Properties

Label 6.15.b.a.5.3
Level $6$
Weight $15$
Character 6.5
Analytic conductor $7.460$
Analytic rank $0$
Dimension $4$
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] = [6,15,Mod(5,6)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6.5");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.45973808911\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-35})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} + 23x^{2} - 22x + 51 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.3
Root \(0.500000 + 1.54383i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.15.b.a.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+90.5097i q^{2} +(-2023.79 + 829.000i) q^{3} -8192.00 q^{4} -40425.0i q^{5} +(-75032.5 - 183173. i) q^{6} +388872. q^{7} -741455. i q^{8} +(3.40849e6 - 3.35545e6i) q^{9} +O(q^{10})\) \(q+90.5097i q^{2} +(-2023.79 + 829.000i) q^{3} -8192.00 q^{4} -40425.0i q^{5} +(-75032.5 - 183173. i) q^{6} +388872. q^{7} -741455. i q^{8} +(3.40849e6 - 3.35545e6i) q^{9} +3.65885e6 q^{10} -3.20747e7i q^{11} +(1.65789e7 - 6.79117e6i) q^{12} -5.64146e7 q^{13} +3.51967e7i q^{14} +(3.35123e7 + 8.18117e7i) q^{15} +6.71089e7 q^{16} +2.36470e8i q^{17} +(3.03700e8 + 3.08501e8i) q^{18} -1.43439e9 q^{19} +3.31162e8i q^{20} +(-7.86996e8 + 3.22375e8i) q^{21} +2.90307e9 q^{22} -6.74668e9i q^{23} +(6.14666e8 + 1.50055e9i) q^{24} +4.46934e9 q^{25} -5.10607e9i q^{26} +(-4.11640e9 + 9.61635e9i) q^{27} -3.18564e9 q^{28} -8.00214e9i q^{29} +(-7.40475e9 + 3.03319e9i) q^{30} -7.26470e9 q^{31} +6.07400e9i q^{32} +(2.65899e10 + 6.49124e10i) q^{33} -2.14028e10 q^{34} -1.57202e10i q^{35} +(-2.79223e10 + 2.74878e10i) q^{36} +2.67765e10 q^{37} -1.29826e11i q^{38} +(1.14171e11 - 4.67677e10i) q^{39} -2.99733e10 q^{40} -1.45007e11i q^{41} +(-2.91781e10 - 7.12308e10i) q^{42} -1.21747e11 q^{43} +2.62756e11i q^{44} +(-1.35644e11 - 1.37788e11i) q^{45} +6.10639e11 q^{46} +5.48796e11i q^{47} +(-1.35814e11 + 5.56333e10i) q^{48} -5.27001e11 q^{49} +4.04518e11i q^{50} +(-1.96034e11 - 4.78566e11i) q^{51} +4.62148e11 q^{52} +8.99111e11i q^{53} +(-8.70373e11 - 3.72574e11i) q^{54} -1.29662e12 q^{55} -2.88331e11i q^{56} +(2.90290e12 - 1.18911e12i) q^{57} +7.24271e11 q^{58} -1.29697e12i q^{59} +(-2.74533e11 - 6.70202e11i) q^{60} +1.73638e12 q^{61} -6.57526e11i q^{62} +(1.32547e12 - 1.30484e12i) q^{63} -5.49756e11 q^{64} +2.28056e12i q^{65} +(-5.87520e12 + 2.40664e12i) q^{66} -7.50142e12 q^{67} -1.93716e12i q^{68} +(5.59300e12 + 1.36539e13i) q^{69} +1.42283e12 q^{70} -4.94522e12i q^{71} +(-2.48791e12 - 2.52724e12i) q^{72} +9.76842e12 q^{73} +2.42353e12i q^{74} +(-9.04500e12 + 3.70508e12i) q^{75} +1.17505e13 q^{76} -1.24730e13i q^{77} +(4.23293e12 + 1.03336e13i) q^{78} -2.22658e13 q^{79} -2.71288e12i q^{80} +(3.58768e11 - 2.28740e13i) q^{81} +1.31245e13 q^{82} -2.67183e13i q^{83} +(6.44707e12 - 2.64090e12i) q^{84} +9.55930e12 q^{85} -1.10192e13i q^{86} +(6.63378e12 + 1.61947e13i) q^{87} -2.37819e13 q^{88} +7.12613e13i q^{89} +(1.24712e13 - 1.22771e13i) q^{90} -2.19381e13 q^{91} +5.52688e13i q^{92} +(1.47022e13 - 6.02244e12i) q^{93} -4.96713e13 q^{94} +5.79852e13i q^{95} +(-5.03535e12 - 1.22925e13i) q^{96} +8.75400e13 q^{97} -4.76987e13i q^{98} +(-1.07625e14 - 1.09326e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3276 q^{3} - 32768 q^{4} + 239616 q^{6} - 1654072 q^{7} - 2153628 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3276 q^{3} - 32768 q^{4} + 239616 q^{6} - 1654072 q^{7} - 2153628 q^{9} - 11735040 q^{10} + 26836992 q^{12} - 248212120 q^{13} + 520179840 q^{15} + 268435456 q^{16} + 908070912 q^{18} - 1252067608 q^{19} - 2512164312 q^{21} + 2708779008 q^{22} - 1962934272 q^{24} - 1010496860 q^{25} - 18844787052 q^{27} + 13550157824 q^{28} - 22159872000 q^{30} + 48544485512 q^{31} + 126848191104 q^{33} - 73181085696 q^{34} + 17642520576 q^{36} - 229361099608 q^{37} + 176113271880 q^{39} + 96133447680 q^{40} - 532172648448 q^{42} - 475123816024 q^{43} + 78358129920 q^{45} + 1407078998016 q^{46} - 219848638464 q^{48} + 546417874380 q^{49} + 330389632512 q^{51} + 2033353687040 q^{52} - 3372586813440 q^{54} - 6195118383360 q^{55} + 6429522003912 q^{57} + 3954244177920 q^{58} - 4261313249280 q^{60} - 8008506933784 q^{61} + 13558362184584 q^{63} - 2199023255552 q^{64} - 12945338929152 q^{66} - 5706498189208 q^{67} + 6766877922048 q^{69} + 26012049530880 q^{70} - 7438916911104 q^{72} + 28135799923400 q^{73} - 21928288537260 q^{75} + 10256937844736 q^{76} - 17912213729280 q^{78} - 80292052723192 q^{79} + 35435631821508 q^{81} + 12944796721152 q^{82} + 20579650043904 q^{84} - 16204620119040 q^{85} - 46328672200320 q^{87} - 22190317633536 q^{88} + 110399597015040 q^{90} + 120737034068560 q^{91} + 53737779031272 q^{93} - 219496277852160 q^{94} + 16080357556224 q^{96} + 178244166574856 q^{97} - 158408610377472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 90.5097i 0.707107i
\(3\) −2023.79 + 829.000i −0.925373 + 0.379058i
\(4\) −8192.00 −0.500000
\(5\) 40425.0i 0.517440i −0.965952 0.258720i \(-0.916699\pi\)
0.965952 0.258720i \(-0.0833007\pi\)
\(6\) −75032.5 183173.i −0.268035 0.654337i
\(7\) 388872. 0.472194 0.236097 0.971729i \(-0.424132\pi\)
0.236097 + 0.971729i \(0.424132\pi\)
\(8\) 741455.i 0.353553i
\(9\) 3.40849e6 3.35545e6i 0.712630 0.701540i
\(10\) 3.65885e6 0.365885
\(11\) 3.20747e7i 1.64594i −0.568086 0.822969i \(-0.692316\pi\)
0.568086 0.822969i \(-0.307684\pi\)
\(12\) 1.65789e7 6.79117e6i 0.462686 0.189529i
\(13\) −5.64146e7 −0.899059 −0.449529 0.893266i \(-0.648408\pi\)
−0.449529 + 0.893266i \(0.648408\pi\)
\(14\) 3.51967e7i 0.333892i
\(15\) 3.35123e7 + 8.18117e7i 0.196140 + 0.478825i
\(16\) 6.71089e7 0.250000
\(17\) 2.36470e8i 0.576280i 0.957588 + 0.288140i \(0.0930369\pi\)
−0.957588 + 0.288140i \(0.906963\pi\)
\(18\) 3.03700e8 + 3.08501e8i 0.496064 + 0.503905i
\(19\) −1.43439e9 −1.60469 −0.802347 0.596858i \(-0.796415\pi\)
−0.802347 + 0.596858i \(0.796415\pi\)
\(20\) 3.31162e8i 0.258720i
\(21\) −7.86996e8 + 3.22375e8i −0.436956 + 0.178989i
\(22\) 2.90307e9 1.16385
\(23\) 6.74668e9i 1.98150i −0.135684 0.990752i \(-0.543323\pi\)
0.135684 0.990752i \(-0.456677\pi\)
\(24\) 6.14666e8 + 1.50055e9i 0.134017 + 0.327169i
\(25\) 4.46934e9 0.732256
\(26\) 5.10607e9i 0.635731i
\(27\) −4.11640e9 + 9.61635e9i −0.393524 + 0.919314i
\(28\) −3.18564e9 −0.236097
\(29\) 8.00214e9i 0.463896i −0.972728 0.231948i \(-0.925490\pi\)
0.972728 0.231948i \(-0.0745099\pi\)
\(30\) −7.40475e9 + 3.03319e9i −0.338580 + 0.138692i
\(31\) −7.26470e9 −0.264050 −0.132025 0.991246i \(-0.542148\pi\)
−0.132025 + 0.991246i \(0.542148\pi\)
\(32\) 6.07400e9i 0.176777i
\(33\) 2.65899e10 + 6.49124e10i 0.623906 + 1.52311i
\(34\) −2.14028e10 −0.407492
\(35\) 1.57202e10i 0.244332i
\(36\) −2.79223e10 + 2.74878e10i −0.356315 + 0.350770i
\(37\) 2.67765e10 0.282060 0.141030 0.990005i \(-0.454959\pi\)
0.141030 + 0.990005i \(0.454959\pi\)
\(38\) 1.29826e11i 1.13469i
\(39\) 1.14171e11 4.67677e10i 0.831965 0.340796i
