Properties

Label 65.5.g.a.34.10
Level $65$
Weight $5$
Character 65.34
Analytic conductor $6.719$
Analytic rank $0$
Dimension $52$
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] = [65,5,Mod(34,65)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(65, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("65.34");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 65.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.71904760045\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 34.10
Character \(\chi\) \(=\) 65.34
Dual form 65.5.g.a.44.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.96266 + 1.96266i) q^{2} +11.7087i q^{3} +8.29597i q^{4} +(-20.0793 + 14.8937i) q^{5} +(-22.9802 - 22.9802i) q^{6} +(49.2380 + 49.2380i) q^{7} +(-47.6846 - 47.6846i) q^{8} -56.0939 q^{9} +O(q^{10})\) \(q+(-1.96266 + 1.96266i) q^{2} +11.7087i q^{3} +8.29597i q^{4} +(-20.0793 + 14.8937i) q^{5} +(-22.9802 - 22.9802i) q^{6} +(49.2380 + 49.2380i) q^{7} +(-47.6846 - 47.6846i) q^{8} -56.0939 q^{9} +(10.1776 - 68.6399i) q^{10} +(36.9838 - 36.9838i) q^{11} -97.1351 q^{12} +(167.514 - 22.3654i) q^{13} -193.275 q^{14} +(-174.386 - 235.103i) q^{15} +54.4414 q^{16} +2.83570 q^{17} +(110.093 - 110.093i) q^{18} +(-74.4440 - 74.4440i) q^{19} +(-123.558 - 166.577i) q^{20} +(-576.514 + 576.514i) q^{21} +145.173i q^{22} -858.183 q^{23} +(558.325 - 558.325i) q^{24} +(181.357 - 598.109i) q^{25} +(-284.876 + 372.667i) q^{26} +291.618i q^{27} +(-408.477 + 408.477i) q^{28} +1280.13 q^{29} +(803.685 + 119.166i) q^{30} +(975.637 + 975.637i) q^{31} +(656.104 - 656.104i) q^{32} +(433.033 + 433.033i) q^{33} +(-5.56551 + 5.56551i) q^{34} +(-1722.00 - 255.330i) q^{35} -465.353i q^{36} +(573.577 + 573.577i) q^{37} +292.216 q^{38} +(261.869 + 1961.37i) q^{39} +(1667.67 + 247.274i) q^{40} +(276.665 + 276.665i) q^{41} -2263.00i q^{42} -3340.52 q^{43} +(306.817 + 306.817i) q^{44} +(1126.33 - 835.445i) q^{45} +(1684.32 - 1684.32i) q^{46} +(345.914 + 345.914i) q^{47} +637.439i q^{48} +2447.77i q^{49} +(817.942 + 1529.82i) q^{50} +33.2024i q^{51} +(185.542 + 1389.69i) q^{52} -1606.43i q^{53} +(-572.346 - 572.346i) q^{54} +(-191.784 + 1293.43i) q^{55} -4695.79i q^{56} +(871.644 - 871.644i) q^{57} +(-2512.45 + 2512.45i) q^{58} +(-641.576 + 641.576i) q^{59} +(1950.40 - 1446.70i) q^{60} -5200.73 q^{61} -3829.68 q^{62} +(-2761.95 - 2761.95i) q^{63} +3446.47i q^{64} +(-3030.45 + 2943.97i) q^{65} -1699.79 q^{66} +(2958.39 - 2958.39i) q^{67} +23.5249i q^{68} -10048.2i q^{69} +(3880.82 - 2878.57i) q^{70} +(-1343.74 - 1343.74i) q^{71} +(2674.82 + 2674.82i) q^{72} +(1183.61 + 1183.61i) q^{73} -2251.47 q^{74} +(7003.09 + 2123.45i) q^{75} +(617.585 - 617.585i) q^{76} +3642.02 q^{77} +(-4363.45 - 3335.53i) q^{78} +2812.08 q^{79} +(-1093.15 + 810.833i) q^{80} -7958.08 q^{81} -1086.00 q^{82} +(-7138.41 + 7138.41i) q^{83} +(-4782.74 - 4782.74i) q^{84} +(-56.9389 + 42.2340i) q^{85} +(6556.29 - 6556.29i) q^{86} +14988.7i q^{87} -3527.12 q^{88} +(-1031.96 + 1031.96i) q^{89} +(-570.901 + 3850.28i) q^{90} +(9349.26 + 7146.81i) q^{91} -7119.46i q^{92} +(-11423.4 + 11423.4i) q^{93} -1357.82 q^{94} +(2603.53 + 386.039i) q^{95} +(7682.13 + 7682.13i) q^{96} +(8066.83 - 8066.83i) q^{97} +(-4804.12 - 4804.12i) q^{98} +(-2074.57 + 2074.57i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96266 + 1.96266i −0.490664 + 0.490664i −0.908515 0.417852i \(-0.862783\pi\)
0.417852 + 0.908515i \(0.362783\pi\)
\(3\) 11.7087i 1.30097i 0.759520 + 0.650484i \(0.225434\pi\)
−0.759520 + 0.650484i \(0.774566\pi\)
\(4\) 8.29597i 0.518498i
\(5\) −20.0793 + 14.8937i −0.803172 + 0.595747i
\(6\) −22.9802 22.9802i −0.638338 0.638338i
\(7\) 49.2380 + 49.2380i 1.00486 + 1.00486i 0.999988 + 0.00486952i \(0.00155002\pi\)
0.00486952 + 0.999988i \(0.498450\pi\)
\(8\) −47.6846 47.6846i −0.745072 0.745072i
\(9\) −56.0939 −0.692517
\(10\) 10.1776 68.6399i 0.101776 0.686399i
\(11\) 36.9838 36.9838i 0.305652 0.305652i −0.537569 0.843220i \(-0.680657\pi\)
0.843220 + 0.537569i \(0.180657\pi\)
\(12\) −97.1351 −0.674549
\(13\) 167.514 22.3654i 0.991204 0.132339i
\(14\) −193.275 −0.986095
\(15\) −174.386 235.103i −0.775048 1.04490i
\(16\) 54.4414 0.212662
\(17\) 2.83570 0.00981212 0.00490606 0.999988i \(-0.498438\pi\)
0.00490606 + 0.999988i \(0.498438\pi\)
\(18\) 110.093 110.093i 0.339793 0.339793i
\(19\) −74.4440 74.4440i −0.206216 0.206216i 0.596441 0.802657i \(-0.296581\pi\)
−0.802657 + 0.596441i \(0.796581\pi\)
\(20\) −123.558 166.577i −0.308894 0.416443i
\(21\) −576.514 + 576.514i −1.30729 + 1.30729i
\(22\) 145.173i 0.299944i
\(23\) −858.183 −1.62227 −0.811137 0.584856i \(-0.801151\pi\)
−0.811137 + 0.584856i \(0.801151\pi\)
\(24\) 558.325 558.325i 0.969315 0.969315i
\(25\) 181.357 598.109i 0.290171 0.956975i
\(26\) −284.876 + 372.667i −0.421414 + 0.551282i
\(27\) 291.618i 0.400025i
\(28\) −408.477 + 408.477i −0.521017 + 0.521017i
\(29\) 1280.13 1.52215 0.761076 0.648663i \(-0.224671\pi\)
0.761076 + 0.648663i \(0.224671\pi\)
\(30\) 803.685 + 119.166i 0.892983 + 0.132407i
\(31\) 975.637 + 975.637i 1.01523 + 1.01523i 0.999882 + 0.0153483i \(0.00488572\pi\)
0.0153483 + 0.999882i \(0.495114\pi\)
\(32\) 656.104 656.104i 0.640727 0.640727i
\(33\) 433.033 + 433.033i 0.397643 + 0.397643i
\(34\) −5.56551 + 5.56551i −0.00481445 + 0.00481445i
