Properties

Label 60.7.f.a.19.34
Level $60$
Weight $7$
Character 60.19
Analytic conductor $13.803$
Analytic rank $0$
Dimension $36$
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] = [60,7,Mod(19,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.19");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.f (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.8032450172\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.34
Character \(\chi\) \(=\) 60.19
Dual form 60.7.f.a.19.33

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.65640 + 2.31937i) q^{2} +15.5885 q^{3} +(53.2410 + 35.5161i) q^{4} +(87.3911 - 89.3745i) q^{5} +(119.352 + 36.1554i) q^{6} +36.3122 q^{7} +(325.260 + 395.411i) q^{8} +243.000 q^{9} +O(q^{10})\) \(q+(7.65640 + 2.31937i) q^{2} +15.5885 q^{3} +(53.2410 + 35.5161i) q^{4} +(87.3911 - 89.3745i) q^{5} +(119.352 + 36.1554i) q^{6} +36.3122 q^{7} +(325.260 + 395.411i) q^{8} +243.000 q^{9} +(876.394 - 481.595i) q^{10} -995.783i q^{11} +(829.945 + 553.641i) q^{12} +105.943i q^{13} +(278.021 + 84.2215i) q^{14} +(1362.29 - 1393.21i) q^{15} +(1573.21 + 3781.83i) q^{16} -1286.27i q^{17} +(1860.51 + 563.607i) q^{18} +9085.22i q^{19} +(7827.02 - 1654.60i) q^{20} +566.051 q^{21} +(2309.59 - 7624.12i) q^{22} +1331.63 q^{23} +(5070.30 + 6163.85i) q^{24} +(-350.602 - 15621.1i) q^{25} +(-245.722 + 811.144i) q^{26} +3788.00 q^{27} +(1933.30 + 1289.67i) q^{28} -14223.4 q^{29} +(13661.6 - 7507.32i) q^{30} +40502.0i q^{31} +(3273.70 + 32604.1i) q^{32} -15522.7i q^{33} +(2983.33 - 9848.19i) q^{34} +(3173.36 - 3245.39i) q^{35} +(12937.6 + 8630.41i) q^{36} -71359.6i q^{37} +(-21072.0 + 69560.1i) q^{38} +1651.49i q^{39} +(63764.5 + 5485.49i) q^{40} -68453.6 q^{41} +(4333.92 + 1312.88i) q^{42} +6391.48 q^{43} +(35366.3 - 53016.5i) q^{44} +(21236.0 - 21718.0i) q^{45} +(10195.5 + 3088.55i) q^{46} -56471.4 q^{47} +(24524.0 + 58952.8i) q^{48} -116330. q^{49} +(33546.7 - 120414. i) q^{50} -20050.9i q^{51} +(-3762.69 + 5640.53i) q^{52} -62845.9i q^{53} +(29002.4 + 8785.77i) q^{54} +(-88997.6 - 87022.5i) q^{55} +(11810.9 + 14358.3i) q^{56} +141624. i q^{57} +(-108900. - 32989.3i) q^{58} -132995. i q^{59} +(122011. - 25792.7i) q^{60} -387193. q^{61} +(-93939.2 + 310100. i) q^{62} +8823.87 q^{63} +(-50556.2 + 257223. i) q^{64} +(9468.63 + 9258.50i) q^{65} +(36003.0 - 118848. i) q^{66} -476348. q^{67} +(45683.2 - 68482.2i) q^{68} +20758.1 q^{69} +(31823.8 - 17487.8i) q^{70} +483101. i q^{71} +(79038.1 + 96084.9i) q^{72} -654838. i q^{73} +(165509. - 546358. i) q^{74} +(-5465.35 - 243508. i) q^{75} +(-322671. + 483706. i) q^{76} -36159.1i q^{77} +(-3830.42 + 12644.5i) q^{78} +80187.9i q^{79} +(475484. + 189893. i) q^{80} +59049.0 q^{81} +(-524108. - 158769. i) q^{82} +1.03615e6 q^{83} +(30137.2 + 20103.9i) q^{84} +(-114960. - 112408. i) q^{85} +(48935.8 + 14824.2i) q^{86} -221721. q^{87} +(393744. - 323888. i) q^{88} +1.20220e6 q^{89} +(212964. - 117028. i) q^{90} +3847.03i q^{91} +(70897.4 + 47294.4i) q^{92} +631363. i q^{93} +(-432368. - 130978. i) q^{94} +(811987. + 793967. i) q^{95} +(51031.9 + 508247. i) q^{96} +1.45683e6i q^{97} +(-890673. - 269814. i) q^{98} -241975. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.65640 + 2.31937i 0.957050 + 0.289921i
\(3\) 15.5885 0.577350
\(4\) 53.2410 + 35.5161i 0.831891 + 0.554939i
\(5\) 87.3911 89.3745i 0.699129 0.714996i
\(6\) 119.352 + 36.1554i 0.552553 + 0.167386i
\(7\) 36.3122 0.105866 0.0529332 0.998598i \(-0.483143\pi\)
0.0529332 + 0.998598i \(0.483143\pi\)
\(8\) 325.260 + 395.411i 0.635273 + 0.772288i
\(9\) 243.000 0.333333
\(10\) 876.394 481.595i 0.876394 0.481595i
\(11\) 995.783i 0.748146i −0.927399 0.374073i \(-0.877961\pi\)
0.927399 0.374073i \(-0.122039\pi\)
\(12\) 829.945 + 553.641i 0.480293 + 0.320394i
\(13\) 105.943i 0.0482218i 0.999709 + 0.0241109i \(0.00767548\pi\)
−0.999709 + 0.0241109i \(0.992325\pi\)
\(14\) 278.021 + 84.2215i 0.101320 + 0.0306930i
\(15\) 1362.29 1393.21i 0.403642 0.412803i
\(16\) 1573.21 + 3781.83i 0.384085 + 0.923298i
\(17\) 1286.27i 0.261809i −0.991395 0.130905i \(-0.958212\pi\)
0.991395 0.130905i \(-0.0417881\pi\)
\(18\) 1860.51 + 563.607i 0.319017 + 0.0966405i
\(19\) 9085.22i 1.32457i 0.749253 + 0.662284i \(0.230413\pi\)
−0.749253 + 0.662284i \(0.769587\pi\)
\(20\) 7827.02 1654.60i 0.978378 0.206825i
\(21\) 566.051 0.0611221
\(22\) 2309.59 7624.12i 0.216904 0.716014i
\(23\) 1331.63 0.109446 0.0547231 0.998502i \(-0.482572\pi\)
0.0547231 + 0.998502i \(0.482572\pi\)
\(24\) 5070.30 + 6163.85i 0.366775 + 0.445880i
\(25\) −350.602 15621.1i −0.0224386 0.999748i
\(26\) −245.722 + 811.144i −0.0139805 + 0.0461507i
\(27\) 3788.00 0.192450
\(28\) 1933.30 + 1289.67i 0.0880694 + 0.0587494i
\(29\) −14223.4 −0.583188 −0.291594 0.956542i \(-0.594186\pi\)
−0.291594 + 0.956542i \(0.594186\pi\)
\(30\) 13661.6 7507.32i 0.505986 0.278049i
\(31\) 40502.0i 1.35954i 0.733426 + 0.679769i \(0.237920\pi\)
−0.733426 + 0.679769i \(0.762080\pi\)
\(32\) 3273.70 + 32604.1i 0.0999054 + 0.994997i
\(33\) 15522.7i 0.431943i
\(34\) 2983.33 9848.19i 0.0759041 0.250565i
\(35\) 3173.36 3245.39i 0.0740143 0.0756941i
\(36\) 12937.6 + 8630.41i 0.277297 + 0.184980i
\(37\) 71359.6i 1.40879i −0.709807 0.704396i \(-0.751218\pi\)
0.709807 0.704396i \(-0.248782\pi\)
\(38\) −21072.0 + 69560.1i −0.384021 + 1.26768i
\(39\) 1651.49i 0.0278409i
\(40\) 63764.5 + 5485.49i 0.996320 + 0.0857107i
\(41\) −68453.6 −0.993218 −0.496609 0.867974i \(-0.665422\pi\)
−0.496609 + 0.867974i \(0.665422\pi\)
\(42\) 4333.92 + 1312.88i 0.0584969 + 0.0177206i
\(43\) 6391.48 0.0803889 0.0401945 0.999192i \(-0.487202\pi\)
0.0401945 + 0.999192i \(0.487202\pi\)
\(44\) 35366.3 53016.5i 0.415176 0.622376i
\(45\) 21236.0 21718.0i 0.233043 0.238332i
\(46\) 10195.5 + 3088.55i 0.104746 + 0.0317308i
\(47\) −56471.4 −0.543920 −0.271960 0.962309i \(-0.587672\pi\)
−0.271960 + 0.962309i \(0.587672\pi\)
\(48\) 24524.0 + 58952.8i 0.221752 + 0.533066i
\(49\) −116330. −0.988792
\(50\) 33546.7 120414.i 0.268374 0.963315i
\(51\) 20050.9i 0.151156i
\(52\) −3762.69 + 5640.53i −0.0267601 + 0.0401153i
\(53\) 62845.9i 0.422133i −0.977472 0.211066i \(-0.932306\pi\)
0.977472 0.211066i \(-0.0676936\pi\)
\(54\) 29002.4 + 8785.77i 0.184184 + 0.0557954i
\(55\) −88997.6 87022.5i −0.534922 0.523051i
\(56\) 11810.9 + 14358.3i 0.0672541 + 0.0817594i
\(57\) 141624.i 0.764740i
\(58\) −108900. 32989.3i −0.558141 0.169079i
\(59\) 132995.i 0.647561i −0.946132 0.323780i \(-0.895046\pi\)
0.946132 0.323780i \(-0.104954\pi\)
\(60\) 122011. 25792.7i 0.564867 0.119411i
\(61\) −387193. −1.70584 −0.852920 0.522042i \(-0.825171\pi\)
−0.852920 + 0.522042i \(0.825171\pi\)
\(62\) −93939.2 + 310100.i −0.394159 + 1.30115i
\(63\) 8823.87 0.0352888
\(64\) −50556.2 + 257223.i −0.192857 + 0.981227i
\(65\) 9468.63 + 9258.50i 0.0344784 + 0.0337132i
\(66\) 36003.0 118848.i 0.125229 0.413391i
\(67\) −476348. −1.58380 −0.791899 0.610653i \(-0.790907\pi\)
−0.791899 + 0.610653i \(0.790907\pi\)
\(68\) 45683.2 68482.2i 0.145288 0.217797i
\(69\) 20758.1 0.0631888
\(70\) 31823.8 17487.8i 0.0927808 0.0509848i
\(71\) 483101.i 1.34978i 0.737919 + 0.674889i \(0.235809\pi\)
−0.737919 + 0.674889i \(0.764191\pi\)
\(72\) 79038.1 + 96084.9i 0.211758 + 0.257429i
\(73\) 654838.i 1.68331i −0.540012 0.841657i \(-0.681580\pi\)
