Properties

Label 63.6.p.b.26.11
Level $63$
Weight $6$
Character 63.26
Analytic conductor $10.104$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,6,Mod(17,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.17");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 63.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.1041806482\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.11
Character \(\chi\) \(=\) 63.26
Dual form 63.6.p.b.17.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(8.14327 + 4.70152i) q^{2} +(28.2086 + 48.8587i) q^{4} +(-33.1882 + 57.4837i) q^{5} +(-116.271 + 57.3420i) q^{7} +229.595i q^{8} +O(q^{10})\) \(q+(8.14327 + 4.70152i) q^{2} +(28.2086 + 48.8587i) q^{4} +(-33.1882 + 57.4837i) q^{5} +(-116.271 + 57.3420i) q^{7} +229.595i q^{8} +(-540.521 + 312.070i) q^{10} +(383.606 - 221.475i) q^{11} +437.107i q^{13} +(-1216.42 - 79.6982i) q^{14} +(-176.771 + 306.177i) q^{16} +(476.524 + 825.364i) q^{17} +(1934.59 + 1116.94i) q^{19} -3744.77 q^{20} +4165.07 q^{22} +(-2096.62 - 1210.49i) q^{23} +(-640.416 - 1109.23i) q^{25} +(-2055.06 + 3559.48i) q^{26} +(-6081.48 - 4063.30i) q^{28} -6381.19i q^{29} +(5912.80 - 3413.76i) q^{31} +(3483.73 - 2011.33i) q^{32} +8961.54i q^{34} +(562.593 - 8586.75i) q^{35} +(-7604.18 + 13170.8i) q^{37} +(10502.6 + 18191.0i) q^{38} +(-13198.0 - 7619.85i) q^{40} +1729.95 q^{41} +13717.1 q^{43} +(21641.9 + 12495.0i) q^{44} +(-11382.2 - 19714.6i) q^{46} +(-9079.05 + 15725.4i) q^{47} +(10230.8 - 13334.4i) q^{49} -12043.7i q^{50} +(-21356.4 + 12330.1i) q^{52} +(20788.0 - 12002.0i) q^{53} +29401.4i q^{55} +(-13165.4 - 26695.2i) q^{56} +(30001.3 - 51963.8i) q^{58} +(-21226.0 - 36764.5i) q^{59} +(-17731.8 - 10237.5i) q^{61} +64199.4 q^{62} +49138.6 q^{64} +(-25126.5 - 14506.8i) q^{65} +(-290.744 - 503.584i) q^{67} +(-26884.1 + 46564.6i) q^{68} +(44952.1 - 67279.2i) q^{70} -32681.9i q^{71} +(-47409.2 + 27371.7i) q^{73} +(-123846. + 71502.4i) q^{74} +126029. i q^{76} +(-31902.3 + 47747.7i) q^{77} +(-18594.6 + 32206.7i) q^{79} +(-11733.5 - 20322.9i) q^{80} +(14087.5 + 8133.41i) q^{82} +44677.3 q^{83} -63259.9 q^{85} +(111702. + 64491.0i) q^{86} +(50849.5 + 88073.9i) q^{88} +(-12075.8 + 20915.9i) q^{89} +(-25064.6 - 50822.7i) q^{91} -136584. i q^{92} +(-147866. + 85370.6i) q^{94} +(-128411. + 74138.2i) q^{95} +28906.5i q^{97} +(146004. - 60485.3i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49} - 2940 q^{52} + 154300 q^{58} + 48504 q^{61} - 327880 q^{64} + 156324 q^{67} - 9468 q^{70} - 703236 q^{73} + 165756 q^{79} + 1081020 q^{82} - 284448 q^{85} + 582308 q^{88} - 19812 q^{91} - 1481724 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.14327 + 4.70152i 1.43954 + 0.831119i 0.997817 0.0660327i \(-0.0210342\pi\)
0.441723 + 0.897152i \(0.354367\pi\)
\(3\) 0 0
\(4\) 28.2086 + 48.8587i 0.881517 + 1.52683i
\(5\) −33.1882 + 57.4837i −0.593689 + 1.02830i 0.400042 + 0.916497i \(0.368996\pi\)
−0.993730 + 0.111802i \(0.964338\pi\)
\(6\) 0 0
\(7\) −116.271 + 57.3420i −0.896862 + 0.442311i
\(8\) 229.595i 1.26835i
\(9\) 0 0
\(10\) −540.521 + 312.070i −1.70928 + 0.986852i
\(11\) 383.606 221.475i 0.955880 0.551877i 0.0609771 0.998139i \(-0.480578\pi\)
0.894902 + 0.446262i \(0.147245\pi\)
\(12\) 0 0
\(13\) 437.107i 0.717347i 0.933463 + 0.358673i \(0.116771\pi\)
−0.933463 + 0.358673i \(0.883229\pi\)
\(14\) −1216.42 79.6982i −1.65868 0.108675i
\(15\) 0 0
\(16\) −176.771 + 306.177i −0.172628 + 0.299001i
\(17\) 476.524 + 825.364i 0.399910 + 0.692665i 0.993714 0.111945i \(-0.0357080\pi\)
−0.593804 + 0.804609i \(0.702375\pi\)
\(18\) 0 0
\(19\) 1934.59 + 1116.94i 1.22943 + 0.709813i 0.966911 0.255113i \(-0.0821126\pi\)
0.262522 + 0.964926i \(0.415446\pi\)
\(20\) −3744.77 −2.09339
\(21\) 0 0
\(22\) 4165.07 1.83470
\(23\) −2096.62 1210.49i −0.826420 0.477134i 0.0262052 0.999657i \(-0.491658\pi\)
−0.852625 + 0.522523i \(0.824991\pi\)
\(24\) 0 0
\(25\) −640.416 1109.23i −0.204933 0.354954i
\(26\) −2055.06 + 3559.48i −0.596200 + 1.03265i
\(27\) 0 0
\(28\) −6081.48 4063.30i −1.46593 0.979454i
\(29\) 6381.19i 1.40899i −0.709711 0.704493i \(-0.751174\pi\)
0.709711 0.704493i \(-0.248826\pi\)
\(30\) 0 0
\(31\) 5912.80 3413.76i 1.10507 0.638012i 0.167521 0.985869i \(-0.446424\pi\)
0.937548 + 0.347857i \(0.113091\pi\)
\(32\) 3483.73 2011.33i 0.601408 0.347223i
\(33\) 0 0
\(34\) 8961.54i 1.32949i
\(35\) 562.593 8586.75i 0.0776291 1.18484i
\(36\) 0 0
\(37\) −7604.18 + 13170.8i −0.913163 + 1.58164i −0.103594 + 0.994620i \(0.533034\pi\)
−0.809569 + 0.587025i \(0.800299\pi\)
\(38\) 10502.6 + 18191.0i 1.17988 + 2.04361i
\(39\) 0 0
\(40\) −13198.0 7619.85i −1.30424 0.753002i
\(41\) 1729.95 0.160722 0.0803609 0.996766i \(-0.474393\pi\)
0.0803609 + 0.996766i \(0.474393\pi\)
\(42\) 0 0
\(43\) 13717.1 1.13133 0.565666 0.824634i \(-0.308619\pi\)
0.565666 + 0.824634i \(0.308619\pi\)
\(44\) 21641.9 + 12495.0i 1.68525 + 0.972979i
\(45\) 0 0
\(46\) −11382.2 19714.6i −0.793110 1.37371i
\(47\) −9079.05 + 15725.4i −0.599509 + 1.03838i 0.393384 + 0.919374i \(0.371304\pi\)
−0.992894 + 0.119006i \(0.962029\pi\)
\(48\) 0 0
\(49\) 10230.8 13334.4i 0.608722 0.793383i
\(50\) 12043.7i 0.681295i
\(51\) 0 0
\(52\) −21356.4 + 12330.1i −1.09527 + 0.632353i
\(53\) 20788.0 12002.0i 1.01654 0.586898i 0.103439 0.994636i \(-0.467015\pi\)
0.913099 + 0.407738i \(0.133682\pi\)
\(54\) 0 0
\(55\) 29401.4i 1.31057i
\(56\) −13165.4 26695.2i −0.561003 1.13753i
\(57\) 0 0
\(58\) 30001.3 51963.8i 1.17104 2.02829i
\(59\) −21226.0 36764.5i −0.793850 1.37499i −0.923567 0.383437i \(-0.874740\pi\)
0.129718 0.991551i \(-0.458593\pi\)
\(60\) 0 0
\(61\) −17731.8 10237.5i −0.610139 0.352264i 0.162881 0.986646i \(-0.447921\pi\)
−0.773020 + 0.634382i \(0.781255\pi\)
\(62\) 64199.4 2.12105
\(63\) 0 0
\(64\) 49138.6 1.49959
\(65\) −25126.5 14506.8i −0.737647 0.425881i
\(66\) 0 0
\(67\) −290.744 503.584i −0.00791269 0.0137052i 0.862042 0.506837i \(-0.169185\pi\)
−0.869955 + 0.493132i \(0.835852\pi\)
\(68\) −26884.1 + 46564.6i −0.705055 + 1.22119i
\(69\) 0 0
\(70\) 44952.1 67279.2i 1.09649 1.64110i
\(71\) 32681.9i 0.769416i −0.923038 0.384708i \(-0.874302\pi\)
