Properties

Label 108.6.h.a.71.15
Level $108$
Weight $6$
Character 108.71
Analytic conductor $17.321$
Analytic rank $0$
Dimension $56$
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] = [108,6,Mod(35,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, 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("108.35");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not 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: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.15
Character \(\chi\) \(=\) 108.71
Dual form 108.6.h.a.35.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0499164 + 5.65663i) q^{2} +(-31.9950 + 0.564717i) q^{4} +(-70.1957 - 40.5275i) q^{5} +(89.9985 - 51.9607i) q^{7} +(-4.79147 - 180.956i) q^{8} +O(q^{10})\) \(q+(0.0499164 + 5.65663i) q^{2} +(-31.9950 + 0.564717i) q^{4} +(-70.1957 - 40.5275i) q^{5} +(89.9985 - 51.9607i) q^{7} +(-4.79147 - 180.956i) q^{8} +(225.745 - 399.094i) q^{10} +(214.271 + 371.129i) q^{11} +(42.9574 - 74.4044i) q^{13} +(298.415 + 506.495i) q^{14} +(1023.36 - 36.1363i) q^{16} +1509.75i q^{17} +1224.53i q^{19} +(2268.80 + 1257.04i) q^{20} +(-2088.64 + 1230.58i) q^{22} +(1530.14 - 2650.27i) q^{23} +(1722.45 + 2983.38i) q^{25} +(423.023 + 239.280i) q^{26} +(-2850.16 + 1713.31i) q^{28} +(4347.44 - 2510.00i) q^{29} +(-3400.78 - 1963.44i) q^{31} +(255.492 + 5786.98i) q^{32} +(-8540.08 + 75.3610i) q^{34} -8423.34 q^{35} +13035.3 q^{37} +(-6926.71 + 61.1240i) q^{38} +(-6997.35 + 12896.5i) q^{40} +(15071.6 + 8701.62i) q^{41} +(-5754.33 + 3322.27i) q^{43} +(-7065.19 - 11753.3i) q^{44} +(15068.0 + 8523.13i) q^{46} +(10068.4 + 17438.9i) q^{47} +(-3003.68 + 5202.52i) q^{49} +(-16789.9 + 9892.22i) q^{50} +(-1332.41 + 2404.83i) q^{52} +18043.0i q^{53} -34735.5i q^{55} +(-9833.82 - 16036.8i) q^{56} +(14415.1 + 24466.6i) q^{58} +(14736.4 - 25524.2i) q^{59} +(-11989.0 - 20765.6i) q^{61} +(10936.7 - 19335.0i) q^{62} +(-32722.1 + 1734.09i) q^{64} +(-6030.85 + 3481.91i) q^{65} +(-348.663 - 201.301i) q^{67} +(-852.579 - 48304.3i) q^{68} +(-420.463 - 47647.8i) q^{70} +36645.5 q^{71} +58635.9 q^{73} +(650.675 + 73735.9i) q^{74} +(-691.512 - 39178.8i) q^{76} +(38568.2 + 22267.4i) q^{77} +(39354.5 - 22721.3i) q^{79} +(-73300.1 - 38937.7i) q^{80} +(-48469.5 + 85689.1i) q^{82} +(-27253.7 - 47204.9i) q^{83} +(61186.2 - 105978. i) q^{85} +(-19080.1 - 32384.3i) q^{86} +(66131.2 - 40551.9i) q^{88} -45338.5i q^{89} -8928.39i q^{91} +(-47460.1 + 85659.6i) q^{92} +(-98143.1 + 57823.6i) q^{94} +(49627.1 - 85956.6i) q^{95} +(41820.0 + 72434.3i) q^{97} +(-29578.7 - 16731.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0499164 + 5.65663i 0.00882405 + 0.999961i
\(3\) 0 0
\(4\) −31.9950 + 0.564717i −0.999844 + 0.0176474i
\(5\) −70.1957 40.5275i −1.25570 0.724978i −0.283463 0.958983i \(-0.591483\pi\)
−0.972235 + 0.234005i \(0.924817\pi\)
\(6\) 0 0
\(7\) 89.9985 51.9607i 0.694209 0.400802i −0.110978 0.993823i \(-0.535398\pi\)
0.805187 + 0.593021i \(0.202065\pi\)
\(8\) −4.79147 180.956i −0.0264694 0.999650i
\(9\) 0 0
\(10\) 225.745 399.094i 0.713869 1.26205i
\(11\) 214.271 + 371.129i 0.533927 + 0.924789i 0.999214 + 0.0396293i \(0.0126177\pi\)
−0.465287 + 0.885160i \(0.654049\pi\)
\(12\) 0 0
\(13\) 42.9574 74.4044i 0.0704985 0.122107i −0.828621 0.559809i \(-0.810874\pi\)
0.899120 + 0.437702i \(0.144208\pi\)
\(14\) 298.415 + 506.495i 0.406912 + 0.690645i
\(15\) 0 0
\(16\) 1023.36 36.1363i 0.999377 0.0352893i
\(17\) 1509.75i 1.26701i 0.773737 + 0.633507i \(0.218385\pi\)
−0.773737 + 0.633507i \(0.781615\pi\)
\(18\) 0 0
\(19\) 1224.53i 0.778189i 0.921198 + 0.389094i \(0.127212\pi\)
−0.921198 + 0.389094i \(0.872788\pi\)
\(20\) 2268.80 + 1257.04i 1.26830 + 0.702705i
\(21\) 0 0
\(22\) −2088.64 + 1230.58i −0.920042 + 0.542067i
\(23\) 1530.14 2650.27i 0.603129 1.04465i −0.389215 0.921147i \(-0.627254\pi\)
0.992344 0.123503i \(-0.0394130\pi\)
\(24\) 0 0
\(25\) 1722.45 + 2983.38i 0.551186 + 0.954681i
\(26\) 423.023 + 239.280i 0.122724 + 0.0694183i
\(27\) 0 0
\(28\) −2850.16 + 1713.31i −0.687028 + 0.412990i
\(29\) 4347.44 2510.00i 0.959929 0.554215i 0.0637776 0.997964i \(-0.479685\pi\)
0.896151 + 0.443749i \(0.146352\pi\)
\(30\) 0 0
\(31\) −3400.78 1963.44i −0.635587 0.366956i 0.147326 0.989088i \(-0.452933\pi\)
−0.782913 + 0.622132i \(0.786267\pi\)
\(32\) 255.492 + 5786.98i 0.0441065 + 0.999027i
\(33\) 0 0
\(34\) −8540.08 + 75.3610i −1.26696 + 0.0111802i
\(35\) −8423.34 −1.16229
\(36\) 0 0
\(37\) 13035.3 1.56537 0.782684 0.622419i \(-0.213850\pi\)
0.782684 + 0.622419i \(0.213850\pi\)
\(38\) −6926.71 + 61.1240i −0.778158 + 0.00686677i
\(39\) 0 0
\(40\) −6997.35 + 12896.5i −0.691486 + 1.27445i
\(41\) 15071.6 + 8701.62i 1.40024 + 0.808426i 0.994416 0.105527i \(-0.0336531\pi\)
0.405819 + 0.913954i \(0.366986\pi\)
\(42\) 0 0
\(43\) −5754.33 + 3322.27i −0.474596 + 0.274008i −0.718162 0.695876i \(-0.755016\pi\)
0.243566 + 0.969884i \(0.421683\pi\)
\(44\) −7065.19 11753.3i −0.550164 0.915223i
\(45\) 0 0
\(46\) 15068.0 + 8523.13i 1.04993 + 0.593888i
\(47\) 10068.4 + 17438.9i 0.664836 + 1.15153i 0.979330 + 0.202270i \(0.0648319\pi\)
−0.314494 + 0.949260i \(0.601835\pi\)
\(48\) 0 0
\(49\) −3003.68 + 5202.52i −0.178716 + 0.309545i
\(50\) −16789.9 + 9892.22i −0.949781 + 0.559588i
\(51\) 0 0
\(52\) −1332.41 + 2404.83i −0.0683326 + 0.123332i
\(53\) 18043.0i 0.882304i 0.897432 + 0.441152i \(0.145430\pi\)
−0.897432 + 0.441152i \(0.854570\pi\)
\(54\) 0 0
\(55\) 34735.5i 1.54834i
\(56\) −9833.82 16036.8i −0.419037 0.683357i
\(57\) 0 0
\(58\) 14415.1 + 24466.6i 0.562664 + 0.955001i
\(59\) 14736.4 25524.2i 0.551140 0.954602i −0.447053 0.894507i \(-0.647527\pi\)
0.998193 0.0600943i \(-0.0191401\pi\)
\(60\) 0 0
\(61\) −11989.0 20765.6i −0.412533 0.714528i 0.582633 0.812735i \(-0.302023\pi\)
−0.995166 + 0.0982073i \(0.968689\pi\)
\(62\) 10936.7 19335.0i 0.361334 0.638800i
\(63\) 0 0
\(64\) −32722.1 + 1734.09i −0.998599 + 0.0529203i
\(65\) −6030.85 + 3481.91i −0.177050 + 0.102220i
\(66\) 0 0
\(67\) −348.663 201.301i −0.00948897 0.00547846i 0.495248 0.868752i \(-0.335077\pi\)
−0.504737 + 0.863273i \(0.668411\pi\)
\(68\) −852.579 48304.3i −0.0223595 1.26682i
\(69\) 0 0
\(70\) −420.463 47647.8i −0.0102561 1.16224i
\(71\) 36645.5 0.862730 0.431365 0.902178i \(-0.358032\pi\)
0.431365 + 0.902178i \(0.358032\pi\)
\(72\) 0 0