0.540012 0.841657i \(-0.318420\pi\)
\(74\) 165509. 546358.i 0.408439 1.34829i
\(75\) −5465.35 243508.i −0.0129549 0.577205i
\(76\) −322671. + 483706.i −0.735055 + 1.10190i
\(77\) 36159.1i 0.0792036i
\(78\) −3830.42 + 12644.5i −0.00807166 + 0.0266451i
\(79\) 80187.9i 0.162640i 0.996688 + 0.0813200i \(0.0259136\pi\)
−0.996688 + 0.0813200i \(0.974086\pi\)
\(80\) 475484. + 189893.i 0.928679 + 0.370884i
\(81\) 59049.0 0.111111
\(82\) −524108. 158769.i −0.950559 0.287955i
\(83\) 1.03615e6 1.81213 0.906066 0.423137i \(-0.139071\pi\)
0.906066 + 0.423137i \(0.139071\pi\)
\(84\) 30137.2 + 20103.9i 0.0508469 + 0.0339190i
\(85\) −114960. 112408.i −0.187192 0.183038i
\(86\) 48935.8 + 14824.2i 0.0769362 + 0.0233065i
\(87\) −221721. −0.336704
\(88\) 393744. 323888.i 0.577784 0.475277i
\(89\) 1.20220e6 1.70532 0.852662 0.522463i \(-0.174987\pi\)
0.852662 + 0.522463i \(0.174987\pi\)
\(90\) 212964. 117028.i 0.292131 0.160532i
\(91\) 3847.03i 0.00510507i
\(92\) 70897.4 + 47294.4i 0.0910473 + 0.0607360i
\(93\) 631363.i 0.784929i
\(94\) −432368. 130978.i −0.520559 0.157694i
\(95\) 811987. + 793967.i 0.947061 + 0.926044i
\(96\) 51031.9 + 508247.i 0.0576804 + 0.574462i
\(97\) 1.45683e6i 1.59622i 0.602511 + 0.798111i \(0.294167\pi\)
−0.602511 + 0.798111i \(0.705833\pi\)
\(98\) −890673. 269814.i −0.946324 0.286672i
\(99\) 241975.i 0.249382i
\(100\) 536133. 844134.i 0.536133 0.844134i
\(101\) 796216. 0.772800 0.386400 0.922331i \(-0.373718\pi\)
0.386400 + 0.922331i \(0.373718\pi\)
\(102\) 46505.6 153518.i 0.0438232 0.144664i
\(103\) 747900. 0.684435 0.342217 0.939621i \(-0.388822\pi\)
0.342217 + 0.939621i \(0.388822\pi\)
\(104\) −41891.2 + 34459.1i −0.0372411 + 0.0306340i
\(105\) 49467.8 50590.6i 0.0427322 0.0437020i
\(106\) 145763. 481173.i 0.122385 0.404002i
\(107\) 75240.9 0.0614190 0.0307095 0.999528i \(-0.490223\pi\)
0.0307095 + 0.999528i \(0.490223\pi\)
\(108\) 201677. + 134535.i 0.160098 + 0.106798i
\(109\) 905540. 0.699243 0.349622 0.936891i \(-0.386310\pi\)
0.349622 + 0.936891i \(0.386310\pi\)
\(110\) −479564. 872698.i −0.360303 0.655671i
\(111\) 1.11239e6i 0.813367i
\(112\) 57126.9 + 137326.i 0.0406618 + 0.0977463i
\(113\) 799166.i 0.553862i 0.960890 + 0.276931i \(0.0893173\pi\)
−0.960890 + 0.276931i \(0.910683\pi\)
\(114\) −328480. + 1.08433e6i −0.221715 + 0.731895i
\(115\) 116373. 119014.i 0.0765170 0.0782536i
\(116\) −757267. 505159.i −0.485149 0.323634i
\(117\) 25744.2i 0.0160739i
\(118\) 308466. 1.01827e6i 0.187742 0.619748i
\(119\) 46707.2i 0.0277168i
\(120\) 993990. + 85510.3i 0.575226 + 0.0494851i
\(121\) 779977. 0.440277
\(122\) −2.96451e6 898045.i −1.63258 0.494560i
\(123\) −1.06709e6 −0.573434
\(124\) −1.43847e6 + 2.15637e6i −0.754460 + 1.13099i
\(125\) −1.42676e6 1.33381e6i −0.730503 0.682909i
\(126\) 67559.1 + 20465.8i 0.0337732 + 0.0102310i
\(127\) −3.25779e6 −1.59042 −0.795209 0.606335i \(-0.792639\pi\)
−0.795209 + 0.606335i \(0.792639\pi\)
\(128\) −983674. + 1.85214e6i −0.469052 + 0.883170i
\(129\) 99633.3 0.0464126
\(130\) 51021.7 + 92848.0i 0.0232234 + 0.0422613i
\(131\) 208824.i 0.0928893i 0.998921 + 0.0464446i \(0.0147891\pi\)
−0.998921 + 0.0464446i \(0.985211\pi\)
\(132\) 551306. 826446.i 0.239702 0.359329i
\(133\) 329904.i 0.140227i
\(134\) −3.64711e6 1.10483e6i −1.51577 0.459177i
\(135\) 331037. 338550.i 0.134547 0.137601i
\(136\) 508605. 418371.i 0.202192 0.166320i
\(137\) 2.47104e6i 0.960987i 0.876998 + 0.480493i \(0.159542\pi\)
−0.876998 + 0.480493i \(0.840458\pi\)
\(138\) 158932. + 48145.7i 0.0604749 + 0.0183198i
\(139\) 1.93989e6i 0.722327i −0.932503 0.361163i \(-0.882380\pi\)
0.932503 0.361163i \(-0.117620\pi\)
\(140\) 284217. 60082.2i 0.103577 0.0218959i
\(141\) −880303. −0.314033
\(142\) −1.12049e6 + 3.69881e6i −0.391330 + 1.29181i
\(143\) 105496. 0.0360770
\(144\) 382291. + 918984.i 0.128028 + 0.307766i
\(145\) −1.24300e6 + 1.27121e6i −0.407724 + 0.416977i
\(146\) 1.51881e6 5.01370e6i 0.488029 1.61102i
\(147\) −1.81341e6 −0.570879
\(148\) 2.53441e6 3.79926e6i 0.781794 1.17196i
\(149\) 502061. 0.151774 0.0758870 0.997116i \(-0.475821\pi\)
0.0758870 + 0.997116i \(0.475821\pi\)
\(150\) 522941. 1.87707e6i 0.154946 0.556170i
\(151\) 3.91206e6i 1.13625i −0.822941 0.568127i \(-0.807668\pi\)
0.822941 0.568127i \(-0.192332\pi\)
\(152\) −3.59240e6 + 2.95505e6i −1.02295 + 0.841463i
\(153\) 312563.i 0.0872697i
\(154\) 83866.3 276848.i 0.0229628 0.0758019i
\(155\) 3.61984e6 + 3.53951e6i 0.972064 + 0.950492i
\(156\) −58654.5 + 87927.1i −0.0154500 + 0.0231606i
\(157\) 1.57181e6i 0.406163i 0.979162 + 0.203081i \(0.0650956\pi\)
−0.979162 + 0.203081i \(0.934904\pi\)
\(158\) −185986. + 613951.i −0.0471528 + 0.155655i
\(159\) 979670.i 0.243719i
\(160\) 3.20006e6 + 2.55672e6i 0.781266 + 0.624199i
\(161\) 48354.5 0.0115867
\(162\) 452103. + 136957.i 0.106339 + 0.0322135i
\(163\) 3.02276e6 0.697977 0.348989 0.937127i \(-0.386525\pi\)
0.348989 + 0.937127i \(0.386525\pi\)
\(164\) −3.64454e6 2.43120e6i −0.826249 0.551175i
\(165\) −1.38734e6 1.35655e6i −0.308837 0.301983i
\(166\) 7.93321e6 + 2.40323e6i 1.73430 + 0.525376i
\(167\) 1.71951e6 0.369194 0.184597 0.982814i \(-0.440902\pi\)
0.184597 + 0.982814i \(0.440902\pi\)
\(168\) 184114. + 223823.i 0.0388292 + 0.0472038i
\(169\) 4.81559e6 0.997675
\(170\) −619460. 1.12728e6i −0.126086 0.229448i
\(171\) 2.20771e6i 0.441523i
\(172\) 340289. + 227000.i 0.0668748 + 0.0446109i
\(173\) 6.03741e6i 1.16604i −0.812459 0.583019i \(-0.801871\pi\)
0.812459 0.583019i \(-0.198129\pi\)
\(174\) −1.69758e6 514252.i −0.322243 0.0976177i
\(175\) −12731.2 567235.i −0.00237549 0.105840i
\(176\) 3.76588e6 1.56658e6i 0.690762 0.287352i
\(177\) 2.07319e6i 0.373869i
\(178\) 9.20453e6 + 2.78835e6i 1.63208 + 0.494410i
\(179\) 1.11888e7i 1.95086i 0.220311 + 0.975430i \(0.429293\pi\)
−0.220311 + 0.975430i \(0.570707\pi\)
\(180\) 1.90197e6 402068.i 0.326126 0.0689417i
\(181\) −5.54253e6 −0.934700 −0.467350 0.884072i \(-0.654791\pi\)
−0.467350 + 0.884072i \(0.654791\pi\)
\(182\) −8922.70 + 29454.4i −0.00148007 + 0.00488581i
\(183\) −6.03575e6 −0.984867
\(184\) 433126. + 526542.i 0.0695282 + 0.0845239i
\(185\) −6.37773e6 6.23619e6i −1.00728 0.984927i
\(186\) −1.46437e6 + 4.83397e6i −0.227568 + 0.751217i
\(187\) −1.28084e6 −0.195872
\(188\) −3.00660e6 2.00565e6i −0.452483 0.301843i
\(189\) 137550. 0.0203740
\(190\) 4.37539e6 + 7.96223e6i 0.637905 + 1.16084i
\(191\) 4.62646e6i 0.663970i 0.943285 + 0.331985i \(0.107718\pi\)
−0.943285 + 0.331985i \(0.892282\pi\)
\(192\) −788093. + 4.00971e6i −0.111346 + 0.566512i
\(193\) 7.66995e6i 1.06689i −0.845834 0.533446i \(-0.820897\pi\)
0.845834 0.533446i \(-0.179103\pi\)
\(194\) −3.37893e6 + 1.11541e7i −0.462779 + 1.52766i
\(195\) 147601. + 144326.i 0.0199061 + 0.0194643i
\(196\) −6.19355e6 4.13160e6i −0.822567 0.548719i
\(197\) 1.07837e7i 1.41049i −0.708963 0.705246i \(-0.750837\pi\)
0.708963 0.705246i \(-0.249163\pi\)
\(198\) 561231. 1.85266e6i 0.0723012 0.238671i
\(199\) 9.05284e6i 1.14875i −0.818592 0.574375i \(-0.805245\pi\)
0.818592 0.574375i \(-0.194755\pi\)
\(200\) 6.06271e6 5.21954e6i 0.757839 0.652442i
\(201\) −7.42552e6 −0.914406
\(202\) 6.09615e6 + 1.84672e6i 0.739608 + 0.224051i
\(203\) −516482. −0.0617401
\(204\) 712131. 1.06753e6i 0.0838821 0.125745i
\(205\) −5.98223e6 + 6.11800e6i −0.694387 + 0.710147i