0.923038 0.384708i \(-0.125698\pi\)
\(72\) 0 0
\(73\) −47409.2 + 27371.7i −1.04125 + 0.601167i −0.920187 0.391478i \(-0.871964\pi\)
−0.121064 + 0.992645i \(0.538631\pi\)
\(74\) −123846. + 71502.4i −2.62907 + 1.51789i
\(75\) 0 0
\(76\) 126029.i 2.50285i
\(77\) −31902.3 + 47747.7i −0.613191 + 0.917753i
\(78\) 0 0
\(79\) −18594.6 + 32206.7i −0.335211 + 0.580603i −0.983525 0.180770i \(-0.942141\pi\)
0.648314 + 0.761373i \(0.275474\pi\)
\(80\) −11733.5 20322.9i −0.204975 0.355027i
\(81\) 0 0
\(82\) 14087.5 + 8133.41i 0.231365 + 0.133579i
\(83\) 44677.3 0.711855 0.355928 0.934514i \(-0.384165\pi\)
0.355928 + 0.934514i \(0.384165\pi\)
\(84\) 0 0
\(85\) −63259.9 −0.949689
\(86\) 111702. + 64491.0i 1.62860 + 0.940271i
\(87\) 0 0
\(88\) 50849.5 + 88073.9i 0.699971 + 1.21239i
\(89\) −12075.8 + 20915.9i −0.161600 + 0.279899i −0.935443 0.353479i \(-0.884999\pi\)
0.773843 + 0.633378i \(0.218332\pi\)
\(90\) 0 0
\(91\) −25064.6 50822.7i −0.317290 0.643361i
\(92\) 136584.i 1.68241i
\(93\) 0 0
\(94\) −147866. + 85370.6i −1.72603 + 0.996527i
\(95\) −128411. + 74138.2i −1.45980 + 0.842817i
\(96\) 0 0
\(97\) 28906.5i 0.311937i 0.987762 + 0.155968i \(0.0498498\pi\)
−0.987762 + 0.155968i \(0.950150\pi\)
\(98\) 146004. 60485.3i 1.53568 0.636186i
\(99\) 0 0
\(100\) 36130.4 62579.7i 0.361304 0.625797i
\(101\) −49025.4 84914.5i −0.478209 0.828283i 0.521479 0.853264i \(-0.325381\pi\)
−0.999688 + 0.0249816i \(0.992047\pi\)
\(102\) 0 0
\(103\) −101433. 58562.5i −0.942078 0.543909i −0.0514670 0.998675i \(-0.516390\pi\)
−0.890611 + 0.454766i \(0.849723\pi\)
\(104\) −100357. −0.909843
\(105\) 0 0
\(106\) 225710. 1.95113
\(107\) 93124.6 + 53765.5i 0.786330 + 0.453988i 0.838669 0.544642i \(-0.183334\pi\)
−0.0523390 + 0.998629i \(0.516668\pi\)
\(108\) 0 0
\(109\) 6225.96 + 10783.7i 0.0501927 + 0.0869362i 0.890030 0.455902i \(-0.150683\pi\)
−0.839837 + 0.542838i \(0.817350\pi\)
\(110\) −138231. + 239424.i −1.08924 + 1.88662i
\(111\) 0 0
\(112\) 2996.56 45735.9i 0.0225724 0.344518i
\(113\) 11586.2i 0.0853583i 0.999089 + 0.0426792i \(0.0135893\pi\)
−0.999089 + 0.0426792i \(0.986411\pi\)
\(114\) 0 0
\(115\) 139166. 80347.8i 0.981273 0.566538i
\(116\) 311777. 180004.i 2.15129 1.24205i
\(117\) 0 0
\(118\) 399178.i 2.63913i
\(119\) −102734. 68640.9i −0.665037 0.444340i
\(120\) 0 0
\(121\) 17576.6 30443.6i 0.109137 0.189031i
\(122\) −96263.4 166733.i −0.585547 1.01420i
\(123\) 0 0
\(124\) 333583. + 192594.i 1.94827 + 1.12484i
\(125\) −122409. −0.700712
\(126\) 0 0
\(127\) −79605.0 −0.437957 −0.218978 0.975730i \(-0.570272\pi\)
−0.218978 + 0.975730i \(0.570272\pi\)
\(128\) 288670. + 166664.i 1.55731 + 0.899116i
\(129\) 0 0
\(130\) −136408. 236265.i −0.707915 1.22614i
\(131\) 94339.7 163401.i 0.480304 0.831911i −0.519440 0.854507i \(-0.673860\pi\)
0.999745 + 0.0225953i \(0.00719291\pi\)
\(132\) 0 0
\(133\) −288984. 18933.8i −1.41659 0.0928132i
\(134\) 5467.76i 0.0263055i
\(135\) 0 0
\(136\) −189499. + 109407.i −0.878538 + 0.507224i
\(137\) 242004. 139721.i 1.10159 0.636006i 0.164955 0.986301i \(-0.447252\pi\)
0.936639 + 0.350295i \(0.113919\pi\)
\(138\) 0 0
\(139\) 297273.i 1.30502i 0.757778 + 0.652512i \(0.226285\pi\)
−0.757778 + 0.652512i \(0.773715\pi\)
\(140\) 435407. 214732.i 1.87748 0.925928i
\(141\) 0 0
\(142\) 153654. 266137.i 0.639476 1.10760i
\(143\) 96808.1 + 167677.i 0.395887 + 0.685697i
\(144\) 0 0
\(145\) 366815. + 211780.i 1.44886 + 0.836500i
\(146\) −514755. −1.99856
\(147\) 0 0
\(148\) −858012. −3.21988
\(149\) 35158.2 + 20298.6i 0.129736 + 0.0749033i 0.563464 0.826141i \(-0.309469\pi\)
−0.433727 + 0.901044i \(0.642802\pi\)
\(150\) 0 0
\(151\) 29119.5 + 50436.5i 0.103930 + 0.180012i 0.913301 0.407286i \(-0.133525\pi\)
−0.809370 + 0.587298i \(0.800191\pi\)
\(152\) −256443. + 444172.i −0.900288 + 1.55935i
\(153\) 0 0
\(154\) −484276. + 238833.i −1.64547 + 0.811509i
\(155\) 453186.i 1.51512i
\(156\) 0 0
\(157\) 423501. 244508.i 1.37121 0.791671i 0.380133 0.924932i \(-0.375878\pi\)
0.991081 + 0.133261i \(0.0425447\pi\)
\(158\) −302841. + 174845.i −0.965100 + 0.557201i
\(159\) 0 0
\(160\) 267010.i 0.824570i
\(161\) 313188. + 20519.7i 0.952226 + 0.0623887i
\(162\) 0 0
\(163\) 54486.7 94373.8i 0.160628 0.278216i −0.774466 0.632616i \(-0.781981\pi\)
0.935094 + 0.354399i \(0.115315\pi\)
\(164\) 48799.5 + 84523.2i 0.141679 + 0.245395i
\(165\) 0 0
\(166\) 363819. + 210051.i 1.02474 + 0.591636i
\(167\) −78858.6 −0.218805 −0.109403 0.993998i \(-0.534894\pi\)
−0.109403 + 0.993998i \(0.534894\pi\)
\(168\) 0 0
\(169\) 180231. 0.485414
\(170\) −515142. 297418.i −1.36712 0.789304i
\(171\) 0 0
\(172\) 386939. + 670197.i 0.997289 + 1.72735i
\(173\) 211590. 366485.i 0.537502 0.930980i −0.461536 0.887121i \(-0.652701\pi\)
0.999038 0.0438588i \(-0.0139652\pi\)
\(174\) 0 0
\(175\) 138067. + 92248.6i 0.340797 + 0.227701i
\(176\) 156602.i 0.381079i
\(177\) 0 0
\(178\) −196673. + 113549.i −0.465259 + 0.268617i
\(179\) −287231. + 165833.i −0.670036 + 0.386846i −0.796090 0.605178i \(-0.793102\pi\)
0.126054 + 0.992023i \(0.459769\pi\)
\(180\) 0 0
\(181\) 469062.i 1.06423i −0.846673 0.532113i \(-0.821398\pi\)
0.846673 0.532113i \(-0.178602\pi\)
\(182\) 34836.6 531705.i 0.0779575 1.18985i
\(183\) 0 0
\(184\) 277922. 481374.i 0.605170 1.04819i
\(185\) −504738. 874233.i −1.08427 1.87801i
\(186\) 0 0
\(187\) 365594. + 211076.i 0.764532 + 0.441403i
\(188\) −1.02443e6 −2.11391
\(189\) 0 0
\(190\) −1.39425e6 −2.80192
\(191\) 243913. + 140823.i 0.483784 + 0.279313i 0.721992 0.691901i \(-0.243227\pi\)
−0.238208 + 0.971214i \(0.576560\pi\)
\(192\) 0 0
\(193\) −301997. 523075.i −0.583593 1.01081i −0.995049 0.0993830i \(-0.968313\pi\)
0.411456 0.911429i \(-0.365020\pi\)
\(194\) −135905. + 235394.i −0.259256 + 0.449045i
\(195\) 0 0
\(196\) 940096. + 123719.i 1.74796 + 0.230036i
\(197\) 14019.1i 0.0257369i 0.999917 + 0.0128684i \(0.00409626\pi\)
−0.999917 + 0.0128684i \(0.995904\pi\)
\(198\) 0 0
\(199\) 357535. 206423.i 0.640008 0.369509i −0.144610 0.989489i \(-0.546193\pi\)
0.784618 + 0.619980i \(0.212859\pi\)
\(200\) 254674. 147036.i 0.450205 0.259926i