\(73\) 58635.9 1.28782 0.643911 0.765100i \(-0.277311\pi\)
0.643911 + 0.765100i \(0.277311\pi\)
\(74\) 650.675 + 73735.9i 0.0138129 + 1.56531i
\(75\) 0 0
\(76\) −691.512 39178.8i −0.0137330 0.778067i
\(77\) 38568.2 + 22267.4i 0.741314 + 0.427998i
\(78\) 0 0
\(79\) 39354.5 22721.3i 0.709457 0.409605i −0.101403 0.994845i \(-0.532333\pi\)
0.810860 + 0.585240i \(0.199000\pi\)
\(80\) −73300.1 38937.7i −1.28050 0.680213i
\(81\) 0 0
\(82\) −48469.5 + 85689.1i −0.796039 + 1.40731i
\(83\) −27253.7 47204.9i −0.434241 0.752128i 0.562992 0.826462i \(-0.309650\pi\)
−0.997233 + 0.0743344i \(0.976317\pi\)
\(84\) 0 0
\(85\) 61186.2 105978.i 0.918557 1.59099i
\(86\) −19080.1 32384.3i −0.278185 0.472160i
\(87\) 0 0
\(88\) 66131.2 40551.9i 0.910332 0.558219i
\(89\) 45338.5i 0.606726i −0.952875 0.303363i \(-0.901891\pi\)
0.952875 0.303363i \(-0.0981094\pi\)
\(90\) 0 0
\(91\) 8928.39i 0.113024i
\(92\) −47460.1 + 85659.6i −0.584600 + 1.05513i
\(93\) 0 0
\(94\) −98143.1 + 57823.6i −1.14562 + 0.674971i
\(95\) 49627.1 85956.6i 0.564169 0.977170i
\(96\) 0 0
\(97\) 41820.0 + 72434.3i 0.451289 + 0.781655i 0.998466 0.0553615i \(-0.0176311\pi\)
−0.547178 + 0.837016i \(0.684298\pi\)
\(98\) −29578.7 16731.0i −0.311110 0.175977i
\(99\) 0 0
\(100\) −56794.7 94480.6i −0.567947 0.944806i
\(101\) −107672. + 62164.7i −1.05027 + 0.606374i −0.922725 0.385459i \(-0.874043\pi\)
−0.127545 + 0.991833i \(0.540710\pi\)
\(102\) 0 0
\(103\) 57893.0 + 33424.5i 0.537691 + 0.310436i 0.744143 0.668021i \(-0.232858\pi\)
−0.206452 + 0.978457i \(0.566192\pi\)
\(104\) −13669.8 7416.89i −0.123930 0.0672417i
\(105\) 0 0
\(106\) −102062. + 900.639i −0.882270 + 0.00778550i
\(107\) −144038. −1.21624 −0.608119 0.793846i \(-0.708076\pi\)
−0.608119 + 0.793846i \(0.708076\pi\)
\(108\) 0 0
\(109\) −137855. −1.11136 −0.555680 0.831396i \(-0.687542\pi\)
−0.555680 + 0.831396i \(0.687542\pi\)
\(110\) 196486. 1733.87i 1.54828 0.0136626i
\(111\) 0 0
\(112\) 90223.4 56426.8i 0.679633 0.425050i
\(113\) 24697.0 + 14258.8i 0.181948 + 0.105048i 0.588208 0.808710i \(-0.299834\pi\)
−0.406259 + 0.913758i \(0.633167\pi\)
\(114\) 0 0
\(115\) −214818. + 124025.i −1.51470 + 0.874511i
\(116\) −137679. + 82762.5i −0.949999 + 0.571069i
\(117\) 0 0
\(118\) 145117. + 82084.4i 0.959428 + 0.542695i
\(119\) 78447.4 + 135875.i 0.507821 + 0.879573i
\(120\) 0 0
\(121\) −11298.8 + 19570.0i −0.0701565 + 0.121515i
\(122\) 116865. 68854.0i 0.710860 0.418822i
\(123\) 0 0
\(124\) 109917. + 60899.9i 0.641964 + 0.355683i
\(125\) 25930.3i 0.148434i
\(126\) 0 0
\(127\) 74540.3i 0.410093i −0.978752 0.205046i \(-0.934266\pi\)
0.978752 0.205046i \(-0.0657345\pi\)
\(128\) −11442.5 185010.i −0.0617299 0.998093i
\(129\) 0 0
\(130\) −19996.9 33940.5i −0.103778 0.176141i
\(131\) −66965.9 + 115988.i −0.340938 + 0.590522i −0.984607 0.174782i \(-0.944078\pi\)
0.643669 + 0.765304i \(0.277411\pi\)
\(132\) 0 0
\(133\) 63627.3 + 110206.i 0.311899 + 0.540226i
\(134\) 1121.28 1982.31i 0.00539451 0.00953694i
\(135\) 0 0
\(136\) 273197. 7233.90i 1.26657 0.0335371i
\(137\) 143212. 82683.3i 0.651894 0.376371i −0.137287 0.990531i \(-0.543838\pi\)
0.789182 + 0.614160i \(0.210505\pi\)
\(138\) 0 0
\(139\) 105373. + 60837.0i 0.462585 + 0.267074i 0.713131 0.701031i \(-0.247277\pi\)
−0.250546 + 0.968105i \(0.580610\pi\)
\(140\) 269505. 4756.81i 1.16211 0.0205114i
\(141\) 0 0
\(142\) 1829.21 + 207290.i 0.00761277 + 0.862696i
\(143\) 36818.2 0.150564
\(144\) 0 0
\(145\) −406896. −1.60717
\(146\) 2926.89 + 331682.i 0.0113638 + 1.28777i
\(147\) 0 0
\(148\) −417065. + 7361.26i −1.56512 + 0.0276247i
\(149\) 60786.2 + 35094.9i 0.224305 + 0.129503i 0.607942 0.793981i \(-0.291995\pi\)
−0.383637 + 0.923484i \(0.625329\pi\)
\(150\) 0 0
\(151\) 31118.1 17966.1i 0.111064 0.0641225i −0.443439 0.896304i \(-0.646242\pi\)
0.554503 + 0.832182i \(0.312908\pi\)
\(152\) 221586. 5867.29i 0.777916 0.0205982i
\(153\) 0 0
\(154\) −124033. + 219278.i −0.421440 + 0.745062i
\(155\) 159147. + 275651.i 0.532070 + 0.921573i
\(156\) 0 0
\(157\) −84404.3 + 146193.i −0.273285 + 0.473343i −0.969701 0.244295i \(-0.921443\pi\)
0.696416 + 0.717638i \(0.254777\pi\)
\(158\) 130491. + 221480.i 0.415850 + 0.705815i
\(159\) 0 0
\(160\) 216597. 416576.i 0.668888 1.28645i
\(161\) 318028.i 0.966941i
\(162\) 0 0
\(163\) 325623.i 0.959943i −0.877284 0.479972i \(-0.840647\pi\)
0.877284 0.479972i \(-0.159353\pi\)
\(164\) −487131. 269897.i −1.41428 0.783590i
\(165\) 0 0
\(166\) 265660. 156521.i 0.748267 0.440861i
\(167\) −106712. + 184831.i −0.296090 + 0.512843i −0.975238 0.221158i \(-0.929016\pi\)
0.679148 + 0.734002i \(0.262350\pi\)
\(168\) 0 0
\(169\) 181956. + 315157.i 0.490060 + 0.848809i
\(170\) 602531. + 340818.i 1.59903 + 0.904482i
\(171\) 0 0
\(172\) 182234. 109546.i 0.469686 0.282341i
\(173\) 27550.4 15906.2i 0.0699862 0.0404066i −0.464599 0.885521i \(-0.653801\pi\)
0.534585 + 0.845115i \(0.320468\pi\)
\(174\) 0 0
\(175\) 310037. + 179000.i 0.765276 + 0.441832i
\(176\) 232688. + 372056.i 0.566230 + 0.905371i
\(177\) 0 0
\(178\) 256463. 2263.13i 0.606702 0.00535378i
\(179\) −475398. −1.10898 −0.554491 0.832189i \(-0.687087\pi\)
−0.554491 + 0.832189i \(0.687087\pi\)
\(180\) 0 0
\(181\) 4695.48 0.0106533 0.00532664 0.999986i \(-0.498304\pi\)
0.00532664 + 0.999986i \(0.498304\pi\)
\(182\) 50504.6 445.673i 0.113019 0.000997327i
\(183\) 0 0
\(184\) −486914. 264188.i −1.06025 0.575267i
\(185\) −915021. 528288.i −1.96563 1.13486i
\(186\) 0 0
\(187\) −560310. + 323495.i −1.17172 + 0.676493i
\(188\) −331986. 552273.i −0.685054 1.13962i
\(189\) 0 0
\(190\) 488702. + 276431.i 0.982110 + 0.555525i
\(191\) −302770. 524412.i −0.600522 1.04013i −0.992742 0.120263i \(-0.961626\pi\)
0.392220 0.919871i \(-0.371707\pi\)
\(192\) 0 0
\(193\) 46694.6 80877.5i 0.0902347 0.156291i −0.817375 0.576106i \(-0.804572\pi\)
0.907610 + 0.419815i \(0.137905\pi\)
\(194\) −407647. + 240176.i −0.777642 + 0.458168i
\(195\) 0 0
\(196\) 93164.7 168151.i 0.173225 0.312650i
\(197\) 466419.i 0.856270i 0.903715 + 0.428135i \(0.140829\pi\)
−0.903715 + 0.428135i \(0.859171\pi\)
\(198\) 0 0
\(199\) 625885.i 1.12037i 0.828367 + 0.560185i \(0.189270\pi\)
−0.828367 + 0.560185i \(0.810730\pi\)
\(200\) 531607. 325983.i 0.939757 0.576262i
\(201\) 0 0
\(202\) −357018. 605960.i −0.615618 1.04488i
\(203\) 260842. 451792.i 0.444261 0.769482i
\(204\) 0 0