\(40\) −2.99733e10 −0.182943
\(41\) 1.45007e11i 0.744564i −0.928120 0.372282i \(-0.878575\pi\)
0.928120 0.372282i \(-0.121425\pi\)
\(42\) −2.91781e10 7.12308e10i −0.126564 0.308974i
\(43\) −1.21747e11 −0.447896 −0.223948 0.974601i \(-0.571895\pi\)
−0.223948 + 0.974601i \(0.571895\pi\)
\(44\) 2.62756e11i 0.822969i
\(45\) −1.35644e11 1.37788e11i −0.363005 0.368743i
\(46\) 6.10639e11 1.40114
\(47\) 5.48796e11i 1.08324i 0.840623 + 0.541621i \(0.182189\pi\)
−0.840623 + 0.541621i \(0.817811\pi\)
\(48\) −1.35814e11 + 5.56333e10i −0.231343 + 0.0947645i
\(49\) −5.27001e11 −0.777032
\(50\) 4.04518e11i 0.517783i
\(51\) −1.96034e11 4.78566e11i −0.218444 0.533274i
\(52\) 4.62148e11 0.449529
\(53\) 8.99111e11i 0.765389i 0.923875 + 0.382695i \(0.125004\pi\)
−0.923875 + 0.382695i \(0.874996\pi\)
\(54\) −8.70373e11 3.72574e11i −0.650053 0.278263i
\(55\) −1.29662e12 −0.851674
\(56\) 2.88331e11i 0.166946i
\(57\) 2.90290e12 1.18911e12i 1.48494 0.608272i
\(58\) 7.24271e11 0.328024
\(59\) 1.29697e12i 0.521152i −0.965453 0.260576i \(-0.916087\pi\)
0.965453 0.260576i \(-0.0839125\pi\)
\(60\) −2.74533e11 6.70202e11i −0.0980699 0.239412i
\(61\) 1.73638e12 0.552504 0.276252 0.961085i \(-0.410908\pi\)
0.276252 + 0.961085i \(0.410908\pi\)
\(62\) 6.57526e11i 0.186711i
\(63\) 1.32547e12 1.30484e12i 0.336500 0.331263i
\(64\) −5.49756e11 −0.125000
\(65\) 2.28056e12i 0.465209i
\(66\) −5.87520e12 + 2.40664e12i −1.07700 + 0.441168i
\(67\) −7.50142e12 −1.23771 −0.618856 0.785504i \(-0.712404\pi\)
−0.618856 + 0.785504i \(0.712404\pi\)
\(68\) 1.93716e12i 0.288140i
\(69\) 5.59300e12 + 1.36539e13i 0.751105 + 1.83363i
\(70\) 1.42283e12 0.172769
\(71\) 4.94522e12i 0.543722i −0.962336 0.271861i \(-0.912361\pi\)
0.962336 0.271861i \(-0.0876391\pi\)
\(72\) −2.48791e12 2.52724e12i −0.248032 0.251953i
\(73\) 9.76842e12 0.884228 0.442114 0.896959i \(-0.354229\pi\)
0.442114 + 0.896959i \(0.354229\pi\)
\(74\) 2.42353e12i 0.199447i
\(75\) −9.04500e12 + 3.70508e12i −0.677610 + 0.277568i
\(76\) 1.17505e13 0.802347
\(77\) 1.24730e13i 0.777203i
\(78\) 4.23293e12 + 1.03336e13i 0.240979 + 0.588288i
\(79\) −2.22658e13 −1.15944 −0.579721 0.814815i \(-0.696838\pi\)
−0.579721 + 0.814815i \(0.696838\pi\)
\(80\) 2.71288e12i 0.129360i
\(81\) 3.58768e11 2.28740e13i 0.0156826 0.999877i
\(82\) 1.31245e13 0.526486
\(83\) 2.67183e13i 0.984606i −0.870424 0.492303i \(-0.836155\pi\)
0.870424 0.492303i \(-0.163845\pi\)
\(84\) 6.44707e12 2.64090e12i 0.218478 0.0894946i
\(85\) 9.55930e12 0.298190
\(86\) 1.10192e13i 0.316710i
\(87\) 6.63378e12 + 1.61947e13i 0.175843 + 0.429276i
\(88\) −2.37819e13 −0.581927
\(89\) 7.12613e13i 1.61110i 0.592525 + 0.805552i \(0.298131\pi\)
−0.592525 + 0.805552i \(0.701869\pi\)
\(90\) 1.24712e13 1.22771e13i 0.260741 0.256683i
\(91\) −2.19381e13 −0.424531
\(92\) 5.52688e13i 0.990752i
\(93\) 1.47022e13 6.02244e12i 0.244345 0.100090i
\(94\) −4.96713e13 −0.765968
\(95\) 5.79852e13i 0.830333i
\(96\) −5.03535e12 1.22925e13i −0.0670086 0.163584i
\(97\) 8.75400e13 1.08344 0.541719 0.840560i \(-0.317774\pi\)
0.541719 + 0.840560i \(0.317774\pi\)
\(98\) 4.76987e13i 0.549445i
\(99\) −1.07625e14 1.09326e14i −1.15469 1.17294i
\(100\) −3.66128e13 −0.366128
\(101\) 7.53448e12i 0.0702754i 0.999382 + 0.0351377i \(0.0111870\pi\)
−0.999382 + 0.0351377i \(0.988813\pi\)
\(102\) 4.33148e13 1.77429e13i 0.377082 0.154463i
\(103\) 1.12865e14 0.917694 0.458847 0.888515i \(-0.348263\pi\)
0.458847 + 0.888515i \(0.348263\pi\)
\(104\) 4.18289e13i 0.317865i
\(105\) 1.30320e13 + 3.18143e13i 0.0926161 + 0.226098i
\(106\) −8.13782e13 −0.541212
\(107\) 8.18220e13i 0.509546i −0.967001 0.254773i \(-0.917999\pi\)
0.967001 0.254773i \(-0.0820007\pi\)
\(108\) 3.37215e13 7.87772e13i 0.196762 0.459657i
\(109\) 1.73006e14 0.946400 0.473200 0.880955i \(-0.343099\pi\)
0.473200 + 0.880955i \(0.343099\pi\)
\(110\) 1.17357e14i 0.602225i
\(111\) −5.41901e13 + 2.21977e13i −0.261011 + 0.106917i
\(112\) 2.60968e13 0.118049
\(113\) 9.87778e13i 0.419866i −0.977716 0.209933i \(-0.932675\pi\)
0.977716 0.209933i \(-0.0673245\pi\)
\(114\) 1.07626e14 + 2.62741e14i 0.430113 + 1.05001i
\(115\) −2.72734e14 −1.02531
\(116\) 6.55535e13i 0.231948i
\(117\) −1.92288e14 + 1.89296e14i −0.640696 + 0.630726i
\(118\) 1.17388e14 0.368510
\(119\) 9.19567e13i 0.272116i
\(120\) 6.06597e13 2.48479e13i 0.169290 0.0693459i
\(121\) −6.49036e14 −1.70911
\(122\) 1.57159e14i 0.390679i
\(123\) 1.20211e14 + 2.93464e14i 0.282233 + 0.688999i
\(124\) 5.95125e13 0.132025
\(125\) 4.27407e14i 0.896338i
\(126\) 1.18101e14 + 1.19968e14i 0.234239 + 0.237941i
\(127\) 9.57895e14 1.79759 0.898797 0.438364i \(-0.144442\pi\)
0.898797 + 0.438364i \(0.144442\pi\)
\(128\) 4.97582e13i 0.0883883i
\(129\) 2.46389e14 1.00928e14i 0.414471 0.169779i
\(130\) −2.06413e14 −0.328952
\(131\) 3.06170e14i 0.462448i −0.972900 0.231224i \(-0.925727\pi\)
0.972900 0.231224i \(-0.0742731\pi\)
\(132\) −2.17825e14 5.31763e14i −0.311953 0.761553i
\(133\) −5.57795e14 −0.757727
\(134\) 6.78951e14i 0.875195i
\(135\) 3.88741e14 + 1.66405e14i 0.475690 + 0.203625i
\(136\) 1.75332e14 0.203746
\(137\) 1.50579e13i 0.0166235i 0.999965 + 0.00831173i \(0.00264574\pi\)
−0.999965 + 0.00831173i \(0.997354\pi\)
\(138\) −1.23581e15 + 5.06220e14i −1.29657 + 0.531112i
\(139\) 7.56720e14 0.754800 0.377400 0.926050i \(-0.376818\pi\)
0.377400 + 0.926050i \(0.376818\pi\)
\(140\) 1.28780e14i 0.122166i
\(141\) −4.54952e14 1.11065e15i −0.410612 1.00240i
\(142\) 4.47590e14 0.384470
\(143\) 1.80948e15i 1.47980i
\(144\) 2.28740e14 2.25180e14i 0.178157 0.175385i
\(145\) −3.23487e14 −0.240038
\(146\) 8.84137e14i 0.625244i
\(147\) 1.06654e15 4.36884e14i 0.719045 0.294540i
\(148\) −2.19353e14 −0.141030
\(149\) 1.43757e15i 0.881711i 0.897578 + 0.440855i \(0.145325\pi\)
−0.897578 + 0.440855i \(0.854675\pi\)
\(150\) −3.35346e14 8.18660e14i −0.196270 0.479142i
\(151\) −1.35748e15 −0.758393 −0.379197 0.925316i \(-0.623800\pi\)
−0.379197 + 0.925316i \(0.623800\pi\)
\(152\) 1.06354e15i 0.567345i
\(153\) 7.93462e14 + 8.06005e14i 0.404284 + 0.410674i
\(154\) 1.12892e15 0.549566
\(155\) 2.93676e14i 0.136630i
\(156\) −9.35292e14 + 3.83121e14i −0.415982 + 0.170398i
\(157\) −2.68723e15 −1.14290 −0.571449 0.820638i \(-0.693618\pi\)
−0.571449 + 0.820638i \(0.693618\pi\)
\(158\) 2.01527e15i 0.819849i
\(159\) −7.45363e14 1.81961e15i −0.290127 0.708270i
\(160\) 2.45541e14 0.0914713
\(161\) 2.62360e15i 0.935655i
\(162\) 2.07032e15 + 3.24719e13i 0.707020 + 0.0110893i
\(163\) 1.31621e15 0.430540 0.215270 0.976555i \(-0.430937\pi\)
0.215270 + 0.976555i \(0.430937\pi\)
\(164\) 1.18790e15i 0.372282i
\(165\) 2.62409e15 1.07490e15i 0.788116 0.322834i
\(166\) 2.41827e15 0.696222
\(167\) 5.56602e15i 1.53649i −0.640157 0.768244i \(-0.721131\pi\)
0.640157 0.768244i \(-0.278869\pi\)
\(168\) 2.39027e14 + 5.83523e14i 0.0632822 + 0.154487i
\(169\) −7.54768e14 −0.191693
\(170\) 8.65209e14i 0.210852i
\(171\) −4.88910e15 + 4.81302e15i −1.14355 + 1.12576i