\(206\) 5.72623e6 + 1.73466e6i 0.655038 + 0.198432i
\(207\) 323587. 0.0364821
\(208\) −400659. + 166671.i −0.0445231 + 0.0185213i
\(209\) 9.04690e6 0.990971
\(210\) 496084. 272607.i 0.0535670 0.0294361i
\(211\) 1.08423e7i 1.15418i 0.816680 + 0.577090i \(0.195812\pi\)
−0.816680 + 0.577090i \(0.804188\pi\)
\(212\) 2.23204e6 3.34598e6i 0.234258 0.351169i
\(213\) 7.53079e6i 0.779295i
\(214\) 576075. + 174512.i 0.0587811 + 0.0178067i
\(215\) 558558. 571235.i 0.0562022 0.0574777i
\(216\) 1.23208e6 + 1.49782e6i 0.122258 + 0.148627i
\(217\) 1.47072e6i 0.143929i
\(218\) 6.93318e6 + 2.10028e6i 0.669211 + 0.202726i
\(219\) 1.02079e7i 0.971862i
\(220\) −1.64762e6 7.79402e6i −0.154735 0.731970i
\(221\) 136271. 0.0126249
\(222\) 2.58004e6 8.51688e6i 0.235813 0.778433i
\(223\) −6.18382e6 −0.557625 −0.278813 0.960345i \(-0.589941\pi\)
−0.278813 + 0.960345i \(0.589941\pi\)
\(224\) 118875. + 1.18393e6i 0.0105766 + 0.105337i
\(225\) −85196.4 3.79592e6i −0.00747952 0.333249i
\(226\) −1.85356e6 + 6.11874e6i −0.160576 + 0.530074i
\(227\) 1.17330e7 1.00307 0.501534 0.865138i \(-0.332769\pi\)
0.501534 + 0.865138i \(0.332769\pi\)
\(228\) −5.02995e6 + 7.54023e6i −0.424384 + 0.636180i
\(229\) 1.95291e7 1.62621 0.813105 0.582116i \(-0.197775\pi\)
0.813105 + 0.582116i \(0.197775\pi\)
\(230\) 1.16703e6 641307.i 0.0959180 0.0527087i
\(231\) 563664.i 0.0457282i
\(232\) −4.62629e6 5.62409e6i −0.370484 0.450389i
\(233\) 2.06220e7i 1.63029i 0.579260 + 0.815143i \(0.303342\pi\)
−0.579260 + 0.815143i \(0.696658\pi\)
\(234\) −59710.4 + 197108.i −0.00466018 + 0.0153836i
\(235\) −4.93510e6 + 5.04711e6i −0.380270 + 0.388901i
\(236\) 4.72348e6 7.08081e6i 0.359357 0.538700i
\(237\) 1.25001e6i 0.0939003i
\(238\) 108331. 357609.i 0.00803570 0.0265264i
\(239\) 1.82892e7i 1.33968i −0.742506 0.669840i \(-0.766363\pi\)
0.742506 0.669840i \(-0.233637\pi\)
\(240\) 7.41206e6 + 2.96013e6i 0.536173 + 0.214130i
\(241\) −1.88580e7 −1.34724 −0.673620 0.739078i \(-0.735262\pi\)
−0.673620 + 0.739078i \(0.735262\pi\)
\(242\) 5.97182e6 + 1.80906e6i 0.421367 + 0.127646i
\(243\) 920483. 0.0641500
\(244\) −2.06146e7 1.37516e7i −1.41907 0.946637i
\(245\) −1.01662e7 + 1.03970e7i −0.691293 + 0.706983i
\(246\) −8.17004e6 2.47497e6i −0.548806 0.166251i
\(247\) −962517. −0.0638731
\(248\) −1.60149e7 + 1.31737e7i −1.04995 + 0.863678i
\(249\) 1.61520e7 1.04623
\(250\) −7.83029e6 1.35214e7i −0.501139 0.865367i
\(251\) 1.05499e7i 0.667154i −0.942723 0.333577i \(-0.891744\pi\)
0.942723 0.333577i \(-0.108256\pi\)
\(252\) 469792. + 313389.i 0.0293565 + 0.0195831i
\(253\) 1.32602e6i 0.0818818i
\(254\) −2.49429e7 7.55602e6i −1.52211 0.461096i
\(255\) −1.79204e6 1.75227e6i −0.108076 0.105677i
\(256\) −1.18272e7 + 1.18992e7i −0.704957 + 0.709250i
\(257\) 343840.i 0.0202562i 0.999949 + 0.0101281i \(0.00322393\pi\)
−0.999949 + 0.0101281i \(0.996776\pi\)
\(258\) 762833. + 231087.i 0.0444192 + 0.0134560i
\(259\) 2.59122e6i 0.149144i
\(260\) 175294. + 829220.i 0.00997348 + 0.0471791i
\(261\) −3.45628e6 −0.194396
\(262\) −484339. + 1.59884e6i −0.0269306 + 0.0888997i
\(263\) −1.68620e7 −0.926920 −0.463460 0.886118i \(-0.653392\pi\)
−0.463460 + 0.886118i \(0.653392\pi\)
\(264\) 6.13786e6 5.04892e6i 0.333584 0.274401i
\(265\) −5.61682e6 5.49217e6i −0.301823 0.295125i
\(266\) −765171. + 2.52588e6i −0.0406549 + 0.134205i
\(267\) 1.87405e7 0.984569
\(268\) −2.53612e7 1.69180e7i −1.31755 0.878911i
\(269\) 2.06767e7 1.06224 0.531121 0.847296i \(-0.321771\pi\)
0.531121 + 0.847296i \(0.321771\pi\)
\(270\) 3.31978e6 1.82428e6i 0.168662 0.0926830i
\(271\) 1.38151e7i 0.694138i 0.937840 + 0.347069i \(0.112823\pi\)
−0.937840 + 0.347069i \(0.887177\pi\)
\(272\) 4.86444e6 2.02358e6i 0.241728 0.100557i
\(273\) 59969.3i 0.00294741i
\(274\) −5.73125e6 + 1.89193e7i −0.278611 + 0.919713i
\(275\) −1.55552e7 + 349124.i −0.747958 + 0.0167873i
\(276\) 1.10518e6 + 737246.i 0.0525662 + 0.0350659i
\(277\) 2.13872e6i 0.100627i 0.998733 + 0.0503134i \(0.0160220\pi\)
−0.998733 + 0.0503134i \(0.983978\pi\)
\(278\) 4.49934e6 1.48526e7i 0.209418 0.691303i
\(279\) 9.84198e6i 0.453179i
\(280\) 2.31543e6 + 199190.i 0.105477 + 0.00907389i
\(281\) 1.43930e7 0.648685 0.324342 0.945940i \(-0.394857\pi\)
0.324342 + 0.945940i \(0.394857\pi\)
\(282\) −6.73995e6 2.04175e6i −0.300545 0.0910448i
\(283\) 2.56055e7 1.12973 0.564865 0.825183i \(-0.308928\pi\)
0.564865 + 0.825183i \(0.308928\pi\)
\(284\) −1.71578e7 + 2.57208e7i −0.749045 + 1.12287i
\(285\) 1.26576e7 + 1.23767e7i 0.546786 + 0.534652i
\(286\) 807724. + 244686.i 0.0345275 + 0.0104595i
\(287\) −2.48570e6 −0.105148
\(288\) 795509. + 7.92279e6i 0.0333018 + 0.331666i
\(289\) 2.24831e7 0.931456
\(290\) −1.24653e7 + 6.84991e6i −0.511103 + 0.280861i
\(291\) 2.27097e7i 0.921579i
\(292\) 2.32573e7 3.48643e7i 0.934137 1.40033i
\(293\) 8.11800e6i 0.322735i 0.986894 + 0.161367i \(0.0515904\pi\)
−0.986894 + 0.161367i \(0.948410\pi\)
\(294\) −1.38842e7 4.20598e6i −0.546360 0.165510i
\(295\) −1.18864e7 1.16226e7i −0.463003 0.452728i
\(296\) 2.82164e7 2.32104e7i 1.08799 0.894968i
\(297\) 3.77202e6i 0.143981i
\(298\) 3.84398e6 + 1.16447e6i 0.145255 + 0.0440026i
\(299\) 141077.i 0.00527769i
\(300\) 8.35748e6 1.31587e7i 0.309536 0.487361i
\(301\) 232089. 0.00851049
\(302\) 9.07353e6 2.99523e7i 0.329424 1.08745i
\(303\) 1.24118e7 0.446176
\(304\) −3.43587e7 + 1.42930e7i −1.22297 + 0.508748i
\(305\) −3.38372e7 + 3.46052e7i −1.19260 + 1.21967i
\(306\) 724950. 2.39311e6i 0.0253014 0.0835215i
\(307\) 2.07910e7 0.718555 0.359277 0.933231i \(-0.383023\pi\)
0.359277 + 0.933231i \(0.383023\pi\)
\(308\) 1.28423e6 1.92515e6i 0.0439532 0.0658888i
\(309\) 1.16586e7 0.395159
\(310\) 1.95055e7 + 3.54957e7i 0.654746 + 1.19149i
\(311\) 5.61955e7i 1.86819i −0.357026 0.934094i \(-0.616209\pi\)
0.357026 0.934094i \(-0.383791\pi\)
\(312\) −653019. + 537164.i −0.0215012 + 0.0176865i
\(313\) 6.05170e6i 0.197353i −0.995120 0.0986766i \(-0.968539\pi\)
0.995120 0.0986766i \(-0.0314609\pi\)
\(314\) −3.64560e6 + 1.20344e7i −0.117755 + 0.388718i
\(315\) 771127. 788629.i 0.0246714 0.0252314i
\(316\) −2.84796e6 + 4.26929e6i −0.0902553 + 0.135299i
\(317\) 8.06566e6i 0.253199i 0.991954 + 0.126600i \(0.0404063\pi\)
−0.991954 + 0.126600i \(0.959594\pi\)
\(318\) 2.27222e6 7.50075e6i 0.0706592 0.233251i
\(319\) 1.41634e7i 0.436310i
\(320\) 1.85710e7 + 2.69974e7i 0.566742 + 0.823895i
\(321\) 1.17289e6 0.0354603
\(322\) 370221. + 112152.i 0.0110890 + 0.00335923i
\(323\) 1.16860e7 0.346784
\(324\) 3.14383e6 + 2.09719e6i 0.0924323 + 0.0616599i
\(325\) 1.65495e6 37144.0i 0.0482096 0.00108203i
\(326\) 2.31435e7 + 7.01091e6i 0.667999 + 0.202359i
\(327\) 1.41160e7 0.403708
\(328\) −2.22652e7 2.70673e7i −0.630964 0.767050i
\(329\) −2.05060e6 −0.0575829
\(330\) −7.47566e6 1.36040e7i −0.208021 0.378552i
\(331\) 6.79995e6i 0.187509i 0.995595 + 0.0937545i \(0.0298869\pi\)
−0.995595 + 0.0937545i \(0.970113\pi\)
\(332\) 5.51659e7 + 3.68001e7i 1.50750 + 1.00562i
\(333\) 1.73404e7i 0.469598i
\(334\) 1.31652e7 + 3.98817e6i 0.353337 + 0.107037i
\(335\) −4.16285e7 + 4.25733e7i −1.10728 + 1.13241i
\(336\) 890520. + 2.14071e6i 0.0234761 + 0.0564338i
\(337\) 4.63328e7i 1.21059i −0.796000 0.605297i \(-0.793054\pi\)
0.796000 0.605297i \(-0.206946\pi\)
\(338\) 3.68701e7 + 1.11691e7i 0.954825 + 0.289247i
\(339\) 1.24578e7i 0.319772i
