Properties

Label 7.17.b.b.6.8
Level $7$
Weight $17$
Character 7.6
Analytic conductor $11.363$
Analytic rank $0$
Dimension $8$
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] = [7,17,Mod(6,7)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 17, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7.6");
 
S:= CuspForms(chi, 17);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 17 \)
Character orbit: \([\chi]\) \(=\) 7.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: \(11.3627180700\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 5365384x^{6} + 10449491370210x^{4} + 8743024230718881600x^{2} + 2655236149032650377194000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{17}\cdot 3^{5}\cdot 7^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 6.8
Root \(1381.83i\) of defining polynomial
Character \(\chi\) \(=\) 7.6
Dual form 7.17.b.b.6.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+270.026 q^{2} +8290.96i q^{3} +7378.00 q^{4} +234861. i q^{5} +2.23878e6i q^{6} +(-4.98661e6 - 2.89252e6i) q^{7} -1.57042e7 q^{8} -2.56934e7 q^{9} +O(q^{10})\) \(q+270.026 q^{2} +8290.96i q^{3} +7378.00 q^{4} +234861. i q^{5} +2.23878e6i q^{6} +(-4.98661e6 - 2.89252e6i) q^{7} -1.57042e7 q^{8} -2.56934e7 q^{9} +6.34186e7i q^{10} +5.66575e7 q^{11} +6.11708e7i q^{12} +5.49071e8i q^{13} +(-1.34651e9 - 7.81057e8i) q^{14} -1.94722e9 q^{15} -4.72406e9 q^{16} +1.34700e10i q^{17} -6.93787e9 q^{18} -4.64514e8i q^{19} +1.73281e9i q^{20} +(2.39818e10 - 4.13438e10i) q^{21} +1.52990e10 q^{22} +6.50418e10 q^{23} -1.30203e11i q^{24} +9.74282e10 q^{25} +1.48263e11i q^{26} +1.43876e11i q^{27} +(-3.67912e10 - 2.13411e10i) q^{28} +8.11530e10 q^{29} -5.25801e11 q^{30} -1.17487e12i q^{31} -2.46430e11 q^{32} +4.69745e11i q^{33} +3.63725e12i q^{34} +(6.79341e11 - 1.17116e12i) q^{35} -1.89566e11 q^{36} -2.93669e12 q^{37} -1.25431e11i q^{38} -4.55233e12 q^{39} -3.68830e12i q^{40} +7.81827e12i q^{41} +(6.47571e12 - 1.11639e13i) q^{42} +1.54546e13 q^{43} +4.18019e11 q^{44} -6.03437e12i q^{45} +1.75630e13 q^{46} +1.35043e13i q^{47} -3.91670e13i q^{48} +(1.64995e13 + 2.88478e13i) q^{49} +2.63081e13 q^{50} -1.11679e14 q^{51} +4.05105e12i q^{52} -1.02111e14 q^{53} +3.88503e13i q^{54} +1.33066e13i q^{55} +(7.83105e13 + 4.54247e13i) q^{56} +3.85127e12 q^{57} +2.19134e13 q^{58} +1.65302e14i q^{59} -1.43666e13 q^{60} -3.07486e14i q^{61} -3.17245e14i q^{62} +(1.28123e14 + 7.43187e13i) q^{63} +2.43053e14 q^{64} -1.28955e14 q^{65} +1.26843e14i q^{66} +3.75420e13 q^{67} +9.93817e13i q^{68} +5.39259e14i q^{69} +(1.83440e14 - 3.16243e14i) q^{70} -1.78686e14 q^{71} +4.03493e14 q^{72} -8.37004e14i q^{73} -7.92983e14 q^{74} +8.07773e14i q^{75} -3.42719e12i q^{76} +(-2.82529e14 - 1.63883e14i) q^{77} -1.22925e15 q^{78} +2.06130e15 q^{79} -1.10950e15i q^{80} -2.29889e15 q^{81} +2.11114e15i q^{82} +2.72376e15i q^{83} +(1.76938e14 - 3.05034e14i) q^{84} -3.16358e15 q^{85} +4.17314e15 q^{86} +6.72837e14i q^{87} -8.89759e14 q^{88} -6.65516e15i q^{89} -1.62944e15i q^{90} +(1.58820e15 - 2.73800e15i) q^{91} +4.79878e14 q^{92} +9.74079e15 q^{93} +3.64651e15i q^{94} +1.09096e14 q^{95} -2.04314e15i q^{96} -3.48548e15i q^{97} +(4.45530e15 + 7.78964e15i) q^{98} -1.45572e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 544 q^{2} + 18784 q^{4} - 3034472 q^{7} - 35863808 q^{8} - 41933880 q^{9} + 430398704 q^{11} - 2080234240 q^{14} + 83393280 q^{15} - 4357080832 q^{16} - 7232400864 q^{18} + 45847234944 q^{21} - 34275403968 q^{22} + 89765082416 q^{23} + 61966251080 q^{25} - 376785722656 q^{28} - 22437591664 q^{29} - 192018300480 q^{30} + 941689387008 q^{32} + 371925382080 q^{35} - 4527659399328 q^{36} + 5737866534416 q^{37} - 7975804007808 q^{39} - 13160568536640 q^{42} - 3976952110864 q^{43} + 45337613120448 q^{44} + 35817469755072 q^{46} - 27450534789496 q^{49} - 96564765668320 q^{50} + 58670380591488 q^{51} - 108679841507824 q^{53} - 15117119134208 q^{56} - 196163055495360 q^{57} + 650847682404672 q^{58} - 335782392744960 q^{60} + 223739049782808 q^{63} - 460533940742144 q^{64} + 573279455461440 q^{65} - 722120065643024 q^{67} + 12\!\cdots\!60 q^{70}+ \cdots - 15\!\cdots\!92 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 270.026 1.05479 0.527394 0.849621i \(-0.323169\pi\)
0.527394 + 0.849621i \(0.323169\pi\)
\(3\) 8290.96i 1.26367i 0.775101 + 0.631837i \(0.217699\pi\)
−0.775101 + 0.631837i \(0.782301\pi\)
\(4\) 7378.00 0.112579
\(5\) 234861.i 0.601244i 0.953743 + 0.300622i \(0.0971943\pi\)
−0.953743 + 0.300622i \(0.902806\pi\)
\(6\) 2.23878e6i 1.33291i
\(7\) −4.98661e6 2.89252e6i −0.865009 0.501756i
\(8\) −1.57042e7 −0.936041
\(9\) −2.56934e7 −0.596872
\(10\) 6.34186e7i 0.634186i
\(11\) 5.66575e7 0.264311 0.132156 0.991229i \(-0.457810\pi\)
0.132156 + 0.991229i \(0.457810\pi\)
\(12\) 6.11708e7i 0.142264i
\(13\) 5.49071e8i 0.673104i 0.941665 + 0.336552i \(0.109261\pi\)
−0.941665 + 0.336552i \(0.890739\pi\)
\(14\) −1.34651e9 7.81057e8i −0.912402 0.529247i
\(15\) −1.94722e9 −0.759777
\(16\) −4.72406e9 −1.09991
\(17\) 1.34700e10i 1.93097i 0.260453 + 0.965487i \(0.416128\pi\)
−0.260453 + 0.965487i \(0.583872\pi\)
\(18\) −6.93787e9 −0.629573
\(19\) 4.64514e8i 0.0273508i −0.999906 0.0136754i \(-0.995647\pi\)
0.999906 0.0136754i \(-0.00435315\pi\)
\(20\) 1.73281e9i 0.0676877i
\(21\) 2.39818e10 4.13438e10i 0.634056 1.09309i
\(22\) 1.52990e10 0.278793
\(23\) 6.50418e10 0.830557 0.415279 0.909694i \(-0.363684\pi\)
0.415279 + 0.909694i \(0.363684\pi\)
\(24\) 1.30203e11i 1.18285i
\(25\) 9.74282e10 0.638505
\(26\) 1.48263e11i 0.709982i
\(27\) 1.43876e11i 0.509423i
\(28\) −3.67912e10 2.13411e10i −0.0973822 0.0564874i
\(29\) 8.11530e10 0.162226 0.0811130 0.996705i \(-0.474153\pi\)
0.0811130 + 0.996705i \(0.474153\pi\)
\(30\) −5.25801e11 −0.801404
\(31\) 1.17487e12i 1.37751i −0.724993 0.688756i \(-0.758157\pi\)
0.724993 0.688756i \(-0.241843\pi\)
\(32\) −2.46430e11 −0.224126
\(33\) 4.69745e11i 0.334003i
\(34\) 3.63725e12i 2.03677i
\(35\) 6.79341e11 1.17116e12i 0.301678 0.520082i
\(36\) −1.89566e11 −0.0671955
\(37\) −2.93669e12 −0.836074 −0.418037 0.908430i \(-0.637282\pi\)
−0.418037 + 0.908430i \(0.637282\pi\)
\(38\) 1.25431e11i 0.0288493i
\(39\) −4.55233e12 −0.850583
\(40\) 3.68830e12i 0.562790i
\(41\) 7.81827e12i 0.979129i 0.871967 + 0.489564i \(0.162844\pi\)