\(205\) −705309. 1.22163e6i −1.17218 2.03028i
\(206\) −186181. + 329148.i −0.305679 + 0.540409i
\(207\) 0 0
\(208\) 41272.3 77695.0i 0.0661455 0.124519i
\(209\) −454457. + 262381.i −0.719660 + 0.415496i
\(210\) 0 0
\(211\) 756200. + 436592.i 1.16931 + 0.675103i 0.953518 0.301336i \(-0.0974326\pi\)
0.215794 + 0.976439i \(0.430766\pi\)
\(212\) −10189.2 577285.i −0.0155704 0.882167i
\(213\) 0 0
\(214\) −7189.87 814772.i −0.0107321 1.21619i
\(215\) 538572. 0.794599
\(216\) 0 0
\(217\) −408088. −0.588307
\(218\) −6881.20 779793.i −0.00980670 1.11132i
\(219\) 0 0
\(220\) 19615.7 + 1.11136e6i 0.0273242 + 1.54810i
\(221\) 112332. + 64854.8i 0.154711 + 0.0893226i
\(222\) 0 0
\(223\) −419169. + 242007.i −0.564452 + 0.325886i −0.754930 0.655805i \(-0.772329\pi\)
0.190479 + 0.981691i \(0.438996\pi\)
\(224\) 323689. + 507544.i 0.431031 + 0.675856i
\(225\) 0 0
\(226\) −79424.2 + 140414.i −0.103438 + 0.182868i
\(227\) −117910. 204225.i −0.151874 0.263054i 0.780042 0.625727i \(-0.215198\pi\)
−0.931917 + 0.362673i \(0.881864\pi\)
\(228\) 0 0
\(229\) 124091. 214932.i 0.156369 0.270840i −0.777187 0.629269i \(-0.783354\pi\)
0.933557 + 0.358429i \(0.116688\pi\)
\(230\) −712288. 1.20895e6i −0.887842 1.50692i
\(231\) 0 0
\(232\) −475030. 774669.i −0.579430 0.944923i
\(233\) 340275.i 0.410620i −0.978697 0.205310i \(-0.934180\pi\)
0.978697 0.205310i \(-0.0658202\pi\)
\(234\) 0 0
\(235\) 1.63218e6i 1.92797i
\(236\) −457078. + 824969.i −0.534207 + 0.964179i
\(237\) 0 0
\(238\) −764679. + 450531.i −0.875057 + 0.515563i
\(239\) −303908. + 526384.i −0.344149 + 0.596084i −0.985199 0.171415i \(-0.945166\pi\)
0.641049 + 0.767500i \(0.278499\pi\)
\(240\) 0 0
\(241\) 756653. + 1.31056e6i 0.839179 + 1.45350i 0.890582 + 0.454822i \(0.150297\pi\)
−0.0514039 + 0.998678i \(0.516370\pi\)
\(242\) −111265. 62936.1i −0.122129 0.0690815i
\(243\) 0 0
\(244\) 395315. + 657624.i 0.425078 + 0.707137i
\(245\) 421690. 243463.i 0.448826 0.259130i
\(246\) 0 0
\(247\) 91110.3 + 52602.6i 0.0950223 + 0.0548611i
\(248\) −339002. + 624800.i −0.350004 + 0.645077i
\(249\) 0 0
\(250\) 146678. 1294.34i 0.148428 0.00130978i
\(251\) 1.13311e6 1.13524 0.567622 0.823289i \(-0.307864\pi\)
0.567622 + 0.823289i \(0.307864\pi\)
\(252\) 0 0
\(253\) 1.31146e6 1.28811
\(254\) 421647. 3720.78i 0.410077 0.00361868i
\(255\) 0 0
\(256\) 1.04596e6 73961.0i 0.997509 0.0705347i
\(257\) 928992. + 536354.i 0.877362 + 0.506545i 0.869788 0.493426i \(-0.164256\pi\)
0.00757446 + 0.999971i \(0.497589\pi\)
\(258\) 0 0
\(259\) 1.17316e6 677323.i 1.08669 0.627403i
\(260\) 190991. 114810.i 0.175218 0.105328i
\(261\) 0 0
\(262\) −659446. 373012.i −0.593507 0.335714i
\(263\) −341490. 591477.i −0.304430 0.527289i 0.672704 0.739912i \(-0.265133\pi\)
−0.977134 + 0.212623i \(0.931799\pi\)
\(264\) 0 0
\(265\) 731236. 1.26654e6i 0.639651 1.10791i
\(266\) −620218. + 365418.i −0.537452 + 0.316654i
\(267\) 0 0
\(268\) 11269.2 + 6243.72i 0.00958417 + 0.00531015i
\(269\) 931829.i 0.785155i 0.919719 + 0.392577i \(0.128417\pi\)
−0.919719 + 0.392577i \(0.871583\pi\)
\(270\) 0 0
\(271\) 1.76382e6i 1.45892i −0.684023 0.729460i \(-0.739771\pi\)
0.684023 0.729460i \(-0.260229\pi\)
\(272\) 54556.6 + 1.54502e6i 0.0447121 + 1.26622i
\(273\) 0 0
\(274\) 474858. + 805969.i 0.382109 + 0.648548i
\(275\) −738145. + 1.27850e6i −0.588586 + 1.01946i
\(276\) 0 0
\(277\) 309348. + 535806.i 0.242241 + 0.419573i 0.961352 0.275321i \(-0.0887843\pi\)
−0.719111 + 0.694895i \(0.755451\pi\)
\(278\) −338873. + 599092.i −0.262981 + 0.464924i
\(279\) 0 0
\(280\) 40360.2 + 1.52425e6i 0.0307651 + 1.16188i
\(281\) 1.58185e6 913279.i 1.19508 0.689982i 0.235628 0.971843i \(-0.424285\pi\)
0.959455 + 0.281861i \(0.0909518\pi\)
\(282\) 0 0
\(283\) −1.63561e6 944320.i −1.21399 0.700895i −0.250361 0.968153i \(-0.580549\pi\)
−0.963625 + 0.267258i \(0.913883\pi\)
\(284\) −1.17247e6 + 20694.3i −0.862596 + 0.0152249i
\(285\) 0 0
\(286\) 1837.83 + 208267.i 0.00132859 + 0.150558i
\(287\) 1.80857e6 1.29607
\(288\) 0 0
\(289\) −859473. −0.605324
\(290\) −20310.7 2.30166e6i −0.0141818 1.60711i
\(291\) 0 0
\(292\) −1.87606e6 + 33112.7i −1.28762 + 0.0227267i
\(293\) 965146. + 557227.i 0.656786 + 0.379196i 0.791051 0.611750i \(-0.209534\pi\)
−0.134265 + 0.990945i \(0.542867\pi\)
\(294\) 0 0
\(295\) −2.06886e6 + 1.19446e6i −1.38413 + 0.799128i
\(296\) −62458.3 2.35881e6i −0.0414344 1.56482i
\(297\) 0 0
\(298\) −195485. + 345597.i −0.127518 + 0.225439i
\(299\) −131461. 227698.i −0.0850394 0.147293i
\(300\) 0 0
\(301\) −345254. + 597998.i −0.219646 + 0.380438i
\(302\) 103181. + 175127.i 0.0651001 + 0.110493i
\(303\) 0 0
\(304\) 44249.9 + 1.25314e6i 0.0274618 + 0.777704i
\(305\) 1.94354e6i 1.19631i
\(306\) 0 0
\(307\) 1.64394e6i 0.995497i 0.867321 + 0.497749i \(0.165840\pi\)
−0.867321 + 0.497749i \(0.834160\pi\)
\(308\) −1.24656e6 690664.i −0.748752 0.414849i
\(309\) 0 0
\(310\) −1.55131e6 + 913995.i −0.916842 + 0.540182i
\(311\) 363235. 629141.i 0.212954 0.368848i −0.739683 0.672955i \(-0.765025\pi\)
0.952638 + 0.304107i \(0.0983581\pi\)
\(312\) 0 0
\(313\) 702457. + 1.21669e6i 0.405284 + 0.701972i 0.994354 0.106110i \(-0.0338394\pi\)
−0.589071 + 0.808081i \(0.700506\pi\)
\(314\) −831171. 470147.i −0.475736 0.269097i
\(315\) 0 0
\(316\) −1.24632e6 + 749193.i −0.702118 + 0.422062i
\(317\) −1.21701e6 + 702639.i −0.680213 + 0.392721i −0.799935 0.600086i \(-0.795133\pi\)
0.119722 + 0.992807i \(0.461800\pi\)
\(318\) 0 0
\(319\) 1.86306e6 + 1.07564e6i 1.02506 + 0.591821i
\(320\) 2.36723e6 + 1.20442e6i 1.29230 + 0.657510i
\(321\) 0 0
\(322\) 1.79897e6 15874.8i 0.966904 0.00853234i
\(323\) −1.84873e6 −0.985976
\(324\) 0 0
\(325\) 295969. 0.155431
\(326\) 1.84193e6 16253.9i 0.959906 0.00847059i
\(327\) 0 0
\(328\) 1.50239e6 2.76900e6i 0.771080 1.42114i
\(329\) 1.81228e6 + 1.04632e6i 0.923071 + 0.532935i
\(330\) 0 0
\(331\) −214028. + 123569.i −0.107374 + 0.0619926i −0.552725 0.833363i \(-0.686412\pi\)
0.445351 + 0.895356i \(0.353079\pi\)
\(332\) 898642. + 1.49493e6i 0.447447 + 0.744347i
\(333\) 0 0
\(334\) −1.05085e6 594407.i −0.515436 0.291553i
\(335\) 16316.4 + 28260.9i 0.00794352 + 0.0137586i
\(336\) 0 0
\(337\) 1.07901e6 1.86890e6i 0.517549 0.896421i −0.482244 0.876037i \(-0.660178\pi\)
0.999792 0.0203835i \(-0.00648871\pi\)
\(338\) −1.77364e6 + 1.04499e6i −0.844451 + 0.497531i
\(339\) 0 0