\(35\) −1722.00 255.330i −1.40571 0.208432i
\(36\) 465.353i 0.359069i
\(37\) 573.577 + 573.577i 0.418975 + 0.418975i 0.884850 0.465875i \(-0.154260\pi\)
−0.465875 + 0.884850i \(0.654260\pi\)
\(38\) 292.216 0.202366
\(39\) 261.869 + 1961.37i 0.172169 + 1.28953i
\(40\) 1667.67 + 247.274i 1.04230 + 0.154546i
\(41\) 276.665 + 276.665i 0.164584 + 0.164584i 0.784594 0.620010i \(-0.212872\pi\)
−0.620010 + 0.784594i \(0.712872\pi\)
\(42\) 2263.00i 1.28288i
\(43\) −3340.52 −1.80666 −0.903332 0.428942i \(-0.858887\pi\)
−0.903332 + 0.428942i \(0.858887\pi\)
\(44\) 306.817 + 306.817i 0.158480 + 0.158480i
\(45\) 1126.33 835.445i 0.556211 0.412565i
\(46\) 1684.32 1684.32i 0.795991 0.795991i
\(47\) 345.914 + 345.914i 0.156593 + 0.156593i 0.781055 0.624462i \(-0.214682\pi\)
−0.624462 + 0.781055i \(0.714682\pi\)
\(48\) 637.439i 0.276666i
\(49\) 2447.77i 1.01948i
\(50\) 817.942 + 1529.82i 0.327177 + 0.611929i
\(51\) 33.2024i 0.0127652i
\(52\) 185.542 + 1389.69i 0.0686177 + 0.513938i
\(53\) 1606.43i 0.571888i −0.958246 0.285944i \(-0.907693\pi\)
0.958246 0.285944i \(-0.0923071\pi\)
\(54\) −572.346 572.346i −0.196278 0.196278i
\(55\) −191.784 + 1293.43i −0.0633997 + 0.427582i
\(56\) 4695.79i 1.49738i
\(57\) 871.644 871.644i 0.268281 0.268281i
\(58\) −2512.45 + 2512.45i −0.746865 + 0.746865i
\(59\) −641.576 + 641.576i −0.184308 + 0.184308i −0.793230 0.608922i \(-0.791602\pi\)
0.608922 + 0.793230i \(0.291602\pi\)
\(60\) 1950.40 1446.70i 0.541779 0.401861i
\(61\) −5200.73 −1.39767 −0.698836 0.715282i \(-0.746298\pi\)
−0.698836 + 0.715282i \(0.746298\pi\)
\(62\) −3829.68 −0.996274
\(63\) −2761.95 2761.95i −0.695881 0.695881i
\(64\) 3446.47i 0.841424i
\(65\) −3030.45 + 2943.97i −0.717267 + 0.696799i
\(66\) −1699.79 −0.390218
\(67\) 2958.39 2958.39i 0.659031 0.659031i −0.296119 0.955151i \(-0.595693\pi\)
0.955151 + 0.296119i \(0.0956926\pi\)
\(68\) 23.5249i 0.00508756i
\(69\) 10048.2i 2.11053i
\(70\) 3880.82 2878.57i 0.792004 0.587463i
\(71\) −1343.74 1343.74i −0.266562 0.266562i 0.561151 0.827713i \(-0.310359\pi\)
−0.827713 + 0.561151i \(0.810359\pi\)
\(72\) 2674.82 + 2674.82i 0.515975 + 0.515975i
\(73\) 1183.61 + 1183.61i 0.222107 + 0.222107i 0.809385 0.587278i \(-0.199800\pi\)
−0.587278 + 0.809385i \(0.699800\pi\)
\(74\) −2251.47 −0.411152
\(75\) 7003.09 + 2123.45i 1.24499 + 0.377503i
\(76\) 617.585 617.585i 0.106923 0.106923i
\(77\) 3642.02 0.614273
\(78\) −4363.45 3335.53i −0.717201 0.548246i
\(79\) 2812.08 0.450581 0.225291 0.974292i \(-0.427667\pi\)
0.225291 + 0.974292i \(0.427667\pi\)
\(80\) −1093.15 + 810.833i −0.170804 + 0.126693i
\(81\) −7958.08 −1.21294
\(82\) −1086.00 −0.161511