−0.871967 + 0.489564i \(0.837156\pi\)
\(42\) 6.47571e12 1.11639e13i 0.668795 1.15298i
\(43\) 1.54546e13 1.32224 0.661119 0.750281i \(-0.270082\pi\)
0.661119 + 0.750281i \(0.270082\pi\)
\(44\) 4.18019e11 0.0297560
\(45\) 6.03437e12i 0.358866i
\(46\) 1.75630e13 0.876063
\(47\) 1.35043e13i 0.567139i 0.958952 + 0.283569i \(0.0915186\pi\)
−0.958952 + 0.283569i \(0.908481\pi\)
\(48\) 3.91670e13i 1.38992i
\(49\) 1.64995e13 + 2.88478e13i 0.496481 + 0.868047i
\(50\) 2.63081e13 0.673488
\(51\) −1.11679e14 −2.44012
\(52\) 4.05105e12i 0.0757776i
\(53\) −1.02111e14 −1.64008 −0.820038 0.572309i \(-0.806048\pi\)
−0.820038 + 0.572309i \(0.806048\pi\)
\(54\) 3.88503e13i 0.537333i
\(55\) 1.33066e13i 0.158916i
\(56\) 7.83105e13 + 4.54247e13i 0.809684 + 0.469665i
\(57\) 3.85127e12 0.0345625
\(58\) 2.19134e13 0.171114
\(59\) 1.65302e14i 1.12580i 0.826524 + 0.562902i \(0.190315\pi\)
−0.826524 + 0.562902i \(0.809685\pi\)
\(60\) −1.43666e13 −0.0855352
\(61\) 3.07486e14i 1.60394i −0.597368 0.801968i \(-0.703787\pi\)
0.597368 0.801968i \(-0.296213\pi\)
\(62\) 3.17245e14i 1.45298i
\(63\) 1.28123e14 + 7.43187e13i 0.516299 + 0.299484i
\(64\) 2.43053e14 0.863499
\(65\) −1.28955e14 −0.404700
\(66\) 1.26843e14i 0.352303i
\(67\) 3.75420e13 0.0924527 0.0462263 0.998931i \(-0.485280\pi\)
0.0462263 + 0.998931i \(0.485280\pi\)
\(68\) 9.93817e13i 0.217388i
\(69\) 5.39259e14i 1.04955i
\(70\) 1.83440e14 3.16243e14i 0.318207 0.548577i
\(71\) −1.78686e14 −0.276709 −0.138354 0.990383i \(-0.544181\pi\)
−0.138354 + 0.990383i \(0.544181\pi\)
\(72\) 4.03493e14 0.558696
\(73\) 8.37004e14i 1.03787i −0.854812 0.518937i \(-0.826328\pi\)
0.854812 0.518937i \(-0.173672\pi\)
\(74\) −7.92983e14 −0.881881
\(75\) 8.07773e14i 0.806862i
\(76\) 3.42719e12i 0.00307914i
\(77\) −2.82529e14 1.63883e14i −0.228632 0.132620i
\(78\) −1.22925e15 −0.897186
\(79\) 2.06130e15 1.35870 0.679350 0.733815i \(-0.262262\pi\)
0.679350 + 0.733815i \(0.262262\pi\)
\(80\) 1.10950e15i 0.661312i
\(81\) −2.29889e15 −1.24062
\(82\) 2.11114e15i 1.03277i
\(83\) 2.72376e15i 1.20933i 0.796480 + 0.604664i \(0.206693\pi\)
−0.796480 + 0.604664i \(0.793307\pi\)
\(84\) 1.76938e14 3.05034e14i 0.0713817 0.123059i
\(85\) −3.16358e15 −1.16099
\(86\) 4.17314e15 1.39468
\(87\) 6.72837e14i 0.205001i
\(88\) −8.89759e14 −0.247406
\(89\) 6.65516e15i 1.69059i −0.534300 0.845295i \(-0.679425\pi\)
0.534300 0.845295i \(-0.320575\pi\)
\(90\) 1.62944e15i 0.378528i
\(91\) 1.58820e15 2.73800e15i 0.337734 0.582241i
\(92\) 4.79878e14 0.0935037
\(93\) 9.74079e15 1.74073
\(94\) 3.64651e15i 0.598211i
\(95\) 1.09096e14 0.0164445
\(96\) 2.04314e15i 0.283223i
\(97\) 3.48548e15i 0.444722i −0.974964 0.222361i \(-0.928624\pi\)
0.974964 0.222361i \(-0.0713764\pi\)
\(98\) 4.45530e15 + 7.78964e15i 0.523683 + 0.915607i
\(99\) −1.45572e15 −0.157760
\(100\) 7.18825e14 0.0718825
\(101\) 2.00208e15i 0.184889i 0.995718 + 0.0924443i \(0.0294680\pi\)
−0.995718 + 0.0924443i \(0.970532\pi\)
\(102\) −3.01563e16 −2.57381
\(103\) 1.19192e16i 0.940912i 0.882424 + 0.470456i \(0.155911\pi\)
−0.882424 + 0.470456i \(0.844089\pi\)
\(104\) 8.62271e15i 0.630053i
\(105\) 9.71004e15 + 5.63240e15i 0.657214 + 0.381223i
\(106\) −2.75725e16 −1.72993
\(107\) 1.23218e16 0.717141 0.358571 0.933503i \(-0.383264\pi\)
0.358571 + 0.933503i \(0.383264\pi\)
\(108\) 1.06152e15i 0.0573505i
\(109\) −2.59830e16 −1.30400 −0.651999 0.758220i \(-0.726069\pi\)
−0.651999 + 0.758220i \(0.726069\pi\)
\(110\) 3.59314e15i 0.167623i
\(111\) 2.43480e16i 1.05652i
\(112\) 2.35570e16 + 1.36645e16i 0.951428 + 0.551884i
\(113\) 4.55247e16 1.71246 0.856229 0.516596i \(-0.172801\pi\)
0.856229 + 0.516596i \(0.172801\pi\)
\(114\) 1.03994e15 0.0364561
\(115\) 1.52758e16i 0.499368i
\(116\) 5.98747e14 0.0182633
\(117\) 1.41075e16i 0.401756i
\(118\) 4.46359e16i 1.18749i
\(119\) 3.89623e16 6.71696e16i 0.968878 1.67031i
\(120\) 3.05795e16 0.711182
\(121\) −4.27397e16 −0.930139
\(122\) 8.30292e16i 1.69181i
\(123\) −6.48210e16 −1.23730
\(124\) 8.66818e15i 0.155080i
\(125\) 5.87190e16i 0.985142i
\(126\) 3.45964e16 + 2.00680e16i 0.544587 + 0.315892i
\(127\) −4.89229e16 −0.722907 −0.361454 0.932390i \(-0.617719\pi\)
−0.361454 + 0.932390i \(0.617719\pi\)
\(128\) 8.17807e16 1.13494
\(129\) 1.28133e17i 1.67088i
\(130\) −3.48213e16 −0.426873
\(131\) 3.67339e16i 0.423542i −0.977319 0.211771i \(-0.932077\pi\)
0.977319 0.211771i \(-0.0679231\pi\)
\(132\) 3.46578e15i 0.0376019i
\(133\) −1.34362e15 + 2.31635e15i −0.0137234 + 0.0236587i
\(134\) 1.01373e16 0.0975180
\(135\) −3.37909e16 −0.306288
\(136\) 2.11535e17i 1.80747i
\(137\) −6.28808e16 −0.506703 −0.253352 0.967374i \(-0.581533\pi\)
−0.253352 + 0.967374i \(0.581533\pi\)
\(138\) 1.45614e17i 1.10706i
\(139\) 7.02978e16i 0.504456i 0.967668 + 0.252228i \(0.0811633\pi\)
−0.967668 + 0.252228i \(0.918837\pi\)
\(140\) 5.01218e15 8.64082e15i 0.0339627 0.0585505i
\(141\) −1.11964e17 −0.716678
\(142\) −4.82498e16 −0.291869
\(143\) 3.11090e16i 0.177909i
\(144\) 1.21377e17 0.656502
\(145\) 1.90597e16i 0.0975375i
\(146\) 2.26013e17i 1.09474i
\(147\) −2.39176e17 + 1.36797e17i −1.09693 + 0.627391i
\(148\) −2.16669e16 −0.0941247
\(149\) 2.78521e17 1.14649 0.573243 0.819386i \(-0.305685\pi\)
0.573243 + 0.819386i \(0.305685\pi\)
\(150\) 2.18120e17i 0.851069i
\(151\) 2.97192e17 1.09957 0.549784 0.835307i \(-0.314710\pi\)
0.549784 + 0.835307i \(0.314710\pi\)
\(152\) 7.29481e15i 0.0256015i
\(153\) 3.46090e17i 1.15254i
\(154\) −7.62900e16 4.42527e16i −0.241158 0.139886i
\(155\) 2.75931e17 0.828222
\(156\) −3.35871e16 −0.0957582
\(157\) 2.97914e17i 0.807036i 0.914972 + 0.403518i \(0.132213\pi\)
−0.914972 + 0.403518i \(0.867787\pi\)
\(158\) 5.56603e17 1.43314
\(159\) 8.46596e17i 2.07252i
\(160\) 5.78767e16i 0.134755i
\(161\) −3.24338e17 1.88135e17i −0.718440 0.416737i
\(162\) −6.20759e17 −1.30859
\(163\) 1.69831e17 0.340813 0.170406 0.985374i \(-0.445492\pi\)
0.170406 + 0.985374i \(0.445492\pi\)
\(164\) 5.76832e16i 0.110230i
\(165\) −1.10325e17 −0.200818
\(166\) 7.35486e17i 1.27559i
\(167\) 5.70061e17i 0.942300i 0.882053 + 0.471150i \(0.156161\pi\)
−0.882053 + 0.471150i \(0.843839\pi\)
\(168\) −3.76614e17 + 6.49269e17i −0.593503 + 1.02318i
\(169\) 3.63937e17 0.546931
\(170\) −8.54248e17 −1.22460
\(171\) 1.19349e16i 0.0163249i
\(172\) 1.14024e17 0.148857