\(172\) 9.97348e14 0.223948
\(173\) 3.55586e15i 0.766694i 0.923604 + 0.383347i \(0.125229\pi\)
−0.923604 + 0.383347i \(0.874771\pi\)
\(174\) −1.46577e15 + 6.00421e14i −0.303544 + 0.124340i
\(175\) 1.73800e15 0.345767
\(176\) 2.15250e15i 0.411485i
\(177\) 1.07519e15 + 2.62479e15i 0.197547 + 0.482260i
\(178\) −6.44984e15 −1.13922
\(179\) 1.48854e15i 0.252807i 0.991979 + 0.126404i \(0.0403435\pi\)
−0.991979 + 0.126404i \(0.959657\pi\)
\(180\) 1.11119e15 + 1.12876e15i 0.181502 + 0.184372i
\(181\) 3.47684e15 0.546304 0.273152 0.961971i \(-0.411934\pi\)
0.273152 + 0.961971i \(0.411934\pi\)
\(182\) 1.98561e15i 0.300188i
\(183\) −3.51406e15 + 1.43946e15i −0.511272 + 0.209431i
\(184\) −5.00236e15 −0.700568
\(185\) 1.08244e15i 0.145949i
\(186\) 5.45089e14 + 1.33069e15i 0.0707745 + 0.172778i
\(187\) 7.58470e15 0.948522
\(188\) 4.49573e15i 0.541621i
\(189\) −1.60075e15 + 3.73953e15i −0.185820 + 0.434095i
\(190\) −5.24822e15 −0.587134
\(191\) 4.10002e15i 0.442133i 0.975259 + 0.221066i \(0.0709537\pi\)
−0.975259 + 0.221066i \(0.929046\pi\)
\(192\) 1.11259e15 4.55748e14i 0.115672 0.0473823i
\(193\) 7.91819e15 0.793825 0.396913 0.917856i \(-0.370082\pi\)
0.396913 + 0.917856i \(0.370082\pi\)
\(194\) 7.92321e15i 0.766107i
\(195\) −1.89059e15 4.61538e15i −0.176341 0.430492i
\(196\) 4.31719e15 0.388516
\(197\) 1.65493e16i 1.43720i −0.695425 0.718599i \(-0.744784\pi\)
0.695425 0.718599i \(-0.255216\pi\)
\(198\) 9.89507e15 9.74109e15i 0.829397 0.816491i
\(199\) −1.14009e16 −0.922500 −0.461250 0.887270i \(-0.652599\pi\)
−0.461250 + 0.887270i \(0.652599\pi\)
\(200\) 3.31381e15i 0.258892i
\(201\) 1.51813e16 6.21868e15i 1.14535 0.469165i
\(202\) −6.81943e14 −0.0496922
\(203\) 3.11181e15i 0.219049i
\(204\) 1.60591e15 + 3.92041e15i 0.109222 + 0.266637i
\(205\) −5.86191e15 −0.385267
\(206\) 1.02153e16i 0.648907i
\(207\) −2.26381e16 2.29960e16i −1.39011 1.41208i
\(208\) −3.78592e15 −0.224765
\(209\) 4.60076e16i 2.64123i
\(210\) −2.87950e15 + 1.17952e15i −0.159876 + 0.0654895i
\(211\) −9.58039e14 −0.0514524 −0.0257262 0.999669i \(-0.508190\pi\)
−0.0257262 + 0.999669i \(0.508190\pi\)
\(212\) 7.36552e15i 0.382695i
\(213\) 4.09959e15 + 1.00081e16i 0.206102 + 0.503146i
\(214\) 7.40568e15 0.360303
\(215\) 4.92160e15i 0.231759i
\(216\) 7.13010e15 + 3.05212e15i 0.325027 + 0.139132i
\(217\) −2.82504e15 −0.124683
\(218\) 1.56587e16i 0.669206i
\(219\) −1.97692e16 + 8.09802e15i −0.818241 + 0.335174i
\(220\) 1.06219e16 0.425837
\(221\) 1.33404e16i 0.518110i
\(222\) −2.00911e15 4.90473e15i −0.0756019 0.184563i
\(223\) 2.35994e16 0.860532 0.430266 0.902702i \(-0.358420\pi\)
0.430266 + 0.902702i \(0.358420\pi\)
\(224\) 2.36201e15i 0.0834730i
\(225\) 1.52337e16 1.49966e16i 0.521827 0.513707i
\(226\) 8.94035e15 0.296890
\(227\) 1.56244e16i 0.503063i −0.967849 0.251531i \(-0.919066\pi\)
0.967849 0.251531i \(-0.0809342\pi\)
\(228\) −2.37806e16 + 9.74119e15i −0.742470 + 0.304136i
\(229\) −3.99912e16 −1.21092 −0.605461 0.795875i \(-0.707011\pi\)
−0.605461 + 0.795875i \(0.707011\pi\)
\(230\) 2.46851e16i 0.725003i
\(231\) 1.03401e16 + 2.52427e16i 0.294605 + 0.719203i
\(232\) −5.93323e15 −0.164012
\(233\) 2.76210e16i 0.740881i −0.928856 0.370441i \(-0.879207\pi\)
0.928856 0.370441i \(-0.120793\pi\)
\(234\) −1.71331e16 1.74040e16i −0.445991 0.453041i
\(235\) 2.21851e16 0.560513
\(236\) 1.06248e16i 0.260576i
\(237\) 4.50614e16 1.84584e16i 1.07292 0.439496i
\(238\) −8.32297e15 −0.192415
\(239\) 1.77539e16i 0.398574i −0.979941 0.199287i \(-0.936137\pi\)
0.979941 0.199287i \(-0.0638626\pi\)
\(240\) 2.24897e15 + 5.49029e15i 0.0490350 + 0.119706i
\(241\) −7.98776e15 −0.169163 −0.0845816 0.996417i \(-0.526955\pi\)
−0.0845816 + 0.996417i \(0.526955\pi\)
\(242\) 5.87440e16i 1.20853i
\(243\) 1.82365e16 + 4.65896e16i 0.364499 + 0.931204i
\(244\) −1.42244e16 −0.276252
\(245\) 2.13040e16i 0.402068i
\(246\) −2.65613e16 + 1.08802e16i −0.487196 + 0.199569i
\(247\) 8.09206e16 1.44271
\(248\) 5.38645e15i 0.0933557i
\(249\) 2.21495e16 + 5.40723e16i 0.373223 + 0.911128i
\(250\) 3.86845e16 0.633807
\(251\) 1.42116e16i 0.226426i 0.993571 + 0.113213i \(0.0361142\pi\)
−0.993571 + 0.113213i \(0.963886\pi\)
\(252\) −1.08582e16 + 1.06893e16i −0.168250 + 0.165632i
\(253\) −2.16398e17 −3.26143
\(254\) 8.66987e16i 1.27109i
\(255\) −1.93460e16 + 7.92466e15i −0.275937 + 0.113031i
\(256\) 4.50360e15 0.0625000
\(257\) 9.79504e16i 1.32274i −0.750060 0.661369i \(-0.769976\pi\)
0.750060 0.661369i \(-0.230024\pi\)
\(258\) 9.13495e15 + 2.23006e16i 0.120052 + 0.293075i
\(259\) 1.04127e16 0.133187
\(260\) 1.86824e16i 0.232605i
\(261\) −2.68507e16 2.72752e16i −0.325441 0.330586i
\(262\) 2.77113e16 0.327000
\(263\) 1.56067e17i 1.79316i 0.442880 + 0.896581i \(0.353957\pi\)
−0.442880 + 0.896581i \(0.646043\pi\)
\(264\) 4.81297e16 1.97152e16i 0.538500 0.220584i
\(265\) 3.63466e16 0.396043
\(266\) 5.04858e16i 0.535794i
\(267\) −5.90756e16 1.44218e17i −0.610702 1.49087i
\(268\) 6.14516e16 0.618856
\(269\) 2.69565e16i 0.264483i −0.991218 0.132241i \(-0.957783\pi\)
0.991218 0.132241i \(-0.0422174\pi\)
\(270\) −1.50613e16 + 3.51848e16i −0.143985 + 0.336364i
\(271\) 1.23902e17 1.15423 0.577117 0.816662i \(-0.304178\pi\)
0.577117 + 0.816662i \(0.304178\pi\)
\(272\) 1.58692e16i 0.144070i
\(273\) 4.43981e16 1.81867e16i 0.392849 0.160922i
\(274\) −1.36289e15 −0.0117546
\(275\) 1.43353e17i 1.20525i
\(276\) −4.58178e16 1.11852e17i −0.375553 0.916815i
\(277\) −3.99146e16 −0.318987 −0.159494 0.987199i \(-0.550986\pi\)
−0.159494 + 0.987199i \(0.550986\pi\)
\(278\) 6.84905e16i 0.533724i
\(279\) −2.47616e16 + 2.43763e16i −0.188170 + 0.185242i
\(280\) −1.16558e16 −0.0863845
\(281\) 2.39181e17i 1.72895i 0.502677 + 0.864474i \(0.332349\pi\)
−0.502677 + 0.864474i \(0.667651\pi\)
\(282\) 1.00524e17 4.11775e16i 0.708806 0.290346i
\(283\) 8.74437e15 0.0601483 0.0300741 0.999548i \(-0.490426\pi\)
0.0300741 + 0.999548i \(0.490426\pi\)
\(284\) 4.05112e16i 0.271861i
\(285\) −4.80698e16 1.17350e17i −0.314744 0.768367i
\(286\) −1.63776e17 −1.04637
\(287\) 5.63892e16i 0.351579i
\(288\) 2.03810e16 + 2.07032e16i 0.124016 + 0.125976i
\(289\) 1.12460e17 0.667901
\(290\) 2.92787e16i 0.169733i
\(291\) −1.77163e17 + 7.25706e16i −1.00258 + 0.410686i
\(292\) −8.00229e16 −0.442114
\(293\) 2.23167e16i 0.120381i −0.998187 0.0601904i \(-0.980829\pi\)
0.998187 0.0601904i \(-0.0191708\pi\)
\(294\) 3.95422e16 + 9.65322e16i 0.208272 + 0.508441i
\(295\) −5.24299e16 −0.269665
\(296\) 1.98536e16i 0.0997234i
\(297\) 3.08442e17 + 1.32032e17i 1.51314 + 0.647716i
\(298\) −1.30114e17 −0.623464
\(299\) 3.80611e17i 1.78149i
\(300\) 7.40966e16 3.03520e16i 0.338805 0.138784i
\(301\) −4.73439e16 −0.211494
\(302\) 1.22865e17i 0.536265i
\(303\) −6.24608e15 1.52482e16i −0.0266385 0.0650310i
\(304\) −9.62603e16 −0.401173
\(305\) 7.01930e16i 0.285887i
\(306\) −7.29512e16 + 7.18160e16i −0.290391 + 0.285872i
\(307\) 2.99304e17 1.16451 0.582255 0.813006i \(-0.302171\pi\)
0.582255 + 0.813006i \(0.302171\pi\)