\(340\) −1.89781e6 + 3.42531e6i −0.890337 + 1.60695i
\(341\) 1.68284e6i 0.783712i
\(342\) 0 0
\(343\) 2.37090e6i 1.08812i
\(344\) 628755. + 1.02536e6i 0.286474 + 0.467177i
\(345\) 0 0
\(346\) 91350.9 + 155048.i 0.0410225 + 0.0696269i
\(347\) 804114. 1.39277e6i 0.358504 0.620947i −0.629207 0.777237i \(-0.716620\pi\)
0.987711 + 0.156291i \(0.0499537\pi\)
\(348\) 0 0
\(349\) 233867. + 405070.i 0.102779 + 0.178019i 0.912829 0.408343i \(-0.133893\pi\)
−0.810049 + 0.586362i \(0.800560\pi\)
\(350\) −997061. + 1.76270e6i −0.435062 + 0.769145i
\(351\) 0 0
\(352\) −2.09297e6 + 1.33480e6i −0.900339 + 0.574197i
\(353\) −397710. + 229618.i −0.169875 + 0.0980773i −0.582527 0.812811i \(-0.697936\pi\)
0.412652 + 0.910889i \(0.364603\pi\)
\(354\) 0 0
\(355\) −2.57236e6 1.48515e6i −1.08333 0.625460i
\(356\) 25603.4 + 1.45061e6i 0.0107071 + 0.606631i
\(357\) 0 0
\(358\) −23730.1 2.68915e6i −0.00978572 1.10894i
\(359\) −2.21493e6 −0.907037 −0.453518 0.891247i \(-0.649831\pi\)
−0.453518 + 0.891247i \(0.649831\pi\)
\(360\) 0 0
\(361\) 976629. 0.394423
\(362\) 234.381 + 26560.6i 9.40050e−5 + 0.0106529i
\(363\) 0 0
\(364\) 5042.01 + 285664.i 0.00199458 + 0.113006i
\(365\) −4.11598e6 2.37636e6i −1.61712 0.933643i
\(366\) 0 0
\(367\) 2.54558e6 1.46969e6i 0.986555 0.569588i 0.0823124 0.996607i \(-0.473769\pi\)
0.904243 + 0.427019i \(0.140436\pi\)
\(368\) 1.47011e6 2.76748e6i 0.565889 1.06528i
\(369\) 0 0
\(370\) 2.94266e6 5.20231e6i 1.11747 1.97557i
\(371\) 937525. + 1.62384e6i 0.353629 + 0.612504i
\(372\) 0 0
\(373\) −830424. + 1.43834e6i −0.309049 + 0.535289i −0.978155 0.207878i \(-0.933344\pi\)
0.669105 + 0.743168i \(0.266678\pi\)
\(374\) −1.85786e6 3.15332e6i −0.686806 1.16571i
\(375\) 0 0
\(376\) 3.10744e6 1.90549e6i 1.13353 0.695083i
\(377\) 431292.i 0.156285i
\(378\) 0 0
\(379\) 4.69152e6i 1.67770i −0.544360 0.838852i \(-0.683227\pi\)
0.544360 0.838852i \(-0.316773\pi\)
\(380\) −1.53928e6 + 2.77821e6i −0.546837 + 0.986974i
\(381\) 0 0
\(382\) 2.95129e6 1.73883e6i 1.03479 0.609677i
\(383\) 2.64821e6 4.58683e6i 0.922476 1.59777i 0.126904 0.991915i \(-0.459496\pi\)
0.795571 0.605860i \(-0.207171\pi\)
\(384\) 0 0
\(385\) −1.80488e6 3.12614e6i −0.620578 1.07487i
\(386\) 459825. + 260097.i 0.157081 + 0.0888521i
\(387\) 0 0
\(388\) −1.37894e6 2.29392e6i −0.465013 0.773569i
\(389\) 1.59537e6 921088.i 0.534549 0.308622i −0.208318 0.978061i \(-0.566799\pi\)
0.742867 + 0.669439i \(0.233465\pi\)
\(390\) 0 0
\(391\) 4.00124e6 + 2.31011e6i 1.32359 + 0.764173i
\(392\) 955818. + 518605.i 0.314167 + 0.170460i
\(393\) 0 0
\(394\) −2.63836e6 + 23281.9i −0.856236 + 0.00755576i
\(395\) −3.68335e6 −1.18782
\(396\) 0 0
\(397\) 75711.5 0.0241094 0.0120547 0.999927i \(-0.496163\pi\)
0.0120547 + 0.999927i \(0.496163\pi\)
\(398\) −3.54040e6 + 31241.9i −1.12033 + 0.00988620i
\(399\) 0 0
\(400\) 1.87050e6 + 2.99083e6i 0.584532 + 0.934636i
\(401\) −2.92456e6 1.68849e6i −0.908237 0.524371i −0.0283735 0.999597i \(-0.509033\pi\)
−0.879863 + 0.475227i \(0.842366\pi\)
\(402\) 0 0
\(403\) −292178. + 168689.i −0.0896158 + 0.0517397i
\(404\) 3.40988e6 2.04977e6i 1.03941 0.624814i
\(405\) 0 0
\(406\) 2.56864e6 + 1.45294e6i 0.773373 + 0.437454i
\(407\) 2.79309e6 + 4.83777e6i 0.835793 + 1.44764i
\(408\) 0 0
\(409\) −1.75008e6 + 3.03123e6i −0.517310 + 0.896007i 0.482488 + 0.875902i \(0.339733\pi\)
−0.999798 + 0.0201041i \(0.993600\pi\)
\(410\) 6.87512e6 4.05066e6i 2.01986 1.19005i
\(411\) 0 0
\(412\) −1.87116e6 1.03673e6i −0.543086 0.300899i
\(413\) 3.06285e6i 0.883591i
\(414\) 0 0
\(415\) 4.41810e6i 1.25926i
\(416\) 441552. + 229584.i 0.125098 + 0.0650442i
\(417\) 0 0
\(418\) −1.50688e6 2.55760e6i −0.421830 0.715966i
\(419\) −2.65830e6 + 4.60430e6i −0.739721 + 1.28123i 0.212899 + 0.977074i \(0.431709\pi\)
−0.952621 + 0.304161i \(0.901624\pi\)
\(420\) 0 0
\(421\) −2.59023e6 4.48640e6i −0.712250 1.23365i −0.964011 0.265864i \(-0.914343\pi\)
0.251761 0.967790i \(-0.418990\pi\)
\(422\) −2.43190e6 + 4.29934e6i −0.664758 + 1.17522i
\(423\) 0 0
\(424\) 3.26498e6 86452.4i 0.881995 0.0233541i
\(425\) −4.50414e6 + 2.60047e6i −1.20959 + 0.698360i
\(426\) 0 0
\(427\) −2.15799e6 1.24591e6i −0.572768 0.330688i
\(428\) 4.60851e6 81340.9i 1.21605 0.0214635i
\(429\) 0 0
\(430\) 26883.6 + 3.04651e6i 0.00701158 + 0.794568i
\(431\) 5.72244e6 1.48384 0.741922 0.670486i \(-0.233914\pi\)
0.741922 + 0.670486i \(0.233914\pi\)
\(432\) 0 0
\(433\) −6.17405e6 −1.58252 −0.791262 0.611478i \(-0.790575\pi\)
−0.791262 + 0.611478i \(0.790575\pi\)
\(434\) −20370.2 2.30840e6i −0.00519125 0.588284i
\(435\) 0 0
\(436\) 4.41066e6 77848.8i 1.11119 0.0196126i
\(437\) 3.24533e6 + 1.87369e6i 0.812935 + 0.469348i
\(438\) 0 0
\(439\) 5.02340e6 2.90026e6i 1.24405 0.718251i 0.274131 0.961692i \(-0.411610\pi\)
0.969915 + 0.243442i \(0.0782765\pi\)
\(440\) −6.28559e6 + 166434.i −1.54780 + 0.0409837i
\(441\) 0 0
\(442\) −361252. + 638657.i −0.0879539 + 0.155493i
\(443\) −2.08981e6 3.61966e6i −0.505939 0.876312i −0.999976 0.00687158i \(-0.997813\pi\)
0.494037 0.869441i \(-0.335521\pi\)
\(444\) 0 0
\(445\) −1.83746e6 + 3.18257e6i −0.439863 + 0.761864i
\(446\) −1.38987e6 2.35900e6i −0.330854 0.561554i
\(447\) 0 0
\(448\) −2.85484e6 + 1.85633e6i −0.672026 + 0.436978i
\(449\) 970936.i 0.227287i −0.993522 0.113644i \(-0.963748\pi\)
0.993522 0.113644i \(-0.0362522\pi\)
\(450\) 0 0
\(451\) 7.45802e6i 1.72656i
\(452\) −798233. 442265.i −0.183774 0.101821i
\(453\) 0 0
\(454\) 1.14934e6 677166.i 0.261704 0.154190i
\(455\) −361845. + 626734.i −0.0819397 + 0.141924i
\(456\) 0 0
\(457\) −1.03810e6 1.79803e6i −0.232513 0.402724i 0.726034 0.687659i \(-0.241361\pi\)
−0.958547 + 0.284935i \(0.908028\pi\)
\(458\) 1.22199e6 + 691209.i 0.272209 + 0.153973i
\(459\) 0 0
\(460\) 6.80306e6 4.08950e6i 1.49903 0.901105i
\(461\) −2.52767e6 + 1.45935e6i −0.553947 + 0.319821i −0.750712 0.660629i \(-0.770290\pi\)
0.196766 + 0.980451i \(0.436956\pi\)
\(462\) 0 0
\(463\) −5.02987e6 2.90400e6i −1.09045 0.629569i −0.156751 0.987638i \(-0.550102\pi\)
−0.933695 + 0.358069i \(0.883435\pi\)
\(464\) 4.35831e6 2.72574e6i 0.939773 0.587745i
\(465\) 0 0
\(466\) 1.92481e6 16985.3i 0.410604 0.00362333i
\(467\) −8.31962e6 −1.76527 −0.882636 0.470058i \(-0.844233\pi\)
−0.882636 + 0.470058i \(0.844233\pi\)
\(468\) 0 0
\(469\) −41838.9 −0.00878311
\(470\) 9.23266e6 81472.6i 1.92789 0.0170125i