\(173\) 2.23303e17i 0.278308i 0.990271 + 0.139154i \(0.0444383\pi\)
−0.990271 + 0.139154i \(0.955562\pi\)
\(174\) 1.81683e17i 0.216233i
\(175\) −4.85836e17 2.81813e17i −0.552313 0.320374i
\(176\) −2.67653e17 −0.290718
\(177\) −1.37052e18 −1.42265
\(178\) 1.79707e18i 1.78322i
\(179\) 1.28169e18 1.21607 0.608033 0.793911i \(-0.291959\pi\)
0.608033 + 0.793911i \(0.291959\pi\)
\(180\) 4.45216e16i 0.0404009i
\(181\) 7.40013e17i 0.642408i 0.947010 + 0.321204i \(0.104087\pi\)
−0.947010 + 0.321204i \(0.895913\pi\)
\(182\) 4.28856e17 7.39332e17i 0.356238 0.614141i
\(183\) 2.54936e18 2.02685
\(184\) −1.02143e18 −0.777436
\(185\) 6.89715e17i 0.502685i
\(186\) 2.63027e18 1.83610
\(187\) 7.63177e17i 0.510378i
\(188\) 9.96348e16i 0.0638481i
\(189\) 4.16165e17 7.17453e17i 0.255606 0.440655i
\(190\) 2.94588e16 0.0173455
\(191\) −5.02202e17 −0.283538 −0.141769 0.989900i \(-0.545279\pi\)
−0.141769 + 0.989900i \(0.545279\pi\)
\(192\) 2.01515e18i 1.09118i
\(193\) −1.78225e18 −0.925787 −0.462893 0.886414i \(-0.653189\pi\)
−0.462893 + 0.886414i \(0.653189\pi\)
\(194\) 9.41171e17i 0.469088i
\(195\) 1.06917e18i 0.511409i
\(196\) 1.21734e17 + 2.12839e17i 0.0558936 + 0.0977243i
\(197\) −4.91399e16 −0.0216623 −0.0108311 0.999941i \(-0.503448\pi\)
−0.0108311 + 0.999941i \(0.503448\pi\)
\(198\) −3.93083e17 −0.166403
\(199\) 9.47298e16i 0.0385179i −0.999815 0.0192589i \(-0.993869\pi\)
0.999815 0.0192589i \(-0.00613069\pi\)
\(200\) −1.53003e18 −0.597667
\(201\) 3.11260e17i 0.116830i
\(202\) 5.40613e17i 0.195019i
\(203\) −4.04678e17 2.34737e17i −0.140327 0.0813979i
\(204\) −8.23970e17 −0.274707
\(205\) −1.83621e18 −0.588696
\(206\) 3.21849e18i 0.992463i
\(207\) −1.67114e18 −0.495736
\(208\) 2.59384e18i 0.740350i
\(209\) 2.63182e16i 0.00722913i
\(210\) 2.62196e18 + 1.52089e18i 0.693222 + 0.402109i
\(211\) 3.32011e18 0.845070 0.422535 0.906347i \(-0.361140\pi\)
0.422535 + 0.906347i \(0.361140\pi\)
\(212\) −7.53373e17 −0.184639
\(213\) 1.48148e18i 0.349670i
\(214\) 3.32721e18 0.756433
\(215\) 3.62968e18i 0.794988i
\(216\) 2.25945e18i 0.476841i
\(217\) −3.39833e18 + 5.85860e18i −0.691175 + 1.19156i
\(218\) −7.01607e18 −1.37544
\(219\) 6.93957e18 1.31153
\(220\) 9.81765e16i 0.0178906i
\(221\) −7.39599e18 −1.29975
\(222\) 6.57459e18i 1.11441i
\(223\) 9.94156e18i 1.62561i −0.582538 0.812804i \(-0.697940\pi\)
0.582538 0.812804i \(-0.302060\pi\)
\(224\) 1.22885e18 + 7.12804e17i 0.193871 + 0.112457i
\(225\) −2.50326e18 −0.381106
\(226\) 1.22929e19 1.80628
\(227\) 1.66245e18i 0.235799i −0.993026 0.117899i \(-0.962384\pi\)
0.993026 0.117899i \(-0.0376161\pi\)
\(228\) 2.84147e16 0.00389103
\(229\) 8.16261e18i 1.07931i 0.841887 + 0.539654i \(0.181445\pi\)
−0.841887 + 0.539654i \(0.818555\pi\)
\(230\) 4.12486e18i 0.526728i
\(231\) 1.35875e18 2.34243e18i 0.167588 0.288916i
\(232\) −1.27444e18 −0.151850
\(233\) 8.50556e18 0.979164 0.489582 0.871957i \(-0.337149\pi\)
0.489582 + 0.871957i \(0.337149\pi\)
\(234\) 3.80939e18i 0.423768i
\(235\) −3.17163e18 −0.340989
\(236\) 1.21960e18i 0.126742i
\(237\) 1.70901e19i 1.71695i
\(238\) 1.05208e19 1.81375e19i 1.02196 1.76182i
\(239\) −1.32313e18 −0.124285 −0.0621425 0.998067i \(-0.519793\pi\)
−0.0621425 + 0.998067i \(0.519793\pi\)
\(240\) 9.19880e18 0.835683
\(241\) 6.05493e17i 0.0532075i 0.999646 + 0.0266037i \(0.00846923\pi\)
−0.999646 + 0.0266037i \(0.991531\pi\)
\(242\) −1.15408e19 −0.981101
\(243\) 1.28666e19i 1.05831i
\(244\) 2.26863e18i 0.180570i
\(245\) −6.77522e18 + 3.87510e18i −0.521909 + 0.298507i
\(246\) −1.75033e19 −1.30509
\(247\) 2.55051e17 0.0184099
\(248\) 1.84503e19i 1.28941i
\(249\) −2.25826e19 −1.52820
\(250\) 1.58557e19i 1.03912i
\(251\) 1.98557e18i 0.126036i −0.998012 0.0630180i \(-0.979927\pi\)
0.998012 0.0630180i \(-0.0200725\pi\)
\(252\) 9.45290e17 + 5.48324e17i 0.0581247 + 0.0337157i
\(253\) 3.68510e18 0.219526
\(254\) −1.32105e19 −0.762515
\(255\) 2.62291e19i 1.46711i
\(256\) 6.15417e18 0.333618
\(257\) 6.45607e18i 0.339237i 0.985510 + 0.169618i \(0.0542535\pi\)
−0.985510 + 0.169618i \(0.945746\pi\)
\(258\) 3.45993e19i 1.76242i
\(259\) 1.46441e19 + 8.49445e18i 0.723211 + 0.419505i
\(260\) −9.51434e17 −0.0455609
\(261\) −2.08509e18 −0.0968281
\(262\) 9.91911e18i 0.446748i
\(263\) 1.26128e19 0.551019 0.275510 0.961298i \(-0.411153\pi\)
0.275510 + 0.961298i \(0.411153\pi\)
\(264\) 7.37696e18i 0.312641i
\(265\) 2.39818e19i 0.986087i
\(266\) −3.62812e17 + 6.25474e17i −0.0144753 + 0.0249549i
\(267\) 5.51777e19 2.13635
\(268\) 2.76985e17 0.0104083
\(269\) 3.28477e18i 0.119808i −0.998204 0.0599041i \(-0.980921\pi\)
0.998204 0.0599041i \(-0.0190795\pi\)
\(270\) −9.12442e18 −0.323069
\(271\) 2.99307e19i 1.02888i −0.857528 0.514438i \(-0.828001\pi\)
0.857528 0.514438i \(-0.171999\pi\)
\(272\) 6.36331e19i 2.12389i
\(273\) 2.27007e19 + 1.31677e19i 0.735762 + 0.426786i
\(274\) −1.69795e19 −0.534465
\(275\) 5.52004e18 0.168764
\(276\) 3.97866e18i 0.118158i
\(277\) −1.52132e18 −0.0438918 −0.0219459 0.999759i \(-0.506986\pi\)
−0.0219459 + 0.999759i \(0.506986\pi\)
\(278\) 1.89822e19i 0.532095i
\(279\) 3.01863e19i 0.822198i
\(280\) −1.06685e19 + 1.83921e19i −0.282383 + 0.486818i
\(281\) 1.56025e19 0.401368 0.200684 0.979656i \(-0.435684\pi\)
0.200684 + 0.979656i \(0.435684\pi\)
\(282\) −3.02331e19 −0.755944
\(283\) 7.38749e19i 1.79558i 0.440422 + 0.897791i \(0.354829\pi\)
−0.440422 + 0.897791i \(0.645171\pi\)
\(284\) −1.31834e18 −0.0311517
\(285\) 9.04513e17i 0.0207805i
\(286\) 8.40024e18i 0.187656i
\(287\) 2.26145e19 3.89866e19i 0.491284 0.846955i
\(288\) 6.33161e18 0.133775
\(289\) −1.32780e20 −2.72866
\(290\) 5.14661e18i 0.102881i
\(291\) 2.88980e19 0.561984
\(292\) 6.17542e18i 0.116843i
\(293\) 5.85744e19i 1.07837i −0.842188 0.539184i \(-0.818733\pi\)
0.842188 0.539184i \(-0.181267\pi\)
\(294\) −6.45836e19 + 3.69387e19i −1.15703 + 0.661765i
\(295\) −3.88231e19 −0.676883
\(296\) 4.61183e19 0.782600
\(297\) 8.15166e18i 0.134646i
\(298\) 7.52080e19 1.20930
\(299\) 3.57126e19i 0.559051i
\(300\) 5.95976e18i 0.0908361i
\(301\) −7.70659e19 4.47027e19i −1.14375 0.663441i
\(302\) 8.02496e19 1.15981
\(303\) −1.65992e19 −0.233639
\(304\) 2.19439e18i 0.0300833i
\(305\) 7.22165e19 0.964357
\(306\) 9.34532e19i 1.21569i
\(307\) 6.40668e19i 0.811944i 0.913885 + 0.405972i \(0.133067\pi\)