\(308\) 1.02178e17i 0.388602i
\(309\) −2.28415e17 + 9.35649e16i −0.849209 + 0.347859i
\(310\) −2.65805e16 −0.0966120
\(311\) 4.57198e17i 1.62473i −0.583149 0.812365i \(-0.698180\pi\)
0.583149 0.812365i \(-0.301820\pi\)
\(312\) −3.46762e16 8.46529e16i −0.120489 0.294144i
\(313\) 2.39273e17 0.812986 0.406493 0.913654i \(-0.366751\pi\)
0.406493 + 0.913654i \(0.366751\pi\)
\(314\) 2.43220e17i 0.808151i
\(315\) −5.27482e16 5.35820e16i −0.171409 0.174118i
\(316\) 1.82402e17 0.579721
\(317\) 3.46468e17i 1.07708i −0.842599 0.538541i \(-0.818976\pi\)
0.842599 0.538541i \(-0.181024\pi\)
\(318\) 1.64693e17 6.74626e16i 0.500823 0.205151i
\(319\) −2.56666e17 −0.763544
\(320\) 2.22239e16i 0.0646800i
\(321\) 6.78304e16 + 1.65590e17i 0.193148 + 0.471520i
\(322\) 2.37461e17 0.661608
\(323\) 3.39190e17i 0.924753i
\(324\) −2.93902e15 + 1.87384e17i −0.00784130 + 0.499939i
\(325\) −2.52136e17 −0.658341
\(326\) 1.19130e17i 0.304437i
\(327\) −3.50127e17 + 1.43422e17i −0.875773 + 0.358741i
\(328\) −1.07516e17 −0.263243
\(329\) 2.13411e17i 0.511501i
\(330\) 9.72886e16 + 2.37505e17i 0.228278 + 0.557282i
\(331\) −2.72422e17 −0.625816 −0.312908 0.949783i \(-0.601303\pi\)
−0.312908 + 0.949783i \(0.601303\pi\)
\(332\) 2.18877e17i 0.492303i
\(333\) 9.12674e16 8.98472e16i 0.201005 0.197877i
\(334\) 5.03778e17 1.08646
\(335\) 3.03245e17i 0.640442i
\(336\) −5.28144e16 + 2.16342e16i −0.109239 + 0.0447473i
\(337\) 4.80474e17 0.973330 0.486665 0.873589i \(-0.338213\pi\)
0.486665 + 0.873589i \(0.338213\pi\)
\(338\) 6.83138e16i 0.135548i
\(339\) 8.18868e16 + 1.99906e17i 0.159154 + 0.388532i
\(340\) −7.83098e16 −0.149095
\(341\) 2.33013e17i 0.434610i
\(342\) −4.35625e17 4.42511e17i −0.796030 0.808614i
\(343\) −4.68679e17 −0.839105
\(344\) 9.02696e16i 0.158355i
\(345\) 5.51957e17 2.26097e17i 0.948794 0.388652i
\(346\) −3.21840e17 −0.542134
\(347\) 3.71323e17i 0.612979i 0.951874 + 0.306490i \(0.0991545\pi\)
−0.951874 + 0.306490i \(0.900846\pi\)
\(348\) −5.43439e16 1.32667e17i −0.0879217 0.214638i
\(349\) −6.63718e17 −1.05246 −0.526230 0.850342i \(-0.676395\pi\)
−0.526230 + 0.850342i \(0.676395\pi\)
\(350\) 1.57306e17i 0.244494i
\(351\) 2.32225e17 5.42503e17i 0.353801 0.826518i
\(352\) 1.94822e17 0.290964
\(353\) 8.30669e17i 1.21620i 0.793861 + 0.608100i \(0.208068\pi\)
−0.793861 + 0.608100i \(0.791932\pi\)
\(354\) −2.37569e17 + 9.73147e16i −0.341010 + 0.139687i
\(355\) −1.99910e17 −0.281344
\(356\) 5.83773e17i 0.805552i
\(357\) −7.62321e16 1.86101e17i −0.103148 0.251809i
\(358\) −1.34727e17 −0.178762
\(359\) 7.84251e17i 1.02045i −0.860040 0.510227i \(-0.829561\pi\)
0.860040 0.510227i \(-0.170439\pi\)
\(360\) −1.02164e17 + 1.00574e17i −0.130370 + 0.128342i
\(361\) 1.25847e18 1.57504
\(362\) 3.14687e17i 0.386295i
\(363\) 1.31351e18 5.38051e17i 1.58157 0.647853i
\(364\) 1.79717e17 0.212265
\(365\) 3.94888e17i 0.457535i
\(366\) −1.30285e17 3.18057e17i −0.148090 0.361524i
\(367\) −1.84129e17 −0.205333 −0.102667 0.994716i \(-0.532738\pi\)
−0.102667 + 0.994716i \(0.532738\pi\)
\(368\) 4.52762e17i 0.495376i
\(369\) −4.86563e17 4.94254e17i −0.522341 0.530598i
\(370\) 9.79714e16 0.103202
\(371\) 3.49640e17i 0.361412i
\(372\) −1.20441e17 + 4.93358e16i −0.122172 + 0.0500451i
\(373\) 3.45886e16 0.0344327 0.0172164 0.999852i \(-0.494520\pi\)
0.0172164 + 0.999852i \(0.494520\pi\)
\(374\) 6.86489e17i 0.670706i
\(375\) 3.54321e17 + 8.64983e17i 0.339764 + 0.829447i
\(376\) 4.06907e17 0.382984
\(377\) 4.51438e17i 0.417069i
\(378\) −3.38464e17 1.44884e17i −0.306952 0.131394i
\(379\) −3.21511e17 −0.286234 −0.143117 0.989706i \(-0.545713\pi\)
−0.143117 + 0.989706i \(0.545713\pi\)
\(380\) 4.75015e17i 0.415166i
\(381\) −1.93858e18 + 7.94095e17i −1.66345 + 0.681393i
\(382\) −3.71092e17 −0.312635
\(383\) 8.54161e17i 0.706559i 0.935518 + 0.353279i \(0.114933\pi\)
−0.935518 + 0.353279i \(0.885067\pi\)
\(384\) 4.12496e16 + 1.00700e17i 0.0335043 + 0.0817922i
\(385\) −5.04219e17 −0.402156
\(386\) 7.16673e17i 0.561319i
\(387\) −4.14971e17 + 4.08514e17i −0.319184 + 0.314217i
\(388\) −7.17127e17 −0.541719
\(389\) 1.95449e18i 1.45006i −0.688716 0.725031i \(-0.741825\pi\)
0.688716 0.725031i \(-0.258175\pi\)
\(390\) 4.17736e17 1.71116e17i 0.304404 0.124692i
\(391\) 1.59539e18 1.14190
\(392\) 3.90748e17i 0.274722i
\(393\) 2.53815e17 + 6.19624e17i 0.175295 + 0.427937i
\(394\) 1.49787e18 1.01625
\(395\) 9.00096e17i 0.599942i
\(396\) 8.81663e17 + 8.95600e17i 0.577346 + 0.586472i
\(397\) −2.77977e18 −1.78844 −0.894221 0.447625i \(-0.852270\pi\)
−0.894221 + 0.447625i \(0.852270\pi\)
\(398\) 1.03189e18i 0.652306i
\(399\) 1.12886e18 4.62412e17i 0.701180 0.287223i
\(400\) 2.99932e17 0.183064
\(401\) 2.16906e18i 1.30095i −0.759526 0.650477i \(-0.774569\pi\)
0.759526 0.650477i \(-0.225431\pi\)
\(402\) 5.62850e17 + 1.37405e18i 0.331750 + 0.809882i
\(403\) 4.09835e17 0.237396
\(404\) 6.17224e16i 0.0351377i
\(405\) −9.24681e17 1.45032e16i −0.517376 0.00811481i
\(406\) 2.81649e17 0.154891
\(407\) 8.58849e17i 0.464254i
\(408\) −3.54835e17 + 1.45350e17i −0.188541 + 0.0772315i
\(409\) 1.41898e18 0.741163 0.370581 0.928800i \(-0.379158\pi\)
0.370581 + 0.928800i \(0.379158\pi\)
\(410\) 5.30559e17i 0.272425i
\(411\) −1.24830e16 3.04741e16i −0.00630126 0.0153829i
\(412\) −9.24588e17 −0.458847
\(413\) 5.04355e17i 0.246085i
\(414\) 2.08136e18 2.04897e18i 0.998491 0.982953i
\(415\) −1.08009e18 −0.509475
\(416\) 3.42662e17i 0.158933i
\(417\) −1.53144e18 + 6.27321e17i −0.698471 + 0.286113i
\(418\) −4.16413e18 −1.86763
\(419\) 1.61537e18i 0.712481i −0.934394 0.356241i \(-0.884058\pi\)
0.934394 0.356241i \(-0.115942\pi\)
\(420\) −1.06758e17 2.60623e17i −0.0463081 0.113049i
\(421\) 3.64786e18 1.55619 0.778097 0.628144i \(-0.216185\pi\)
0.778097 + 0.628144i \(0.216185\pi\)
\(422\) 8.67117e16i 0.0363824i
\(423\) 1.84145e18 + 1.87056e18i 0.759938 + 0.771951i
\(424\) 6.66651e17 0.270606
\(425\) 1.05686e18i 0.421984i
\(426\) −9.05829e17 + 3.71052e17i −0.355778 + 0.145736i
\(427\) 6.75229e17 0.260889
\(428\) 6.70285e17i 0.254773i
\(429\) −1.50006e18 3.66201e18i −0.560929 1.36936i
\(430\) −4.45453e17 −0.163879
\(431\) 3.81936e18i 1.38245i 0.722640 + 0.691225i \(0.242929\pi\)
−0.722640 + 0.691225i \(0.757071\pi\)
\(432\) −2.76247e17 + 6.45343e17i −0.0983809 + 0.229829i
\(433\) 1.76262e18 0.617653 0.308827 0.951118i \(-0.400064\pi\)
0.308827 + 0.951118i \(0.400064\pi\)
\(434\) 2.55694e17i 0.0881641i
\(435\) 6.54669e17 2.68170e17i 0.222125 0.0909884i
\(436\) −1.41726e18 −0.473200
\(437\) 9.67737e18i 3.17971i
\(438\) −7.32949e17 1.78931e18i −0.237004 0.578584i
\(439\) −2.33405e18 −0.742778 −0.371389 0.928477i \(-0.621118\pi\)
−0.371389 + 0.928477i \(0.621118\pi\)
\(440\) 9.61385e17i 0.301112i
\(441\) −1.79628e18 + 1.76832e18i −0.553736 + 0.545119i
\(442\) 1.20743e18 0.366359
\(443\) 5.51352e18i 1.64665i −0.567567 0.823327i \(-0.692115\pi\)
0.567567 0.823327i \(-0.307885\pi\)
\(444\) 4.43925e17 1.81844e17i 0.130506 0.0534587i
\(445\) 2.88074e18 0.833650