\(340\) −2.12826e6 1.00677e7i −0.0541487 0.256148i
\(341\) 4.03312e7 1.01713
\(342\) −5.12049e6 + 1.69031e7i −0.128007 + 0.422560i
\(343\) −8.49631e6 −0.210546
\(344\) 2.07889e6 + 2.52726e6i 0.0510689 + 0.0620834i
\(345\) 1.81407e6 1.85524e6i 0.0441771 0.0451797i
\(346\) 1.40030e7 4.62249e7i 0.338059 1.11596i
\(347\) 6.18772e6 0.148096 0.0740478 0.997255i \(-0.476408\pi\)
0.0740478 + 0.997255i \(0.476408\pi\)
\(348\) −1.18046e7 7.87465e6i −0.280101 0.186850i
\(349\) −9.57198e6 −0.225178 −0.112589 0.993642i \(-0.535914\pi\)
−0.112589 + 0.993642i \(0.535914\pi\)
\(350\) 1.21816e6 4.37251e6i 0.0284118 0.101983i
\(351\) 401313.i 0.00928029i
\(352\) 3.24666e7 3.25989e6i 0.744403 0.0747439i
\(353\) 4.38759e7i 0.997474i −0.866753 0.498737i \(-0.833797\pi\)
0.866753 0.498737i \(-0.166203\pi\)
\(354\) 4.80850e6 1.58732e7i 0.108393 0.357812i
\(355\) 4.31769e7 + 4.22187e7i 0.965086 + 0.943669i
\(356\) 6.40064e7 + 4.26975e7i 1.41864 + 0.946351i
\(357\) 728094.i 0.0160023i
\(358\) −2.59511e7 + 8.56663e7i −0.565596 + 1.86707i
\(359\) 6.69337e7i 1.44664i −0.690511 0.723322i \(-0.742614\pi\)
0.690511 0.723322i \(-0.257386\pi\)
\(360\) 1.54948e7 + 1.33297e6i 0.332107 + 0.0285702i
\(361\) −3.54953e7 −0.754482
\(362\) −4.24359e7 1.28552e7i −0.894555 0.270990i
\(363\) 1.21586e7 0.254194
\(364\) −136632. + 204820.i −0.00283300 + 0.00424686i
\(365\) −5.85258e7 5.72270e7i −1.20356 1.17685i
\(366\) −4.62121e7 1.39991e7i −0.942568 0.285534i
\(367\) −5.48058e7 −1.10874 −0.554369 0.832271i \(-0.687040\pi\)
−0.554369 + 0.832271i \(0.687040\pi\)
\(368\) 2.09494e6 + 5.03600e6i 0.0420367 + 0.101051i
\(369\) −1.66342e7 −0.331073
\(370\) −3.43664e7 6.25391e7i −0.678467 1.23466i
\(371\) 2.28207e6i 0.0446897i
\(372\) −2.24236e7 + 3.36144e7i −0.435588 + 0.652976i
\(373\) 3.78565e7i 0.729482i 0.931109 + 0.364741i \(0.118842\pi\)
−0.931109 + 0.364741i \(0.881158\pi\)
\(374\) −9.80666e6 2.97075e6i −0.187459 0.0567874i
\(375\) −2.22411e7 2.07920e7i −0.421756 0.394278i
\(376\) −1.83679e7 2.23294e7i −0.345538 0.420063i
\(377\) 1.50687e6i 0.0281224i
\(378\) 1.05314e6 + 319031.i 0.0194990 + 0.00590687i
\(379\) 3.60927e7i 0.662982i 0.943458 + 0.331491i \(0.107552\pi\)
−0.943458 + 0.331491i \(0.892448\pi\)
\(380\) 1.50324e7 + 7.11102e7i 0.273954 + 1.29593i
\(381\) −5.07839e7 −0.918229
\(382\) −1.07305e7 + 3.54220e7i −0.192499 + 0.635453i
\(383\) −5.97603e7 −1.06369 −0.531847 0.846841i \(-0.678502\pi\)
−0.531847 + 0.846841i \(0.678502\pi\)
\(384\) −1.53340e7 + 2.88720e7i −0.270807 + 0.509899i
\(385\) −3.23170e6 3.15998e6i −0.0566303 0.0553735i
\(386\) 1.77895e7 5.87243e7i 0.309315 1.02107i
\(387\) 1.55313e6 0.0267963
\(388\) −5.17409e7 + 7.75630e7i −0.885806 + 1.32788i
\(389\) −6.96398e7 −1.18306 −0.591532 0.806281i \(-0.701477\pi\)
−0.591532 + 0.806281i \(0.701477\pi\)
\(390\) 795350. + 1.44736e6i 0.0134080 + 0.0243996i
\(391\) 1.71284e6i 0.0286540i
\(392\) −3.78376e7 4.59984e7i −0.628153 0.763632i
\(393\) 3.25524e6i 0.0536297i
\(394\) 2.50115e7 8.25646e7i 0.408932 1.34991i
\(395\) 7.16675e6 + 7.00770e6i 0.116287 + 0.113706i
\(396\) 8.59402e6 1.28830e7i 0.138392 0.207459i
\(397\) 2.84760e7i 0.455101i 0.973766 + 0.227551i \(0.0730717\pi\)
−0.973766 + 0.227551i \(0.926928\pi\)
\(398\) 2.09969e7 6.93122e7i 0.333047 1.09941i
\(399\) 5.14270e6i 0.0809603i
\(400\) 5.85246e7 2.59012e7i 0.914447 0.404706i
\(401\) −1.00700e6 −0.0156170 −0.00780848 0.999970i \(-0.502486\pi\)
−0.00780848 + 0.999970i \(0.502486\pi\)
\(402\) −5.68528e7 1.72226e7i −0.875132 0.265106i
\(403\) −4.29091e6 −0.0655593
\(404\) 4.23914e7 + 2.82785e7i 0.642885 + 0.428857i
\(405\) 5.16036e6 5.27747e6i 0.0776809 0.0794440i
\(406\) −3.95440e6 1.19791e6i −0.0590884 0.0178998i
\(407\) −7.10587e7 −1.05398
\(408\) 7.92837e6 6.52176e6i 0.116736 0.0960251i
\(409\) 3.61611e7 0.528532 0.264266 0.964450i \(-0.414870\pi\)
0.264266 + 0.964450i \(0.414870\pi\)
\(410\) −5.99923e7 + 3.29669e7i −0.870450 + 0.478329i
\(411\) 3.85196e7i 0.554826i
\(412\) 3.98190e7 + 2.65625e7i 0.569375 + 0.379819i
\(413\) 4.82936e6i 0.0685550i
\(414\) 2.47751e6 + 750517.i 0.0349152 + 0.0105769i
\(415\) 9.05505e7 9.26057e7i 1.26691 1.29567i
\(416\) −3.45418e6 + 346826.i −0.0479805 + 0.00481762i
\(417\) 3.02400e7i 0.417036i
\(418\) 6.92667e7 + 2.09831e7i 0.948409 + 0.287304i
\(419\) 7.71961e7i 1.04943i 0.851278 + 0.524715i \(0.175828\pi\)
−0.851278 + 0.524715i \(0.824172\pi\)
\(420\) 4.43050e6 936589.i 0.0598005 0.0126416i
\(421\) 1.80523e6 0.0241928 0.0120964 0.999927i \(-0.496150\pi\)
0.0120964 + 0.999927i \(0.496150\pi\)
\(422\) −2.51473e7 + 8.30130e7i −0.334622 + 1.10461i
\(423\) −1.37226e7 −0.181307
\(424\) 2.48500e7 2.04412e7i 0.326008 0.268170i
\(425\) −2.00929e7 + 450969.i −0.261743 + 0.00587462i
\(426\) −1.74667e7 + 5.76588e7i −0.225934 + 0.745825i
\(427\) −1.40598e7 −0.180591
\(428\) 4.00590e6 + 2.67226e6i 0.0510939 + 0.0340838i
\(429\) 1.64453e6 0.0208290
\(430\) 5.60145e6 3.07810e6i 0.0704523 0.0387149i
\(431\) 8.38390e7i 1.04716i −0.851976 0.523581i \(-0.824596\pi\)
0.851976 0.523581i \(-0.175404\pi\)
\(432\) 5.95933e6 + 1.43255e7i 0.0739173 + 0.177689i
\(433\) 3.21731e7i 0.396305i 0.980171 + 0.198153i \(0.0634942\pi\)
−0.980171 + 0.198153i \(0.936506\pi\)
\(434\) −3.41114e6 + 1.12604e7i −0.0417283 + 0.137748i
\(435\) −1.93764e7 + 1.98162e7i −0.235399 + 0.240742i
\(436\) 4.82119e7 + 3.21613e7i 0.581694 + 0.388037i
\(437\) 1.20982e7i 0.144969i
\(438\) 2.36760e7 7.81559e7i 0.281764 0.930121i
\(439\) 1.14441e8i 1.35266i −0.736597 0.676332i \(-0.763569\pi\)
0.736597 0.676332i \(-0.236431\pi\)
\(440\) 5.46235e6 6.34956e7i 0.0641242 0.745393i
\(441\) −2.82683e7 −0.329597
\(442\) 1.04335e6 + 316064.i 0.0120827 + 0.00366023i
\(443\) 3.67575e7 0.422799 0.211400 0.977400i \(-0.432198\pi\)
0.211400 + 0.977400i \(0.432198\pi\)
\(444\) 3.95076e7 5.92246e7i 0.451369 0.676633i
\(445\) 1.05062e8 1.07446e8i 1.19224 1.21930i
\(446\) −4.73459e7 1.43426e7i −0.533676 0.161668i
\(447\) 7.82636e6 0.0876268
\(448\) −1.83581e6 + 9.34033e6i −0.0204170 + 0.103879i
\(449\) 4.64770e6 0.0513451 0.0256725 0.999670i \(-0.491827\pi\)
0.0256725 + 0.999670i \(0.491827\pi\)
\(450\) 8.15185e6 2.92607e7i 0.0894579 0.321105i
\(451\) 6.81649e7i 0.743072i
\(452\) −2.83832e7 + 4.25484e7i −0.307360 + 0.460753i
\(453\) 6.09830e7i 0.656016i
\(454\) 8.98323e7 + 2.72131e7i 0.959987 + 0.290811i
\(455\) 343827. + 336196.i 0.00365011 + 0.00356910i
\(456\) −5.59999e7 + 4.60647e7i −0.590599 + 0.485819i
\(457\) 1.37829e8i 1.44408i 0.691851 + 0.722040i \(0.256795\pi\)
−0.691851 + 0.722040i \(0.743205\pi\)
\(458\) 1.49523e8 + 4.52954e7i 1.55637 + 0.471474i
\(459\) 4.87238e6i 0.0503852i
\(460\) 1.04227e7 2.20332e6i 0.107080 0.0226362i
\(461\) 6.11454e7 0.624110 0.312055 0.950064i \(-0.398983\pi\)
0.312055 + 0.950064i \(0.398983\pi\)
\(462\) 1.30735e6 4.31564e6i 0.0132576 0.0437642i
\(463\) 8.92817e6 0.0899538 0.0449769 0.998988i \(-0.485679\pi\)
0.0449769 + 0.998988i \(0.485679\pi\)
\(464\) −2.23764e7 5.37904e7i −0.223994 0.538456i
\(465\) 5.64278e7 + 5.51755e7i 0.561221 + 0.548767i
\(466\) −4.78302e7 + 1.57891e8i −0.472655 + 1.56027i
\(467\) 9.31715e7 0.914814 0.457407 0.889258i \(-0.348778\pi\)
0.457407 + 0.889258i \(0.348778\pi\)
\(468\) −914334. + 1.37065e6i −0.00892005 + 0.0133718i
\(469\) −1.72972e7 −0.167671