−0.913885 + 0.405972i \(0.866933\pi\)
\(308\) −2.08450e18 1.20913e18i −0.0257392 0.0149303i
\(309\) −9.88216e19 −1.18901
\(310\) 7.45085e19 0.873599
\(311\) 8.73913e19i 0.998585i −0.866434 0.499292i \(-0.833593\pi\)
0.866434 0.499292i \(-0.166407\pi\)
\(312\) 7.14906e19 0.796181
\(313\) 1.21318e20i 1.31696i 0.752599 + 0.658479i \(0.228800\pi\)
−0.752599 + 0.658479i \(0.771200\pi\)
\(314\) 8.04444e19i 0.851253i
\(315\) −1.74546e19 + 3.00910e19i −0.180063 + 0.310422i
\(316\) 1.52082e19 0.152962
\(317\) 3.88718e19 0.381207 0.190603 0.981667i \(-0.438956\pi\)
0.190603 + 0.981667i \(0.438956\pi\)
\(318\) 2.28603e20i 2.18607i
\(319\) 4.59793e18 0.0428782
\(320\) 5.70838e19i 0.519174i
\(321\) 1.02160e20i 0.906233i
\(322\) −8.75796e19 5.08013e19i −0.757802 0.439570i
\(323\) 6.25701e18 0.0528137
\(324\) −1.69612e19 −0.139668
\(325\) 5.34950e19i 0.429780i
\(326\) 4.58588e19 0.359486
\(327\) 2.15424e20i 1.64783i
\(328\) 1.22779e20i 0.916505i
\(329\) 3.90615e19 6.73406e19i 0.284565 0.490580i
\(330\) −2.97906e19 −0.211820
\(331\) −3.75319e19 −0.260481 −0.130241 0.991482i \(-0.541575\pi\)
−0.130241 + 0.991482i \(0.541575\pi\)
\(332\) 2.00959e19i 0.136146i
\(333\) 7.54535e19 0.499029
\(334\) 1.53931e20i 0.993928i
\(335\) 8.81716e18i 0.0555866i
\(336\) −1.13291e20 + 1.95310e20i −0.697402 + 1.20229i
\(337\) 1.01717e20 0.611438 0.305719 0.952122i \(-0.401103\pi\)
0.305719 + 0.952122i \(0.401103\pi\)
\(338\) 9.82725e19 0.576897
\(339\) 3.77444e20i 2.16399i
\(340\) −2.33409e19 −0.130703
\(341\) 6.65651e19i 0.364092i
\(342\) 3.22274e18i 0.0172193i
\(343\) 1.16619e18 1.91578e20i 0.00608719 0.999981i
\(344\) −2.42701e20 −1.23767
\(345\) −1.26651e20 −0.631038
\(346\) 6.02977e19i 0.293556i
\(347\) −9.51178e19 −0.452508 −0.226254 0.974068i \(-0.572648\pi\)
−0.226254 + 0.974068i \(0.572648\pi\)
\(348\) 4.96419e18i 0.0230789i
\(349\) 9.81841e19i 0.446106i −0.974806 0.223053i \(-0.928398\pi\)
0.974806 0.223053i \(-0.0716022\pi\)
\(350\) −1.31188e20 7.60969e19i −0.582573 0.337927i
\(351\) −7.89982e19 −0.342894
\(352\) −1.39621e19 −0.0592392
\(353\) 1.35608e20i 0.562454i −0.959641 0.281227i \(-0.909259\pi\)
0.959641 0.281227i \(-0.0907414\pi\)
\(354\) −3.70075e20 −1.50059
\(355\) 4.19663e19i 0.166370i
\(356\) 4.91018e19i 0.190326i
\(357\) 5.56901e20 + 3.23035e20i 2.11073 + 1.22435i
\(358\) 3.46088e20 1.28269
\(359\) −3.41215e20 −1.23672 −0.618362 0.785894i \(-0.712203\pi\)
−0.618362 + 0.785894i \(0.712203\pi\)
\(360\) 9.47648e19i 0.335913i
\(361\) 2.88226e20 0.999252
\(362\) 1.99823e20i 0.677604i
\(363\) 3.54353e20i 1.17539i
\(364\) 1.17178e19 2.02010e19i 0.0380219 0.0655483i
\(365\) 1.96580e20 0.624016
\(366\) 6.88392e20 2.13790
\(367\) 2.98843e20i 0.908061i −0.890986 0.454030i \(-0.849986\pi\)
0.890986 0.454030i \(-0.150014\pi\)
\(368\) −3.07261e20 −0.913535
\(369\) 2.00878e20i 0.584414i
\(370\) 1.86241e20i 0.530226i
\(371\) 5.09186e20 + 2.95358e20i 1.41868 + 0.822919i
\(372\) 7.18676e19 0.195970
\(373\) −1.02024e20 −0.272291 −0.136146 0.990689i \(-0.543471\pi\)
−0.136146 + 0.990689i \(0.543471\pi\)
\(374\) 2.06077e20i 0.538341i
\(375\) −4.86837e20 −1.24490
\(376\) 2.12074e20i 0.530865i
\(377\) 4.45588e19i 0.109195i
\(378\) 1.12375e20 1.93731e20i 0.269610 0.464798i
\(379\) −5.93003e19 −0.139297 −0.0696487 0.997572i \(-0.522188\pi\)
−0.0696487 + 0.997572i \(0.522188\pi\)
\(380\) 8.04913e17 0.00185131
\(381\) 4.05618e20i 0.913519i
\(382\) −1.35607e20 −0.299073
\(383\) 3.25031e20i 0.701996i 0.936376 + 0.350998i \(0.114158\pi\)
−0.936376 + 0.350998i \(0.885842\pi\)
\(384\) 6.78041e20i 1.43419i
\(385\) 3.84898e19 6.63550e19i 0.0797370 0.137464i
\(386\) −4.81255e20 −0.976510
\(387\) −3.97080e20 −0.789206
\(388\) 2.57159e19i 0.0500666i
\(389\) −7.32963e20 −1.39793 −0.698964 0.715156i \(-0.746355\pi\)
−0.698964 + 0.715156i \(0.746355\pi\)
\(390\) 2.88702e20i 0.539428i
\(391\) 8.76113e20i 1.60378i
\(392\) −2.59111e20 4.53030e20i −0.464727 0.812528i
\(393\) 3.04559e20 0.535219
\(394\) −1.32690e19 −0.0228491
\(395\) 4.84118e20i 0.816910i
\(396\) −1.07403e19 −0.0177605
\(397\) 5.24892e20i 0.850640i 0.905043 + 0.425320i \(0.139839\pi\)
−0.905043 + 0.425320i \(0.860161\pi\)
\(398\) 2.55795e19i 0.0406282i
\(399\) −1.92048e19 1.11399e19i −0.0298969 0.0173419i
\(400\) −4.60256e20 −0.702295
\(401\) 5.73775e20 0.858196 0.429098 0.903258i \(-0.358831\pi\)
0.429098 + 0.903258i \(0.358831\pi\)
\(402\) 8.40482e19i 0.123231i
\(403\) 6.45086e20 0.927209
\(404\) 1.47714e19i 0.0208147i
\(405\) 5.39919e20i 0.745913i
\(406\) −1.09274e20 6.33851e19i −0.148015 0.0858576i
\(407\) −1.66386e20 −0.220984
\(408\) 1.75383e21 2.28405
\(409\) 6.43164e20i 0.821363i −0.911779 0.410682i \(-0.865291\pi\)
0.911779 0.410682i \(-0.134709\pi\)
\(410\) −4.95824e20 −0.620950
\(411\) 5.21343e20i 0.640308i
\(412\) 8.79398e19i 0.105927i
\(413\) 4.78141e20 8.24297e20i 0.564879 0.973831i
\(414\) −4.51252e20 −0.522897
\(415\) −6.39706e20 −0.727102
\(416\) 1.35307e20i 0.150860i
\(417\) −5.82837e20 −0.637468
\(418\) 7.10660e18i 0.00762520i
\(419\) 1.00606e20i 0.105903i 0.998597 + 0.0529517i \(0.0168630\pi\)
−0.998597 + 0.0529517i \(0.983137\pi\)
\(420\) 7.16407e19 + 4.15558e19i 0.0739887 + 0.0429178i
\(421\) 4.89798e20 0.496318 0.248159 0.968719i \(-0.420174\pi\)
0.248159 + 0.968719i \(0.420174\pi\)
\(422\) 8.96516e20 0.891371
\(423\) 3.46971e20i 0.338509i
\(424\) 1.60356e21 1.53518
\(425\) 1.31236e21i 1.23294i
\(426\) 4.00037e20i 0.368828i
\(427\) −8.89411e20 + 1.53331e21i −0.804784 + 1.38742i
\(428\) 9.09105e19 0.0807354
\(429\) −2.57924e20 −0.224819
\(430\) 9.80107e20i 0.838544i
\(431\) −6.28051e20 −0.527445 −0.263722 0.964599i \(-0.584950\pi\)
−0.263722 + 0.964599i \(0.584950\pi\)
\(432\) 6.79679e20i 0.560317i
\(433\) 2.17005e21i 1.75617i −0.478503 0.878086i \(-0.658820\pi\)
0.478503 0.878086i \(-0.341180\pi\)
\(434\) −9.17638e20 + 1.58197e21i −0.729044 + 1.25684i
\(435\) −1.58023e20 −0.123256
\(436\) −1.91702e20 −0.146803
\(437\) 3.02128e19i 0.0227164i
\(438\) 1.87386e21 1.38339
\(439\) 3.99198e19i 0.0289383i −0.999895 0.0144691i \(-0.995394\pi\)
0.999895 0.0144691i \(-0.00460583\pi\)
\(440\) 2.08970e20i 0.148752i
\(441\) −4.23929e20 7.41196e20i −0.296336 0.518113i
\(442\) −1.99711e21 −1.37096
\(443\) −8.43902e20 −0.568934 −0.284467 0.958686i \(-0.591817\pi\)