\(201\) 0 0
\(202\) 921976.i 1.58979i
\(203\) 365910. + 741947.i 0.623210 + 1.26367i
\(204\) 0 0
\(205\) −57414.1 + 99444.1i −0.0954187 + 0.165270i
\(206\) −550665. 953780.i −0.904106 1.56596i
\(207\) 0 0
\(208\) −133832. 77267.9i −0.214487 0.123834i
\(209\) 989492. 1.56692
\(210\) 0 0
\(211\) 729963. 1.12874 0.564371 0.825521i \(-0.309119\pi\)
0.564371 + 0.825521i \(0.309119\pi\)
\(212\) 1.17280e6 + 677116.i 1.79219 + 1.03472i
\(213\) 0 0
\(214\) 505559. + 875654.i 0.754636 + 1.30707i
\(215\) −455245. + 788507.i −0.671659 + 1.16335i
\(216\) 0 0
\(217\) −491735. + 735972.i −0.708894 + 1.06099i
\(218\) 117086.i 0.166864i
\(219\) 0 0
\(220\) −1.43651e6 + 829371.i −2.00103 + 1.15529i
\(221\) −360772. + 208292.i −0.496881 + 0.286874i
\(222\) 0 0
\(223\) 494953.i 0.666503i 0.942838 + 0.333251i \(0.108146\pi\)
−0.942838 + 0.333251i \(0.891854\pi\)
\(224\) −289722. + 433623.i −0.385800 + 0.577421i
\(225\) 0 0
\(226\) −54472.8 + 94349.7i −0.0709429 + 0.122877i
\(227\) 141019. + 244252.i 0.181641 + 0.314611i 0.942439 0.334377i \(-0.108526\pi\)
−0.760799 + 0.648988i \(0.775192\pi\)
\(228\) 0 0
\(229\) −971368. 560820.i −1.22404 0.706699i −0.258262 0.966075i \(-0.583150\pi\)
−0.965777 + 0.259376i \(0.916483\pi\)
\(230\) 1.51103e6 1.88344
\(231\) 0 0
\(232\) 1.46509e6 1.78708
\(233\) 81173.9 + 46865.8i 0.0979550 + 0.0565544i 0.548177 0.836362i \(-0.315322\pi\)
−0.450222 + 0.892917i \(0.648655\pi\)
\(234\) 0 0
\(235\) −602635. 1.04379e6i −0.711844 1.23295i
\(236\) 1.19751e6 2.07415e6i 1.39958 2.42415i
\(237\) 0 0
\(238\) −513873. 1.04197e6i −0.588048 1.19237i
\(239\) 666306.i 0.754534i −0.926104 0.377267i \(-0.876864\pi\)
0.926104 0.377267i \(-0.123136\pi\)
\(240\) 0 0
\(241\) −154322. + 89097.9i −0.171153 + 0.0988155i −0.583130 0.812379i \(-0.698172\pi\)
0.411976 + 0.911195i \(0.364839\pi\)
\(242\) 286263. 165274.i 0.314214 0.181412i
\(243\) 0 0
\(244\) 1.15514e6i 1.24211i
\(245\) 426968. + 1.03065e6i 0.454444 + 1.09697i
\(246\) 0 0
\(247\) −488220. + 845622.i −0.509182 + 0.881929i
\(248\) 783782. + 1.35755e6i 0.809219 + 1.40161i
\(249\) 0 0
\(250\) −996812. 575510.i −1.00870 0.582375i
\(251\) 265419. 0.265918 0.132959 0.991122i \(-0.457552\pi\)
0.132959 + 0.991122i \(0.457552\pi\)
\(252\) 0 0
\(253\) −1.07237e6 −1.05328
\(254\) −648245. 374264.i −0.630456 0.363994i
\(255\) 0 0
\(256\) 780926. + 1.35260e6i 0.744749 + 1.28994i
\(257\) 349659. 605628.i 0.330227 0.571969i −0.652329 0.757936i \(-0.726208\pi\)
0.982556 + 0.185966i \(0.0595415\pi\)
\(258\) 0 0
\(259\) 128903. 1.96742e6i 0.119403 1.82242i
\(260\) 1.63686e6i 1.50168i
\(261\) 0 0
\(262\) 1.53647e6 887080.i 1.38283 0.798380i
\(263\) −1.51168e6 + 872769.i −1.34763 + 0.778054i −0.987913 0.155007i \(-0.950460\pi\)
−0.359716 + 0.933062i \(0.617127\pi\)
\(264\) 0 0
\(265\) 1.59330e6i 1.39374i
\(266\) −2.26425e6 1.51284e6i −1.96210 1.31096i
\(267\) 0 0
\(268\) 16402.9 28410.7i 0.0139503 0.0241627i
\(269\) 83991.2 + 145477.i 0.0707707 + 0.122578i 0.899239 0.437457i \(-0.144121\pi\)
−0.828469 + 0.560036i \(0.810787\pi\)
\(270\) 0 0
\(271\) 1.69618e6 + 979291.i 1.40297 + 0.810006i 0.994697 0.102853i \(-0.0327970\pi\)
0.408275 + 0.912859i \(0.366130\pi\)
\(272\) −336943. −0.276143
\(273\) 0 0
\(274\) 2.62761e6 2.11439
\(275\) −491334. 283672.i −0.391783 0.226196i
\(276\) 0 0
\(277\) −924728. 1.60168e6i −0.724126 1.25422i −0.959333 0.282278i \(-0.908910\pi\)
0.235206 0.971946i \(-0.424423\pi\)
\(278\) −1.39764e6 + 2.42078e6i −1.08463 + 1.87864i
\(279\) 0 0
\(280\) 1.97148e6 + 129169.i 1.50278 + 0.0984605i
\(281\) 431966.i 0.326350i −0.986597 0.163175i \(-0.947826\pi\)
0.986597 0.163175i \(-0.0521735\pi\)
\(282\) 0 0
\(283\) −288875. + 166782.i −0.214409 + 0.123789i −0.603359 0.797470i \(-0.706171\pi\)
0.388950 + 0.921259i \(0.372838\pi\)
\(284\) 1.59679e6 921908.i 1.17477 0.678253i
\(285\) 0 0
\(286\) 1.82058e6i 1.31612i
\(287\) −201143. + 99198.9i −0.144145 + 0.0710890i
\(288\) 0 0
\(289\) 255779. 443021.i 0.180144 0.312018i
\(290\) 1.99138e6 + 3.44917e6i 1.39046 + 2.40835i
\(291\) 0 0
\(292\) −2.67469e6 1.54423e6i −1.83576 1.05988i
\(293\) −1.89373e6 −1.28869 −0.644347 0.764733i \(-0.722871\pi\)
−0.644347 + 0.764733i \(0.722871\pi\)
\(294\) 0 0
\(295\) 2.81781e6 1.88520
\(296\) −3.02396e6 1.74588e6i −2.00607 1.15821i
\(297\) 0 0
\(298\) 190869. + 330594.i 0.124507 + 0.215653i
\(299\) 529112. 916448.i 0.342270 0.592830i
\(300\) 0 0
\(301\) −1.59489e6 + 786564.i −1.01465 + 0.500400i
\(302\) 547624.i 0.345513i
\(303\) 0 0
\(304\) −683960. + 394885.i −0.424470 + 0.245068i
\(305\) 1.17698e6 679527.i 0.724466 0.418271i
\(306\) 0 0
\(307\) 2.37284e6i 1.43689i 0.695585 + 0.718443i \(0.255145\pi\)
−0.695585 + 0.718443i \(0.744855\pi\)
\(308\) −3.23281e6 211810.i −1.94179 0.127224i
\(309\) 0 0
\(310\) −2.13066e6 + 3.69042e6i −1.25925 + 2.18108i
\(311\) −430680. 745960.i −0.252496 0.437335i 0.711717 0.702467i \(-0.247918\pi\)
−0.964212 + 0.265131i \(0.914585\pi\)
\(312\) 0 0
\(313\) −2.49997e6 1.44336e6i −1.44236 0.832747i −0.444353 0.895852i \(-0.646566\pi\)
−0.998007 + 0.0631051i \(0.979900\pi\)
\(314\) 4.59824e6 2.63189
\(315\) 0 0
\(316\) −2.09810e6 −1.18198
\(317\) −1.38969e6 802336.i −0.776727 0.448444i 0.0585418 0.998285i \(-0.481355\pi\)
−0.835269 + 0.549841i \(0.814688\pi\)
\(318\) 0 0
\(319\) −1.41327e6 2.44786e6i −0.777588 1.34682i
\(320\) −1.63082e6 + 2.82467e6i −0.890291 + 1.54203i
\(321\) 0 0
\(322\) 2.45390e6 + 1.63956e6i 1.31892 + 0.881224i
\(323\) 2.12899e6i 1.13545i
\(324\) 0 0
\(325\) 484853. 279930.i 0.254625 0.147008i
\(326\) 887400. 512341.i 0.462461 0.267002i
\(327\) 0 0
\(328\) 397189.i 0.203851i
\(329\) 153904. 2.34901e6i 0.0783901 1.19645i
\(330\) 0 0
\(331\) −1.05295e6 + 1.82376e6i −0.528248 + 0.914952i 0.471210 + 0.882021i \(0.343817\pi\)
−0.999458 + 0.0329309i \(0.989516\pi\)
\(332\) 1.26028e6 + 2.18287e6i 0.627513 + 1.08688i
\(333\) 0 0
\(334\) −642167. 370755.i −0.314979 0.181853i
\(335\) 38597.1 0.0187907
\(336\) 0 0
\(337\) 3.17015e6 1.52056 0.760282 0.649593i \(-0.225061\pi\)
0.760282 + 0.649593i \(0.225061\pi\)