\(470\) −4.94912e7 + 2.71964e7i −0.476689 + 0.261949i
\(471\) 2.45020e7i 0.234498i
\(472\) 5.25879e7 4.32580e7i 0.500103 0.411378i
\(473\) 6.36453e6i 0.0601427i
\(474\) −2.89923e6 + 9.57055e6i −0.0272237 + 0.0898673i
\(475\) 1.41921e8 3.18530e6i 1.32424 0.0297214i
\(476\) 1.65886e6 2.48674e6i 0.0153811 0.0230574i
\(477\) 1.52715e7i 0.140711i
\(478\) 4.24195e7 1.40030e8i 0.388402 1.28214i
\(479\) 7.79984e7i 0.709707i 0.934922 + 0.354854i \(0.115469\pi\)
−0.934922 + 0.354854i \(0.884531\pi\)
\(480\) 4.98841e7 + 3.98553e7i 0.451064 + 0.360381i
\(481\) 7.56007e6 0.0679345
\(482\) −1.44385e8 4.37388e7i −1.28938 0.390594i
\(483\) 753772. 0.00668958
\(484\) 4.15268e7 + 2.77018e7i 0.366262 + 0.244327i
\(485\) 1.30203e8 + 1.27314e8i 1.14129 + 1.11596i
\(486\) 7.04759e6 + 2.13494e6i 0.0613948 + 0.0185985i
\(487\) −1.84100e8 −1.59392 −0.796962 0.604030i \(-0.793561\pi\)
−0.796962 + 0.604030i \(0.793561\pi\)
\(488\) −1.25938e8 1.53101e8i −1.08367 1.31740i
\(489\) 4.71202e7 0.402977
\(490\) −1.01951e8 + 5.60241e7i −0.866572 + 0.476197i
\(491\) 1.36182e8i 1.15047i 0.817987 + 0.575236i \(0.195090\pi\)
−0.817987 + 0.575236i \(0.804910\pi\)
\(492\) −5.68127e7 3.78987e7i −0.477035 0.318221i
\(493\) 1.82951e7i 0.152684i
\(494\) −7.36942e6 2.23244e6i −0.0611297 0.0185182i
\(495\) −2.16264e7 2.11465e7i −0.178307 0.174350i
\(496\) −1.53171e8 + 6.37183e7i −1.25526 + 0.522179i
\(497\) 1.75424e7i 0.142896i
\(498\) 1.23666e8 + 3.74626e7i 1.00130 + 0.303326i
\(499\) 5.25199e7i 0.422690i 0.977412 + 0.211345i \(0.0677844\pi\)
−0.977412 + 0.211345i \(0.932216\pi\)
\(500\) −2.85908e7 1.21686e8i −0.228726 0.973491i
\(501\) 2.68044e7 0.213154
\(502\) 2.44691e7 8.07741e7i 0.193422 0.638500i
\(503\) 7.30908e7 0.574326 0.287163 0.957882i \(-0.407288\pi\)
0.287163 + 0.957882i \(0.407288\pi\)
\(504\) 2.87005e6 + 3.48906e6i 0.0224180 + 0.0272531i
\(505\) 6.95822e7 7.11614e7i 0.540286 0.552549i
\(506\) 3.07552e6 1.01525e7i 0.0237393 0.0783650i
\(507\) 7.50675e7 0.576008
\(508\) −1.73448e8 1.15704e8i −1.32305 0.882585i
\(509\) −1.93773e8 −1.46940 −0.734699 0.678393i \(-0.762677\pi\)
−0.734699 + 0.678393i \(0.762677\pi\)
\(510\) −9.65643e6 1.75725e7i −0.0727957 0.132472i
\(511\) 2.37786e7i 0.178207i
\(512\) −1.18153e8 + 6.36737e7i −0.880306 + 0.474406i
\(513\) 3.44148e7i 0.254913i
\(514\) −797494. + 2.63258e6i −0.00587270 + 0.0193862i
\(515\) 6.53598e7 6.68432e7i 0.478508 0.489368i
\(516\) 5.30458e6 + 3.53859e6i 0.0386102 + 0.0257561i
\(517\) 5.62333e7i 0.406932i
\(518\) 6.01001e6 1.98395e7i 0.0432400 0.142738i
\(519\) 9.41139e7i 0.673212i
\(520\) −581150. + 6.75542e6i −0.00413312 + 0.0480443i
\(521\) 2.38564e8 1.68691 0.843453 0.537203i \(-0.180519\pi\)
0.843453 + 0.537203i \(0.180519\pi\)
\(522\) −2.64627e7 8.01640e6i −0.186047 0.0563596i
\(523\) 4.75494e7 0.332384 0.166192 0.986093i \(-0.446853\pi\)
0.166192 + 0.986093i \(0.446853\pi\)
\(524\) −7.41660e6 + 1.11180e7i −0.0515479 + 0.0772738i
\(525\) −198459. 8.84233e6i −0.00137149 0.0611067i
\(526\) −1.29102e8 3.91093e7i −0.887109 0.268734i
\(527\) 5.20964e7 0.355939
\(528\) 5.87042e7 2.44206e7i 0.398811 0.165903i
\(529\) −1.46263e8 −0.988022
\(530\) −3.02663e7 5.50777e7i −0.203297 0.369955i
\(531\) 3.23179e7i 0.215854i
\(532\) −1.17169e7 + 1.75644e7i −0.0778177 + 0.116654i
\(533\) 7.25219e6i 0.0478947i
\(534\) 1.43484e8 + 4.34661e7i 0.942282 + 0.285448i
\(535\) 6.57539e6 6.72462e6i 0.0429398 0.0439144i
\(536\) −1.54937e8 1.88353e8i −1.00614 1.22315i
\(537\) 1.74417e8i 1.12633i
\(538\) 1.58309e8 + 4.79568e7i 1.01662 + 0.307967i
\(539\) 1.15840e8i 0.739761i
\(540\) 2.96487e7 6.26762e6i 0.188289 0.0398035i
\(541\) 7.93945e6 0.0501417 0.0250708 0.999686i \(-0.492019\pi\)
0.0250708 + 0.999686i \(0.492019\pi\)
\(542\) −3.20423e7 + 1.05774e8i −0.201246 + 0.664325i
\(543\) −8.63995e7 −0.539649
\(544\) 4.19376e7 4.21086e6i 0.260499 0.0261561i
\(545\) 7.91361e7 8.09322e7i 0.488861 0.499956i
\(546\) −139091. + 459149.i −0.000854519 + 0.00282082i
\(547\) −2.71214e8 −1.65711 −0.828554 0.559909i \(-0.810836\pi\)
−0.828554 + 0.559909i \(0.810836\pi\)
\(548\) −8.77616e7 + 1.31561e8i −0.533289 + 0.799436i
\(549\) −9.40880e7 −0.568613
\(550\) −1.19907e8 3.34052e7i −0.720701 0.200783i
\(551\) 1.29222e8i 0.772473i
\(552\) 6.75177e6 + 8.20798e6i 0.0401421 + 0.0487999i
\(553\) 2.91180e6i 0.0172181i
\(554\) −4.96048e6 + 1.63749e7i −0.0291739 + 0.0963049i
\(555\) −9.94189e7 9.72126e7i −0.581554 0.568648i
\(556\) 6.88975e7 1.03282e8i 0.400847 0.600897i
\(557\) 2.95321e7i 0.170895i 0.996343 + 0.0854474i \(0.0272320\pi\)
−0.996343 + 0.0854474i \(0.972768\pi\)
\(558\) −2.28272e7 + 7.53542e7i −0.131386 + 0.433715i
\(559\) 677134.i 0.00387650i
\(560\) 1.72659e7 + 6.89542e6i 0.0983160 + 0.0392642i
\(561\) −1.99664e7 −0.113087
\(562\) 1.10199e8 + 3.33828e7i 0.620824 + 0.188068i
\(563\) 3.69382e7 0.206991 0.103495 0.994630i \(-0.466997\pi\)
0.103495 + 0.994630i \(0.466997\pi\)
\(564\) −4.68682e7 3.12649e7i −0.261241 0.174269i
\(565\) 7.14250e7 + 6.98399e7i 0.396009 + 0.387221i
\(566\) 1.96046e8 + 5.93888e7i 1.08121 + 0.327533i
\(567\) 2.14420e6 0.0117629
\(568\) −1.91023e8 + 1.57133e8i −1.04242 + 0.857478i
\(569\) −4.40705e7 −0.239227 −0.119614 0.992821i \(-0.538166\pi\)
−0.119614 + 0.992821i \(0.538166\pi\)
\(570\) 6.82056e7 + 1.24119e8i 0.368295 + 0.670214i
\(571\) 1.86429e8i 1.00139i −0.865623 0.500697i \(-0.833077\pi\)
0.865623 0.500697i \(-0.166923\pi\)
\(572\) 5.61674e6 + 3.74682e6i 0.0300121 + 0.0200205i
\(573\) 7.21193e7i 0.383343i
\(574\) −1.90315e7 5.76526e6i −0.100632 0.0304848i
\(575\) −466873. 2.08015e7i −0.00245581 0.109419i
\(576\) −1.22852e7 + 6.25051e7i −0.0642855 + 0.327076i
\(577\) 9.75841e7i 0.507986i −0.967206 0.253993i \(-0.918256\pi\)
0.967206 0.253993i \(-0.0817440\pi\)
\(578\) 1.72140e8 + 5.21466e7i 0.891450 + 0.270049i
\(579\) 1.19563e8i 0.615971i
\(580\) −1.11327e8 + 2.35340e7i −0.570579 + 0.120618i
\(581\) 3.76250e7 0.191844
\(582\) −5.26723e7 + 1.73875e8i −0.267186 + 0.881998i
\(583\) −6.25808e7 −0.315817
\(584\) 2.58930e8 2.12992e8i 1.30000 1.06936i
\(585\) 2.30088e6 + 2.24981e6i 0.0114928 + 0.0112377i
\(586\) −1.88287e7 + 6.21547e7i −0.0935678 + 0.308874i
\(587\) 2.62750e8 1.29906 0.649529 0.760337i \(-0.274966\pi\)
0.649529 + 0.760337i \(0.274966\pi\)
\(588\) −9.65479e7 6.44053e7i −0.474910 0.316803i
\(589\) −3.67969e8 −1.80080
\(590\) −6.40499e7 1.16556e8i −0.311862 0.567518i
\(591\) 1.68102e8i 0.814347i
\(592\) 2.69870e8 1.12264e8i 1.30074 0.541097i
\(593\) 1.29038e8i 0.618806i 0.950931 + 0.309403i \(0.100129\pi\)
−0.950931 + 0.309403i \(0.899871\pi\)
\(594\) 8.74872e6 2.88801e7i 0.0417431 0.137797i
\(595\) −4.17444e6 4.08180e6i −0.0198174 0.0193776i
\(596\) 2.67302e7 + 1.78312e7i 0.126260 + 0.0842254i
\(597\) 1.41120e8i 0.663231i
\(598\) −327211. + 1.08015e6i −0.00153012 + 0.00505102i
\(599\) 3.16683e8i 1.47348i 0.676176 + 0.736740i \(0.263636\pi\)
−0.676176 + 0.736740i \(0.736364\pi\)
\(600\) 9.45083e7 8.13645e7i 0.437538 0.376688i
\(601\) −6.91171e7 −0.318392 −0.159196 0.987247i \(-0.550890\pi\)
−0.159196 + 0.987247i \(0.550890\pi\)
\(602\) 1.77697e6 + 538300.i 0.00814497 + 0.00246737i
\(603\) −1.15752e8 −0.527932
\(604\) 1.38941e8 2.08282e8i 0.630551 0.945239i
\(605\) 6.81631e7 6.97101e7i 0.307810 0.314796i
\(606\) 9.50296e7 + 2.87875e7i 0.427013 + 0.129356i