−0.284467 + 0.958686i \(0.591817\pi\)
\(444\) 1.79640e20i 0.118943i
\(445\) 1.56304e21 1.01646
\(446\) 2.68448e21i 1.71467i
\(447\) 2.30921e21i 1.44878i
\(448\) −1.21201e21 7.03038e20i −0.746935 0.433266i
\(449\) 1.36329e21 0.825309 0.412654 0.910888i \(-0.364602\pi\)
0.412654 + 0.910888i \(0.364602\pi\)
\(450\) −6.75944e20 −0.401986
\(451\) 4.42964e20i 0.258795i
\(452\) 3.35882e20 0.192788
\(453\) 2.46401e21i 1.38950i
\(454\) 4.48905e20i 0.248718i
\(455\) 6.43050e20 + 3.73007e20i 0.350069 + 0.203061i
\(456\) −6.04810e19 −0.0323519
\(457\) −3.30364e21 −1.73645 −0.868227 0.496166i \(-0.834741\pi\)
−0.868227 + 0.496166i \(0.834741\pi\)
\(458\) 2.20412e21i 1.13844i
\(459\) −1.93801e21 −0.983682
\(460\) 1.12705e20i 0.0562186i
\(461\) 2.21453e20i 0.108561i −0.998526 0.0542805i \(-0.982713\pi\)
0.998526 0.0542805i \(-0.0172865\pi\)
\(462\) 3.66898e20 6.32518e20i 0.176770 0.304745i
\(463\) 3.87674e21 1.83577 0.917886 0.396844i \(-0.129895\pi\)
0.917886 + 0.396844i \(0.129895\pi\)
\(464\) −3.83371e20 −0.178433
\(465\) 2.28773e21i 1.04660i
\(466\) 2.29672e21 1.03281
\(467\) 4.03114e21i 1.78194i −0.454062 0.890970i \(-0.650025\pi\)
0.454062 0.890970i \(-0.349975\pi\)
\(468\) 1.04085e20i 0.0452295i
\(469\) −1.87207e20 1.08591e20i −0.0799724 0.0463887i
\(470\) −8.56424e20 −0.359671
\(471\) −2.46999e21 −1.01983
\(472\) 2.59593e21i 1.05380i
\(473\) 8.75618e20 0.349482
\(474\) 4.61478e21i 1.81102i
\(475\) 4.52568e19i 0.0174636i
\(476\) 2.87464e20 4.95577e20i 0.109076 0.188042i
\(477\) 2.62357e21 0.978915
\(478\) −3.57279e20 −0.131094
\(479\) 4.96713e21i 1.79235i −0.443706 0.896173i \(-0.646336\pi\)
0.443706 0.896173i \(-0.353664\pi\)
\(480\) 4.79854e20 0.170286
\(481\) 1.61245e21i 0.562764i
\(482\) 1.63499e20i 0.0561226i
\(483\) 1.55982e21 2.68907e21i 0.526620 0.907874i
\(484\) −3.15333e20 −0.104715
\(485\) 8.18604e20 0.267387
\(486\) 3.47431e21i 1.11629i
\(487\) 3.86397e21 1.22124 0.610621 0.791923i \(-0.290920\pi\)
0.610621 + 0.791923i \(0.290920\pi\)
\(488\) 4.82881e21i 1.50135i
\(489\) 1.40806e21i 0.430676i
\(490\) −1.82948e21 + 1.04638e21i −0.550503 + 0.314861i
\(491\) 4.87646e21 1.44362 0.721810 0.692091i \(-0.243310\pi\)
0.721810 + 0.692091i \(0.243310\pi\)
\(492\) −4.78250e20 −0.139294
\(493\) 1.09313e21i 0.313254i
\(494\) 6.88705e19 0.0194186
\(495\) 3.41892e20i 0.0948523i
\(496\) 5.55014e21i 1.51513i
\(497\) 8.91035e20 + 5.16853e20i 0.239356 + 0.138840i
\(498\) −6.09789e21 −1.61193
\(499\) −4.46501e21 −1.16150 −0.580749 0.814083i \(-0.697240\pi\)
−0.580749 + 0.814083i \(0.697240\pi\)
\(500\) 4.33229e20i 0.110907i
\(501\) −4.72635e21 −1.19076
\(502\) 5.36154e20i 0.132941i
\(503\) 7.17394e20i 0.175071i 0.996161 + 0.0875354i \(0.0278991\pi\)
−0.996161 + 0.0875354i \(0.972101\pi\)
\(504\) −2.01206e21 1.16711e21i −0.483278 0.280329i
\(505\) −4.70211e20 −0.111163
\(506\) 9.95074e20 0.231553
\(507\) 3.01739e21i 0.691143i
\(508\) −3.60954e20 −0.0813845
\(509\) 3.26039e21i 0.723648i −0.932247 0.361824i \(-0.882154\pi\)
0.932247 0.361824i \(-0.117846\pi\)
\(510\) 7.08254e21i 1.54749i
\(511\) −2.42105e21 + 4.17381e21i −0.520760 + 0.897770i
\(512\) −3.69780e21 −0.783039
\(513\) 6.68325e19 0.0139331
\(514\) 1.74331e21i 0.357823i
\(515\) −2.79935e21 −0.565718
\(516\) 9.45368e20i 0.188106i
\(517\) 7.65120e20i 0.149901i
\(518\) 3.95429e21 + 2.29372e21i 0.762835 + 0.442489i
\(519\) −1.85140e21 −0.351691
\(520\) 2.02514e21 0.378816
\(521\) 6.65810e21i 1.22645i 0.789909 + 0.613224i \(0.210128\pi\)
−0.789909 + 0.613224i \(0.789872\pi\)
\(522\) −5.63029e20 −0.102133
\(523\) 5.30443e21i 0.947600i −0.880632 0.473800i \(-0.842882\pi\)
0.880632 0.473800i \(-0.157118\pi\)
\(524\) 2.71023e20i 0.0476821i
\(525\) 2.33650e21 4.02805e21i 0.404848 0.697943i
\(526\) 3.40579e21 0.581209
\(527\) 1.58255e22 2.65994
\(528\) 2.21910e21i 0.367372i
\(529\) −1.90218e21 −0.310174
\(530\) 6.47571e21i 1.04011i
\(531\) 4.24717e21i 0.671960i
\(532\) −9.91322e18 + 1.70900e19i −0.00154498 + 0.00266348i
\(533\) −4.29279e21 −0.659055
\(534\) 1.48994e22 2.25340
\(535\) 2.89392e21i 0.431177i
\(536\) −5.89566e20 −0.0865395
\(537\) 1.06264e22i 1.53671i
\(538\) 8.86973e20i 0.126372i
\(539\) 9.34822e20 + 1.63444e21i 0.131226 + 0.229435i
\(540\) −2.49309e20 −0.0344817
\(541\) −7.19478e21 −0.980481 −0.490241 0.871587i \(-0.663091\pi\)
−0.490241 + 0.871587i \(0.663091\pi\)
\(542\) 8.08207e21i 1.08525i
\(543\) −6.13542e21 −0.811794
\(544\) 3.31941e21i 0.432782i
\(545\) 6.10239e21i 0.784021i
\(546\) 6.12977e21 + 3.55563e21i 0.776074 + 0.450169i
\(547\) −5.53194e21 −0.690206 −0.345103 0.938565i \(-0.612156\pi\)
−0.345103 + 0.938565i \(0.612156\pi\)
\(548\) −4.63935e20 −0.0570444
\(549\) 7.90035e21i 0.957343i
\(550\) 1.49055e21 0.178011
\(551\) 3.76967e19i 0.00443701i
\(552\) 8.46861e21i 0.982426i
\(553\) −1.02789e22 5.96235e21i −1.17529 0.681736i
\(554\) −4.10797e20 −0.0462966
\(555\) 5.71840e21 0.635229
\(556\) 5.18658e20i 0.0567914i
\(557\) −8.43664e21 −0.910600 −0.455300 0.890338i \(-0.650468\pi\)
−0.455300 + 0.890338i \(0.650468\pi\)
\(558\) 8.15109e21i 0.867245i
\(559\) 8.48566e21i 0.890003i
\(560\) −3.20925e21 + 5.53262e21i −0.331817 + 0.572041i
\(561\) −6.32747e21 −0.644952
\(562\) 4.21307e21 0.423359
\(563\) 1.43830e22i 1.42489i −0.701728 0.712444i \(-0.747588\pi\)
0.701728 0.712444i \(-0.252412\pi\)
\(564\) −8.26068e20 −0.0806832
\(565\) 1.06920e22i 1.02961i
\(566\) 1.99481e22i 1.89396i
\(567\) 1.14636e22 + 6.64959e21i 1.07314 + 0.622487i
\(568\) 2.80611e21 0.259011
\(569\) −4.27027e21 −0.388648 −0.194324 0.980937i \(-0.562251\pi\)
−0.194324 + 0.980937i \(0.562251\pi\)
\(570\) 2.44242e20i 0.0219190i
\(571\) 5.15155e21 0.455879 0.227939 0.973675i \(-0.426801\pi\)
0.227939 + 0.973675i \(0.426801\pi\)
\(572\) 2.29522e20i 0.0200289i
\(573\) 4.16374e21i 0.358299i
\(574\) 6.10651e21 1.05274e22i 0.518201 0.893359i
\(575\) 6.33690e21 0.530315
\(576\) −6.24486e21 −0.515398
\(577\) 9.03400e21i 0.735316i −0.929961 0.367658i \(-0.880160\pi\)
0.929961 0.367658i \(-0.119840\pi\)
\(578\) −3.58540e22 −2.87816
\(579\) 1.47766e22i 1.16989i
\(580\) 1.40622e20i 0.0109807i
\(581\) 7.87855e21 1.35823e22i 0.606788 1.04608i
\(582\) 7.80321e21 0.592775
\(583\) −5.78533e21 −0.433491
\(584\) 1.31445e22i 0.971493i
\(585\) 3.31330e21 0.241554
\(586\) 1.58166e22i 1.13745i