\(338\) 1.46767e6 + 847358.i 0.698773 + 0.403437i
\(339\) 0 0
\(340\) −1.78447e6 3.09079e6i −0.837167 1.45002i
\(341\) 1.51212e6 2.61907e6i 0.704208 1.21972i
\(342\) 0 0
\(343\) −424923. + 2.13705e6i −0.195018 + 0.980800i
\(344\) 3.14937e6i 1.43492i
\(345\) 0 0
\(346\) 3.44607e6 1.98959e6i 1.54751 0.893456i
\(347\) −1.65067e6 + 953013.i −0.735928 + 0.424888i −0.820587 0.571522i \(-0.806353\pi\)
0.0846587 + 0.996410i \(0.473020\pi\)
\(348\) 0 0
\(349\) 3.96883e6i 1.74421i 0.489317 + 0.872106i \(0.337246\pi\)
−0.489317 + 0.872106i \(0.662754\pi\)
\(350\) 690610. + 1.40033e6i 0.301344 + 0.611027i
\(351\) 0 0
\(352\) 890919. 1.54312e6i 0.383249 0.663807i
\(353\) −1.18997e6 2.06109e6i −0.508275 0.880359i −0.999954 0.00958205i \(-0.996950\pi\)
0.491679 0.870777i \(-0.336383\pi\)
\(354\) 0 0
\(355\) 1.87867e6 + 1.08465e6i 0.791190 + 0.456794i
\(356\) −1.36256e6 −0.569812
\(357\) 0 0
\(358\) −3.11866e6 −1.28606
\(359\) 2.27068e6 + 1.31098e6i 0.929865 + 0.536858i 0.886769 0.462213i \(-0.152944\pi\)
0.0430964 + 0.999071i \(0.486278\pi\)
\(360\) 0 0
\(361\) 1.25704e6 + 2.17726e6i 0.507670 + 0.879310i
\(362\) 2.20530e6 3.81970e6i 0.884498 1.53200i
\(363\) 0 0
\(364\) 1.77610e6 2.65826e6i 0.702608 1.05158i
\(365\) 3.63367e6i 1.42762i
\(366\) 0 0
\(367\) 2.12630e6 1.22762e6i 0.824060 0.475771i −0.0277546 0.999615i \(-0.508836\pi\)
0.851815 + 0.523844i \(0.175502\pi\)
\(368\) 741246. 427959.i 0.285327 0.164734i
\(369\) 0 0
\(370\) 9.49215e6i 3.60463i
\(371\) −1.72882e6 + 2.58750e6i −0.652102 + 0.975992i
\(372\) 0 0
\(373\) 1.60705e6 2.78349e6i 0.598077 1.03590i −0.395027 0.918669i \(-0.629265\pi\)
0.993105 0.117231i \(-0.0374018\pi\)
\(374\) 1.98476e6 + 3.43770e6i 0.733716 + 1.27083i
\(375\) 0 0
\(376\) −3.61047e6 2.08450e6i −1.31702 0.760384i
\(377\) 2.78926e6 1.01073
\(378\) 0 0
\(379\) −1.46777e6 −0.524879 −0.262440 0.964948i \(-0.584527\pi\)
−0.262440 + 0.964948i \(0.584527\pi\)
\(380\) −7.24459e6 4.18266e6i −2.57368 1.48591i
\(381\) 0 0
\(382\) 1.32417e6 + 2.29352e6i 0.464284 + 0.804164i
\(383\) 1.22044e6 2.11387e6i 0.425129 0.736345i −0.571304 0.820739i \(-0.693562\pi\)
0.996432 + 0.0843939i \(0.0268954\pi\)
\(384\) 0 0
\(385\) −1.68593e6 3.41853e6i −0.579681 1.17540i
\(386\) 5.67939e6i 1.94014i
\(387\) 0 0
\(388\) −1.41233e6 + 815411.i −0.476275 + 0.274978i
\(389\) −295356. + 170524.i −0.0989629 + 0.0571362i −0.548665 0.836043i \(-0.684864\pi\)
0.449702 + 0.893179i \(0.351530\pi\)
\(390\) 0 0
\(391\) 2.30730e6i 0.763243i
\(392\) 3.06151e6 + 2.34894e6i 1.00628 + 0.772070i
\(393\) 0 0
\(394\) −65911.2 + 114162.i −0.0213904 + 0.0370492i
\(395\) −1.23424e6 2.13777e6i −0.398022 0.689395i
\(396\) 0 0
\(397\) −185747. 107241.i −0.0591488 0.0341496i 0.470134 0.882595i \(-0.344206\pi\)
−0.529283 + 0.848445i \(0.677539\pi\)
\(398\) 3.88200e6 1.22842
\(399\) 0 0
\(400\) 452829. 0.141509
\(401\) −1.94476e6 1.12281e6i −0.603957 0.348695i 0.166640 0.986018i \(-0.446708\pi\)
−0.770597 + 0.637323i \(0.780042\pi\)
\(402\) 0 0
\(403\) 1.49218e6 + 2.58453e6i 0.457675 + 0.792717i
\(404\) 2.76587e6 4.79063e6i 0.843099 1.46029i
\(405\) 0 0
\(406\) −508570. + 7.76220e6i −0.153121 + 2.33706i
\(407\) 6.73654e6i 2.01582i
\(408\) 0 0
\(409\) −938943. + 542099.i −0.277543 + 0.160240i −0.632311 0.774715i \(-0.717893\pi\)
0.354767 + 0.934955i \(0.384560\pi\)
\(410\) −935076. + 539866.i −0.274718 + 0.158609i
\(411\) 0 0
\(412\) 6.60785e6i 1.91786i
\(413\) 4.57611e6 + 3.05750e6i 1.32015 + 0.882046i
\(414\) 0 0
\(415\) −1.48276e6 + 2.56822e6i −0.422621 + 0.732000i
\(416\) 879167. + 1.52276e6i 0.249079 + 0.431418i
\(417\) 0 0
\(418\) 8.05770e6 + 4.65212e6i 2.25564 + 1.30230i
\(419\) −5.00675e6 −1.39322 −0.696612 0.717448i \(-0.745310\pi\)
−0.696612 + 0.717448i \(0.745310\pi\)
\(420\) 0 0
\(421\) −3.58647e6 −0.986192 −0.493096 0.869975i \(-0.664135\pi\)
−0.493096 + 0.869975i \(0.664135\pi\)
\(422\) 5.94429e6 + 3.43194e6i 1.62487 + 0.938119i
\(423\) 0 0
\(424\) 2.75559e6 + 4.77283e6i 0.744390 + 1.28932i
\(425\) 610347. 1.05715e6i 0.163910 0.283900i
\(426\) 0 0
\(427\) 2.64873e6 + 173542.i 0.703021 + 0.0460611i
\(428\) 6.06659e6i 1.60079i
\(429\) 0 0
\(430\) −7.41436e6 + 4.28069e6i −1.93376 + 1.11646i
\(431\) −1.00224e6 + 578644.i −0.259884 + 0.150044i −0.624281 0.781200i \(-0.714608\pi\)
0.364398 + 0.931243i \(0.381275\pi\)
\(432\) 0 0
\(433\) 3.11440e6i 0.798279i −0.916890 0.399140i \(-0.869309\pi\)
0.916890 0.399140i \(-0.130691\pi\)
\(434\) −7.46452e6 + 3.68132e6i −1.90229 + 0.938165i
\(435\) 0 0
\(436\) −351251. + 608384.i −0.0884914 + 0.153272i
\(437\) −2.70407e6 4.68359e6i −0.677352 1.17321i
\(438\) 0 0
\(439\) −1.95943e6 1.13128e6i −0.485254 0.280162i 0.237349 0.971424i \(-0.423721\pi\)
−0.722603 + 0.691263i \(0.757055\pi\)
\(440\) −6.75042e6 −1.66226
\(441\) 0 0
\(442\) −3.91715e6 −0.953706
\(443\) 1.62039e6 + 935535.i 0.392294 + 0.226491i 0.683154 0.730275i \(-0.260608\pi\)
−0.290860 + 0.956766i \(0.593941\pi\)
\(444\) 0 0
\(445\) −801548. 1.38832e6i −0.191880 0.332346i
\(446\) −2.32703e6 + 4.03054e6i −0.553943 + 0.959457i
\(447\) 0 0
\(448\) −5.71339e6 + 2.81771e6i −1.34493 + 0.663286i
\(449\) 5.11523e6i 1.19743i 0.800963 + 0.598714i \(0.204321\pi\)
−0.800963 + 0.598714i \(0.795679\pi\)
\(450\) 0 0
\(451\) 663619. 383141.i 0.153631 0.0886987i
\(452\) −566087. + 326831.i −0.130328 + 0.0752448i
\(453\) 0 0
\(454\) 2.65202e6i 0.603861i
\(455\) 3.75333e6 + 245913.i 0.849939 + 0.0556869i
\(456\) 0 0
\(457\) −1.56673e6 + 2.71366e6i −0.350916 + 0.607805i −0.986410 0.164301i \(-0.947463\pi\)
0.635494 + 0.772106i \(0.280796\pi\)
\(458\) −5.27341e6 9.13381e6i −1.17470 2.03464i
\(459\) 0 0
\(460\) 7.85137e6 + 4.53299e6i 1.73002 + 0.998826i
\(461\) −1.57943e6 −0.346137 −0.173068 0.984910i \(-0.555368\pi\)
−0.173068 + 0.984910i \(0.555368\pi\)
\(462\) 0 0
\(463\) −1.73622e6 −0.376402 −0.188201 0.982131i \(-0.560266\pi\)
−0.188201 + 0.982131i \(0.560266\pi\)
\(464\) 1.95377e6 + 1.12801e6i 0.421288 + 0.243231i
\(465\) 0 0
\(466\) 440681. + 763281.i 0.0940068 + 0.162825i
\(467\) −920630. + 1.59458e6i −0.195341 + 0.338340i −0.947012 0.321198i \(-0.895915\pi\)