\(446\) 2.13597e18i 0.608488i
\(447\) −1.19175e18 2.90935e18i −0.334220 0.815911i
\(448\) −2.13785e17 −0.0590243
\(449\) 1.61107e18i 0.437916i −0.975734 0.218958i \(-0.929734\pi\)
0.975734 0.218958i \(-0.0702657\pi\)
\(450\) 1.35734e18 + 1.37879e18i 0.363246 + 0.368988i
\(451\) −4.65105e18 −1.22551
\(452\) 8.09188e17i 0.209933i
\(453\) 2.74725e18 1.12535e18i 0.701796 0.287475i
\(454\) 1.41416e18 0.355719
\(455\) 8.86847e17i 0.219669i
\(456\) −8.81671e17 2.15237e18i −0.215057 0.525005i
\(457\) 2.15795e18 0.518357 0.259178 0.965829i \(-0.416548\pi\)
0.259178 + 0.965829i \(0.416548\pi\)
\(458\) 3.61959e18i 0.856252i
\(459\) −2.27398e18 9.73405e17i −0.529783 0.226780i
\(460\) 2.23424e18 0.512655
\(461\) 7.87564e18i 1.77983i −0.456122 0.889917i \(-0.650762\pi\)
0.456122 0.889917i \(-0.349238\pi\)
\(462\) −2.28470e18 + 9.35878e17i −0.508553 + 0.208317i
\(463\) 6.63457e17 0.145461 0.0727304 0.997352i \(-0.476829\pi\)
0.0727304 + 0.997352i \(0.476829\pi\)
\(464\) 5.37015e17i 0.115974i
\(465\) −2.43457e17 5.94338e17i −0.0517907 0.126434i
\(466\) 2.49997e18 0.523882
\(467\) 4.86419e18i 1.00414i 0.864828 + 0.502068i \(0.167427\pi\)
−0.864828 + 0.502068i \(0.832573\pi\)
\(468\) 1.57523e18 1.55071e18i 0.320348 0.315363i
\(469\) −2.91710e18 −0.584441
\(470\) 2.00796e18i 0.396342i
\(471\) 5.43839e18 2.22771e18i 1.05761 0.433225i
\(472\) −9.61643e17 −0.184255
\(473\) 3.90498e18i 0.737210i
\(474\) 1.67066e18 + 4.07849e18i 0.310771 + 0.758666i
\(475\) −6.41077e18 −1.17505
\(476\) 7.53309e17i 0.136058i
\(477\) 3.01692e18 + 3.06461e18i 0.536951 + 0.545439i
\(478\) 1.60690e18 0.281834
\(479\) 4.20027e18i 0.725987i −0.931792 0.362994i \(-0.881755\pi\)
0.931792 0.362994i \(-0.118245\pi\)
\(480\) −4.96925e17 + 2.03554e17i −0.0846451 + 0.0346730i
\(481\) −1.51059e18 −0.253589
\(482\) 7.22970e17i 0.119616i
\(483\) 2.17496e18 + 5.30961e18i 0.354668 + 0.865830i
\(484\) 5.31690e18 0.854557
\(485\) 3.53880e18i 0.560614i
\(486\) −4.21681e18 + 1.65058e18i −0.658460 + 0.257740i
\(487\) −7.32539e18 −1.12753 −0.563765 0.825935i \(-0.690648\pi\)
−0.563765 + 0.825935i \(0.690648\pi\)
\(488\) 1.28745e18i 0.195340i
\(489\) −2.66374e18 + 1.09114e18i −0.398410 + 0.163200i
\(490\) −1.92822e18 −0.284305
\(491\) 1.51721e18i 0.220533i −0.993902 0.110267i \(-0.964830\pi\)
0.993902 0.110267i \(-0.0351705\pi\)
\(492\) −9.84767e17 2.40405e18i −0.141116 0.344499i
\(493\) 1.89227e18 0.267334
\(494\) 7.32409e18i 1.02015i
\(495\) −4.41951e18 + 4.35073e18i −0.606929 + 0.597484i
\(496\) −4.87526e17 −0.0660125
\(497\) 1.92306e18i 0.256743i
\(498\) −4.89407e18 + 2.00474e18i −0.644265 + 0.263909i
\(499\) 7.25157e18 0.941300 0.470650 0.882320i \(-0.344019\pi\)
0.470650 + 0.882320i \(0.344019\pi\)
\(500\) 3.50132e18i 0.448169i
\(501\) 4.61423e18 + 1.12645e19i 0.582418 + 1.42182i
\(502\) −1.28628e18 −0.160107
\(503\) 8.22025e17i 0.100904i −0.998726 0.0504521i \(-0.983934\pi\)
0.998726 0.0504521i \(-0.0160662\pi\)
\(504\) −9.67480e17 9.82774e17i −0.117119 0.118971i
\(505\) 3.04581e17 0.0363633
\(506\) 1.95861e19i 2.30618i
\(507\) 1.52749e18 6.25703e17i 0.177388 0.0726628i
\(508\) −7.84707e18 −0.898797
\(509\) 6.28539e18i 0.710081i 0.934851 + 0.355040i \(0.115533\pi\)
−0.934851 + 0.355040i \(0.884467\pi\)
\(510\) −7.17258e17 1.75100e18i −0.0799253 0.195117i
\(511\) 3.79867e18 0.417528
\(512\) 4.07619e17i 0.0441942i
\(513\) 5.90452e18 1.37936e19i 0.631485 1.47522i
\(514\) 8.86545e18 0.935318
\(515\) 4.56256e18i 0.474851i
\(516\) −2.01842e18 + 8.26801e17i −0.207235 + 0.0848894i
\(517\) 1.76024e19 1.78295
\(518\) 9.42446e17i 0.0941777i
\(519\) −2.94781e18 7.19631e18i −0.290621 0.709477i
\(520\) 1.69093e18 0.164476
\(521\) 1.31562e18i 0.126260i −0.998005 0.0631299i \(-0.979892\pi\)
0.998005 0.0631299i \(-0.0201083\pi\)
\(522\) 2.46867e18 2.43025e18i 0.233759 0.230122i
\(523\) 8.43843e18 0.788406 0.394203 0.919023i \(-0.371021\pi\)
0.394203 + 0.919023i \(0.371021\pi\)
\(524\) 2.50814e18i 0.231224i
\(525\) −3.51735e18 + 1.44080e18i −0.319964 + 0.131066i
\(526\) −1.41255e19 −1.26796
\(527\) 1.71788e18i 0.152167i
\(528\) 1.78442e18 + 4.35620e18i 0.155977 + 0.380777i
\(529\) −3.39248e19 −2.92636
\(530\) 3.28972e18i 0.280045i
\(531\) −4.35190e18 4.42069e18i −0.365609 0.371389i
\(532\) 4.56945e18 0.378864
\(533\) 8.18051e18i 0.669407i
\(534\) 1.30531e19 5.34692e18i 1.05421 0.431832i
\(535\) −3.30765e18 −0.263659
\(536\) 5.56197e18i 0.437598i
\(537\) −1.23400e18 3.01250e18i −0.0958287 0.233941i
\(538\) 2.43982e18 0.187017
\(539\) 1.69034e19i 1.27895i
\(540\) −3.18457e18 1.36319e18i −0.237845 0.101812i
\(541\) 4.60856e17 0.0339769 0.0169885 0.999856i \(-0.494592\pi\)
0.0169885 + 0.999856i \(0.494592\pi\)
\(542\) 1.12143e19i 0.816166i
\(543\) −7.03639e18 + 2.88230e18i −0.505535 + 0.207081i
\(544\) −1.43632e18 −0.101873
\(545\) 6.99375e18i 0.489705i
\(546\) 1.64607e18 + 4.01846e18i 0.113789 + 0.277786i
\(547\) 1.04234e19 0.711376 0.355688 0.934605i \(-0.384247\pi\)
0.355688 + 0.934605i \(0.384247\pi\)
\(548\) 1.23355e17i 0.00831173i
\(549\) 5.91842e18 5.82632e18i 0.393731 0.387603i
\(550\) 1.29748e19 0.852239
\(551\) 1.14782e19i 0.744410i
\(552\) 1.01237e19 4.14696e18i 0.648286 0.265556i
\(553\) −8.65856e18 −0.547482
\(554\) 3.61266e18i 0.225558i
\(555\) 8.97344e17 + 2.19063e18i 0.0553233 + 0.135058i
\(556\) −6.19905e18 −0.377400
\(557\) 5.90126e16i 0.00354779i 0.999998 + 0.00177390i \(0.000564649\pi\)
−0.999998 + 0.00177390i \(0.999435\pi\)
\(558\) −2.20629e18 2.24117e18i −0.130986 0.133056i
\(559\) 6.86828e18 0.402685
\(560\) 1.05496e18i 0.0610831i
\(561\) −1.53498e19 + 6.28772e18i −0.877736 + 0.359545i
\(562\) −2.16482e19 −1.22255
\(563\) 7.69233e18i 0.429041i 0.976719 + 0.214521i \(0.0688189\pi\)
−0.976719 + 0.214521i \(0.931181\pi\)
\(564\) 3.72696e18 + 9.09842e18i 0.205306 + 0.501202i
\(565\) −3.99309e18 −0.217255
\(566\) 7.91450e17i 0.0425313i
\(567\) 1.39515e17 8.89506e18i 0.00740524 0.472136i
\(568\) −3.66666e18 −0.192235
\(569\) 1.74875e19i 0.905612i −0.891609 0.452806i \(-0.850423\pi\)
0.891609 0.452806i \(-0.149577\pi\)
\(570\) 1.06213e19 4.35078e18i 0.543318 0.222558i
\(571\) 3.30803e19 1.67154 0.835769 0.549081i \(-0.185022\pi\)
0.835769 + 0.549081i \(0.185022\pi\)
\(572\) 1.48233e19i 0.739898i
\(573\) −3.39892e18 8.29758e18i −0.167594 0.409137i
\(574\) 5.10377e18 0.248604
\(575\) 3.01532e19i 1.45097i
\(576\) −1.87384e18 + 1.84468e18i −0.0890787 + 0.0876925i
\(577\) −1.68751e19 −0.792530 −0.396265 0.918136i \(-0.629694\pi\)
−0.396265 + 0.918136i \(0.629694\pi\)
\(578\) 1.01787e19i 0.472278i
\(579\) −1.60248e19 + 6.56418e18i −0.734584 + 0.300906i
\(580\) 2.65000e18 0.120019
\(581\) 1.03900e19i 0.464926i
\(582\) −6.56834e18 1.60349e19i −0.290399 0.708934i
\(583\) 2.88387e19 1.25978
\(584\) 7.24285e18i 0.312622i
\(585\) 7.65230e18 + 7.77326e18i 0.326363 + 0.331522i
\(586\) 2.01988e18 0.0851221
\(587\) 2.61913e18i 0.109066i −0.998512 0.0545331i \(-0.982633\pi\)
0.998512 0.0545331i \(-0.0173670\pi\)