\(607\) −3.08877e8 −1.38108 −0.690542 0.723292i \(-0.742628\pi\)
−0.690542 + 0.723292i \(0.742628\pi\)
\(608\) −2.96215e8 + 2.97423e7i −1.31794 + 0.132332i
\(609\) −8.05116e6 −0.0356457
\(610\) −3.39334e8 + 1.86470e8i −1.49499 + 0.821524i
\(611\) 5.98277e6i 0.0262288i
\(612\) 1.11010e7 1.66412e7i 0.0484294 0.0725989i
\(613\) 2.65213e8i 1.15137i −0.817673 0.575683i \(-0.804736\pi\)
0.817673 0.575683i \(-0.195264\pi\)
\(614\) 1.59184e8 + 4.82220e7i 0.687693 + 0.208324i
\(615\) −9.32537e7 + 9.53702e7i −0.400904 + 0.410003i
\(616\) 1.42977e7 1.17611e7i 0.0611680 0.0503159i
\(617\) 3.68044e8i 1.56691i −0.621449 0.783455i \(-0.713456\pi\)
0.621449 0.783455i \(-0.286544\pi\)
\(618\) 8.92630e7 + 2.70407e7i 0.378187 + 0.114565i
\(619\) 9.59461e7i 0.404534i 0.979330 + 0.202267i \(0.0648309\pi\)
−0.979330 + 0.202267i \(0.935169\pi\)
\(620\) 6.70146e7 + 3.17010e8i 0.281187 + 1.33014i
\(621\) 5.04421e6 0.0210629
\(622\) 1.30338e8 4.30256e8i 0.541628 1.78795i
\(623\) 4.36546e7 0.180537
\(624\) −6.24566e6 + 2.59815e6i −0.0257054 + 0.0106933i
\(625\) −2.43895e8 + 1.09536e7i −0.998993 + 0.0448658i
\(626\) 1.40361e7 4.63342e7i 0.0572169 0.188877i
\(627\) 1.41027e8 0.572137
\(628\) −5.58244e7 + 8.36846e7i −0.225396 + 0.337883i
\(629\) −9.17876e7 −0.368835
\(630\) 7.73318e6 4.24953e6i 0.0309269 0.0169949i
\(631\) 2.46173e8i 0.979832i 0.871770 + 0.489916i \(0.162973\pi\)
−0.871770 + 0.489916i \(0.837027\pi\)
\(632\) −3.17072e7 + 2.60819e7i −0.125605 + 0.103321i
\(633\) 1.69015e8i 0.666367i
\(634\) −1.87073e7 + 6.17539e7i −0.0734078 + 0.242324i
\(635\) −2.84701e8 + 2.91163e8i −1.11191 + 1.13714i
\(636\) 3.47941e7 5.21587e7i 0.135249 0.202747i
\(637\) 1.23244e7i 0.0476813i
\(638\) −3.28502e7 + 1.08441e8i −0.126496 + 0.417571i
\(639\) 1.17393e8i 0.449926i
\(640\) 7.95700e7 + 2.49776e8i 0.303536 + 0.952820i
\(641\) −1.40284e8 −0.532641 −0.266321 0.963884i \(-0.585808\pi\)
−0.266321 + 0.963884i \(0.585808\pi\)
\(642\) 8.98012e6 + 2.72037e6i 0.0339373 + 0.0102807i
\(643\) 1.91656e8 0.720924 0.360462 0.932774i \(-0.382619\pi\)
0.360462 + 0.932774i \(0.382619\pi\)
\(644\) 2.57444e6 + 1.71736e6i 0.00963886 + 0.00642990i
\(645\) 8.70706e6 8.90468e6i 0.0324483 0.0331848i
\(646\) 8.94729e7 + 2.71042e7i 0.331890 + 0.100540i
\(647\) 4.33268e8 1.59972 0.799860 0.600187i \(-0.204907\pi\)
0.799860 + 0.600187i \(0.204907\pi\)
\(648\) 1.92063e7 + 2.33486e7i 0.0705859 + 0.0858097i
\(649\) −1.32435e8 −0.484470
\(650\) 1.27571e7 + 3.55405e6i 0.0464528 + 0.0129415i
\(651\) 2.29262e7i 0.0830977i
\(652\) 1.60935e8 + 1.07357e8i 0.580641 + 0.387335i
\(653\) 1.61233e8i 0.579048i −0.957171 0.289524i \(-0.906503\pi\)
0.957171 0.289524i \(-0.0934969\pi\)
\(654\) 1.08078e8 + 3.27402e7i 0.386369 + 0.117044i
\(655\) 1.86635e7 + 1.82493e7i 0.0664155 + 0.0649415i
\(656\) −1.07692e8 2.58879e8i −0.381480 0.917035i
\(657\) 1.59126e8i 0.561105i
\(658\) −1.57002e7 4.75611e6i −0.0551098 0.0166945i
\(659\) 2.39459e8i 0.836711i −0.908283 0.418356i \(-0.862607\pi\)
0.908283 0.418356i \(-0.137393\pi\)
\(660\) −2.56839e7 1.21497e8i −0.0893366 0.422603i
\(661\) 3.06751e8 1.06214 0.531071 0.847328i \(-0.321790\pi\)
0.531071 + 0.847328i \(0.321790\pi\)
\(662\) −1.57716e7 + 5.20632e7i −0.0543629 + 0.179456i
\(663\) 2.12426e6 0.00728899
\(664\) 3.37019e8 + 4.09707e8i 1.15120 + 1.39949i
\(665\) 2.94850e7 + 2.88307e7i 0.100262 + 0.0980370i
\(666\) 4.02188e7 1.32765e8i 0.136146 0.449429i
\(667\) −1.89403e7 −0.0638277
\(668\) 9.15483e7 + 6.10701e7i 0.307129 + 0.204880i
\(669\) −9.63963e7 −0.321945
\(670\) −4.17468e8 + 2.29407e8i −1.38803 + 0.762749i
\(671\) 3.85560e8i 1.27622i
\(672\) 1.85308e6 + 1.84556e7i 0.00610642 + 0.0608163i
\(673\) 4.75380e8i 1.55954i −0.626068 0.779769i \(-0.715337\pi\)
0.626068 0.779769i \(-0.284663\pi\)
\(674\) 1.07463e8 3.54742e8i 0.350977 1.15860i
\(675\) −1.32808e6 5.91725e7i −0.00431830 0.192402i
\(676\) 2.56387e8 + 1.71031e8i 0.829957 + 0.553649i
\(677\) 1.03793e8i 0.334505i −0.985914 0.167252i \(-0.946511\pi\)
0.985914 0.167252i \(-0.0534895\pi\)
\(678\) −2.88942e7 + 9.53816e7i −0.0927089 + 0.306038i
\(679\) 5.29007e7i 0.168986i
\(680\) 7.05581e6 8.20182e7i 0.0224399 0.260846i
\(681\) 1.82899e8 0.579122
\(682\) 3.08792e8 + 9.35430e7i 0.973448 + 0.294889i
\(683\) −1.94870e8 −0.611621 −0.305810 0.952092i \(-0.598927\pi\)
−0.305810 + 0.952092i \(0.598927\pi\)
\(684\) −7.84091e7 + 1.17541e8i −0.245018 + 0.367299i
\(685\) 2.20848e8 + 2.15947e8i 0.687102 + 0.671853i
\(686\) −6.50512e7 1.97061e7i −0.201504 0.0610419i
\(687\) 3.04429e8 0.938893
\(688\) 1.00552e7 + 2.41715e7i 0.0308762 + 0.0742229i
\(689\) 6.65810e6 0.0203560
\(690\) 1.81923e7 9.99699e6i 0.0553783 0.0304314i
\(691\) 4.76743e8i 1.44494i −0.691402 0.722471i \(-0.743006\pi\)
0.691402 0.722471i \(-0.256994\pi\)
\(692\) 2.14425e8 3.21438e8i 0.647079 0.970016i
\(693\) 8.78666e6i 0.0264012i
\(694\) 4.73757e7 + 1.43516e7i 0.141735 + 0.0429361i
\(695\) −1.73377e8 1.69529e8i −0.516461 0.504999i
\(696\) −7.21168e7 8.76708e7i −0.213899 0.260032i
\(697\) 8.80496e7i 0.260033i
\(698\) −7.32869e7 2.22010e7i −0.215506 0.0652838i
\(699\) 3.21466e8i 0.941246i
\(700\) 1.94682e7 3.06524e7i 0.0567585 0.0893655i
\(701\) −1.50161e8 −0.435915 −0.217958 0.975958i \(-0.569939\pi\)
−0.217958 + 0.975958i \(0.569939\pi\)
\(702\) −930793. + 3.07261e6i −0.00269055 + 0.00888170i
\(703\) 6.48317e8 1.86604
\(704\) 2.56138e8 + 5.03430e7i 0.734101 + 0.144285i
\(705\) −7.69306e7 + 7.86766e7i −0.219549 + 0.224532i
\(706\) 1.01764e8 3.35931e8i 0.289189 0.954633i
\(707\) 2.89124e7 0.0818136
\(708\) 7.36317e7 1.10379e8i 0.207475 0.311019i
\(709\) 2.76865e8 0.776836 0.388418 0.921483i \(-0.373022\pi\)
0.388418 + 0.921483i \(0.373022\pi\)
\(710\) 2.32659e8 + 4.23386e8i 0.650046 + 1.18294i
\(711\) 1.94857e7i 0.0542133i
\(712\) 3.91027e8 + 4.75364e8i 1.08335 + 1.31700i
\(713\) 5.39337e7i 0.148796i
\(714\) 1.68872e6 5.57458e6i 0.00463941 0.0153150i
\(715\) 9.21945e6 9.42870e6i 0.0252224 0.0257949i
\(716\) −3.97384e8 + 5.95705e8i −1.08261 + 1.62290i
\(717\) 2.85100e8i 0.773465i
\(718\) 1.55244e8 5.12472e8i 0.419413 1.38451i
\(719\) 4.05407e8i 1.09070i −0.838209 0.545349i \(-0.816397\pi\)
0.838209 0.545349i \(-0.183603\pi\)
\(720\) 1.15543e8 + 4.61439e7i 0.309560 + 0.123628i
\(721\) 2.71579e7 0.0724587
\(722\) −2.71766e8 8.23267e7i −0.722077 0.218740i
\(723\) −2.93967e8 −0.777829
\(724\) −2.95090e8 1.96849e8i −0.777569 0.518702i
\(725\) 4.98675e6 + 2.22184e8i 0.0130859 + 0.583042i
\(726\) 9.30915e7 + 2.82004e7i 0.243276 + 0.0736963i
\(727\) −2.43401e8 −0.633460 −0.316730 0.948516i \(-0.602585\pi\)
−0.316730 + 0.948516i \(0.602585\pi\)
\(728\) −1.52116e6 + 1.25129e6i −0.00394258 + 0.00324311i
\(729\) 1.43489e7 0.0370370
\(730\) −3.15367e8 5.73896e8i −0.810676 1.47525i
\(731\) 8.22116e6i 0.0210465i
\(732\) −3.21349e8 2.14366e8i −0.819302 0.546541i
\(733\) 6.38589e8i 1.62147i 0.585411 + 0.810737i \(0.300933\pi\)
−0.585411 + 0.810737i \(0.699067\pi\)
\(734\) −4.19616e8 1.27115e8i −1.06112 0.321447i
\(735\) −1.58476e8 + 1.62073e8i −0.399118 + 0.408177i
\(736\) 4.35936e6 + 4.34166e7i 0.0109343 + 0.108899i
\(737\) 4.74339e8i 1.18491i
\(738\) −1.27358e8 3.85809e7i −0.316853 0.0959850i
\(739\) 1.88890e7i 0.0468031i 0.999726 + 0.0234016i \(0.00744963\pi\)
−0.999726 + 0.0234016i \(0.992550\pi\)