\(471\) 0 0
\(472\) −4.68936e6 2.54434e6i −0.968856 0.525679i
\(473\) −2.46598e6 1.42373e6i −0.506799 0.292601i
\(474\) 0 0
\(475\) −3.65323e6 + 2.10919e6i −0.742922 + 0.428926i
\(476\) −2.58666e6 4.30302e6i −0.523265 0.870474i
\(477\) 0 0
\(478\) −2.99273e6 1.69282e6i −0.599098 0.338876i
\(479\) 57304.6 + 99254.5i 0.0114117 + 0.0197657i 0.871675 0.490085i \(-0.163034\pi\)
−0.860263 + 0.509850i \(0.829701\pi\)
\(480\) 0 0
\(481\) 559963. 969884.i 0.110356 0.191142i
\(482\) −7.37560e6 + 4.34553e6i −1.44604 + 0.851972i
\(483\) 0 0
\(484\) 350453. 632524.i 0.0680011 0.122734i
\(485\) 6.77943e6i 1.30870i
\(486\) 0 0
\(487\) 2.72517e6i 0.520681i 0.965517 + 0.260340i \(0.0838348\pi\)
−0.965517 + 0.260340i \(0.916165\pi\)
\(488\) −3.70021e6 + 2.26898e6i −0.703358 + 0.431302i
\(489\) 0 0
\(490\) 1.39823e6 + 2.37319e6i 0.263080 + 0.446522i
\(491\) −2.94851e6 + 5.10696e6i −0.551948 + 0.956002i 0.446186 + 0.894940i \(0.352782\pi\)
−0.998134 + 0.0610621i \(0.980551\pi\)
\(492\) 0 0
\(493\) 3.78946e6 + 6.56353e6i 0.702198 + 1.21624i
\(494\) −293006. + 518004.i −0.0540205 + 0.0955027i
\(495\) 0 0
\(496\) −3.55119e6 1.88642e6i −0.648141 0.344298i
\(497\) 3.29804e6 1.90413e6i 0.598915 0.345784i
\(498\) 0 0
\(499\) −6.34312e6 3.66220e6i −1.14039 0.658402i −0.193860 0.981029i \(-0.562101\pi\)
−0.946526 + 0.322627i \(0.895434\pi\)
\(500\) 14643.3 + 829640.i 0.00261947 + 0.148410i
\(501\) 0 0
\(502\) 56560.9 + 6.40961e6i 0.0100174 + 1.13520i
\(503\) 5.80816e6 1.02357 0.511786 0.859113i \(-0.328984\pi\)
0.511786 + 0.859113i \(0.328984\pi\)
\(504\) 0 0
\(505\) 1.00775e7 1.75843
\(506\) 65463.1 + 7.41843e6i 0.0113663 + 1.28806i
\(507\) 0 0
\(508\) 42094.2 + 2.38492e6i 0.00723707 + 0.410029i
\(509\) 3.70500e6 + 2.13908e6i 0.633861 + 0.365960i 0.782246 0.622970i \(-0.214074\pi\)
−0.148385 + 0.988930i \(0.547407\pi\)
\(510\) 0 0
\(511\) 5.27714e6 3.04676e6i 0.894018 0.516162i
\(512\) 470581. + 5.91295e6i 0.0793340 + 0.996848i
\(513\) 0 0
\(514\) −2.98758e6 + 5.28174e6i −0.498784 + 0.881798i
\(515\) −2.70922e6 4.69251e6i −0.450119 0.779628i
\(516\) 0 0
\(517\) −4.31472e6 + 7.47332e6i −0.709948 + 1.22967i
\(518\) 3.88993e6 + 6.60231e6i 0.636967 + 1.08111i
\(519\) 0 0
\(520\) 658969. + 1.07463e6i 0.106870 + 0.174282i
\(521\) 6.07298e6i 0.980184i 0.871671 + 0.490092i \(0.163037\pi\)
−0.871671 + 0.490092i \(0.836963\pi\)
\(522\) 0 0
\(523\) 525817.i 0.0840583i −0.999116 0.0420291i \(-0.986618\pi\)
0.999116 0.0420291i \(-0.0133822\pi\)
\(524\) 2.07707e6 3.74886e6i 0.330464 0.596446i
\(525\) 0 0
\(526\) 3.32872e6 1.96121e6i 0.524582 0.309071i
\(527\) 2.96430e6 5.13432e6i 0.464939 0.805297i
\(528\) 0 0
\(529\) −1.46446e6 2.53652e6i −0.227530 0.394093i
\(530\) 7.20085e6 + 4.07312e6i 1.11351 + 0.629850i
\(531\) 0 0
\(532\) −2.09799e6 3.49010e6i −0.321384 0.534637i
\(533\) 1.29488e6 747598.i 0.197429 0.113986i
\(534\) 0 0
\(535\) 1.01109e7 + 5.83751e6i 1.52723 + 0.881746i
\(536\) −34756.0 + 64057.2i −0.00522537 + 0.00963066i
\(537\) 0 0
\(538\) −5.27101e6 + 46513.5i −0.785124 + 0.00692825i
\(539\) −2.57440e6 −0.381685
\(540\) 0 0
\(541\) 1.11917e7 1.64400 0.822000 0.569488i \(-0.192858\pi\)
0.822000 + 0.569488i \(0.192858\pi\)
\(542\) 9.97730e6 88043.6i 1.45886 0.0128736i
\(543\) 0 0
\(544\) −8.73687e6 + 385728.i −1.26578 + 0.0558836i
\(545\) 9.67679e6 + 5.58690e6i 1.39553 + 0.805711i
\(546\) 0 0
\(547\) 776917. 448553.i 0.111021 0.0640982i −0.443461 0.896294i \(-0.646250\pi\)
0.554482 + 0.832195i \(0.312916\pi\)
\(548\) −4.53537e6 + 2.72633e6i −0.645151 + 0.387817i
\(549\) 0 0
\(550\) −7.26888e6 4.11160e6i −1.02461 0.579567i
\(551\) 3.07356e6 + 5.32357e6i 0.431284 + 0.747006i
\(552\) 0 0
\(553\) 2.36123e6 4.08977e6i 0.328341 0.568704i
\(554\) −3.01542e6 + 1.77661e6i −0.417420 + 0.245934i
\(555\) 0 0
\(556\) −3.40576e6 1.88698e6i −0.467226 0.258869i
\(557\) 2.91603e6i 0.398249i 0.979974 + 0.199124i \(0.0638098\pi\)
−0.979974 + 0.199124i \(0.936190\pi\)
\(558\) 0 0
\(559\) 570864.i 0.0772686i
\(560\) −8.62013e6 + 304388.i −1.16157 + 0.0410164i
\(561\) 0 0
\(562\) 5.24504e6 + 8.90233e6i 0.700500 + 1.18895i
\(563\) 1.88482e6 3.26460e6i 0.250610 0.434070i −0.713084 0.701079i \(-0.752702\pi\)
0.963694 + 0.267009i \(0.0860354\pi\)
\(564\) 0 0
\(565\) −1.15575e6 2.00182e6i −0.152315 0.263817i
\(566\) 5.26003e6 9.29918e6i 0.690156 1.22012i
\(567\) 0 0
\(568\) −175586. 6.63122e6i −0.0228359 0.862428i
\(569\) 578222. 333836.i 0.0748710 0.0432268i −0.462097 0.886829i \(-0.652903\pi\)
0.536968 + 0.843603i \(0.319570\pi\)
\(570\) 0 0
\(571\) −5.54218e6 3.19978e6i −0.711361 0.410704i 0.100204 0.994967i \(-0.468051\pi\)
−0.811565 + 0.584262i \(0.801384\pi\)
\(572\) −1.17800e6 + 20791.8i −0.150541 + 0.00265707i
\(573\) 0 0
\(574\) 90277.1 + 1.02304e7i 0.0114366 + 1.29602i
\(575\) 1.05424e7 1.32974
\(576\) 0 0
\(577\) −8.64788e6 −1.08136 −0.540680 0.841229i \(-0.681833\pi\)
−0.540680 + 0.841229i \(0.681833\pi\)
\(578\) −42901.8 4.86173e6i −0.00534141 0.605300i
\(579\) 0 0
\(580\) 1.30186e7 229781.i 1.60692 0.0283625i
\(581\) −4.90560e6 2.83225e6i −0.602908 0.348089i
\(582\) 0 0
\(583\) −6.69626e6 + 3.86609e6i −0.815945 + 0.471086i
\(584\) −280952. 1.06105e7i −0.0340879 1.28737i
\(585\) 0 0
\(586\) −3.10385e6 + 5.48729e6i −0.373385 + 0.660107i
\(587\) 358200. + 620420.i 0.0429072 + 0.0743175i 0.886681 0.462381i \(-0.153005\pi\)
−0.843774 + 0.536698i \(0.819671\pi\)
\(588\) 0 0
\(589\) 2.40429e6 4.16436e6i 0.285561 0.494606i
\(590\) −6.85989e6 1.16432e7i −0.811310 1.37702i
\(591\) 0 0
\(592\) 1.33398e7 471047.i 1.56439 0.0552408i
\(593\) 6.55369e6i 0.765331i 0.923887 + 0.382665i \(0.124994\pi\)
−0.923887 + 0.382665i \(0.875006\pi\)
\(594\) 0 0
\(595\) 1.27171e7i 1.47264i
\(596\) −1.96467e6 1.08854e6i −0.226556 0.125524i
\(597\) 0 0
\(598\) 1.28144e6 754995.i 0.146536 0.0863358i
\(599\) 1.04139e6 1.80373e6i 0.118589 0.205402i −0.800620 0.599173i \(-0.795496\pi\)
0.919209 + 0.393771i \(0.128830\pi\)
\(600\) 0 0
\(601\) 392578. + 679965.i 0.0443343 + 0.0767893i 0.887341 0.461114i \(-0.152550\pi\)
−0.843007 + 0.537903i \(0.819217\pi\)
\(602\) −3.39989e6 1.92313e6i −0.382361 0.216280i
\(603\) 0 0
\(604\) −985480. + 592398.i −0.109915 + 0.0660725i
\(605\) 1.58625e6 915822.i 0.176191 0.101724i
\(606\) 0 0
\(607\) −8.67650e6 5.00938e6i −0.955812 0.551838i −0.0609306 0.998142i \(-0.519407\pi\)