\(588\) −8.73710e18 + 3.57896e18i −0.359522 + 0.147270i
\(589\) 1.04204e19 0.423719
\(590\) 4.74541e18i 0.190682i
\(591\) 1.37194e19 + 3.34923e19i 0.544781 + 1.32994i
\(592\) 1.79694e18 0.0705151
\(593\) 1.72412e19i 0.668628i 0.942462 + 0.334314i \(0.108505\pi\)
−0.942462 + 0.334314i \(0.891495\pi\)
\(594\) −1.19502e19 + 2.79169e19i −0.458004 + 1.06995i
\(595\) 3.71735e18 0.140804
\(596\) 1.17766e19i 0.440855i
\(597\) 2.30730e19 9.45132e18i 0.853656 0.349681i
\(598\) −3.44490e19 −1.25970
\(599\) 1.31700e19i 0.475992i 0.971266 + 0.237996i \(0.0764905\pi\)
−0.971266 + 0.237996i \(0.923510\pi\)
\(600\) 2.74715e18 + 6.70646e18i 0.0981349 + 0.239571i
\(601\) −2.22713e19 −0.786366 −0.393183 0.919460i \(-0.628626\pi\)
−0.393183 + 0.919460i \(0.628626\pi\)
\(602\) 4.28508e18i 0.149549i
\(603\) −2.55685e19 + 2.51706e19i −0.882031 + 0.868305i
\(604\) 1.11205e19 0.379197
\(605\) 2.62373e19i 0.884364i
\(606\) 1.38011e18 5.65331e17i 0.0459838 0.0188362i
\(607\) −9.19398e18 −0.302819 −0.151409 0.988471i \(-0.548381\pi\)
−0.151409 + 0.988471i \(0.548381\pi\)
\(608\) 8.71249e18i 0.283672i
\(609\) 2.57969e18 + 6.29766e18i 0.0830323 + 0.202702i
\(610\) 6.35315e18 0.202153
\(611\) 3.09601e19i 0.973899i
\(612\) −6.50004e18 6.60279e18i −0.202142 0.205337i
\(613\) −1.27074e19 −0.390691 −0.195346 0.980734i \(-0.562583\pi\)
−0.195346 + 0.980734i \(0.562583\pi\)
\(614\) 2.70899e19i 0.823433i
\(615\) 1.18633e19 4.85952e18i 0.356516 0.146039i
\(616\) −9.24814e18 −0.274783
\(617\) 3.04798e19i 0.895399i −0.894184 0.447699i \(-0.852243\pi\)
0.894184 0.447699i \(-0.147757\pi\)
\(618\) −8.46853e18 2.06737e19i −0.245974 0.600481i
\(619\) −5.37193e19 −1.54275 −0.771375 0.636380i \(-0.780431\pi\)
−0.771375 + 0.636380i \(0.780431\pi\)
\(620\) 2.40579e18i 0.0683150i
\(621\) 6.48784e19 + 2.77720e19i 1.82163 + 0.779769i
\(622\) 4.13808e19 1.14886
\(623\) 2.77116e19i 0.760755i
\(624\) 7.66191e18 3.13853e18i 0.207991 0.0851989i
\(625\) 1.00007e19 0.268454
\(626\) 2.16565e19i 0.574868i
\(627\) −3.81403e19 9.31098e19i −1.00118 2.44412i
\(628\) 2.20138e19 0.571449
\(629\) 6.33185e18i 0.162546i
\(630\) 4.84969e18 4.77422e18i 0.123120 0.121204i
\(631\) −4.49810e19 −1.12934 −0.564669 0.825318i \(-0.690996\pi\)
−0.564669 + 0.825318i \(0.690996\pi\)
\(632\) 1.65091e19i 0.409925i
\(633\) 1.93887e18 7.94214e17i 0.0476127 0.0195035i
\(634\) 3.13587e19 0.761612
\(635\) 3.87229e19i 0.930147i
\(636\) 6.10602e18 + 1.49063e19i 0.145063 + 0.354135i
\(637\) 2.97306e19 0.698598
\(638\) 2.32308e19i 0.539907i
\(639\) −1.65934e19 1.68557e19i −0.381443 0.387473i
\(640\) −2.01148e18 −0.0457357
\(641\) 1.10795e19i 0.249180i 0.992208 + 0.124590i \(0.0397615\pi\)
−0.992208 + 0.124590i \(0.960238\pi\)
\(642\) −1.49875e19 + 6.13931e18i −0.333415 + 0.136576i
\(643\) 5.52622e19 1.21605 0.608025 0.793918i \(-0.291962\pi\)
0.608025 + 0.793918i \(0.291962\pi\)
\(644\) 2.14925e19i 0.467828i
\(645\) −4.08001e18 9.96029e18i −0.0878503 0.214464i
\(646\) 3.07000e19 0.653899
\(647\) 1.49668e19i 0.315355i 0.987491 + 0.157678i \(0.0504007\pi\)
−0.987491 + 0.157678i \(0.949599\pi\)
\(648\) −1.69600e19 2.66010e17i −0.353510 0.00554464i
\(649\) −4.15998e19 −0.857785
\(650\) 2.28207e19i 0.465517i
\(651\) 5.71729e18 2.34196e18i 0.115378 0.0472621i
\(652\) −1.07824e19 −0.215270
\(653\) 1.04550e19i 0.206506i 0.994655 + 0.103253i \(0.0329251\pi\)
−0.994655 + 0.103253i \(0.967075\pi\)
\(654\) −1.29811e19 3.16899e19i −0.253668 0.619265i
\(655\) −1.23769e19 −0.239289
\(656\) 9.73125e18i 0.186141i
\(657\) 3.32955e19 3.27774e19i 0.630127 0.620322i
\(658\) −1.93158e19 −0.361686
\(659\) 1.04417e20i 1.93452i 0.253789 + 0.967260i \(0.418323\pi\)
−0.253789 + 0.967260i \(0.581677\pi\)
\(660\) −2.14965e19 + 8.80556e18i −0.394058 + 0.161417i
\(661\) 1.08289e18 0.0196415 0.00982073 0.999952i \(-0.496874\pi\)
0.00982073 + 0.999952i \(0.496874\pi\)
\(662\) 2.46568e19i 0.442519i
\(663\) 1.10592e19 + 2.69981e19i 0.196394 + 0.479445i
\(664\) −1.98104e19 −0.348111
\(665\) 2.25489e19i 0.392078i
\(666\) 8.13204e18 + 8.26058e18i 0.139920 + 0.142132i
\(667\) −5.39879e19 −0.919211
\(668\) 4.55968e19i 0.768244i
\(669\) −4.77602e19 + 1.95639e19i −0.796313 + 0.326192i
\(670\) −2.74466e19 −0.452861
\(671\) 5.56937e19i 0.909387i
\(672\) −1.95811e18 4.78022e18i −0.0316411 0.0772436i
\(673\) 9.20725e19 1.47239 0.736197 0.676767i \(-0.236620\pi\)
0.736197 + 0.676767i \(0.236620\pi\)
\(674\) 4.34875e19i 0.688248i
\(675\) −1.83976e19 + 4.29787e19i −0.288160 + 0.673173i
\(676\) 6.18306e18 0.0958466
\(677\) 5.38915e19i 0.826799i 0.910550 + 0.413399i \(0.135659\pi\)
−0.910550 + 0.413399i \(0.864341\pi\)
\(678\) −1.80934e19 + 7.41155e18i −0.274734 + 0.112539i
\(679\) 3.40419e19 0.511594
\(680\) 7.08779e18i 0.105426i
\(681\) 1.29526e19 + 3.16205e19i 0.190690 + 0.465521i
\(682\) −2.10899e19 −0.307316
\(683\) 5.26049e19i 0.758719i −0.925249 0.379360i \(-0.876144\pi\)
0.925249 0.379360i \(-0.123856\pi\)
\(684\) 4.00515e19 3.94282e19i 0.571776 0.562878i
\(685\) 6.08717e17 0.00860164
\(686\) 4.24199e19i 0.593337i
\(687\) 8.09339e19 3.31527e19i 1.12055 0.459010i
\(688\) −8.17027e18 −0.111974
\(689\) 5.07230e19i 0.688130i
\(690\) 2.04640e19 + 4.99575e19i 0.274818 + 0.670898i
\(691\) 1.69293e19 0.225057 0.112529 0.993648i \(-0.464105\pi\)
0.112529 + 0.993648i \(0.464105\pi\)
\(692\) 2.91296e19i 0.383347i
\(693\) −4.18523e19 4.25139e19i −0.545239 0.553858i
\(694\) −3.36083e19 −0.433442
\(695\) 3.05904e19i 0.390564i
\(696\) 1.20076e19 4.91865e18i 0.151772 0.0621700i
\(697\) 3.42898e19 0.429077
\(698\) 6.00729e19i 0.744202i
\(699\) 2.28978e19 + 5.58992e19i 0.280837 + 0.685591i
\(700\) −1.42377e19 −0.172884
\(701\) 1.46538e20i 1.76166i −0.473430 0.880831i \(-0.656984\pi\)
0.473430 0.880831i \(-0.343016\pi\)
\(702\) 4.91018e19 + 2.10186e19i 0.584436 + 0.250175i
\(703\) −3.84080e19 −0.452621
\(704\) 1.76332e19i 0.205742i
\(705\) −4.48979e19 + 1.83914e19i −0.518683 + 0.212467i
\(706\) −7.51835e19 −0.859983
\(707\) 2.92995e18i 0.0331837i
\(708\) −8.80792e18 2.15023e19i −0.0987735 0.241130i
\(709\) −6.40379e19 −0.711072 −0.355536 0.934663i \(-0.615702\pi\)
−0.355536 + 0.934663i \(0.615702\pi\)
\(710\) 1.80938e19i 0.198940i
\(711\) −7.58928e19 + 7.47117e19i −0.826253 + 0.813395i
\(712\) 5.28371e19 0.569611
\(713\) 4.90126e19i 0.523216i
\(714\) 1.68439e19 6.89974e18i 0.178056 0.0729366i
\(715\) 7.31483e19 0.765705
\(716\) 1.21941e19i 0.126404i
\(717\) 1.47180e19 + 3.59302e19i 0.151083 + 0.368830i
\(718\) 7.09823e19 0.721570
\(719\) 7.12152e18i 0.0716920i −0.999357 0.0358460i \(-0.988587\pi\)
0.999357 0.0358460i \(-0.0114126\pi\)
\(720\) −9.10291e18 9.24680e18i −0.0907512 0.0921858i
\(721\) 4.38900e19 0.433330
\(722\) 1.13904e20i 1.11372i
\(723\) 1.61656e19 6.62186e18i 0.156539 0.0641227i
\(724\) −2.84822e19 −0.273152
\(725\) 3.57643e19i 0.339690i
\(726\) 4.86988e19 + 1.18886e20i 0.458102 + 1.11834i
\(727\) −6.63685e19 −0.618331 −0.309165 0.951008i \(-0.600050\pi\)
−0.309165 + 0.951008i \(0.600050\pi\)