\(83\) −7138.41 + 7138.41i −1.03620 + 1.03620i −0.0368852 + 0.999320i \(0.511744\pi\)
−0.999320 + 0.0368852i \(0.988256\pi\)
\(84\) −4782.74 4782.74i −0.677826 0.677826i
\(85\) −56.9389 + 42.2340i −0.00788082 + 0.00584554i
\(86\) 6556.29 6556.29i 0.886465 0.886465i
\(87\) 14988.7i 1.98027i
\(88\) −3527.12 −0.455465
\(89\) −1031.96 + 1031.96i −0.130282 + 0.130282i −0.769241 0.638959i \(-0.779365\pi\)
0.638959 + 0.769241i \(0.279365\pi\)
\(90\) −570.901 + 3850.28i −0.0704815 + 0.475343i
\(91\) 9349.26 + 7146.81i 1.12900 + 0.863037i
\(92\) 7119.46i 0.841146i
\(93\) −11423.4 + 11423.4i −1.32078 + 1.32078i
\(94\) −1357.82 −0.153669
\(95\) 2603.53 + 386.039i 0.288480 + 0.0427744i
\(96\) 7682.13 + 7682.13i 0.833565 + 0.833565i
\(97\) 8066.83 8066.83i 0.857353 0.857353i −0.133673 0.991026i \(-0.542677\pi\)
0.991026 + 0.133673i \(0.0426770\pi\)
\(98\) −4804.12 4804.12i −0.500221 0.500221i
\(99\) −2074.57 + 2074.57i −0.211669 + 0.211669i
\(100\) 4961.90 + 1504.53i 0.496190 + 0.150453i
\(101\) 3934.27i 0.385675i −0.981231 0.192838i \(-0.938231\pi\)
0.981231 0.192838i \(-0.0617691\pi\)
\(102\) −65.1649 65.1649i −0.00626345 0.00626345i
\(103\) 15584.3 1.46897 0.734485 0.678625i \(-0.237424\pi\)
0.734485 + 0.678625i \(0.237424\pi\)
\(104\) −9054.30 6921.34i −0.837121 0.639916i
\(105\) 2989.58 20162.4i 0.271164 1.82879i
\(106\) 3152.87 + 3152.87i 0.280605 + 0.280605i
\(107\) 4354.40i 0.380330i −0.981752 0.190165i \(-0.939098\pi\)
0.981752 0.190165i \(-0.0609024\pi\)
\(108\) −2419.26 −0.207412
\(109\) 14256.5 + 14256.5i 1.19994 + 1.19994i 0.974185 + 0.225752i \(0.0724840\pi\)
0.225752 + 0.974185i \(0.427516\pi\)
\(110\) −2162.16 2914.97i −0.178691 0.240907i
\(111\) −6715.85 + 6715.85i −0.545073 + 0.545073i
\(112\) 2680.59 + 2680.59i 0.213695 + 0.213695i
\(113\) 18625.6i 1.45866i −0.684162 0.729330i \(-0.739832\pi\)
0.684162 0.729330i \(-0.260168\pi\)
\(114\) 3421.47i 0.263271i
\(115\) 17231.7 12781.5i 1.30297 0.966465i
\(116\) 10619.9i 0.789233i
\(117\) −9396.49 + 1254.56i −0.686426 + 0.0916473i
\(118\) 2518.38i 0.180866i
\(119\) 139.624 + 139.624i 0.00985978 + 0.00985978i
\(120\) −2895.26 + 19526.3i −0.201060 + 1.35599i
\(121\) 11905.4i 0.813154i
\(122\) 10207.2 10207.2i 0.685787 0.685787i
\(123\) −3239.39 + 3239.39i −0.214118 + 0.214118i
\(124\) −8093.85 + 8093.85i −0.526395 + 0.526395i
\(125\) 5266.54 + 14710.7i 0.337058 + 0.941484i
\(126\) 10841.5 0.682888
\(127\) −20800.0 −1.28961 −0.644803 0.764349i \(-0.723060\pi\)
−0.644803 + 0.764349i \(0.723060\pi\)
\(128\) 3733.42 + 3733.42i 0.227870 + 0.227870i
\(129\) 39113.2i 2.35041i
\(130\) 169.728 11725.7i 0.0100431 0.693831i