\(587\) 1.47426e22i 1.04585i 0.852378 + 0.522926i \(0.175160\pi\)
−0.852378 + 0.522926i \(0.824840\pi\)
\(588\) −1.76464e21 + 1.00929e21i −0.123492 + 0.0706313i
\(589\) −5.45743e20 −0.0376761
\(590\) −1.04832e22 −0.713969
\(591\) 4.07417e20i 0.0273741i
\(592\) 1.38731e22 0.919602
\(593\) 1.70778e22i 1.11685i 0.829555 + 0.558425i \(0.188594\pi\)
−0.829555 + 0.558425i \(0.811406\pi\)
\(594\) 2.20116e21i 0.142023i
\(595\) 1.57755e22 + 9.15073e21i 1.00426 + 0.582532i
\(596\) 2.05493e21 0.129071
\(597\) 7.85402e20 0.0486740
\(598\) 9.64332e21i 0.589681i
\(599\) 2.23629e22 1.34931 0.674657 0.738131i \(-0.264292\pi\)
0.674657 + 0.738131i \(0.264292\pi\)
\(600\) 1.26854e22i 0.755256i
\(601\) 1.53685e21i 0.0902890i 0.998980 + 0.0451445i \(0.0143748\pi\)
−0.998980 + 0.0451445i \(0.985625\pi\)
\(602\) −2.08098e22 1.20709e22i −1.20641 0.699790i
\(603\) −9.64581e20 −0.0551824
\(604\) 2.19269e21 0.123789
\(605\) 1.00379e22i 0.559241i
\(606\) −4.48221e21 −0.246440
\(607\) 6.64708e21i 0.360680i −0.983604 0.180340i \(-0.942280\pi\)
0.983604 0.180340i \(-0.0577198\pi\)
\(608\) 1.14470e20i 0.00613004i
\(609\) 1.94620e21 3.35517e21i 0.102860 0.177328i
\(610\) 1.95003e22 1.01719
\(611\) −7.41482e21 −0.381743
\(612\) 2.55345e21i 0.129753i
\(613\) 2.31810e22 1.16265 0.581325 0.813672i \(-0.302535\pi\)
0.581325 + 0.813672i \(0.302535\pi\)
\(614\) 1.72997e22i 0.856430i
\(615\) 1.52239e22i 0.743919i
\(616\) 4.43688e21 + 2.57365e21i 0.214009 + 0.124138i
\(617\) 7.42512e21 0.353527 0.176763 0.984253i \(-0.443437\pi\)
0.176763 + 0.984253i \(0.443437\pi\)
\(618\) −2.66844e22 −1.25415
\(619\) 3.07234e22i 1.42543i −0.701456 0.712713i \(-0.747466\pi\)
0.701456 0.712713i \(-0.252534\pi\)
\(620\) 2.03582e21 0.0932407
\(621\) 9.35795e21i 0.423105i
\(622\) 2.35979e22i 1.05330i
\(623\) −1.92502e22 + 3.31866e22i −0.848264 + 1.46238i
\(624\) 2.15055e22 0.935561
\(625\) 1.07554e21 0.0461940
\(626\) 3.27591e22i 1.38911i
\(627\) 2.18203e20 0.00913526
\(628\) 2.19801e21i 0.0908557i
\(629\) 3.95572e22i 1.61444i
\(630\) −4.71319e21 + 8.12536e21i −0.189929 + 0.327430i
\(631\) −4.05650e22 −1.61405 −0.807024 0.590519i \(-0.798923\pi\)
−0.807024 + 0.590519i \(0.798923\pi\)
\(632\) −3.23709e22 −1.27180
\(633\) 2.75269e22i 1.06789i
\(634\) 1.04964e22 0.402093
\(635\) 1.14901e22i 0.434644i
\(636\) 6.24619e21i 0.233323i
\(637\) −1.58395e22 + 9.05942e21i −0.584286 + 0.334183i
\(638\) 1.24156e21 0.0452274
\(639\) 4.59104e21 0.165160
\(640\) 1.92071e22i 0.682374i
\(641\) −3.39412e21 −0.119087 −0.0595434 0.998226i \(-0.518964\pi\)
−0.0595434 + 0.998226i \(0.518964\pi\)
\(642\) 2.75858e22i 0.955884i
\(643\) 3.99482e22i 1.36713i 0.729890 + 0.683564i \(0.239571\pi\)
−0.729890 + 0.683564i \(0.760429\pi\)
\(644\) −2.39296e21 1.38806e21i −0.0808815 0.0469160i
\(645\) −3.00935e22 −1.00461
\(646\) 1.68955e21 0.0557073
\(647\) 1.45003e21i 0.0472219i 0.999721 + 0.0236109i \(0.00751630\pi\)
−0.999721 + 0.0236109i \(0.992484\pi\)
\(648\) 3.61021e22 1.16127
\(649\) 9.36561e21i 0.297563i
\(650\) 1.44450e22i 0.453327i
\(651\) −4.85735e22 2.81755e22i −1.50574 0.873420i
\(652\) 1.25301e21 0.0383685
\(653\) 5.55769e22 1.68108 0.840541 0.541747i \(-0.182237\pi\)
0.840541 + 0.541747i \(0.182237\pi\)
\(654\) 5.81700e22i 1.73811i
\(655\) 8.62736e21 0.254652
\(656\) 3.69340e22i 1.07695i
\(657\) 2.15054e22i 0.619478i
\(658\) 1.05476e22 1.81837e22i 0.300156 0.517458i
\(659\) 1.64988e22 0.463842 0.231921 0.972735i \(-0.425499\pi\)
0.231921 + 0.972735i \(0.425499\pi\)
\(660\) −8.13977e20 −0.0226079
\(661\) 2.01529e22i 0.553001i 0.961014 + 0.276500i \(0.0891747\pi\)
−0.961014 + 0.276500i \(0.910825\pi\)
\(662\) −1.01346e22 −0.274753
\(663\) 6.13199e22i 1.64245i
\(664\) 4.27744e22i 1.13198i
\(665\) −5.44020e20 3.15564e20i −0.0142247 0.00825114i
\(666\) 2.03744e22 0.526370
\(667\) 5.27834e21 0.134738
\(668\) 4.20591e21i 0.106084i
\(669\) 8.24251e22 2.05424
\(670\) 2.38086e21i 0.0586322i
\(671\) 1.74214e22i 0.423938i
\(672\) −5.90983e21 + 1.01883e22i −0.142109 + 0.244990i
\(673\) −2.75005e22 −0.653462 −0.326731 0.945117i \(-0.605947\pi\)
−0.326731 + 0.945117i \(0.605947\pi\)
\(674\) 2.74661e22 0.644938
\(675\) 1.40176e22i 0.325269i
\(676\) 2.68513e21 0.0615732
\(677\) 2.28197e22i 0.517131i 0.965994 + 0.258566i \(0.0832498\pi\)
−0.965994 + 0.258566i \(0.916750\pi\)
\(678\) 1.01920e23i 2.28255i
\(679\) −1.00818e22 + 1.73807e22i −0.223142 + 0.384689i
\(680\) 4.96814e22 1.08673
\(681\) 1.37833e22 0.297973
\(682\) 1.79743e22i 0.384040i
\(683\) 1.27757e22 0.269786 0.134893 0.990860i \(-0.456931\pi\)
0.134893 + 0.990860i \(0.456931\pi\)
\(684\) 8.80560e19i 0.00183785i
\(685\) 1.47683e22i 0.304652i
\(686\) 3.14902e20 5.17309e22i 0.00642070 1.05477i
\(687\) −6.76759e22 −1.36389
\(688\) −7.30083e22 −1.45434
\(689\) 5.60660e22i 1.10394i
\(690\) −3.41990e22 −0.665612
\(691\) 9.51389e22i 1.83035i 0.403058 + 0.915175i \(0.367947\pi\)
−0.403058 + 0.915175i \(0.632053\pi\)
\(692\) 1.64753e21i 0.0313318i
\(693\) 7.25911e21 + 4.21071e21i 0.136464 + 0.0791570i
\(694\) −2.56843e22 −0.477300
\(695\) −1.65102e22 −0.303302
\(696\) 1.05663e22i 0.191889i
\(697\) −1.05312e23 −1.89067
\(698\) 2.65123e22i 0.470547i
\(699\) 7.05193e22i 1.23734i
\(700\) −3.58450e21 2.07922e21i −0.0621790 0.0360675i
\(701\) 3.40641e22 0.584188 0.292094 0.956390i \(-0.405648\pi\)
0.292094 + 0.956390i \(0.405648\pi\)
\(702\) −2.13316e22 −0.361681
\(703\) 1.36413e21i 0.0228673i
\(704\) 1.37708e22 0.228233
\(705\) 2.62959e22i 0.430899i
\(706\) 3.66176e22i 0.593270i
\(707\) 5.79106e21 9.98358e21i 0.0927690 0.159930i
\(708\) −1.01117e22 −0.160161
\(709\) 5.37960e22 0.842520 0.421260 0.906940i \(-0.361588\pi\)
0.421260 + 0.906940i \(0.361588\pi\)
\(710\) 1.13320e22i 0.175485i
\(711\) −5.29616e22 −0.810969
\(712\) 1.04514e23i 1.58246i
\(713\) 7.64155e22i 1.14410i
\(714\) 1.50378e23 + 8.72279e22i 2.22637 + 1.29143i
\(715\) −7.30630e21 −0.106967
\(716\) 9.45628e21 0.136904
\(717\) 1.09700e22i 0.157056i
\(718\) −9.21369e22 −1.30448
\(719\) 2.58679e22i 0.362184i 0.983466 + 0.181092i \(0.0579632\pi\)
−0.983466 + 0.181092i \(0.942037\pi\)
\(720\) 2.85067e22i 0.394718i
\(721\) 3.44765e22 5.94363e22i 0.472108 0.813897i
\(722\) 7.78284e22 1.05400
\(723\) −5.02012e21 −0.0672369
\(724\) 5.45982e21i 0.0723219i
\(725\) 7.90659e21 0.103582
\(726\) 9.56845e22i 1.23979i