0.751671 + 0.659538i \(0.229248\pi\)
\(468\) 0 0
\(469\) 62681.5 + 41880.2i 0.0131585 + 0.00879178i
\(470\) 1.13332e7i 2.36651i
\(471\) 0 0
\(472\) 8.44095e6 4.87338e6i 1.74396 1.00688i
\(473\) 5.26194e6 3.03798e6i 1.08142 0.624356i
\(474\) 0 0
\(475\) 2.86121e6i 0.581857i
\(476\) 455728. 6.95569e6i 0.0921910 1.40709i
\(477\) 0 0
\(478\) 3.13265e6 5.42591e6i 0.627108 1.08618i
\(479\) 2.47327e6 + 4.28383e6i 0.492530 + 0.853088i 0.999963 0.00860373i \(-0.00273869\pi\)
−0.507433 + 0.861691i \(0.669405\pi\)
\(480\) 0 0
\(481\) −5.75706e6 3.32384e6i −1.13459 0.655054i
\(482\) −1.67558e6 −0.328510
\(483\) 0 0
\(484\) 1.98325e6 0.384825
\(485\) −1.66165e6 959356.i −0.320764 0.185193i
\(486\) 0 0
\(487\) −1.49950e6 2.59722e6i −0.286500 0.496233i 0.686472 0.727157i \(-0.259159\pi\)
−0.972972 + 0.230924i \(0.925825\pi\)
\(488\) 2.35047e6 4.07114e6i 0.446792 0.773867i
\(489\) 0 0
\(490\) −1.36870e6 + 1.04002e7i −0.257524 + 1.95683i
\(491\) 5.51530e6i 1.03244i 0.856455 + 0.516221i \(0.172662\pi\)
−0.856455 + 0.516221i \(0.827338\pi\)
\(492\) 0 0
\(493\) 5.26680e6 3.04079e6i 0.975955 0.563468i
\(494\) −7.95141e6 + 4.59075e6i −1.46598 + 0.846382i
\(495\) 0 0
\(496\) 2.41382e6i 0.440555i
\(497\) 1.87404e6 + 3.79995e6i 0.340321 + 0.690060i
\(498\) 0 0
\(499\) 987310. 1.71007e6i 0.177502 0.307442i −0.763523 0.645781i \(-0.776532\pi\)
0.941024 + 0.338339i \(0.109865\pi\)
\(500\) −3.45299e6 5.98076e6i −0.617690 1.06987i
\(501\) 0 0
\(502\) 2.16138e6 + 1.24787e6i 0.382799 + 0.221009i
\(503\) −9.81653e6 −1.72997 −0.864984 0.501800i \(-0.832671\pi\)
−0.864984 + 0.501800i \(0.832671\pi\)
\(504\) 0 0
\(505\) 6.50827e6 1.13563
\(506\) −8.73259e6 5.04176e6i −1.51624 0.875399i
\(507\) 0 0
\(508\) −2.24554e6 3.88939e6i −0.386066 0.668686i
\(509\) −4.74859e6 + 8.22480e6i −0.812401 + 1.40712i 0.0987782 + 0.995109i \(0.468507\pi\)
−0.911179 + 0.412010i \(0.864827\pi\)
\(510\) 0 0
\(511\) 3.94276e6 5.90107e6i 0.667956 0.999720i
\(512\) 4.01968e6i 0.677667i
\(513\) 0 0
\(514\) 5.69474e6 3.28786e6i 0.950749 0.548915i
\(515\) 6.73277e6 3.88717e6i 1.11860 0.645826i
\(516\) 0 0
\(517\) 8.04312e6i 1.32342i
\(518\) 1.02996e7 1.54152e7i 1.68653 2.52421i
\(519\) 0 0
\(520\) 3.33069e6 5.76892e6i 0.540164 0.935591i
\(521\) 4.99494e6 + 8.65149e6i 0.806188 + 1.39636i 0.915486 + 0.402349i \(0.131806\pi\)
−0.109298 + 0.994009i \(0.534860\pi\)
\(522\) 0 0
\(523\) 5.77282e6 + 3.33294e6i 0.922856 + 0.532811i 0.884545 0.466455i \(-0.154469\pi\)
0.0383108 + 0.999266i \(0.487802\pi\)
\(524\) 1.06448e7 1.69359
\(525\) 0 0
\(526\) −1.64134e7 −2.58662
\(527\) 5.63518e6 + 3.25347e6i 0.883856 + 0.510295i
\(528\) 0 0
\(529\) −287618. 498168.i −0.0446865 0.0773993i
\(530\) −7.49091e6 + 1.29746e7i −1.15836 + 2.00634i
\(531\) 0 0
\(532\) −7.22673e6 1.46534e7i −1.10704 2.24471i
\(533\) 756174.i 0.115293i
\(534\) 0 0
\(535\) −6.18128e6 + 3.56876e6i −0.933671 + 0.539055i
\(536\) 115620. 66753.4i 0.0173829 0.0100360i
\(537\) 0 0
\(538\) 1.57955e6i 0.235275i
\(539\) 971359. 7.38101e6i 0.144015 1.09432i
\(540\) 0 0
\(541\) −1.73070e6 + 2.99766e6i −0.254231 + 0.440341i −0.964686 0.263401i \(-0.915156\pi\)
0.710456 + 0.703742i \(0.248489\pi\)
\(542\) 9.20831e6 + 1.59493e7i 1.34642 + 2.33207i
\(543\) 0 0
\(544\) 3.32016e6 + 1.91690e6i 0.481018 + 0.277716i
\(545\) −826514. −0.119195
\(546\) 0 0
\(547\) −6.12419e6 −0.875146 −0.437573 0.899183i \(-0.644162\pi\)
−0.437573 + 0.899183i \(0.644162\pi\)
\(548\) 1.36532e7 + 7.88267e6i 1.94215 + 1.12130i
\(549\) 0 0
\(550\) −2.66738e6 4.62003e6i −0.375991 0.651236i
\(551\) 7.12738e6 1.23450e7i 1.00012 1.73225i
\(552\) 0 0
\(553\) 315208. 4.81095e6i 0.0438313 0.668988i
\(554\) 1.73905e7i 2.40734i
\(555\) 0 0
\(556\) −1.45244e7 + 8.38565e6i −1.99255 + 1.15040i
\(557\) 7.46159e6 4.30795e6i 1.01905 0.588346i 0.105218 0.994449i \(-0.466446\pi\)
0.913827 + 0.406103i \(0.133113\pi\)
\(558\) 0 0
\(559\) 5.99582e6i 0.811557i
\(560\) 2.52962e6 + 1.69015e6i 0.340867 + 0.227748i
\(561\) 0 0
\(562\) 2.03090e6 3.51762e6i 0.271236 0.469794i
\(563\) −3.67238e6 6.36075e6i −0.488288 0.845740i 0.511621 0.859211i \(-0.329045\pi\)
−0.999909 + 0.0134710i \(0.995712\pi\)
\(564\) 0 0
\(565\) −666019. 384526.i −0.0877739 0.0506763i
\(566\) −3.13651e6 −0.411534
\(567\) 0 0
\(568\) 7.50359e6 0.975885
\(569\) −7.23229e6 4.17556e6i −0.936472 0.540672i −0.0476195 0.998866i \(-0.515164\pi\)
−0.888853 + 0.458193i \(0.848497\pi\)
\(570\) 0 0
\(571\) 503910. + 872798.i 0.0646789 + 0.112027i 0.896552 0.442939i \(-0.146064\pi\)
−0.831873 + 0.554967i \(0.812731\pi\)
\(572\) −5.46163e6 + 9.45982e6i −0.697963 + 1.20891i
\(573\) 0 0
\(574\) −2.10435e6 137874.i −0.266586 0.0174664i
\(575\) 3.10086e6i 0.391122i
\(576\) 0 0
\(577\) −8.77180e6 + 5.06440e6i −1.09685 + 0.633269i −0.935393 0.353610i \(-0.884954\pi\)
−0.161462 + 0.986879i \(0.551621\pi\)
\(578\) 4.16575e6 2.40510e6i 0.518649 0.299442i
\(579\) 0 0
\(580\) 2.38961e7i 2.94956i
\(581\) −5.19466e6 + 2.56188e6i −0.638436 + 0.314861i
\(582\) 0 0
\(583\) 5.31627e6 9.20804e6i 0.647792 1.12201i
\(584\) −6.28441e6 1.08849e7i −0.762487 1.32067i
\(585\) 0 0
\(586\) −1.54212e7 8.90342e6i −1.85513 1.07106i
\(587\) 1.07648e7 1.28947 0.644733 0.764408i \(-0.276969\pi\)
0.644733 + 0.764408i \(0.276969\pi\)
\(588\) 0 0
\(589\) 1.52518e7 1.81148
\(590\) 2.29462e7 + 1.32480e7i 2.71382 + 1.56682i
\(591\) 0 0
\(592\) −2.68840e6 4.65645e6i −0.315275 0.546073i
\(593\) −3.25915e6 + 5.64502e6i −0.380600 + 0.659218i −0.991148 0.132761i \(-0.957616\pi\)
0.610549 + 0.791979i \(0.290949\pi\)
\(594\) 0 0
\(595\) 7.35528e6 3.62745e6i 0.851740 0.420058i
\(596\) 2.29038e6i 0.264114i
\(597\) 0 0
\(598\) 8.61740e6 4.97526e6i 0.985424 0.568935i
\(599\) −2.97856e6 + 1.71967e6i −0.339187 + 0.195830i −0.659913 0.751342i \(-0.729407\pi\)
0.320725 + 0.947172i \(0.396073\pi\)
\(600\) 0 0
\(601\) 6.52015e6i 0.736329i −0.929761 0.368164i \(-0.879986\pi\)
0.929761 0.368164i \(-0.120014\pi\)
\(602\) −1.66857e7 1.09323e6i −1.87652 0.122947i
\(603\) 0 0
\(604\) −1.64284e6 + 2.84548e6i −0.183233 + 0.317368i
\(605\) 1.16667e6 + 2.02074e6i 0.129587 + 0.224451i