\(728\) 1.62661e19i 0.150094i
\(729\) −7.55295e19 7.91695e19i −0.690278 0.723544i
\(730\) 3.57412e19 0.323526
\(731\) 2.87894e19i 0.258114i
\(732\) 2.87872e19 1.17920e19i 0.255636 0.104715i
\(733\) −8.99402e19 −0.791090 −0.395545 0.918447i \(-0.629444\pi\)
−0.395545 + 0.918447i \(0.629444\pi\)
\(734\) 1.66655e19i 0.145193i
\(735\) −1.76610e19 4.31149e19i −0.152407 0.372062i
\(736\) 4.09793e19 0.350284
\(737\) 2.40606e20i 2.03720i
\(738\) 4.47348e19 4.40386e19i 0.375190 0.369351i
\(739\) 1.79121e20 1.48811 0.744056 0.668118i \(-0.232900\pi\)
0.744056 + 0.668118i \(0.232900\pi\)
\(740\) 8.86736e18i 0.0729747i
\(741\) −1.63766e20 + 6.70832e19i −1.33505 + 0.546872i
\(742\) −3.16458e19 −0.255557
\(743\) 8.18780e19i 0.655007i 0.944850 + 0.327503i \(0.106207\pi\)
−0.944850 + 0.327503i \(0.893793\pi\)
\(744\) −4.46537e18 1.09011e19i −0.0353873 0.0863889i
\(745\) 5.81139e19 0.456232
\(746\) 3.13060e18i 0.0243476i
\(747\) −8.96519e19 9.10691e19i −0.690741 0.701660i
\(748\) −6.21339e19 −0.474261
\(749\) 3.18183e19i 0.240605i
\(750\) −7.82893e19 + 3.20695e19i −0.586508 + 0.240250i
\(751\) −1.87139e20 −1.38895 −0.694474 0.719518i \(-0.744363\pi\)
−0.694474 + 0.719518i \(0.744363\pi\)
\(752\) 3.68291e19i 0.270811i
\(753\) −1.17814e19 2.87612e19i −0.0858284 0.209528i
\(754\) −4.08595e19 −0.294913
\(755\) 5.48761e19i 0.392423i
\(756\) 1.31134e19 3.06343e19i 0.0929099 0.217048i
\(757\) 3.06234e18 0.0214972 0.0107486 0.999942i \(-0.496579\pi\)
0.0107486 + 0.999942i \(0.496579\pi\)
\(758\) 2.90999e19i 0.202398i
\(759\) 4.37943e20 1.79394e20i 3.01804 1.23627i
\(760\) 4.29934e19 0.293567
\(761\) 1.96596e20i 1.33009i −0.746801 0.665047i \(-0.768411\pi\)
0.746801 0.665047i \(-0.231589\pi\)
\(762\) −7.18733e19 1.75460e20i −0.481818 1.17623i
\(763\) 6.72771e19 0.446885
\(764\) 3.35874e19i 0.221066i
\(765\) 3.25827e19 3.20757e19i 0.212499 0.209193i
\(766\) −7.73098e19 −0.499612
\(767\) 7.31679e19i 0.468547i
\(768\) −9.11434e18 + 3.73348e18i −0.0578358 + 0.0236911i
\(769\) 2.28748e20 1.43838 0.719190 0.694813i \(-0.244513\pi\)
0.719190 + 0.694813i \(0.244513\pi\)
\(770\) 4.56367e19i 0.284367i
\(771\) 8.12009e19 + 1.98231e20i 0.501395 + 1.22403i
\(772\) −6.48658e19 −0.396913
\(773\) 1.59306e20i 0.965997i −0.875621 0.482999i \(-0.839548\pi\)
0.875621 0.482999i \(-0.160452\pi\)
\(774\) −3.69744e19 3.75589e19i −0.222185 0.225697i
\(775\) −3.24684e19 −0.193352
\(776\) 6.49070e19i 0.383053i
\(777\) −2.10730e19 + 8.63209e18i −0.123248 + 0.0504858i
\(778\) 1.76900e20 1.02535
\(779\) 2.07997e20i 1.19480i
\(780\) 1.54877e19 + 3.78092e19i 0.0881706 + 0.215246i
\(781\) −1.58616e20 −0.894933
\(782\) 1.44398e20i 0.807446i
\(783\) 7.69514e19 + 3.29400e19i 0.426466 + 0.182554i
\(784\) −3.53665e19 −0.194258
\(785\) 1.08631e20i 0.591381i
\(786\) −5.60819e19 + 2.29727e19i −0.302597 + 0.123952i
\(787\) −1.03633e20 −0.554212 −0.277106 0.960839i \(-0.589375\pi\)
−0.277106 + 0.960839i \(0.589375\pi\)
\(788\) 1.35572e20i 0.718599i
\(789\) −1.29379e20 3.15846e20i −0.679713 1.65934i
\(790\) −8.14674e19 −0.424223
\(791\) 3.84120e19i 0.198258i
\(792\) −8.10604e19 + 7.97990e19i −0.414699 + 0.408245i
\(793\) −9.79570e19 −0.496733
\(794\) 2.51596e20i 1.26462i
\(795\) −7.35578e19 + 3.01313e19i −0.366487 + 0.150123i
\(796\) 9.33959e19 0.461250
\(797\) 3.68547e20i 1.80420i 0.431527 + 0.902100i \(0.357975\pi\)
−0.431527 + 0.902100i \(0.642025\pi\)
\(798\) 4.18528e19 + 1.02173e20i 0.203097 + 0.495809i
\(799\) −1.29774e20 −0.624251
\(800\) 2.71467e19i 0.129446i
\(801\) 2.39113e20 + 2.42893e20i 1.13025 + 1.14812i
\(802\) 1.96321e20 0.919913
\(803\) 3.13319e20i 1.45539i
\(804\) −1.24365e20 + 5.09434e19i −0.572673 + 0.234583i
\(805\) −1.06059e20 −0.484146
\(806\) 3.70941e19i 0.167865i
\(807\) 2.23469e19 + 5.45543e19i 0.100254 + 0.244745i
\(808\) 5.58648e18 0.0248461
\(809\) 1.33306e20i 0.587772i −0.955840 0.293886i \(-0.905051\pi\)
0.955840 0.293886i \(-0.0949486\pi\)
\(810\) 1.31268e18 8.36925e19i 0.00573803 0.365840i
\(811\) 1.22205e20 0.529593 0.264797 0.964304i \(-0.414695\pi\)
0.264797 + 0.964304i \(0.414695\pi\)
\(812\) 2.54920e19i 0.109524i
\(813\) −2.50752e20 + 1.02715e20i −1.06810 + 0.437521i
\(814\) 7.77341e19 0.328277
\(815\) 5.32079e19i 0.222778i
\(816\) −1.31556e19 3.21160e19i −0.0546109 0.133318i
\(817\) 1.74632e20 0.718736
\(818\) 1.28432e20i 0.524081i
\(819\) −7.47757e19 + 7.36120e19i −0.302533 + 0.297825i
\(820\) 4.80207e19 0.192634
\(821\) 2.89339e20i 1.15082i −0.817867 0.575408i \(-0.804843\pi\)
0.817867 0.575408i \(-0.195157\pi\)
\(822\) 2.75820e18 1.12983e18i 0.0108773 0.00445566i
\(823\) −4.11108e20 −1.60752 −0.803761 0.594952i \(-0.797171\pi\)
−0.803761 + 0.594952i \(0.797171\pi\)
\(824\) 8.36841e19i 0.324454i
\(825\) 1.18839e20 + 2.90115e20i 0.456859 + 1.11530i
\(826\) 4.56490e19 0.174009
\(827\) 2.05905e19i 0.0778267i 0.999243 + 0.0389133i \(0.0123896\pi\)
−0.999243 + 0.0389133i \(0.987610\pi\)
\(828\) 1.85451e20 + 1.88383e20i 0.695053 + 0.706040i
\(829\) 4.12783e20 1.53405 0.767025 0.641617i \(-0.221736\pi\)
0.767025 + 0.641617i \(0.221736\pi\)
\(830\) 9.77585e19i 0.360253i
\(831\) 8.07788e19 3.30892e19i 0.295182 0.120915i
\(832\) 3.10143e19 0.112382
\(833\) 1.24620e20i 0.447788i
\(834\) −5.67786e19 1.38610e20i −0.202312 0.493894i
\(835\) −2.25006e20 −0.795040
\(836\) 3.76894e20i 1.32061i
\(837\) 2.99044e19 6.98600e19i 0.103910 0.242745i
\(838\) 1.46207e20 0.503800
\(839\) 3.20024e20i 1.09358i −0.837271 0.546789i \(-0.815850\pi\)
0.837271 0.546789i \(-0.184150\pi\)
\(840\) 2.35889e19 9.66266e18i 0.0799379 0.0327448i
\(841\) 2.33524e20 0.784801
\(842\) 3.30167e20i 1.10039i
\(843\) −1.98281e20 4.84052e20i −0.655372 1.59992i
\(844\) 7.84825e18 0.0257262
\(845\) 3.05115e19i 0.0991897i
\(846\) −1.69304e20 + 1.66669e20i −0.545852 + 0.537357i
\(847\) −2.52392e20 −0.807034
\(848\) 6.03383e19i 0.191347i
\(849\) −1.76968e19 + 7.24908e18i −0.0556596 + 0.0227997i
\(850\) −9.56564e19 −0.298388
\(851\) 1.80653e20i 0.558904i
\(852\) −3.35838e19 8.19863e19i −0.103051 0.251573i
\(853\) −1.37167e18 −0.00417453 −0.00208726 0.999998i \(-0.500664\pi\)
−0.00208726 + 0.999998i \(0.500664\pi\)
\(854\) 6.11148e19i 0.184476i
\(855\) 1.94566e20 + 1.97642e20i 0.582512 + 0.591720i
\(856\) −6.06673e19 −0.180152
\(857\) 1.79112e20i 0.527544i 0.964585 + 0.263772i \(0.0849667\pi\)
−0.964585 + 0.263772i \(0.915033\pi\)
\(858\) 3.31447e20 1.35770e20i 0.968286 0.396636i
\(859\) −1.12363e20 −0.325590 −0.162795 0.986660i \(-0.552051\pi\)
−0.162795 + 0.986660i \(0.552051\pi\)
\(860\) 4.03178e19i 0.115880i
\(861\) 4.67467e19 + 1.14120e20i 0.133269 + 0.325342i
\(862\) −3.45689e20 −0.977540
\(863\) 5.93686e20i 1.66526i 0.553832 + 0.832628i \(0.313165\pi\)
−0.553832 + 0.832628i \(0.686835\pi\)
\(864\) −5.84097e19 2.50030e19i −0.162513 0.0695658i
\(865\) 1.43746e20 0.396718
\(866\) 1.59535e20i 0.436747i
\(867\) −2.27595e20 + 9.32292e19i −0.618058 + 0.253173i
\(868\) 2.31428e19 0.0623415
\(869\) 7.14169e20i 1.90837i