\(727\) 5.69842e22i 0.730263i −0.930956 0.365132i \(-0.881024\pi\)
0.930956 0.365132i \(-0.118976\pi\)
\(728\) −2.49414e22 + 4.29980e22i −0.316133 + 0.545001i
\(729\) 7.71693e21 0.0967441
\(730\) 5.30816e22 0.658205
\(731\) 2.08173e23i 2.55321i
\(732\) 1.88092e22 0.228182
\(733\) 1.16231e23i 1.39473i −0.716718 0.697364i \(-0.754356\pi\)
0.716718 0.697364i \(-0.245644\pi\)
\(734\) 8.06954e22i 0.957812i
\(735\) −3.21283e22 5.61731e22i −0.377215 0.659522i
\(736\) −1.60282e22 −0.186150
\(737\) 2.12704e21 0.0244363
\(738\) 5.42422e22i 0.616433i
\(739\) −7.73065e22 −0.869082 −0.434541 0.900652i \(-0.643089\pi\)
−0.434541 + 0.900652i \(0.643089\pi\)
\(740\) 5.08872e21i 0.0565919i
\(741\) 2.11462e21i 0.0232641i
\(742\) 1.37493e23 + 7.97542e22i 1.49641 + 0.868005i
\(743\) 1.03344e23 1.11269 0.556344 0.830952i \(-0.312204\pi\)
0.556344 + 0.830952i \(0.312204\pi\)
\(744\) −1.52971e23 −1.62939
\(745\) 6.54139e22i 0.689318i
\(746\) −2.75492e22 −0.287210
\(747\) 6.99826e22i 0.721814i
\(748\) 5.63072e21i 0.0574581i
\(749\) −6.14441e22 3.56412e22i −0.620334 0.359830i
\(750\) −1.31459e23 −1.31310
\(751\) 1.59317e23 1.57450 0.787248 0.616636i \(-0.211505\pi\)
0.787248 + 0.616636i \(0.211505\pi\)
\(752\) 6.37951e22i 0.623799i
\(753\) 1.64623e22 0.159268
\(754\) 1.20320e22i 0.115178i
\(755\) 6.97989e22i 0.661109i
\(756\) 3.07047e21 5.29337e21i 0.0287760 0.0496087i
\(757\) 8.52662e22 0.790697 0.395348 0.918531i \(-0.370624\pi\)
0.395348 + 0.918531i \(0.370624\pi\)
\(758\) −1.60126e22 −0.146929
\(759\) 3.05531e22i 0.277409i
\(760\) −1.71327e21 −0.0153927
\(761\) 8.00060e22i 0.711287i 0.934622 + 0.355644i \(0.115738\pi\)
−0.934622 + 0.355644i \(0.884262\pi\)
\(762\) 1.09527e23i 0.963570i
\(763\) 1.29567e23 + 7.51564e22i 1.12797 + 0.654289i
\(764\) −3.70525e21 −0.0319205
\(765\) 8.12830e22 0.692960
\(766\) 8.77669e22i 0.740458i
\(767\) −9.07627e22 −0.757783
\(768\) 5.10240e22i 0.421585i
\(769\) 6.29296e22i 0.514570i 0.966336 + 0.257285i \(0.0828279\pi\)
−0.966336 + 0.257285i \(0.917172\pi\)
\(770\) 1.03932e22 1.79176e22i 0.0841057 0.144995i
\(771\) −5.35270e22 −0.428685
\(772\) −1.31495e22 −0.104225
\(773\) 2.31126e23i 1.81306i −0.422139 0.906531i \(-0.638721\pi\)
0.422139 0.906531i \(-0.361279\pi\)
\(774\) −1.07222e23 −0.832446
\(775\) 1.14465e23i 0.879549i
\(776\) 5.47366e22i 0.416279i
\(777\) −7.04272e22 + 1.21414e23i −0.530118 + 0.913903i
\(778\) −1.97919e23 −1.47452
\(779\) 3.63170e21 0.0267800
\(780\) 7.88831e21i 0.0575741i
\(781\) −1.01239e22 −0.0731373
\(782\) 2.36573e23i 1.69165i
\(783\) 1.16760e22i 0.0826417i
\(784\) −7.79447e22 1.36278e23i −0.546083 0.954770i
\(785\) −6.99683e22 −0.485226
\(786\) 8.22390e22 0.564543
\(787\) 2.83630e23i 1.92732i −0.267133 0.963660i \(-0.586076\pi\)
0.267133 0.963660i \(-0.413924\pi\)
\(788\) −3.62554e20 −0.00243873
\(789\) 1.04573e23i 0.696309i
\(790\) 1.30724e23i 0.861668i
\(791\) −2.27014e23 1.31681e23i −1.48129 0.859237i
\(792\) 2.28609e22 0.147670
\(793\) 1.68832e23 1.07961
\(794\) 1.41734e23i 0.897246i
\(795\) 1.98832e23 1.24609
\(796\) 6.98917e20i 0.00433632i
\(797\) 1.11760e23i 0.686468i 0.939250 + 0.343234i \(0.111522\pi\)
−0.939250 + 0.343234i \(0.888478\pi\)
\(798\) −5.18578e21 3.00806e21i −0.0315349 0.0182921i
\(799\) −1.81903e23 −1.09513
\(800\) −2.40092e22 −0.143106
\(801\) 1.70993e23i 1.00907i
\(802\) 1.54934e23 0.905216
\(803\) 4.74225e22i 0.274322i
\(804\) 2.29648e21i 0.0131527i
\(805\) 4.41856e22 7.61743e22i 0.250561 0.431958i
\(806\) 1.74190e23 0.978009
\(807\) 2.72339e22 0.151399
\(808\) 3.14410e22i 0.173063i
\(809\) −1.09796e23 −0.598407 −0.299203 0.954189i \(-0.596721\pi\)
−0.299203 + 0.954189i \(0.596721\pi\)
\(810\) 1.45792e23i 0.786781i
\(811\) 1.21306e23i 0.648209i −0.946021 0.324105i \(-0.894937\pi\)
0.946021 0.324105i \(-0.105063\pi\)
\(812\) −2.98572e21 1.73189e21i −0.0157979 0.00916373i
\(813\) 2.48154e23 1.30016
\(814\) −4.49284e22 −0.233091
\(815\) 3.98867e22i 0.204912i
\(816\) 5.27579e23 2.68390
\(817\) 7.17887e21i 0.0361643i
\(818\) 1.73671e23i 0.866365i
\(819\) −4.08063e22 + 7.03485e22i −0.201584 + 0.347523i
\(820\) −1.35475e22 −0.0662750
\(821\) −1.80834e23 −0.876064 −0.438032 0.898959i \(-0.644324\pi\)
−0.438032 + 0.898959i \(0.644324\pi\)
\(822\) 1.40776e23i 0.675389i
\(823\) 9.66562e22 0.459231 0.229615 0.973281i \(-0.426253\pi\)
0.229615 + 0.973281i \(0.426253\pi\)
\(824\) 1.87181e23i 0.880732i
\(825\) 4.57664e22i 0.213263i
\(826\) 1.29110e23 2.22582e23i 0.595828 1.02719i
\(827\) 9.96977e22 0.455660 0.227830 0.973701i \(-0.426837\pi\)
0.227830 + 0.973701i \(0.426837\pi\)
\(828\) −1.23297e22 −0.0558097
\(829\) 3.66051e22i 0.164099i 0.996628 + 0.0820494i \(0.0261465\pi\)
−0.996628 + 0.0820494i \(0.973853\pi\)
\(830\) −1.72737e23 −0.766939
\(831\) 1.26132e22i 0.0554650i
\(832\) 1.33454e23i 0.581224i
\(833\) −3.88579e23 + 2.22249e23i −1.67618 + 0.958692i
\(834\) −1.57381e23 −0.672394
\(835\) −1.33885e23 −0.566553
\(836\) 1.94176e20i 0.000813851i
\(837\) 1.69035e23 0.701736
\(838\) 2.71661e22i 0.111706i
\(839\) 1.78047e23i 0.725168i 0.931951 + 0.362584i \(0.118105\pi\)
−0.931951 + 0.362584i \(0.881895\pi\)
\(840\) −1.52488e23 8.84521e22i −0.615179 0.356840i
\(841\) −2.43661e23 −0.973683
\(842\) 1.32258e23 0.523511
\(843\) 1.29360e23i 0.507199i
\(844\) 2.44958e22 0.0951375
\(845\) 8.54747e22i 0.328839i
\(846\) 9.36911e22i 0.357055i
\(847\) 2.13126e23 + 1.23626e23i 0.804579 + 0.466703i
\(848\) 4.82377e23 1.80393
\(849\) −6.12494e23 −2.26903
\(850\) 3.54371e23i 1.30049i
\(851\) −1.91008e23 −0.694407
\(852\) 1.09303e22i 0.0393656i
\(853\) 1.04907e23i 0.374294i −0.982332 0.187147i \(-0.940076\pi\)
0.982332 0.187147i \(-0.0599240\pi\)
\(854\) −2.40164e23 + 4.14034e23i −0.848878 + 1.46343i
\(855\) −2.80305e21 −0.00981527
\(856\) −1.93504e23 −0.671274
\(857\) 1.62445e23i 0.558290i −0.960249 0.279145i \(-0.909949\pi\)
0.960249 0.279145i \(-0.0900510\pi\)
\(858\) −6.96461e22 −0.237136
\(859\) 4.43943e23i 1.49755i 0.662824 + 0.748775i \(0.269358\pi\)
−0.662824 + 0.748775i \(0.730642\pi\)
\(860\) 2.67798e22i 0.0894993i
\(861\) 3.23237e23 + 1.87496e23i 1.07028 + 0.620823i
\(862\) −1.69590e23 −0.556343
\(863\) −6.65298e22 −0.216237 −0.108118 0.994138i \(-0.534483\pi\)
−0.108118 + 0.994138i \(0.534483\pi\)
\(864\) 3.54553e22i 0.114175i