\(606\) 0 0
\(607\) −1.26515e6 730432.i −0.139370 0.0804652i 0.428694 0.903450i \(-0.358974\pi\)
−0.568064 + 0.822985i \(0.692307\pi\)
\(608\) 8.98611e6 0.985855
\(609\) 0 0
\(610\) 1.27792e7 1.39053
\(611\) −6.87367e6 3.96851e6i −0.744878 0.430056i
\(612\) 0 0
\(613\) 8.22442e6 + 1.42451e7i 0.884004 + 1.53114i 0.846851 + 0.531830i \(0.178495\pi\)
0.0371523 + 0.999310i \(0.488171\pi\)
\(614\) −1.11560e7 + 1.93227e7i −1.19422 + 2.06846i
\(615\) 0 0
\(616\) −1.09626e7 7.32461e6i −1.16403 0.777737i
\(617\) 3.81821e6i 0.403782i −0.979408 0.201891i \(-0.935291\pi\)
0.979408 0.201891i \(-0.0647087\pi\)
\(618\) 0 0
\(619\) −2.61645e6 + 1.51061e6i −0.274464 + 0.158462i −0.630915 0.775852i \(-0.717320\pi\)
0.356450 + 0.934314i \(0.383987\pi\)
\(620\) −2.21421e7 + 1.27837e7i −2.31334 + 1.33561i
\(621\) 0 0
\(622\) 8.09940e6i 0.839416i
\(623\) 204704. 3.12436e6i 0.0211303 0.322508i
\(624\) 0 0
\(625\) 6.06385e6 1.05029e7i 0.620938 1.07550i
\(626\) −1.35719e7 2.35073e7i −1.38422 2.39754i
\(627\) 0 0
\(628\) 2.38927e7 + 1.37945e7i 2.41750 + 1.39574i
\(629\) −1.44943e7 −1.46073
\(630\) 0 0
\(631\) 1.62315e7 1.62288 0.811438 0.584439i \(-0.198685\pi\)
0.811438 + 0.584439i \(0.198685\pi\)
\(632\) −7.39451e6 4.26922e6i −0.736405 0.425163i
\(633\) 0 0
\(634\) −7.54439e6 1.30673e7i −0.745420 1.29111i
\(635\) 2.64195e6 4.57599e6i 0.260010 0.450350i
\(636\) 0 0
\(637\) 5.82855e6 + 4.47195e6i 0.569131 + 0.436665i
\(638\) 2.65781e7i 2.58507i
\(639\) 0 0
\(640\) −1.91609e7 + 1.10625e7i −1.84912 + 1.06759i
\(641\) −3.11331e6 + 1.79747e6i −0.299280 + 0.172789i −0.642119 0.766605i \(-0.721945\pi\)
0.342840 + 0.939394i \(0.388611\pi\)
\(642\) 0 0
\(643\) 5.61426e6i 0.535507i −0.963487 0.267754i \(-0.913719\pi\)
0.963487 0.267754i \(-0.0862813\pi\)
\(644\) 7.83201e6 + 1.58808e7i 0.744147 + 1.50889i
\(645\) 0 0
\(646\) −1.00095e7 + 1.73369e7i −0.943691 + 1.63452i
\(647\) −2.93988e6 5.09203e6i −0.276102 0.478222i 0.694311 0.719675i \(-0.255709\pi\)
−0.970413 + 0.241453i \(0.922376\pi\)
\(648\) 0 0
\(649\) −1.62848e7 9.40205e6i −1.51765 0.876215i
\(650\) 5.26438e6 0.488724
\(651\) 0 0
\(652\) 6.14797e6 0.566386
\(653\) 1.50765e7 + 8.70444e6i 1.38363 + 0.798837i 0.992587 0.121537i \(-0.0387824\pi\)
0.391039 + 0.920374i \(0.372116\pi\)
\(654\) 0 0
\(655\) 6.26194e6 + 1.08460e7i 0.570303 + 0.987793i
\(656\) −305806. + 529672.i −0.0277451 + 0.0480560i
\(657\) 0 0
\(658\) 1.22972e7 1.84051e7i 1.10724 1.65719i
\(659\) 5.65316e6i 0.507081i −0.967325 0.253541i \(-0.918405\pi\)
0.967325 0.253541i \(-0.0815952\pi\)
\(660\) 0 0
\(661\) −1.17378e7 + 6.77682e6i −1.04492 + 0.603285i −0.921223 0.389035i \(-0.872809\pi\)
−0.123697 + 0.992320i \(0.539475\pi\)
\(662\) −1.71489e7 + 9.90093e6i −1.52087 + 0.878073i
\(663\) 0 0
\(664\) 1.02577e7i 0.902878i
\(665\) 1.06792e7 1.59835e7i 0.936453 1.40158i
\(666\) 0 0
\(667\) −7.72435e6 + 1.33790e7i −0.672275 + 1.16442i
\(668\) −2.22449e6 3.85293e6i −0.192881 0.334079i
\(669\) 0 0
\(670\) 314307. + 181465.i 0.0270500 + 0.0156173i
\(671\) −9.06937e6 −0.777626
\(672\) 0 0
\(673\) −3.85676e6 −0.328235 −0.164118 0.986441i \(-0.552478\pi\)
−0.164118 + 0.986441i \(0.552478\pi\)
\(674\) 2.58154e7 + 1.49045e7i 2.18891 + 1.26377i
\(675\) 0 0
\(676\) 5.08405e6 + 8.80583e6i 0.427901 + 0.741146i
\(677\) 5.93780e6 1.02846e7i 0.497913 0.862411i −0.502084 0.864819i \(-0.667433\pi\)
0.999997 + 0.00240761i \(0.000766368\pi\)
\(678\) 0 0
\(679\) −1.65756e6 3.36098e6i −0.137973 0.279764i
\(680\) 1.45242e7i 1.20453i
\(681\) 0 0
\(682\) 2.46272e7 1.42185e7i 2.02747 1.17056i
\(683\) −6.89816e6 + 3.98266e6i −0.565824 + 0.326679i −0.755480 0.655172i \(-0.772596\pi\)
0.189656 + 0.981851i \(0.439263\pi\)
\(684\) 0 0
\(685\) 1.85484e7i 1.51036i
\(686\) −1.35077e7 + 1.54048e7i −1.09590 + 1.24982i
\(687\) 0 0
\(688\) −2.42478e6 + 4.19985e6i −0.195300 + 0.338269i
\(689\) 5.24614e6 + 9.08658e6i 0.421009 + 0.729210i
\(690\) 0 0
\(691\) −2.04326e7 1.17968e7i −1.62790 0.939870i −0.984717 0.174160i \(-0.944279\pi\)
−0.643186 0.765710i \(-0.722388\pi\)
\(692\) 2.38746e7 1.89527
\(693\) 0 0
\(694\) −1.79224e7 −1.41253
\(695\) −1.70884e7 9.86597e6i −1.34196 0.774779i
\(696\) 0 0
\(697\) 824364. + 1.42784e6i 0.0642742 + 0.111326i
\(698\) −1.86595e7 + 3.23193e7i −1.44965 + 2.51086i
\(699\) 0 0
\(700\) −612468. + 9.34798e6i −0.0472431 + 0.721062i
\(701\) 1.79714e7i 1.38129i 0.723192 + 0.690647i \(0.242674\pi\)
−0.723192 + 0.690647i \(0.757326\pi\)
\(702\) 0 0
\(703\) −2.94219e7 + 1.69868e7i −2.24534 + 1.29635i
\(704\) 1.88498e7 1.08830e7i 1.43343 0.827591i
\(705\) 0 0
\(706\) 2.23787e7i 1.68975i
\(707\) 1.05694e7 + 7.06187e6i 0.795246 + 0.531338i
\(708\) 0 0
\(709\) 3.36632e6 5.83064e6i 0.251501 0.435613i −0.712438 0.701735i \(-0.752409\pi\)
0.963939 + 0.266122i \(0.0857424\pi\)
\(710\) 1.01990e7 + 1.76652e7i 0.759300 + 1.31515i
\(711\) 0 0
\(712\) −4.80218e6 2.77254e6i −0.355009 0.204964i
\(713\) −1.65292e7 −1.21767
\(714\) 0 0
\(715\) −1.28516e7 −0.940136
\(716\) −1.62047e7 9.35581e6i −1.18130 0.682022i
\(717\) 0 0
\(718\) 1.23272e7 + 2.13513e7i 0.892386 + 1.54566i
\(719\) 5.08775e6 8.81225e6i 0.367032 0.635718i −0.622068 0.782963i \(-0.713707\pi\)
0.989100 + 0.147245i \(0.0470406\pi\)
\(720\) 0 0
\(721\) 1.51518e7 + 992727.i 1.08549 + 0.0711200i
\(722\) 2.36400e7i 1.68774i
\(723\) 0 0
\(724\) 2.29177e7 1.32316e7i 1.62490 0.938134i
\(725\) −7.07823e6 + 4.08662e6i −0.500126 + 0.288748i
\(726\) 0 0
\(727\) 9.35279e6i 0.656304i −0.944625 0.328152i \(-0.893574\pi\)
0.944625 0.328152i \(-0.106426\pi\)
\(728\) 1.16686e7 5.75470e6i 0.816004 0.402433i
\(729\) 0 0
\(730\) 1.70838e7 2.95900e7i 1.18653 2.05512i
\(731\) 6.53651e6 + 1.13216e7i 0.452431 + 0.783634i
\(732\) 0 0
\(733\) 1.30765e7 + 7.54971e6i 0.898940 + 0.519003i 0.876856 0.480753i \(-0.159636\pi\)
0.0220841 + 0.999756i \(0.492970\pi\)
\(734\) 2.30867e7 1.58169
\(735\) 0 0
\(736\) −9.73876e6 −0.662688
\(737\) −223062. 128785.i −0.0151271 0.00873366i
\(738\) 0 0
\(739\) −9.46139e6 1.63876e7i −0.637300 1.10384i −0.986023 0.166610i \(-0.946718\pi\)
0.348723 0.937226i \(-0.386615\pi\)