\(740\) −1.18072e8 5.58533e8i −0.291374 1.37833i
\(741\) −1.50042e7 −0.0368771
\(742\) 5.29298e6 1.74725e7i 0.0129565 0.0427703i
\(743\) −5.63528e8 −1.37388 −0.686940 0.726714i \(-0.741047\pi\)
−0.686940 + 0.726714i \(0.741047\pi\)
\(744\) −2.49648e8 + 2.05357e8i −0.606191 + 0.498644i
\(745\) 4.38756e7 4.48714e7i 0.106110 0.108518i
\(746\) −8.78034e7 + 2.89845e8i −0.211492 + 0.698151i
\(747\) 2.51785e8 0.604044
\(748\) −6.81934e7 4.54906e7i −0.162944 0.108697i
\(749\) 2.73216e6 0.00650222
\(750\) −1.22062e8 2.10777e8i −0.289333 0.499620i
\(751\) 1.95339e8i 0.461178i −0.973051 0.230589i \(-0.925935\pi\)
0.973051 0.230589i \(-0.0740652\pi\)
\(752\) −8.88417e7 2.13565e8i −0.208912 0.502200i
\(753\) 1.64456e8i 0.385182i
\(754\) 3.49500e6 1.15372e7i 0.00815328 0.0269145i
\(755\) −3.49639e8 3.41879e8i −0.812416 0.794387i
\(756\) 7.32333e6 + 4.88526e6i 0.0169490 + 0.0113063i
\(757\) 6.04178e8i 1.39276i 0.717671 + 0.696382i \(0.245208\pi\)
−0.717671 + 0.696382i \(0.754792\pi\)
\(758\) −8.37123e7 + 2.76340e8i −0.192213 + 0.634507i
\(759\) 2.06705e7i 0.0472745i
\(760\) −4.98368e7 + 5.79314e8i −0.113530 + 1.31969i
\(761\) −6.11654e8 −1.38788 −0.693940 0.720033i \(-0.744127\pi\)
−0.693940 + 0.720033i \(0.744127\pi\)
\(762\) −3.88822e8 1.17787e8i −0.878791 0.266214i
\(763\) 3.28822e7 0.0740264
\(764\) −1.64314e8 + 2.46317e8i −0.368463 + 0.552351i
\(765\) −2.79352e7 2.73152e7i −0.0623975 0.0610127i
\(766\) −4.57549e8 1.38606e8i −1.01801 0.308388i
\(767\) 1.40900e7 0.0312265
\(768\) −1.84368e8 + 1.85491e8i −0.407007 + 0.409486i
\(769\) 1.56867e8 0.344948 0.172474 0.985014i \(-0.444824\pi\)
0.172474 + 0.985014i \(0.444824\pi\)
\(770\) −1.74140e7 3.16896e7i −0.0381441 0.0694136i
\(771\) 5.35994e6i 0.0116949i
\(772\) 2.72407e8 4.08356e8i 0.592060 0.887539i
\(773\) 6.26937e8i 1.35733i 0.734448 + 0.678665i \(0.237441\pi\)
−0.734448 + 0.678665i \(0.762559\pi\)
\(774\) 1.18914e7 + 3.60229e6i 0.0256454 + 0.00776882i
\(775\) 6.32684e8 1.42001e7i 1.35920 0.0305061i
\(776\) −5.76046e8 + 4.73848e8i −1.23274 + 1.01404i
\(777\) 4.03932e7i 0.0861083i
\(778\) −5.33190e8 1.61520e8i −1.13225 0.342996i
\(779\) 6.21915e8i 1.31558i
\(780\) 2.73256e6 + 1.29263e7i 0.00575819 + 0.0272389i
\(781\) 4.81063e8 1.00983
\(782\) 3.97270e6 1.31142e7i 0.00830741 0.0274233i
\(783\) −5.38781e7 −0.112235
\(784\) −1.83013e8 4.39942e8i −0.379781 0.912949i
\(785\) 1.40479e8 + 1.37362e8i 0.290405 + 0.283960i
\(786\) −7.55011e6 + 2.49234e7i −0.0155484 + 0.0513263i
\(787\) −4.20122e8 −0.861888 −0.430944 0.902379i \(-0.641819\pi\)
−0.430944 + 0.902379i \(0.641819\pi\)
\(788\) 3.82996e8 5.74137e8i 0.782736 1.17337i
\(789\) −2.62853e8 −0.535157
\(790\) 3.86181e7 + 7.02762e7i 0.0783266 + 0.142537i
\(791\) 2.90195e7i 0.0586354i
\(792\) 9.56797e7 7.87048e7i 0.192595 0.158426i
\(793\) 4.10205e7i 0.0822587i
\(794\) −6.60465e7 + 2.18024e8i −0.131944 + 0.435555i
\(795\) −8.75575e7 8.56144e7i −0.174258 0.170391i
\(796\) 3.21522e8 4.81983e8i 0.637487 0.955635i
\(797\) 8.14269e8i 1.60840i −0.594362 0.804198i \(-0.702595\pi\)
0.594362 0.804198i \(-0.297405\pi\)
\(798\) −1.19278e7 + 3.93746e7i −0.0234721 + 0.0774831i
\(799\) 7.26374e7i 0.142403i
\(800\) 5.08162e8 6.25697e7i 0.992505 0.122207i
\(801\) 2.92135e8 0.568441
\(802\) −7.71000e6 2.33561e6i −0.0149462 0.00452769i
\(803\) −6.52077e8 −1.25937
\(804\) −3.95343e8 2.63726e8i −0.760686 0.507439i
\(805\) 4.22575e6 4.32166e6i 0.00810058 0.00828443i
\(806\) −3.28530e7 9.95222e6i −0.0627436 0.0190071i
\(807\) 3.22317e8 0.613286
\(808\) 2.58977e8 + 3.14833e8i 0.490939 + 0.596824i
\(809\) 1.00451e9 1.89719 0.948594 0.316496i \(-0.102506\pi\)
0.948594 + 0.316496i \(0.102506\pi\)
\(810\) 5.17502e7 2.84377e7i 0.0973771 0.0535105i
\(811\) 9.40317e8i 1.76283i 0.472338 + 0.881417i \(0.343410\pi\)
−0.472338 + 0.881417i \(0.656590\pi\)
\(812\) −2.74981e7 1.83434e7i −0.0513610 0.0342620i
\(813\) 2.15356e8i 0.400761i
\(814\) −5.44054e8 1.64811e8i −1.00872 0.305572i
\(815\) 2.64162e8 2.70158e8i 0.487976 0.499051i
\(816\) 7.58292e7 3.15444e7i 0.139562 0.0580567i
\(817\) 5.80680e7i 0.106481i
\(818\) 2.76864e8 + 8.38710e7i 0.505832 + 0.153233i
\(819\) 934829.i 0.00170169i
\(820\) −5.35788e8 + 1.13263e8i −0.971742 + 0.205422i
\(821\) −5.07811e8 −0.917640 −0.458820 0.888529i \(-0.651728\pi\)
−0.458820 + 0.888529i \(0.651728\pi\)
\(822\) −8.93414e7 + 2.94922e8i −0.160856 + 0.530997i
\(823\) 3.22556e8 0.578637 0.289318 0.957233i \(-0.406571\pi\)
0.289318 + 0.957233i \(0.406571\pi\)
\(824\) 2.43262e8 + 2.95728e8i 0.434803 + 0.528580i
\(825\) −2.42481e8 + 5.44230e6i −0.431834 + 0.00969217i
\(826\) 1.12011e7 3.69755e7i 0.0198756 0.0656106i
\(827\) 4.20915e8 0.744180 0.372090 0.928197i \(-0.378641\pi\)
0.372090 + 0.928197i \(0.378641\pi\)
\(828\) 1.72281e7 + 1.14925e7i 0.0303491 + 0.0202453i
\(829\) 7.22698e8 1.26851 0.634254 0.773125i \(-0.281307\pi\)
0.634254 + 0.773125i \(0.281307\pi\)
\(830\) 9.08079e8 4.99006e8i 1.58814 0.872713i
\(831\) 3.33393e7i 0.0580969i
\(832\) −2.72510e7 5.35609e6i −0.0473165 0.00929989i
\(833\) 1.49632e8i 0.258875i
\(834\) 7.01377e7 2.31529e8i 0.120908 0.399124i
\(835\) 1.50269e8 1.53680e8i 0.258114 0.263972i
\(836\) 4.81666e8 + 3.21311e8i 0.824380 + 0.549929i
\(837\) 1.53421e8i 0.261643i
\(838\) −1.79047e8 + 5.91045e8i −0.304252 + 1.00436i
\(839\) 3.57997e8i 0.606168i 0.952964 + 0.303084i \(0.0980163\pi\)
−0.952964 + 0.303084i \(0.901984\pi\)
\(840\) 3.60940e7 + 3.10507e6i 0.0608971 + 0.00523882i
\(841\) −3.92519e8 −0.659891
\(842\) 1.38216e7 + 4.18699e6i 0.0231537 + 0.00701401i
\(843\) 2.24365e8 0.374518
\(844\) −3.85076e8 + 5.77255e8i −0.640500 + 0.960153i
\(845\) 4.20839e8 4.30391e8i 0.697503 0.713333i
\(846\) −1.05065e8 3.18277e7i −0.173520 0.0525647i
\(847\) 2.83227e7 0.0466106
\(848\) 2.37672e8 9.88700e7i 0.389754 0.162135i
\(849\) 3.99151e8 0.652250
\(850\) −1.54885e8 4.31501e7i −0.252205 0.0702627i
\(851\) 9.50247e7i 0.154187i
\(852\) −2.67464e8 + 4.00947e8i −0.432461 + 0.648289i
\(853\) 1.53019e8i 0.246546i −0.992373 0.123273i \(-0.960661\pi\)
0.992373 0.123273i \(-0.0393390\pi\)
\(854\) −1.07648e8 3.26100e7i −0.172835 0.0523573i
\(855\) 1.97313e8 + 1.92934e8i 0.315687 + 0.308681i
\(856\) 2.44728e7 + 2.97511e7i 0.0390178 + 0.0474332i
\(857\) 2.61817e8i 0.415963i 0.978133 + 0.207982i \(0.0666894\pi\)
−0.978133 + 0.207982i \(0.933311\pi\)
\(858\) 1.25912e7 + 3.81427e6i 0.0199344 + 0.00603879i
\(859\) 6.48325e7i 0.102285i −0.998691 0.0511426i \(-0.983714\pi\)
0.998691 0.0511426i \(-0.0162863\pi\)
\(860\) 5.00263e7 1.05753e7i 0.0786507 0.0166264i
\(861\) −3.87482e7 −0.0607075
\(862\) 1.94454e8 6.41905e8i 0.303595 1.00219i
\(863\) 3.46397e8 0.538942 0.269471 0.963008i \(-0.413151\pi\)
0.269471 + 0.963008i \(0.413151\pi\)
\(864\) 1.24008e7 + 1.23504e8i 0.0192268 + 0.191487i
\(865\) −5.39591e8 5.27616e8i −0.833712 0.815210i
\(866\) −7.46215e7 + 2.46331e8i −0.114897 + 0.379284i
\(867\) 3.50477e8 0.537776
\(868\) −5.22341e7 + 7.83025e7i −0.0798721 + 0.119734i
\(869\) 7.98497e7 0.121679
\(870\) −1.94315e8 + 1.06779e8i −0.295085 + 0.162155i
\(871\) 5.04658e7i 0.0763735i
\(872\) 2.94536e8 + 3.58061e8i 0.444210 + 0.540017i
\(873\) 3.54009e8i 0.532074i
\(874\) −2.80601e7 + 9.26284e7i −0.0420296 + 0.138743i
\(875\) −5.18090e7 4.84335e7i −0.0773358 0.0722972i
\(876\) 3.62545e8 5.43480e8i 0.539324 0.808484i