\(865\) −5.24452e22 −0.167331
\(866\) 5.85970e23i 1.85239i
\(867\) 1.10087e24i 3.44813i
\(868\) −2.50729e22 + 4.32248e22i −0.0778121 + 0.134145i
\(869\) 1.16788e23 0.359120
\(870\) −4.26704e22 −0.130009
\(871\) 2.06133e22i 0.0622302i
\(872\) 4.08041e23 1.22060
\(873\) 8.95538e22i 0.265442i
\(874\) 8.15824e21i 0.0239610i
\(875\) 1.69846e23 2.92809e23i 0.494301 0.852157i
\(876\) 5.12002e22 0.147652
\(877\) −1.76354e23 −0.503952 −0.251976 0.967733i \(-0.581080\pi\)
−0.251976 + 0.967733i \(0.581080\pi\)
\(878\) 1.07794e22i 0.0305237i
\(879\) 4.85638e23 1.36270
\(880\) 6.28613e22i 0.174792i
\(881\) 3.97774e23i 1.09605i 0.836463 + 0.548024i \(0.184620\pi\)
−0.836463 + 0.548024i \(0.815380\pi\)
\(882\) −1.14472e23 2.00142e23i −0.312572 0.546500i
\(883\) 5.80261e23 1.57014 0.785069 0.619408i \(-0.212627\pi\)
0.785069 + 0.619408i \(0.212627\pi\)
\(884\) −5.45677e22 −0.146325
\(885\) 3.21881e23i 0.855360i
\(886\) −2.27875e23 −0.600106
\(887\) 4.52350e23i 1.18055i 0.807201 + 0.590277i \(0.200981\pi\)
−0.807201 + 0.590277i \(0.799019\pi\)
\(888\) 3.82365e23i 0.988951i
\(889\) 2.43959e23 + 1.41511e23i 0.625321 + 0.362723i
\(890\) 4.22061e23 1.07215
\(891\) −1.30249e23 −0.327909
\(892\) 7.33489e22i 0.183010i
\(893\) 6.27294e21 0.0155117
\(894\) 6.23547e23i 1.52816i
\(895\) 3.01018e23i 0.731153i
\(896\) −4.07808e23 2.36553e23i −0.981730 0.569461i
\(897\) −2.96092e23 −0.706458
\(898\) 3.68123e23 0.870527
\(899\) 9.53441e22i 0.223468i
\(900\) −1.84690e22 −0.0429046
\(901\) 1.37543e24i 3.16694i
\(902\) 1.19612e23i 0.272974i
\(903\) 3.70629e23 6.38950e23i 0.838373 1.44532i
\(904\) −7.14928e23 −1.60293
\(905\) −1.73800e23 −0.386244
\(906\) 6.65347e23i 1.46562i
\(907\) 1.51743e23 0.331322 0.165661 0.986183i \(-0.447024\pi\)
0.165661 + 0.986183i \(0.447024\pi\)
\(908\) 1.22656e22i 0.0265461i
\(909\) 5.14402e22i 0.110355i
\(910\) 1.73640e23 + 1.00722e23i 0.369249 + 0.214186i
\(911\) 4.78281e23 1.00817 0.504087 0.863653i \(-0.331829\pi\)
0.504087 + 0.863653i \(0.331829\pi\)
\(912\) −1.81936e22 −0.0380155
\(913\) 1.54322e23i 0.319639i
\(914\) −8.92069e23 −1.83159
\(915\) 5.98745e23i 1.21863i
\(916\) 6.02238e22i 0.121508i
\(917\) −1.06254e23 + 1.83177e23i −0.212515 + 0.366368i
\(918\) −5.23313e23 −1.03758
\(919\) 2.52314e23 0.495926 0.247963 0.968770i \(-0.420239\pi\)
0.247963 + 0.968770i \(0.420239\pi\)
\(920\) 2.39893e23i 0.467429i
\(921\) −5.31176e23 −1.02603
\(922\) 5.97980e22i 0.114509i
\(923\) 9.81112e22i 0.186254i
\(924\) 1.00249e22 1.72825e22i 0.0188670 0.0325260i
\(925\) −2.86117e23 −0.533837
\(926\) 1.04682e24 1.93635
\(927\) 3.06244e23i 0.561603i
\(928\) −1.99985e22 −0.0363592
\(929\) 2.89738e23i 0.522251i −0.965305 0.261125i \(-0.915906\pi\)
0.965305 0.261125i \(-0.0840936\pi\)
\(930\) 6.17747e23i 1.10394i
\(931\) 1.34002e22 7.66427e21i 0.0237418 0.0135792i
\(932\) 6.27541e22 0.110234
\(933\) 7.24558e23 1.26189
\(934\) 1.08851e24i 1.87957i
\(935\) −1.79240e23 −0.306862
\(936\) 2.21546e23i 0.376061i
\(937\) 9.00773e23i 1.51600i 0.652255 + 0.757999i \(0.273823\pi\)
−0.652255 + 0.757999i \(0.726177\pi\)
\(938\) −5.05508e22 2.93225e22i −0.0843540 0.0489303i
\(939\) −1.00585e24 −1.66420
\(940\) −2.34003e22 −0.0383883
\(941\) 5.79898e23i 0.943267i 0.881795 + 0.471634i \(0.156336\pi\)
−0.881795 + 0.471634i \(0.843664\pi\)
\(942\) −6.66962e23 −1.07571
\(943\) 5.08514e23i 0.813223i
\(944\) 7.80897e23i 1.23828i
\(945\) 1.68502e23 + 9.77410e22i 0.264942 + 0.153682i
\(946\) 2.36439e23 0.368630
\(947\) 1.55676e23 0.240669 0.120335 0.992733i \(-0.461603\pi\)
0.120335 + 0.992733i \(0.461603\pi\)
\(948\) 1.26091e23i 0.193294i
\(949\) 4.59575e23 0.698597
\(950\) 1.22205e22i 0.0184204i
\(951\) 3.22285e23i 0.481721i
\(952\) −6.11871e23 + 1.05484e24i −0.906910 + 1.56348i
\(953\) 1.61838e23 0.237869 0.118935 0.992902i \(-0.462052\pi\)
0.118935 + 0.992902i \(0.462052\pi\)
\(954\) 7.08431e23 1.03255
\(955\) 1.17948e23i 0.170476i
\(956\) −9.76205e21 −0.0139919
\(957\) 3.81212e22i 0.0541841i
\(958\) 1.34125e24i 1.89055i
\(959\) 3.13562e23 + 1.81884e23i 0.438303 + 0.254242i
\(960\) −4.73280e23 −0.656067
\(961\) −6.52892e23 −0.897540
\(962\) 4.35404e23i 0.593598i
\(963\) −3.16589e23 −0.428041
\(964\) 4.46733e21i 0.00599006i
\(965\) 4.18582e23i 0.556624i
\(966\) 4.21192e23 7.26119e23i 0.555473 0.957615i
\(967\) −6.22182e23 −0.813778 −0.406889 0.913478i \(-0.633386\pi\)
−0.406889 + 0.913478i \(0.633386\pi\)
\(968\) 6.71191e23 0.870649
\(969\) 5.18766e22i 0.0667393i
\(970\) 2.21044e23 0.282037
\(971\) 1.21529e24i 1.53789i −0.639315 0.768945i \(-0.720782\pi\)
0.639315 0.768945i \(-0.279218\pi\)
\(972\) 9.49298e22i 0.119144i
\(973\) 2.03338e23 3.50548e23i 0.253114 0.436359i
\(974\) 1.04337e24 1.28815
\(975\) −4.43525e23 −0.543102
\(976\) 1.45258e24i 1.76418i
\(977\) −1.14008e24 −1.37334 −0.686671 0.726968i \(-0.740929\pi\)
−0.686671 + 0.726968i \(0.740929\pi\)
\(978\) 3.80213e23i 0.454272i
\(979\) 3.77065e23i 0.446842i
\(980\) −4.99876e22 + 2.85905e22i −0.0587562 + 0.0336057i
\(981\) 6.67590e23 0.778319
\(982\) 1.31677e24 1.52272
\(983\) 5.80105e23i 0.665393i 0.943034 + 0.332696i \(0.107958\pi\)
−0.943034 + 0.332696i \(0.892042\pi\)
\(984\) 1.01796e24 1.15816
\(985\) 1.15410e22i 0.0130243i
\(986\) 2.95174e23i 0.330417i
\(987\) 5.58319e23 + 3.23858e23i 0.619933 + 0.359598i
\(988\) 1.88177e21 0.00207258
\(989\) 1.00519e24 1.09819
\(990\) 9.23198e22i 0.100049i
\(991\) 1.69694e23 0.182422 0.0912111 0.995832i \(-0.470926\pi\)
0.0912111 + 0.995832i \(0.470926\pi\)
\(992\) 2.89522e23i 0.308737i
\(993\) 3.11176e23i 0.329163i
\(994\) 2.40603e23 + 1.39564e23i 0.252470 + 0.146447i
\(995\) 2.22483e22 0.0231586
\(996\) −1.66615e23 −0.172044
\(997\) 1.11057e23i 0.113759i 0.998381 + 0.0568794i \(0.0181150\pi\)
−0.998381 + 0.0568794i \(0.981885\pi\)
\(998\) −1.20567e24 −1.22513
\(999\) 4.22520e23i 0.425915i
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 7.17.b.b.6.8 yes 8
3.2 odd 2 63.17.d.c.55.1 8
4.3 odd 2 112.17.c.b.97.1 8
7.6 odd 2 inner 7.17.b.b.6.7 8
21.20 even 2 63.17.d.c.55.2 8
28.27 even 2 112.17.c.b.97.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.17.b.b.6.7 8 7.6 odd 2 inner
7.17.b.b.6.8 yes 8 1.1 even 1 trivial
63.17.d.c.55.1 8 3.2 odd 2
63.17.d.c.55.2 8 21.20 even 2
112.17.c.b.97.1 8 4.3 odd 2
112.17.c.b.97.8 8 28.27 even 2