\(740\) 2.84759e7 4.93217e7i 1.91160 3.31100i
\(741\) 0 0
\(742\) −2.62435e7 + 1.29427e7i −1.74989 + 0.863005i
\(743\) 1.40170e7i 0.931501i −0.884916 0.465750i \(-0.845784\pi\)
0.884916 0.465750i \(-0.154216\pi\)
\(744\) 0 0
\(745\) −2.33368e6 + 1.34735e6i −0.154046 + 0.0889385i
\(746\) 2.61733e7 1.51112e7i 1.72191 0.994147i
\(747\) 0 0
\(748\) 2.38166e7i 1.55642i
\(749\) −1.39107e7 911411.i −0.906033 0.0593622i
\(750\) 0 0
\(751\) −6.33649e6 + 1.09751e7i −0.409967 + 0.710084i −0.994886 0.101008i \(-0.967793\pi\)
0.584919 + 0.811092i \(0.301126\pi\)
\(752\) −3.20983e6 5.55959e6i −0.206984 0.358508i
\(753\) 0 0
\(754\) 2.27137e7 + 1.31138e7i 1.45499 + 0.840038i
\(755\) −3.86570e6 −0.246809
\(756\) 0 0
\(757\) 8.38368e6 0.531735 0.265867 0.964010i \(-0.414342\pi\)
0.265867 + 0.964010i \(0.414342\pi\)
\(758\) −1.19524e7 6.90074e6i −0.755585 0.436237i
\(759\) 0 0
\(760\) −1.70218e7 2.94826e7i −1.06898 1.85153i
\(761\) −3.94333e6 + 6.83004e6i −0.246832 + 0.427525i −0.962645 0.270767i \(-0.912723\pi\)
0.715813 + 0.698292i \(0.246056\pi\)
\(762\) 0 0
\(763\) −1.34226e6 896818.i −0.0834687 0.0557690i
\(764\) 1.58897e7i 0.984877i
\(765\) 0 0
\(766\) 1.98768e7 1.14759e7i 1.22398 0.706665i
\(767\) 1.60700e7 9.27803e6i 0.986343 0.569465i
\(768\) 0 0
\(769\) 2.85431e7i 1.74055i −0.492568 0.870274i \(-0.663942\pi\)
0.492568 0.870274i \(-0.336058\pi\)
\(770\) 2.34324e6 3.57644e7i 0.142426 2.17382i
\(771\) 0 0
\(772\) 1.70378e7 2.95104e7i 1.02889 1.78210i
\(773\) −9.06870e6 1.57075e7i −0.545879 0.945490i −0.998551 0.0538132i \(-0.982862\pi\)
0.452672 0.891677i \(-0.350471\pi\)
\(774\) 0 0
\(775\) −7.57330e6 4.37245e6i −0.452930 0.261499i
\(776\) −6.63679e6 −0.395643
\(777\) 0 0
\(778\) −3.20689e6 −0.189948
\(779\) 3.34675e6 + 1.93225e6i 0.197597 + 0.114082i
\(780\) 0 0
\(781\) −7.23821e6 1.25369e7i −0.424623 0.735469i
\(782\) 1.08478e7 1.87890e7i 0.634345 1.09872i
\(783\) 0 0
\(784\) 2.27417e6 + 5.48957e6i 0.132140 + 0.318969i
\(785\) 3.24592e7i 1.88003i
\(786\) 0 0
\(787\) 9.29400e6 5.36589e6i 0.534892 0.308820i −0.208115 0.978104i \(-0.566733\pi\)
0.743006 + 0.669285i \(0.233399\pi\)
\(788\) −684956. + 395459.i −0.0392959 + 0.0226875i
\(789\) 0 0
\(790\) 2.32112e7i 1.32322i
\(791\) −664377. 1.34714e6i −0.0377549 0.0765546i
\(792\) 0 0
\(793\) 4.47487e6 7.75070e6i 0.252695 0.437681i
\(794\) −1.00839e6 1.74659e6i −0.0567647 0.0983194i
\(795\) 0 0
\(796\) 2.01711e7 + 1.16458e7i 1.12836 + 0.651457i
\(797\) −2.16530e7 −1.20746 −0.603729 0.797189i \(-0.706319\pi\)
−0.603729 + 0.797189i \(0.706319\pi\)
\(798\) 0 0
\(799\) −1.73055e7 −0.958999
\(800\) −4.46207e6 2.57618e6i −0.246497 0.142315i
\(801\) 0 0
\(802\) −1.05578e7 1.82867e7i −0.579613 1.00392i
\(803\) −1.21243e7 + 2.09999e7i −0.663540 + 1.14929i
\(804\) 0 0
\(805\) −1.15737e7 + 1.73222e7i −0.629480 + 0.942134i
\(806\) 2.80620e7i 1.52153i
\(807\) 0 0
\(808\) 1.94960e7 1.12560e7i 1.05055 0.606534i
\(809\) 2.51511e7 1.45210e7i 1.35109 0.780054i 0.362691 0.931909i \(-0.381858\pi\)
0.988403 + 0.151855i \(0.0485247\pi\)
\(810\) 0 0
\(811\) 1.01783e7i 0.543405i 0.962381 + 0.271703i \(0.0875867\pi\)
−0.962381 + 0.271703i \(0.912413\pi\)
\(812\) −2.59287e7 + 3.88071e7i −1.38004 + 2.06548i
\(813\) 0 0
\(814\) −3.16720e7 + 5.48574e7i −1.67538 + 2.90185i
\(815\) 3.61664e6 + 6.26420e6i 0.190726 + 0.330348i
\(816\) 0 0
\(817\) 2.65369e7 + 1.53211e7i 1.39090 + 0.803035i
\(818\) −1.01948e7 −0.532713
\(819\) 0 0
\(820\) −6.47827e6 −0.336453
\(821\) −2.93963e7 1.69719e7i −1.52207 0.878766i −0.999660 0.0260706i \(-0.991701\pi\)
−0.522408 0.852696i \(-0.674966\pi\)
\(822\) 0 0
\(823\) 383232. + 663777.i 0.0197225 + 0.0341604i 0.875718 0.482823i \(-0.160388\pi\)
−0.855996 + 0.516983i \(0.827055\pi\)
\(824\) 1.34456e7 2.32885e7i 0.689864 1.19488i
\(825\) 0 0
\(826\) 2.28896e7 + 4.64127e7i 1.16732 + 2.36694i
\(827\) 1.50733e7i 0.766381i −0.923669 0.383191i \(-0.874825\pi\)
0.923669 0.383191i \(-0.125175\pi\)
\(828\) 0 0
\(829\) 2.15108e7 1.24192e7i 1.08710 0.627638i 0.154297 0.988024i \(-0.450689\pi\)
0.932803 + 0.360387i \(0.117355\pi\)
\(830\) −2.41490e7 + 1.39424e7i −1.21676 + 0.702496i
\(831\) 0 0
\(832\) 2.14788e7i 1.07573i
\(833\) 1.58809e7 + 2.08997e6i 0.792983 + 0.104358i
\(834\) 0 0
\(835\) 2.61718e6 4.53308e6i 0.129902 0.224997i
\(836\) 2.79121e7 + 4.83453e7i 1.38127 + 2.39242i
\(837\) 0 0
\(838\) −4.07713e7 2.35393e7i −2.00560 1.15793i
\(839\) 1.88795e6 0.0925947 0.0462974 0.998928i \(-0.485258\pi\)
0.0462974 + 0.998928i \(0.485258\pi\)
\(840\) 0 0
\(841\) −2.02085e7 −0.985244
\(842\) −2.92055e7 1.68618e7i −1.41966 0.819643i
\(843\) 0 0
\(844\) 2.05912e7 + 3.56650e7i 0.995006 + 1.72340i
\(845\) −5.98154e6 + 1.03603e7i −0.288185 + 0.499151i
\(846\) 0 0
\(847\) −297952. + 4.54758e6i −0.0142705 + 0.217807i
\(848\) 8.48642e6i 0.405261i
\(849\) 0 0
\(850\) 9.94043e6 5.73911e6i 0.471909 0.272457i
\(851\) 3.18862e7 1.84095e7i 1.50931 0.871402i
\(852\) 0 0
\(853\) 2.82848e6i 0.133101i −0.997783 0.0665504i \(-0.978801\pi\)
0.997783 0.0665504i \(-0.0211993\pi\)
\(854\) 2.07534e7 + 1.38663e7i 0.973745 + 0.650601i
\(855\) 0 0
\(856\) −1.23443e7 + 2.13809e7i −0.575813 + 0.997338i
\(857\) 1.19125e7 + 2.06331e7i 0.554054 + 0.959650i 0.997976 + 0.0635847i \(0.0202533\pi\)
−0.443922 + 0.896065i \(0.646413\pi\)
\(858\) 0 0
\(859\) −9.92340e6 5.72927e6i −0.458857 0.264921i 0.252707 0.967543i \(-0.418679\pi\)
−0.711564 + 0.702622i \(0.752013\pi\)
\(860\) −5.13672e7 −2.36832
\(861\) 0 0
\(862\) −1.08820e7 −0.498817
\(863\) 1.23304e7 + 7.11898e6i 0.563575 + 0.325380i 0.754579 0.656209i \(-0.227841\pi\)
−0.191004 + 0.981589i \(0.561174\pi\)
\(864\) 0 0
\(865\) 1.40446e7 + 2.43259e7i 0.638218 + 1.10543i
\(866\) 1.46424e7 2.53614e7i 0.663465 1.14916i
\(867\) 0 0
\(868\) −4.98297e7 3.26478e6i −2.24486 0.147080i
\(869\) 1.64729e7i 0.739982i
\(870\) 0 0
\(871\) 220120. 127086.i 0.00983136 0.00567614i
\(872\) −2.47588e6 + 1.42945e6i −0.110265 + 0.0636616i
\(873\) 0 0
\(874\) 5.08530e7i 2.25184i
\(875\) 1.42326e7 7.01919e6i 0.628442 0.309932i
\(876\) 0 0
\(877\) −1.73898e7 + 3.01200e7i −0.763477 + 1.32238i 0.177571 + 0.984108i \(0.443176\pi\)