−0.894882 + 0.446304i \(0.852740\pi\)
\(608\) −7.08632e6 + 312857.i −0.777431 + 0.0343232i
\(609\) 0 0
\(610\) −1.09939e7 + 97014.3i −1.19626 + 0.0105563i
\(611\) 1.73005e6 0.187480
\(612\) 0 0
\(613\) −4.81550e6 −0.517595 −0.258797 0.965932i \(-0.583326\pi\)
−0.258797 + 0.965932i \(0.583326\pi\)
\(614\) −9.29917e6 + 82059.5i −0.995458 + 0.00878432i
\(615\) 0 0
\(616\) 3.84461e6 7.08583e6i 0.408226 0.752383i
\(617\) −8.76037e6 5.05780e6i −0.926423 0.534871i −0.0407445 0.999170i \(-0.512973\pi\)
−0.885678 + 0.464299i \(0.846306\pi\)
\(618\) 0 0
\(619\) 1.10769e7 6.39527e6i 1.16196 0.670860i 0.210190 0.977661i \(-0.432592\pi\)
0.951774 + 0.306800i \(0.0992584\pi\)
\(620\) −5.24757e6 8.72957e6i −0.548251 0.912040i
\(621\) 0 0
\(622\) 3.57695e6 + 2.02328e6i 0.370712 + 0.209691i
\(623\) −2.35582e6 4.08040e6i −0.243177 0.421195i
\(624\) 0 0
\(625\) 4.33178e6 7.50287e6i 0.443575 0.768294i
\(626\) −6.84731e6 + 4.03428e6i −0.698368 + 0.411462i
\(627\) 0 0
\(628\) 2.61796e6 4.72510e6i 0.264889 0.478092i
\(629\) 1.96800e7i 1.98334i
\(630\) 0 0
\(631\) 1.13313e7i 1.13294i 0.824082 + 0.566471i \(0.191692\pi\)
−0.824082 + 0.566471i \(0.808308\pi\)
\(632\) −4.30012e6 7.01256e6i −0.428241 0.698367i
\(633\) 0 0
\(634\) −4.03532e6 6.84909e6i −0.398708 0.676721i
\(635\) −3.02093e6 + 5.23241e6i −0.297308 + 0.514953i
\(636\) 0 0
\(637\) 258060. + 446974.i 0.0251984 + 0.0436449i
\(638\) −5.99151e6 + 1.05924e7i −0.582753 + 1.03025i
\(639\) 0 0
\(640\) −6.69479e6 + 1.34507e7i −0.646081 + 1.29806i
\(641\) 1.30074e7 7.50980e6i 1.25039 0.721910i 0.279200 0.960233i \(-0.409931\pi\)
0.971186 + 0.238323i \(0.0765976\pi\)
\(642\) 0 0
\(643\) −2.31540e6 1.33680e6i −0.220851 0.127508i 0.385493 0.922711i \(-0.374031\pi\)
−0.606344 + 0.795202i \(0.707365\pi\)
\(644\) 179596. + 1.01753e7i 0.0170640 + 0.966791i
\(645\) 0 0
\(646\) −92281.7 1.04576e7i −0.00870030 0.985937i
\(647\) −1.55764e7 −1.46288 −0.731438 0.681908i \(-0.761150\pi\)
−0.731438 + 0.681908i \(0.761150\pi\)
\(648\) 0 0
\(649\) 1.26303e7 1.17707
\(650\) 14773.7 + 1.67419e6i 0.00137153 + 0.155425i
\(651\) 0 0
\(652\) 183885. + 1.04183e7i 0.0169405 + 0.959794i
\(653\) −415132. 239677.i −0.0380981 0.0219959i 0.480830 0.876814i \(-0.340335\pi\)
−0.518928 + 0.854818i \(0.673669\pi\)
\(654\) 0 0
\(655\) 9.40143e6 5.42792e6i 0.856230 0.494345i
\(656\) 1.57382e7 + 8.36027e6i 1.42789 + 0.758509i
\(657\) 0 0
\(658\) −5.82818e6 + 1.03036e7i −0.524769 + 0.927737i
\(659\) −155358. 269087.i −0.0139354 0.0241368i 0.858974 0.512020i \(-0.171103\pi\)
−0.872909 + 0.487883i \(0.837769\pi\)
\(660\) 0 0
\(661\) 1.04750e7 1.81433e7i 0.932505 1.61515i 0.153482 0.988151i \(-0.450951\pi\)
0.779023 0.626995i \(-0.215715\pi\)
\(662\) −709668. 1.20451e6i −0.0629376 0.106823i
\(663\) 0 0
\(664\) −8.41142e6 + 5.15791e6i −0.740370 + 0.453997i
\(665\) 1.03146e7i 0.904481i
\(666\) 0 0
\(667\) 1.53625e7i 1.33705i
\(668\) 3.30989e6 5.97395e6i 0.286994 0.517989i
\(669\) 0 0
\(670\) −159047. + 93706.7i −0.0136880 + 0.00806462i
\(671\) 5.13780e6 8.89893e6i 0.440525 0.763012i
\(672\) 0 0
\(673\) 6.73764e6 + 1.16699e7i 0.573417 + 0.993187i 0.996212 + 0.0869616i \(0.0277157\pi\)
−0.422795 + 0.906225i \(0.638951\pi\)
\(674\) 1.06256e7 + 6.01028e6i 0.900953 + 0.509619i
\(675\) 0 0
\(676\) −5.99965e6 9.98069e6i −0.504963 0.840028i
\(677\) −3.38026e6 + 1.95159e6i −0.283451 + 0.163650i −0.634985 0.772525i \(-0.718994\pi\)
0.351534 + 0.936175i \(0.385660\pi\)
\(678\) 0 0
\(679\) 7.52747e6 + 4.34599e6i 0.626577 + 0.361755i
\(680\) −1.94704e7 1.05642e7i −1.61474 0.876123i
\(681\) 0 0
\(682\) 9.51920e6 84001.1i 0.783681 0.00691551i
\(683\) 1.55558e7 1.27597 0.637985 0.770048i \(-0.279768\pi\)
0.637985 + 0.770048i \(0.279768\pi\)
\(684\) 0 0
\(685\) −1.34038e7 −1.09144
\(686\) −1.34113e7 + 118347.i −1.08808 + 0.00960164i
\(687\) 0 0
\(688\) −5.76871e6 + 3.60782e6i −0.464631 + 0.290586i
\(689\) 1.34248e6 + 775080.i 0.107736 + 0.0622011i
\(690\) 0 0
\(691\) −9.52435e6 + 5.49889e6i −0.758823 + 0.438107i −0.828873 0.559437i \(-0.811017\pi\)
0.0700501 + 0.997543i \(0.477684\pi\)
\(692\) −872493. + 524478.i −0.0692622 + 0.0416353i
\(693\) 0 0
\(694\) 7.91850e6 + 4.47905e6i 0.624086 + 0.353010i
\(695\) −4.93114e6 8.54099e6i −0.387245 0.670728i
\(696\) 0 0
\(697\) −1.31372e7 + 2.27543e7i −1.02429 + 1.77412i
\(698\) −2.27966e6 + 1.34312e6i −0.177105 + 0.104346i
\(699\) 0 0
\(700\) −1.00207e7 5.55202e6i −0.772954 0.428258i
\(701\) 1.51787e7i 1.16665i −0.812239 0.583324i \(-0.801752\pi\)
0.812239 0.583324i \(-0.198248\pi\)
\(702\) 0 0
\(703\) 1.59621e7i 1.21815i
\(704\) −7.65497e6 1.17725e7i −0.582119 0.895238i
\(705\) 0 0
\(706\) −1.31872e6 2.23824e6i −0.0995725 0.169003i
\(707\) −6.46024e6 + 1.11895e7i −0.486071 + 0.841900i
\(708\) 0 0
\(709\) −6.34771e6 1.09946e7i −0.474244 0.821414i 0.525321 0.850904i \(-0.323945\pi\)
−0.999565 + 0.0294896i \(0.990612\pi\)
\(710\) 8.27255e6 1.46250e7i 0.615876 1.08881i
\(711\) 0 0
\(712\) −8.20427e6 + 217238.i −0.606513 + 0.0160597i
\(713\) −1.04073e7 + 6.00867e6i −0.766682 + 0.442644i
\(714\) 0 0
\(715\) −2.58447e6 1.49215e6i −0.189063 0.109156i
\(716\) 1.52104e7 268465.i 1.10881 0.0195707i
\(717\) 0 0
\(718\) −110561. 1.25291e7i −0.00800374 0.907001i
\(719\) 1.30901e7 0.944324 0.472162 0.881512i \(-0.343474\pi\)
0.472162 + 0.881512i \(0.343474\pi\)
\(720\) 0 0
\(721\) 6.94705e6 0.497693
\(722\) 48749.8 + 5.52443e6i 0.00348040 + 0.394407i
\(723\) 0 0
\(724\) −150232. + 2651.62i −0.0106516 + 0.000188003i
\(725\) 1.49766e7 + 8.64672e6i 1.05820 + 0.610951i
\(726\) 0 0
\(727\) −6.63075e6 + 3.82826e6i −0.465293 + 0.268637i −0.714267 0.699873i \(-0.753240\pi\)
0.248974 + 0.968510i \(0.419907\pi\)
\(728\) −1.61564e6 + 42780.1i −0.112984 + 0.00299167i
\(729\) 0 0
\(730\) 1.32368e7 2.34012e7i 0.919337 1.62529i
\(731\) −5.01578e6 8.68758e6i −0.347172 0.601319i
\(732\) 0 0
\(733\) 9.24808e6 1.60181e7i 0.635757 1.10116i −0.350597 0.936527i \(-0.614021\pi\)
0.986354 0.164638i \(-0.0526455\pi\)
\(734\) 8.44057e6 + 1.43260e7i 0.578271 + 0.981491i
\(735\) 0 0
\(736\) 1.57280e7 + 8.17774e6i 1.07024 + 0.556466i
\(737\) 172532.i 0.0117004i
\(738\) 0 0
\(739\) 3.75594e6i 0.252992i −0.991967 0.126496i \(-0.959627\pi\)
0.991967 0.126496i \(-0.0403732\pi\)
\(740\) 2.95745e7 + 1.63859e7i 1.98535 + 1.09999i