\(870\) 2.42720e19 + 5.92539e19i 0.0643385 + 0.157066i
\(871\) 4.23190e20 1.11278
\(872\) 1.28276e20i 0.334603i
\(873\) 2.98379e20 2.93736e20i 0.772090 0.760076i
\(874\) −8.75895e20 −2.24839
\(875\) 1.66207e20i 0.423246i
\(876\) 1.61950e20 6.63390e19i 0.409120 0.167587i
\(877\) −2.81536e20 −0.705565 −0.352783 0.935705i \(-0.614764\pi\)
−0.352783 + 0.935705i \(0.614764\pi\)
\(878\) 2.11254e20i 0.525223i
\(879\) 1.85006e19 + 4.51644e19i 0.0456313 + 0.111397i
\(880\) −8.70146e19 −0.212919
\(881\) 4.59687e20i 1.11592i 0.829869 + 0.557958i \(0.188415\pi\)
−0.829869 + 0.557958i \(0.811585\pi\)
\(882\) −1.60050e20 1.62580e20i −0.385458 0.391551i
\(883\) 5.05033e20 1.20669 0.603343 0.797482i \(-0.293835\pi\)
0.603343 + 0.797482i \(0.293835\pi\)
\(884\) 1.09284e20i 0.259055i
\(885\) 1.06107e20 4.34644e19i 0.249541 0.102219i
\(886\) 4.99027e20 1.16436
\(887\) 2.84488e20i 0.658564i 0.944232 + 0.329282i \(0.106807\pi\)
−0.944232 + 0.329282i \(0.893193\pi\)
\(888\) 1.64586e19 + 4.01795e19i 0.0378010 + 0.0922813i
\(889\) 3.72499e20 0.848814
\(890\) 2.60735e20i 0.589480i
\(891\) −7.33676e20 1.15074e19i −1.64574 0.0258126i
\(892\) −1.93326e20 −0.430266
\(893\) 7.87187e20i 1.73827i
\(894\) 2.63324e20 1.07865e20i 0.576936 0.236329i
\(895\) 6.01743e19 0.130813
\(896\) 1.93496e19i 0.0417365i
\(897\) −3.15527e20 7.70277e20i −0.675288 1.64854i
\(898\) 1.45818e20 0.309653
\(899\) 5.81332e19i 0.122492i
\(900\) −1.24794e20 + 1.22852e20i −0.260914 + 0.256853i
\(901\) −2.12613e20 −0.441078
\(902\) 4.20965e20i 0.866564i
\(903\) 9.58141e19 3.92481e19i 0.195711 0.0801686i
\(904\) −7.32393e19 −0.148445
\(905\) 1.40551e20i 0.282679i
\(906\) 1.01855e20 + 2.48653e20i 0.203276 + 0.496245i
\(907\) 3.38318e20 0.669999 0.335000 0.942218i \(-0.391264\pi\)
0.335000 + 0.942218i \(0.391264\pi\)
\(908\) 1.27995e20i 0.251531i
\(909\) 2.52815e19 + 2.56812e19i 0.0493010 + 0.0500804i
\(910\) −8.02682e19 −0.155330
\(911\) 4.84530e20i 0.930449i −0.885193 0.465224i \(-0.845974\pi\)
0.885193 0.465224i \(-0.154026\pi\)
\(912\) 1.94811e20 7.97998e19i 0.371235 0.152068i
\(913\) −8.56982e20 −1.62060
\(914\) 1.95316e20i 0.366534i
\(915\) 5.81900e19 + 1.42056e20i 0.108368 + 0.264552i
\(916\) 3.27608e20 0.605461
\(917\) 1.19061e20i 0.218366i
\(918\) 8.81025e19 2.05817e20i 0.160358 0.374613i
\(919\) 2.01048e20 0.363155 0.181577 0.983377i \(-0.441880\pi\)
0.181577 + 0.983377i \(0.441880\pi\)
\(920\) 2.02220e20i 0.362502i
\(921\) −6.05728e20 + 2.48123e20i −1.07761 + 0.441417i
\(922\) 7.12822e20 1.25853
\(923\) 2.78983e20i 0.488838i
\(924\) −8.47060e19 2.06788e20i −0.147303 0.359601i
\(925\) 1.19673e20 0.206540
\(926\) 6.00492e19i 0.102856i
\(927\) 3.84698e20 3.78711e20i 0.653976 0.643799i
\(928\) 4.86050e19 0.0820059
\(929\) 1.15283e20i 0.193044i −0.995331 0.0965220i \(-0.969228\pi\)
0.995331 0.0965220i \(-0.0307718\pi\)
\(930\) 5.37933e19 2.20352e19i 0.0894021 0.0366216i
\(931\) 7.55925e20 1.24690
\(932\) 2.26272e20i 0.370441i
\(933\) 3.79017e20 + 9.25272e20i 0.615867 + 1.50348i
\(934\) −4.40256e20 −0.710031
\(935\) 3.06612e20i 0.490803i
\(936\) 1.40355e20 + 1.42573e20i 0.222995 + 0.226520i
\(937\) −4.45216e20 −0.702091 −0.351046 0.936358i \(-0.614174\pi\)
−0.351046 + 0.936358i \(0.614174\pi\)
\(938\) 2.64025e20i 0.413262i
\(939\) −4.84238e20 + 1.98357e20i −0.752316 + 0.308169i
\(940\) −1.81740e20 −0.280256
\(941\) 3.84694e20i 0.588828i −0.955678 0.294414i \(-0.904876\pi\)
0.955678 0.294414i \(-0.0951244\pi\)
\(942\) 2.01630e20 + 4.92227e20i 0.306336 + 0.747841i
\(943\) −9.78315e20 −1.47536
\(944\) 8.70380e19i 0.130288i
\(945\) 1.51171e20 + 6.47105e19i 0.224618 + 0.0961506i
\(946\) −3.53439e20 −0.521286
\(947\) 8.36588e20i 1.22479i 0.790552 + 0.612395i \(0.209794\pi\)
−0.790552 + 0.612395i \(0.790206\pi\)
\(948\) −3.69143e20 + 1.51211e20i −0.536458 + 0.219748i
\(949\) −5.51082e20 −0.794973
\(950\) 5.80237e20i 0.830883i
\(951\) 2.87222e20 + 7.01179e20i 0.408277 + 0.996702i
\(952\) 6.81817e19 0.0962076
\(953\) 1.09883e20i 0.153915i 0.997034 + 0.0769575i \(0.0245206\pi\)
−0.997034 + 0.0769575i \(0.975479\pi\)
\(954\) −2.77377e20 + 2.73060e20i −0.385684 + 0.379682i
\(955\) 1.65743e20 0.228777
\(956\) 1.45440e20i 0.199287i
\(957\) 5.19439e20 2.12776e20i 0.706563 0.289427i
\(958\) 3.80165e20 0.513350
\(959\) 5.85561e18i 0.00784950i
\(960\) −1.84236e19 4.49765e19i −0.0245175 0.0598531i
\(961\) −7.04168e20 −0.930278
\(962\) 1.36723e20i 0.179314i
\(963\) −2.74549e20 2.78889e20i −0.357467 0.363118i
\(964\) 6.54357e19 0.0845816
\(965\) 3.20093e20i 0.410757i
\(966\) −4.80571e20 + 1.96855e20i −0.612234 + 0.250788i
\(967\) 2.27258e20 0.287431 0.143715 0.989619i \(-0.454095\pi\)
0.143715 + 0.989619i \(0.454095\pi\)
\(968\) 4.81231e20i 0.604263i
\(969\) 2.81189e20 + 6.86450e20i 0.350535 + 0.855741i
\(970\) 3.20296e20 0.396414
\(971\) 7.80153e20i 0.958618i −0.877646 0.479309i \(-0.840887\pi\)
0.877646 0.479309i \(-0.159113\pi\)
\(972\) −1.49393e20 3.81662e20i −0.182250 0.465602i
\(973\) 2.94268e20 0.356412
\(974\) 6.63019e20i 0.797284i
\(975\) 5.10270e20 2.09021e20i 0.609211 0.249550i
\(976\) 1.16526e20 0.138126
\(977\) 1.06441e21i 1.25270i −0.779541 0.626352i \(-0.784547\pi\)
0.779541 0.626352i \(-0.215453\pi\)
\(978\) −9.87588e19 2.41094e20i −0.115399 0.281718i
\(979\) 2.28568e21 2.65178
\(980\) 1.74523e20i 0.201034i
\(981\) 5.89687e20 5.80511e20i 0.674433 0.663938i
\(982\) 1.37322e20 0.155941
\(983\) 4.92533e20i 0.555343i 0.960676 + 0.277671i \(0.0895626\pi\)
−0.960676 + 0.277671i \(0.910437\pi\)
\(984\) 2.17590e20 8.91309e19i 0.243598 0.0997844i
\(985\) −6.69006e20 −0.743663
\(986\) 1.71268e20i 0.189034i
\(987\) −1.76918e20 4.31900e20i −0.193889 0.473329i
\(988\) −6.62901e20 −0.721357
\(989\) 8.21384e20i 0.887508i
\(990\) −3.93784e20 4.00008e20i −0.422485 0.429163i
\(991\) −1.28336e21 −1.36720 −0.683601 0.729856i \(-0.739587\pi\)
−0.683601 + 0.729856i \(0.739587\pi\)
\(992\) 4.41258e19i 0.0466779i
\(993\) 5.51325e20 2.25838e20i 0.579113 0.237221i
\(994\) 1.74055e20 0.181544
\(995\) 4.60880e20i 0.477338i
\(996\) −1.81449e20 4.42960e20i −0.186612 0.455564i
\(997\) 6.77562e20 0.691963 0.345982 0.938241i \(-0.387546\pi\)
0.345982 + 0.938241i \(0.387546\pi\)
\(998\) 6.56337e20i 0.665600i
\(999\) −1.10223e20 + 2.57493e20i −0.110997 + 0.259302i
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 6.15.b.a.5.3 yes 4
3.2 odd 2 inner 6.15.b.a.5.1 4
4.3 odd 2 48.15.e.d.17.3 4
5.2 odd 4 150.15.b.a.149.4 8
5.3 odd 4 150.15.b.a.149.5 8
5.4 even 2 150.15.d.a.101.2 4
12.11 even 2 48.15.e.d.17.4 4
15.2 even 4 150.15.b.a.149.6 8
15.8 even 4 150.15.b.a.149.3 8
15.14 odd 2 150.15.d.a.101.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.15.b.a.5.1 4 3.2 odd 2 inner
6.15.b.a.5.3 yes 4 1.1 even 1 trivial
48.15.e.d.17.3 4 4.3 odd 2
48.15.e.d.17.4 4 12.11 even 2
150.15.b.a.149.3 8 15.8 even 4
150.15.b.a.149.4 8 5.2 odd 4
150.15.b.a.149.5 8 5.3 odd 4
150.15.b.a.149.6 8 15.2 even 4
150.15.d.a.101.2 4 5.4 even 2
150.15.d.a.101.4 4 15.14 odd 2