\(877\) 3.86932e8i 0.573635i 0.957985 + 0.286817i \(0.0925973\pi\)
−0.957985 + 0.286817i \(0.907403\pi\)
\(878\) 2.65432e8 8.76210e8i 0.392166 1.29457i
\(879\) 1.26547e8i 0.186331i
\(880\) 1.89092e8 4.73479e8i 0.277476 0.694788i
\(881\) −7.55475e7 −0.110482 −0.0552411 0.998473i \(-0.517593\pi\)
−0.0552411 + 0.998473i \(0.517593\pi\)
\(882\) −2.16433e8 6.55647e7i −0.315441 0.0955574i
\(883\) −1.09819e8 −0.159513 −0.0797563 0.996814i \(-0.525414\pi\)
−0.0797563 + 0.996814i \(0.525414\pi\)
\(884\) 7.25523e6 + 4.83983e6i 0.0105025 + 0.00700605i
\(885\) −1.85291e8 1.81179e8i −0.267315 0.261383i
\(886\) 2.81430e8 + 8.52542e7i 0.404640 + 0.122579i
\(887\) −4.08975e8 −0.586038 −0.293019 0.956107i \(-0.594660\pi\)
−0.293019 + 0.956107i \(0.594660\pi\)
\(888\) 4.39850e8 3.61814e8i 0.628153 0.516710i
\(889\) −1.18297e8 −0.168372
\(890\) 1.05360e9 5.78974e8i 1.49454 0.821275i
\(891\) 5.88000e7i 0.0831274i
\(892\) −3.29233e8 2.19625e8i −0.463884 0.309448i
\(893\) 5.13055e8i 0.720460i
\(894\) 5.99217e7 + 1.81522e7i 0.0838633 + 0.0254049i
\(895\) 9.99997e8 + 9.77805e8i 1.39486 + 1.36390i
\(896\) −3.57194e7 + 6.72554e7i −0.0496569 + 0.0934982i
\(897\) 2.19918e6i 0.00304708i
\(898\) 3.55846e7 + 1.07797e7i 0.0491398 + 0.0148860i
\(899\) 5.76075e8i 0.792867i
\(900\) 1.30280e8 2.05124e8i 0.178711 0.281378i
\(901\) −8.08367e7 −0.110518
\(902\) −1.58100e8 + 5.21898e8i −0.215433 + 0.711158i
\(903\) 3.61791e6 0.00491353
\(904\) −3.15999e8 + 2.59936e8i −0.427741 + 0.351854i
\(905\) −4.84368e8 + 4.95361e8i −0.653476 + 0.668307i
\(906\) 1.41442e8 4.66911e8i 0.190193 0.627840i
\(907\) −1.19298e9 −1.59886 −0.799429 0.600761i \(-0.794864\pi\)
−0.799429 + 0.600761i \(0.794864\pi\)
\(908\) 6.24675e8 + 4.16709e8i 0.834443 + 0.556641i
\(909\) 1.93481e8 0.257600
\(910\) 1.85271e6 + 3.37152e6i 0.00245858 + 0.00447405i
\(911\) 6.51943e8i 0.862292i 0.902282 + 0.431146i \(0.141891\pi\)
−0.902282 + 0.431146i \(0.858109\pi\)
\(912\) −5.35599e8 + 2.22806e8i −0.706083 + 0.293726i
\(913\) 1.03178e9i 1.35574i
\(914\) −3.19676e8 + 1.05527e9i −0.418670 + 1.38206i
\(915\) −5.27470e8 + 5.39442e8i −0.688549 + 0.704176i
\(916\) 1.03975e9 + 6.93599e8i 1.35283 + 0.902448i
\(917\) 7.58284e6i 0.00983386i
\(918\) 1.13009e7 3.73049e7i 0.0146077 0.0482212i
\(919\) 5.07991e7i 0.0654500i 0.999464 + 0.0327250i \(0.0104185\pi\)
−0.999464 + 0.0327250i \(0.989581\pi\)
\(920\) 8.49108e7 + 7.30465e6i 0.109043 + 0.00938071i
\(921\) 3.24099e8 0.414858
\(922\) 4.68154e8 + 1.41819e8i 0.597305 + 0.180943i
\(923\) −5.11813e7 −0.0650887
\(924\) 2.00192e7 3.00101e7i 0.0253764 0.0380409i
\(925\) −1.11471e9 + 2.50188e7i −1.40844 + 0.0316113i
\(926\) 6.83577e7 + 2.07077e7i 0.0860903 + 0.0260795i
\(927\) 1.81740e8 0.228145
\(928\) −4.65631e7 4.63740e8i −0.0582637 0.580271i
\(929\) 5.44046e8 0.678560 0.339280 0.940685i \(-0.389817\pi\)
0.339280 + 0.940685i \(0.389817\pi\)
\(930\) 3.04061e8 + 5.53323e8i 0.378018 + 0.687907i
\(931\) 1.05689e9i 1.30972i
\(932\) −7.32414e8 + 1.09794e9i −0.904709 + 1.35622i
\(933\) 8.76002e8i 1.07860i
\(934\) 7.13359e8 + 2.16099e8i 0.875523 + 0.265224i
\(935\) −1.11934e8 + 1.14475e8i −0.136939 + 0.140047i
\(936\) −1.01796e7 + 8.37356e6i −0.0124137 + 0.0102113i
\(937\) 1.23031e9i 1.49553i −0.663963 0.747765i \(-0.731127\pi\)
0.663963 0.747765i \(-0.268873\pi\)
\(938\) −1.32435e8 4.01187e7i −0.160470 0.0486114i
\(939\) 9.43366e7i 0.113942i
\(940\) −4.42003e8 + 9.34377e7i −0.532160 + 0.112496i
\(941\) −1.04638e9 −1.25580 −0.627901 0.778293i \(-0.716086\pi\)
−0.627901 + 0.778293i \(0.716086\pi\)
\(942\) −5.68293e7 + 1.87597e8i −0.0679860 + 0.224427i
\(943\) −9.11549e7 −0.108704
\(944\) 5.02965e8 2.09230e8i 0.597891 0.248719i
\(945\) 1.20207e7 1.22935e7i 0.0142441 0.0145673i
\(946\) 1.47617e7 4.87294e7i 0.0174367 0.0575596i
\(947\) −1.05258e9 −1.23938 −0.619692 0.784845i \(-0.712743\pi\)
−0.619692 + 0.784845i \(0.712743\pi\)
\(948\) −4.43953e7 + 6.65516e7i −0.0521089 + 0.0781148i
\(949\) 6.93757e7 0.0811725
\(950\) 1.09399e9 + 3.04779e8i 1.27598 + 0.355479i
\(951\) 1.25731e8i 0.146185i
\(952\) 1.84686e7 1.51920e7i 0.0214054 0.0176077i
\(953\) 1.26282e8i 0.145902i 0.997336 + 0.0729512i \(0.0232417\pi\)
−0.997336 + 0.0729512i \(0.976758\pi\)
\(954\) 3.54204e7 1.16925e8i 0.0407951 0.134667i
\(955\) 4.13487e8 + 4.04311e8i 0.474736 + 0.464200i
\(956\) 6.49561e8 9.73736e8i 0.743441 1.11447i
\(957\) 2.20786e8i 0.251904i
\(958\) −1.80907e8 + 5.97187e8i −0.205759 + 0.679225i
\(959\) 8.97288e7i 0.101736i
\(960\) 2.89493e8 + 4.20848e8i 0.327209 + 0.475676i
\(961\) −7.52907e8 −0.848343
\(962\) 5.78829e7 + 1.75346e7i 0.0650168 + 0.0196957i
\(963\) 1.82835e7 0.0204730
\(964\) −1.00402e9 6.69763e8i −1.12076 0.747636i
\(965\) −6.85498e8 6.70285e8i −0.762824 0.745895i
\(966\) 5.77118e6 + 1.74828e6i 0.00640226 + 0.00193945i
\(967\) −1.32116e9 −1.46108 −0.730542 0.682868i \(-0.760732\pi\)
−0.730542 + 0.682868i \(0.760732\pi\)
\(968\) 2.53695e8 + 3.08412e8i 0.279696 + 0.340020i
\(969\) 1.82167e8 0.200216
\(970\) 7.01601e8 + 1.27676e9i 0.768732 + 1.39892i
\(971\) 6.03829e8i 0.659563i −0.944057 0.329781i \(-0.893025\pi\)
0.944057 0.329781i \(-0.106975\pi\)
\(972\) 4.90075e7 + 3.26920e7i 0.0533658 + 0.0355994i
\(973\) 7.04419e7i 0.0764702i
\(974\) −1.40955e9 4.26997e8i −1.52547 0.462113i
\(975\) 2.57981e7 579017.i 0.0278339 0.000624709i
\(976\) −6.09138e8 1.46430e9i −0.655188 1.57500i
\(977\) 9.72123e8i 1.04241i 0.853432 + 0.521204i \(0.174517\pi\)
−0.853432 + 0.521204i \(0.825483\pi\)
\(978\) 3.60771e8 + 1.09289e8i 0.385670 + 0.116832i
\(979\) 1.19713e9i 1.27583i
\(980\) −9.10521e8 + 1.92480e8i −0.967413 + 0.204507i
\(981\) 2.20046e8 0.233081
\(982\) −3.15858e8 + 1.04267e9i −0.333547 + 1.10106i
\(983\) 5.59576e8 0.589112 0.294556 0.955634i \(-0.404828\pi\)
0.294556 + 0.955634i \(0.404828\pi\)
\(984\) −3.47080e8 4.21938e8i −0.364287 0.442856i
\(985\) −9.63791e8 9.42402e8i −1.00850 0.986115i
\(986\) −4.24331e7 + 1.40075e8i −0.0442664 + 0.146126i
\(987\) −3.19657e7 −0.0332455
\(988\) −5.12454e7 3.41849e7i −0.0531354 0.0354457i
\(989\) 8.51110e6 0.00879826
\(990\) −1.16534e8 2.12066e8i −0.120101 0.218557i
\(991\) 1.32095e9i 1.35727i 0.734477 + 0.678634i \(0.237428\pi\)
−0.734477 + 0.678634i \(0.762572\pi\)
\(992\) −1.32053e9 + 1.32591e8i −1.35274 + 0.135825i
\(993\) 1.06001e8i 0.108258i
\(994\) −4.06875e7 + 1.34312e8i −0.0414287 + 0.136759i
\(995\) −8.09093e8 7.91138e8i −0.821352 0.803124i
\(996\) 8.59951e8 + 5.73657e8i 0.870353 + 0.580596i
\(997\) 8.80146e8i 0.888115i 0.895998 + 0.444058i \(0.146461\pi\)
−0.895998 + 0.444058i \(0.853539\pi\)
\(998\) −1.21813e8 + 4.02113e8i −0.122547 + 0.404536i
\(999\) 2.70310e8i 0.271122i
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 60.7.f.a.19.34 yes 36
3.2 odd 2 180.7.f.g.19.3 36
4.3 odd 2 inner 60.7.f.a.19.4 yes 36
5.4 even 2 inner 60.7.f.a.19.3 36
12.11 even 2 180.7.f.g.19.33 36
15.14 odd 2 180.7.f.g.19.34 36
20.19 odd 2 inner 60.7.f.a.19.33 yes 36
60.59 even 2 180.7.f.g.19.4 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.7.f.a.19.3 36 5.4 even 2 inner
60.7.f.a.19.4 yes 36 4.3 odd 2 inner
60.7.f.a.19.33 yes 36 20.19 odd 2 inner
60.7.f.a.19.34 yes 36 1.1 even 1 trivial
180.7.f.g.19.3 36 3.2 odd 2
180.7.f.g.19.4 36 60.59 even 2
180.7.f.g.19.33 36 12.11 even 2
180.7.f.g.19.34 36 15.14 odd 2