\(741\) 0 0
\(742\) −9.13868e6 + 5.38429e6i −0.609359 + 0.359020i
\(743\) −22492.7 + 38958.6i −0.00149476 + 0.00258899i −0.866772 0.498705i \(-0.833809\pi\)
0.865277 + 0.501294i \(0.167142\pi\)
\(744\) 0 0
\(745\) −2.84462e6 4.92702e6i −0.187773 0.325232i
\(746\) −8.17760e6 4.62561e6i −0.537996 0.304314i
\(747\) 0 0
\(748\) 1.77444e7 1.06666e7i 1.15960 0.697066i
\(749\) −1.29632e7 + 7.48433e6i −0.844324 + 0.487471i
\(750\) 0 0
\(751\) 2.26479e7 + 1.30757e7i 1.46530 + 0.845993i 0.999248 0.0387633i \(-0.0123418\pi\)
0.466054 + 0.884756i \(0.345675\pi\)
\(752\) 1.09338e7 + 1.74825e7i 0.705059 + 1.12735i
\(753\) 0 0
\(754\) 2.43966e6 21528.5i 0.156279 0.00137907i
\(755\) −2.91248e6 −0.185950
\(756\) 0 0
\(757\) −8.60555e6 −0.545807 −0.272903 0.962041i \(-0.587984\pi\)
−0.272903 + 0.962041i \(0.587984\pi\)
\(758\) 2.65382e7 234183.i 1.67764 0.0148041i
\(759\) 0 0
\(760\) −1.57921e7 8.56845e6i −0.991761 0.538107i
\(761\) −2.15910e7 1.24656e7i −1.35148 0.780280i −0.363027 0.931779i \(-0.618257\pi\)
−0.988458 + 0.151498i \(0.951590\pi\)
\(762\) 0 0
\(763\) −1.24067e7 + 7.16302e6i −0.771516 + 0.445435i
\(764\) 9.98326e6 + 1.66076e7i 0.618784 + 1.02937i
\(765\) 0 0
\(766\) 2.60782e7 + 1.47510e7i 1.60585 + 0.908341i
\(767\) −1.26608e6 2.19291e6i −0.0777090 0.134596i
\(768\) 0 0
\(769\) −1.62777e7 + 2.81939e7i −0.992610 + 1.71925i −0.391212 + 0.920300i \(0.627944\pi\)
−0.601398 + 0.798950i \(0.705389\pi\)
\(770\) 1.75934e7 1.03656e7i 1.06935 0.630039i
\(771\) 0 0
\(772\) −1.44832e6 + 2.61405e6i −0.0874625 + 0.157859i
\(773\) 1.64551e6i 0.0990493i 0.998773 + 0.0495246i \(0.0157706\pi\)
−0.998773 + 0.0495246i \(0.984229\pi\)
\(774\) 0 0
\(775\) 1.35278e7i 0.809044i
\(776\) 1.29070e7 7.91464e6i 0.769436 0.471820i
\(777\) 0 0
\(778\) 5.28989e6 + 8.97845e6i 0.313327 + 0.531805i
\(779\) −1.06554e7 + 1.84557e7i −0.629108 + 1.08965i
\(780\) 0 0
\(781\) 7.85208e6 + 1.36002e7i 0.460635 + 0.797843i
\(782\) −1.28677e7 + 2.27488e7i −0.752464 + 1.33028i
\(783\) 0 0
\(784\) −2.88585e6 + 5.43260e6i −0.167681 + 0.315659i
\(785\) 1.18496e7 6.84139e6i 0.686326 0.396251i
\(786\) 0 0
\(787\) 1.68858e7 + 9.74900e6i 0.971816 + 0.561078i 0.899789 0.436325i \(-0.143720\pi\)
0.0720264 + 0.997403i \(0.477053\pi\)
\(788\) −263395. 1.49231e7i −0.0151109 0.856136i
\(789\) 0 0
\(790\) −183859. 2.08354e7i −0.0104814 1.18777i
\(791\) 2.96359e6 0.168414
\(792\) 0 0
\(793\) −2.06007e6 −0.116332
\(794\) 3779.24 + 428272.i 0.000212742 + 0.0241084i
\(795\) 0 0
\(796\) −353448. 2.00252e7i −0.0197716 1.12020i
\(797\) 318483. + 183876.i 0.0177599 + 0.0102537i 0.508854 0.860853i \(-0.330069\pi\)
−0.491094 + 0.871107i \(0.663403\pi\)
\(798\) 0 0
\(799\) −2.63283e7 + 1.52007e7i −1.45900 + 0.842356i
\(800\) −1.68247e7 + 1.07300e7i −0.929441 + 0.592757i
\(801\) 0 0
\(802\) 9.40521e6 1.66274e7i 0.516336 0.912829i
\(803\) 1.25640e7 + 2.17614e7i 0.687604 + 1.19096i
\(804\) 0 0
\(805\) −1.28889e7 + 2.23242e7i −0.701011 + 1.21419i
\(806\) −968796. 1.64432e6i −0.0525285 0.0891558i
\(807\) 0 0
\(808\) 1.17650e7 + 1.91861e7i 0.633961 + 1.03385i
\(809\) 5.76347e6i 0.309609i 0.987945 + 0.154804i \(0.0494747\pi\)
−0.987945 + 0.154804i \(0.950525\pi\)
\(810\) 0 0
\(811\) 819789.i 0.0437673i 0.999761 + 0.0218837i \(0.00696634\pi\)
−0.999761 + 0.0218837i \(0.993034\pi\)
\(812\) −8.09052e6 + 1.46024e7i −0.430612 + 0.777203i
\(813\) 0 0
\(814\) −2.72261e7 + 1.60410e7i −1.44020 + 0.848534i
\(815\) −1.31967e7 + 2.28573e7i −0.695938 + 1.20540i
\(816\) 0 0
\(817\) −4.06821e6 7.04635e6i −0.213230 0.369325i
\(818\) −1.72339e7 9.74827e6i −0.900536 0.509383i
\(819\) 0 0
\(820\) 2.32563e7 + 3.86878e7i 1.20783 + 2.00928i
\(821\) 631565. 364634.i 0.0327009 0.0188799i −0.483560 0.875311i \(-0.660657\pi\)
0.516261 + 0.856431i \(0.327323\pi\)
\(822\) 0 0
\(823\) −1.52844e7 8.82447e6i −0.786592 0.454139i 0.0521692 0.998638i \(-0.483386\pi\)
−0.838762 + 0.544499i \(0.816720\pi\)
\(824\) 5.77097e6 1.06362e7i 0.296095 0.545720i
\(825\) 0 0
\(826\) 1.73254e7 152887.i 0.883557 0.00779685i
\(827\) −2.90788e7 −1.47847 −0.739236 0.673447i \(-0.764813\pi\)
−0.739236 + 0.673447i \(0.764813\pi\)
\(828\) 0 0
\(829\) −1.37334e7 −0.694051 −0.347026 0.937856i \(-0.612808\pi\)
−0.347026 + 0.937856i \(0.612808\pi\)
\(830\) −2.49916e7 + 220536.i −1.25921 + 0.0111118i
\(831\) 0 0
\(832\) −1.27663e6 + 2.50916e6i −0.0639378 + 0.125667i
\(833\) −7.85448e6 4.53478e6i −0.392197 0.226435i
\(834\) 0 0
\(835\) 1.49815e7 8.64958e6i 0.743600 0.429318i
\(836\) 1.43922e7 8.65153e6i 0.712216 0.428131i
\(837\) 0 0
\(838\) −2.61775e7 1.48072e7i −1.28771 0.728387i
\(839\) 5.44148e6 + 9.42491e6i 0.266877 + 0.462245i 0.968054 0.250743i \(-0.0806748\pi\)
−0.701176 + 0.712988i \(0.747341\pi\)
\(840\) 0 0
\(841\) 2.34460e6 4.06097e6i 0.114309 0.197989i
\(842\) 2.52487e7 1.48759e7i 1.22732 0.723108i
\(843\) 0 0
\(844\) −2.44412e7 1.35417e7i −1.18104 0.654362i
\(845\) 2.94969e7i 1.42113i
\(846\) 0 0
\(847\) 2.34837e6i 0.112475i
\(848\) 652006. + 1.84645e7i 0.0311359 + 0.881755i
\(849\) 0 0
\(850\) −1.49347e7 2.53485e7i −0.709006 1.20339i
\(851\) 1.99458e7 3.45471e7i 0.944119 1.63526i
\(852\) 0 0
\(853\) 1.39626e6 + 2.41839e6i 0.0657043 + 0.113803i 0.897006 0.442018i \(-0.145737\pi\)
−0.831302 + 0.555821i \(0.812404\pi\)
\(854\) 6.93996e6 1.22691e7i 0.325621 0.575664i
\(855\) 0 0
\(856\) 690156. + 2.60646e7i 0.0321931 + 1.21581i
\(857\) 2.22286e7 1.28337e7i 1.03386 0.596898i 0.115770 0.993276i \(-0.463066\pi\)
0.918087 + 0.396378i \(0.129733\pi\)
\(858\) 0 0
\(859\) −4.15701e6 2.40005e6i −0.192220 0.110978i 0.400802 0.916165i \(-0.368732\pi\)
−0.593021 + 0.805187i \(0.702065\pi\)
\(860\) −1.72316e7 + 304141.i −0.794475 + 0.0140226i
\(861\) 0 0
\(862\) 285644. + 3.23698e7i 0.0130935 + 1.48379i
\(863\) −2.59610e7 −1.18658 −0.593288 0.804991i \(-0.702170\pi\)
−0.593288 + 0.804991i \(0.702170\pi\)
\(864\) 0 0
\(865\) −2.57856e6 −0.117175
\(866\) −308186. 3.49243e7i −0.0139643 1.58246i
\(867\) 0 0
\(868\) 1.30568e7 230454.i 0.588215 0.0103821i
\(869\) 1.68651e7 + 9.73705e6i 0.757597 + 0.437399i
\(870\) 0 0
\(871\) −29955.3 + 17294.7i −0.00133792 + 0.000772446i
\(872\) 660526. + 2.49456e7i 0.0294170 + 1.11097i
\(873\) 0 0
\(874\) −1.04368e7 + 1.84512e7i −0.462157 + 0.817045i
\(875\) −1.34735e6 2.33369e6i −0.0594924 0.103044i
\(876\) 0 0