−0.941048 + 0.338273i \(0.890157\pi\)
\(878\) −1.06375e7 1.84246e7i −0.465695 0.806608i
\(879\) 0 0
\(880\) −9.00204e6 5.19733e6i −0.391863 0.226242i
\(881\) 9.40367e6 0.408186 0.204093 0.978952i \(-0.434576\pi\)
0.204093 + 0.978952i \(0.434576\pi\)
\(882\) 0 0
\(883\) 1.30301e7 0.562399 0.281199 0.959649i \(-0.409268\pi\)
0.281199 + 0.959649i \(0.409268\pi\)
\(884\) −2.03537e7 1.17512e7i −0.876018 0.505769i
\(885\) 0 0
\(886\) 8.79687e6 + 1.52366e7i 0.376482 + 0.652086i
\(887\) 6.51276e6 1.12804e7i 0.277943 0.481411i −0.692930 0.721004i \(-0.743681\pi\)
0.970873 + 0.239593i \(0.0770140\pi\)
\(888\) 0 0
\(889\) 9.25574e6 4.56471e6i 0.392787 0.193713i
\(890\) 1.50740e7i 0.637900i
\(891\) 0 0
\(892\) −2.41827e7 + 1.39619e7i −1.01764 + 0.587534i
\(893\) −3.51285e7 + 2.02814e7i −1.47411 + 0.851079i
\(894\) 0 0
\(895\) 2.20148e7i 0.918664i
\(896\) −4.31207e7 2.82521e6i −1.79438 0.117566i
\(897\) 0 0
\(898\) −2.40493e7 + 4.16547e7i −0.995205 + 1.72374i
\(899\) −2.17839e7 3.77307e7i −0.898950 1.55703i
\(900\) 0 0
\(901\) 1.98120e7 + 1.14384e7i 0.813047 + 0.469413i
\(902\) 7.20538e6 0.294877
\(903\) 0 0
\(904\) −2.66014e6 −0.108264
\(905\) 2.69634e7 + 1.55673e7i 1.09434 + 0.631819i
\(906\) 0 0
\(907\) 9.82796e6 + 1.70225e7i 0.396685 + 0.687078i 0.993315 0.115439i \(-0.0368273\pi\)
−0.596630 + 0.802516i \(0.703494\pi\)
\(908\) −7.95590e6 + 1.37800e7i −0.320239 + 0.554671i
\(909\) 0 0
\(910\) 2.94082e7 + 1.96489e7i 1.17724 + 0.786564i
\(911\) 2.66058e7i 1.06214i −0.847329 0.531069i \(-0.821791\pi\)
0.847329 0.531069i \(-0.178209\pi\)
\(912\) 0 0
\(913\) 1.71385e7 9.89489e6i 0.680448 0.392857i
\(914\) −2.55166e7 + 1.47320e7i −1.01032 + 0.583306i
\(915\) 0 0
\(916\) 6.32797e7i 2.49187i
\(917\) −1.59921e6 + 2.44084e7i −0.0628032 + 0.958553i
\(918\) 0 0
\(919\) 1.42661e7 2.47096e7i 0.557206 0.965109i −0.440522 0.897742i \(-0.645207\pi\)
0.997728 0.0673674i \(-0.0214600\pi\)
\(920\) 1.84474e7 + 3.19519e7i 0.718566 + 1.24459i
\(921\) 0 0
\(922\) −1.28617e7 7.42571e6i −0.498278 0.287681i
\(923\) 1.42855e7 0.551938
\(924\) 0 0
\(925\) 1.94793e7 0.748549
\(926\) −1.41385e7 8.16286e6i −0.541846 0.312835i
\(927\) 0 0
\(928\) −1.28347e7 2.22304e7i −0.489233 0.847376i
\(929\) 2.01679e7 3.49319e7i 0.766694 1.32795i −0.172653 0.984983i \(-0.555234\pi\)
0.939347 0.342969i \(-0.111433\pi\)
\(930\) 0 0
\(931\) 3.46861e7 1.43694e7i 1.31154 0.543332i
\(932\) 5.28806e6i 0.199415i
\(933\) 0 0
\(934\) −1.49939e7 + 8.65672e6i −0.562402 + 0.324703i
\(935\) −2.42669e7 + 1.40105e7i −0.907788 + 0.524112i
\(936\) 0 0
\(937\) 2.03556e7i 0.757417i 0.925516 + 0.378708i \(0.123632\pi\)
−0.925516 + 0.378708i \(0.876368\pi\)
\(938\) 313532. + 635740.i 0.0116352 + 0.0235924i
\(939\) 0 0
\(940\) 3.39989e7 5.88879e7i 1.25501 2.17373i
\(941\) 1.74195e7 + 3.01714e7i 0.641299 + 1.11076i 0.985143 + 0.171736i \(0.0549376\pi\)
−0.343844 + 0.939027i \(0.611729\pi\)
\(942\) 0 0
\(943\) −3.62706e6 2.09408e6i −0.132824 0.0766858i
\(944\) 1.50086e7 0.548164
\(945\) 0 0
\(946\) 5.71326e7 2.07566
\(947\) −6.18612e6 3.57156e6i −0.224153 0.129415i 0.383719 0.923450i \(-0.374643\pi\)
−0.607872 + 0.794035i \(0.707976\pi\)
\(948\) 0 0
\(949\) −1.19644e7 2.07229e7i −0.431245 0.746938i
\(950\) 1.34520e7 2.32996e7i 0.483592 0.837606i
\(951\) 0 0
\(952\) 1.57596e7 2.35872e7i 0.563576 0.843497i
\(953\) 6.28996e6i 0.224344i 0.993689 + 0.112172i \(0.0357808\pi\)
−0.993689 + 0.112172i \(0.964219\pi\)
\(954\) 0 0
\(955\) −1.61901e7 + 9.34735e6i −0.574435 + 0.331650i
\(956\) 3.25548e7 1.87955e7i 1.15205 0.665135i
\(957\) 0 0
\(958\) 4.65125e7i 1.63741i
\(959\) −2.01261e7 + 3.01225e7i −0.706666 + 1.05766i
\(960\) 0 0
\(961\) 8.99292e6 1.55762e7i 0.314118 0.544068i
\(962\) −3.12542e7 5.41338e7i −1.08886 1.88595i
\(963\) 0 0
\(964\) −8.70641e6 5.02665e6i −0.301749 0.174215i
\(965\) 4.00910e7 1.38589
\(966\) 0 0
\(967\) 3.55035e7 1.22097 0.610485 0.792028i \(-0.290975\pi\)
0.610485 + 0.792028i \(0.290975\pi\)
\(968\) 6.98970e6 + 4.03551e6i 0.239757 + 0.138423i
\(969\) 0 0
\(970\) −9.02086e6 1.56246e7i −0.307835 0.533187i
\(971\) 1.32813e7 2.30038e7i 0.452055 0.782982i −0.546459 0.837486i \(-0.684025\pi\)
0.998514 + 0.0545043i \(0.0173578\pi\)
\(972\) 0 0
\(973\) −1.70462e7 3.45642e7i −0.577226 1.17043i
\(974\) 2.81998e7i 0.952463i
\(975\) 0 0
\(976\) 6.26896e6 3.61939e6i 0.210655 0.121622i
\(977\) 3.05413e7 1.76330e7i 1.02365 0.591004i 0.108490 0.994098i \(-0.465398\pi\)
0.915159 + 0.403093i \(0.132065\pi\)
\(978\) 0 0
\(979\) 1.06979e7i 0.356733i
\(980\) −3.83119e7 + 4.99342e7i −1.27429 + 1.66086i
\(981\) 0 0
\(982\) −2.59303e7 + 4.49126e7i −0.858082 + 1.48624i
\(983\) −1.59341e7 2.75987e7i −0.525951 0.910973i −0.999543 0.0302290i \(-0.990376\pi\)
0.473592 0.880744i \(-0.342957\pi\)
\(984\) 0 0
\(985\) −805871. 465270.i −0.0264652 0.0152797i
\(986\) 5.71853e7 1.87324
\(987\) 0 0
\(988\) −5.50879e7 −1.79541
\(989\) −2.87595e7 1.66043e7i −0.934956 0.539797i
\(990\) 0 0
\(991\) 2.80173e7 + 4.85275e7i 0.906239 + 1.56965i 0.819245 + 0.573444i \(0.194393\pi\)
0.0869941 + 0.996209i \(0.472274\pi\)
\(992\) 1.37324e7 2.37852e7i 0.443065 0.767411i
\(993\) 0 0
\(994\) −2.60469e6 + 3.97548e7i −0.0836161 + 1.27622i
\(995\) 2.74032e7i 0.877493i
\(996\) 0 0
\(997\) 5.15391e6 2.97561e6i 0.164210 0.0948065i −0.415643 0.909528i \(-0.636443\pi\)
0.579853 + 0.814721i \(0.303110\pi\)
\(998\) 1.60799e7 9.28372e6i 0.511041 0.295050i
\(999\) 0 0
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 63.6.p.b.26.11 yes 24
3.2 odd 2 inner 63.6.p.b.26.2 yes 24
7.2 even 3 441.6.c.b.440.17 24
7.3 odd 6 inner 63.6.p.b.17.2 24
7.5 odd 6 441.6.c.b.440.7 24
21.2 odd 6 441.6.c.b.440.8 24
21.5 even 6 441.6.c.b.440.18 24
21.17 even 6 inner 63.6.p.b.17.11 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.6.p.b.17.2 24 7.3 odd 6 inner
63.6.p.b.17.11 yes 24 21.17 even 6 inner
63.6.p.b.26.2 yes 24 3.2 odd 2 inner
63.6.p.b.26.11 yes 24 1.1 even 1 trivial
441.6.c.b.440.7 24 7.5 odd 6
441.6.c.b.440.8 24 21.2 odd 6
441.6.c.b.440.17 24 7.2 even 3
441.6.c.b.440.18 24 21.5 even 6