\(877\) 1.75890e7 3.04651e7i 0.772222 1.33753i −0.164120 0.986440i \(-0.552478\pi\)
0.936343 0.351088i \(-0.114188\pi\)
\(878\) 1.66565e7 + 2.82708e7i 0.729200 + 1.23766i
\(879\) 0 0
\(880\) −1.25521e6 3.55470e7i −0.0546399 1.54738i
\(881\) 1.34812e7i 0.585177i −0.956238 0.292588i \(-0.905483\pi\)
0.956238 0.292588i \(-0.0945166\pi\)
\(882\) 0 0
\(883\) 1.27557e7i 0.550557i −0.961364 0.275279i \(-0.911230\pi\)
0.961364 0.275279i \(-0.0887701\pi\)
\(884\) −3.63068e6 2.01159e6i −0.156263 0.0865784i
\(885\) 0 0
\(886\) 2.03708e7 1.20020e7i 0.871814 0.513652i
\(887\) 9.47111e6 1.64044e7i 0.404196 0.700088i −0.590032 0.807380i \(-0.700885\pi\)
0.994228 + 0.107292i \(0.0342180\pi\)
\(888\) 0 0
\(889\) −3.87317e6 6.70852e6i −0.164366 0.284690i
\(890\) −1.80943e7 1.02350e7i −0.765716 0.433123i
\(891\) 0 0
\(892\) 1.32746e7 7.97973e6i 0.558613 0.335797i
\(893\) −2.13545e7 + 1.23290e7i −0.896107 + 0.517368i
\(894\) 0 0
\(895\) 3.33709e7 + 1.92667e7i 1.39255 + 0.803988i
\(896\) −1.06431e7 1.60561e7i −0.442891 0.668144i
\(897\) 0 0
\(898\) 5.49223e6 48465.6i 0.227278 0.00200559i
\(899\) −1.97130e7 −0.813491
\(900\) 0 0
\(901\) −2.72403e7 −1.11789
\(902\) −4.21873e7 + 372277.i −1.72650 + 0.0152353i
\(903\) 0 0
\(904\) 2.46188e6 4.53739e6i 0.100195 0.184665i
\(905\) −329602. 190296.i −0.0133773 0.00772339i
\(906\) 0 0
\(907\) −3.65444e7 + 2.10989e7i −1.47504 + 0.851613i −0.999604 0.0281382i \(-0.991042\pi\)
−0.475434 + 0.879752i \(0.657709\pi\)
\(908\) 3.88785e6 + 6.46761e6i 0.156493 + 0.260333i
\(909\) 0 0
\(910\) −3.56327e6 2.01554e6i −0.142641 0.0806841i
\(911\) 1.29463e7 + 2.24236e7i 0.516831 + 0.895177i 0.999809 + 0.0195449i \(0.00622174\pi\)
−0.482978 + 0.875632i \(0.660445\pi\)
\(912\) 0 0
\(913\) 1.16794e7 2.02293e7i 0.463706 0.803163i
\(914\) 1.01190e7 5.96188e6i 0.400657 0.236057i
\(915\) 0 0
\(916\) −3.84892e6 + 6.94683e6i −0.151565 + 0.273557i
\(917\) 1.39184e7i 0.546594i
\(918\) 0 0
\(919\) 3.59722e7i 1.40501i −0.711681 0.702503i \(-0.752066\pi\)
0.711681 0.702503i \(-0.247934\pi\)
\(920\) 2.34724e7 + 3.82783e7i 0.914297 + 1.49102i
\(921\) 0 0
\(922\) −8.38118e6 1.42253e7i −0.324697 0.551103i
\(923\) 1.57420e6 2.72659e6i 0.0608212 0.105345i
\(924\) 0 0
\(925\) 2.24527e7 + 3.88892e7i 0.862809 + 1.49443i
\(926\) 1.61758e7 2.85971e7i 0.619923 1.09596i
\(927\) 0 0
\(928\) 1.56360e7 + 2.45173e7i 0.596015 + 0.934550i
\(929\) −3.28939e7 + 1.89913e7i −1.25048 + 0.721964i −0.971204 0.238248i \(-0.923427\pi\)
−0.279273 + 0.960212i \(0.590094\pi\)
\(930\) 0 0
\(931\) −6.37063e6 3.67809e6i −0.240884 0.139075i
\(932\) 192159. + 1.08871e7i 0.00724637 + 0.410556i
\(933\) 0 0
\(934\) −415285. 4.70611e7i −0.0155768 1.76520i
\(935\) 5.24417e7 1.96177
\(936\) 0 0
\(937\) −1.87349e7 −0.697111 −0.348555 0.937288i \(-0.613328\pi\)
−0.348555 + 0.937288i \(0.613328\pi\)
\(938\) −2088.45 236667.i −7.75026e−5 0.00878276i
\(939\) 0 0
\(940\) 921722. + 5.22217e7i 0.0340236 + 1.92767i
\(941\) −1.73547e7 1.00197e7i −0.638915 0.368878i 0.145281 0.989390i \(-0.453591\pi\)
−0.784196 + 0.620513i \(0.786925\pi\)
\(942\) 0 0
\(943\) 4.61233e7 2.66293e7i 1.68905 0.975171i
\(944\) 1.41583e7 2.66530e7i 0.517109 0.973456i
\(945\) 0 0
\(946\) 7.93044e6 1.40202e7i 0.288117 0.509361i
\(947\) −1.05215e7 1.82237e7i −0.381243 0.660332i 0.609997 0.792404i \(-0.291171\pi\)
−0.991240 + 0.132071i \(0.957837\pi\)
\(948\) 0 0
\(949\) 2.51885e6 4.36277e6i 0.0907896 0.157252i
\(950\) −1.21133e7 2.05597e7i −0.435465 0.739108i
\(951\) 0 0
\(952\) 2.42115e7 1.48466e7i 0.865823 0.530925i
\(953\) 3.31281e6i 0.118158i −0.998253 0.0590792i \(-0.981184\pi\)
0.998253 0.0590792i \(-0.0188164\pi\)
\(954\) 0 0
\(955\) 4.90820e7i 1.74146i
\(956\) 9.42628e6 1.70133e7i 0.333577 0.602065i
\(957\) 0 0
\(958\) −558586. + 329106.i −0.0196642 + 0.0115857i
\(959\) 8.59256e6 1.48828e7i 0.301701 0.522561i
\(960\) 0 0
\(961\) −6.60435e6 1.14391e7i −0.230686 0.399560i
\(962\) 5.51423e6 + 3.11909e6i 0.192109 + 0.108665i
\(963\) 0 0
\(964\) −2.49492e7 4.15042e7i −0.864698 1.43846i
\(965\) −6.55552e6 + 3.78483e6i −0.226615 + 0.130836i
\(966\) 0 0
\(967\) −1.14131e7 6.58936e6i −0.392498 0.226609i 0.290744 0.956801i \(-0.406097\pi\)
−0.683242 + 0.730192i \(0.739431\pi\)
\(968\) 3.59545e6 + 1.95081e6i 0.123329 + 0.0669155i
\(969\) 0 0
\(970\) 3.83488e7 338405.i 1.30865 0.0115480i
\(971\) −5.16587e6 −0.175831 −0.0879155 0.996128i \(-0.528021\pi\)
−0.0879155 + 0.996128i \(0.528021\pi\)
\(972\) 0 0
\(973\) 1.26445e7 0.428174
\(974\) −1.54153e7 + 136031.i −0.520660 + 0.00459451i
\(975\) 0 0
\(976\) −1.30195e7 2.08175e7i −0.437491 0.699525i
\(977\) −1.37911e6 796228.i −0.0462234 0.0266871i 0.476710 0.879060i \(-0.341829\pi\)
−0.522934 + 0.852373i \(0.675162\pi\)
\(978\) 0 0
\(979\) 1.68264e7 9.71474e6i 0.561093 0.323947i
\(980\) −1.33545e7 + 8.02773e6i −0.444183 + 0.267010i
\(981\) 0 0
\(982\) −2.90354e7 1.64237e7i −0.960836 0.543491i
\(983\) 7.65007e6 + 1.32503e7i 0.252512 + 0.437363i 0.964217 0.265115i \(-0.0854101\pi\)
−0.711705 + 0.702478i \(0.752077\pi\)
\(984\) 0 0
\(985\) 1.89028e7 3.27406e7i 0.620776 1.07522i
\(986\) −3.69383e7 + 2.17632e7i −1.21000 + 0.712903i
\(987\) 0 0
\(988\) −2.94478e6 1.63157e6i −0.0959756 0.0531757i
\(989\) 2.03341e7i 0.661049i
\(990\) 0 0
\(991\) 4.54893e7i 1.47138i −0.677317 0.735691i \(-0.736858\pi\)
0.677317 0.735691i \(-0.263142\pi\)
\(992\) 1.04935e7 2.01819e7i 0.338566 0.651153i
\(993\) 0 0
\(994\) 1.09356e7 + 1.85608e7i 0.351055 + 0.595840i
\(995\) 2.53655e7 4.39344e7i 0.812244 1.40685i
\(996\) 0 0
\(997\) −1.16700e7 2.02131e7i −0.371821 0.644013i 0.618025 0.786159i \(-0.287933\pi\)
−0.989846 + 0.142146i \(0.954600\pi\)
\(998\) 2.03991e7 3.60635e7i 0.648314 1.14615i
\(999\) 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 108.6.h.a.71.15 56
3.2 odd 2 36.6.h.a.23.14 yes 56
4.3 odd 2 inner 108.6.h.a.71.5 56
9.2 odd 6 inner 108.6.h.a.35.5 56
9.7 even 3 36.6.h.a.11.24 yes 56
12.11 even 2 36.6.h.a.23.24 yes 56
36.7 odd 6 36.6.h.a.11.14 56
36.11 even 6 inner 108.6.h.a.35.15 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.6.h.a.11.14 56 36.7 odd 6
36.6.h.a.11.24 yes 56 9.7 even 3
36.6.h.a.23.14 yes 56 3.2 odd 2
36.6.h.a.23.24 yes 56 12.11 even 2
108.6.h.a.35.5 56 9.2 odd 6 inner
108.6.h.a.35.15 56 36.11 even 6 inner
108.6.h.a.71.5 56 4.3 odd 2 inner
108.6.h.a.71.15 56 1.1 even 1 trivial