\(131\) 7041.46 0.410317 0.205159 0.978729i \(-0.434229\pi\)
0.205159 + 0.978729i \(0.434229\pi\)
\(132\) −3592.43 + 3592.43i −0.206177 + 0.206177i
\(133\) 7330.95i 0.414436i
\(134\) 11612.6i 0.646726i
\(135\) −4343.27 5855.49i −0.238314 0.321289i
\(136\) −135.219 135.219i −0.00731073 0.00731073i
\(137\) 15382.9 + 15382.9i 0.819591 + 0.819591i 0.986049 0.166457i \(-0.0532328\pi\)
−0.166457 + 0.986049i \(0.553233\pi\)
\(138\) 19721.2 + 19721.2i 1.03556 + 1.03556i
\(139\) 14481.8 0.749539 0.374769 0.927118i \(-0.377722\pi\)
0.374769 + 0.927118i \(0.377722\pi\)
\(140\) 2118.21 14285.7i 0.108072 0.728860i
\(141\) −4050.21 + 4050.21i −0.203722 + 0.203722i
\(142\) 5274.60 0.261585
\(143\) 5368.14 7022.45i 0.262513 0.343413i
\(144\) −3053.83 −0.147272
\(145\) −25704.1 + 19065.8i −1.22255 + 0.906818i
\(146\) −4646.03 −0.217960
\(147\) −28660.2 −1.32631
\(148\) −4758.38 + 4758.38i −0.217238 + 0.217238i
\(149\) −12147.7 12147.7i −0.547170 0.547170i 0.378451 0.925621i \(-0.376457\pi\)
−0.925621 + 0.378451i \(0.876457\pi\)
\(150\) −17912.3 + 9577.05i −0.796100 + 0.425646i
\(151\) −6761.45 + 6761.45i −0.296542 + 0.296542i −0.839658 0.543116i \(-0.817244\pi\)
0.543116 + 0.839658i \(0.317244\pi\)
\(152\) 7099.67i 0.307292i
\(153\) −159.066 −0.00679506
\(154\) −7148.03 + 7148.03i −0.301401 + 0.301401i
\(155\) −34120.9 5059.28i −1.42023 0.210584i
\(156\) −16271.4 + 2172.46i −0.668616 + 0.0892694i
\(157\) 12263.3i 0.497519i −0.968565 0.248759i \(-0.919977\pi\)
0.968565 0.248759i \(-0.0800228\pi\)
\(158\) −5519.14 + 5519.14i −0.221084 + 0.221084i
\(159\) 18809.3 0.744008
\(160\) −3402.31 + 22945.9i −0.132903 + 0.896325i
\(161\) −42255.2 42255.2i −1.63015 1.63015i
\(162\) 15619.0 15619.0i 0.595144 0.595144i
\(163\) 2052.00 + 2052.00i 0.0772329 + 0.0772329i 0.744668 0.667435i \(-0.232608\pi\)
−0.667435 + 0.744668i \(0.732608\pi\)
\(164\) −2295.21 + 2295.21i −0.0853364 + 0.0853364i
\(165\) −15144.5 2245.54i −0.556270 0.0824810i
\(166\) 28020.5i 1.01686i
\(167\) 21065.0 + 21065.0i 0.755316 + 0.755316i 0.975466 0.220150i \(-0.0706546\pi\)
−0.220150 + 0.975466i \(0.570655\pi\)
\(168\) 54981.7 1.94805
\(169\) 27560.6 7493.00i 0.964973 0.262351i
\(170\) 28.8606 194.642i 0.000998637 0.00673503i
\(171\) 4175.86 + 4175.86i 0.142808 + 0.142808i
\(172\) 27712.9i 0.936752i
\(173\) −6229.06 −0.208128 −0.104064 0.994571i \(-0.533185\pi\)
−0.104064 + 0.994571i \(0.533185\pi\)
\(174\) −29417.6 29417.6i −0.971647 0.971647i
\(175\) 38379.4 20520.1i 1.25320 0.670043i
\(176\) 2013.45 2013.45i 0.0650004 0.0650004i
\(177\) −7512.03 7512.03i −0.239779 0.239779i
\(178\) 4050.78i 0.127849i
\(179\) 38292.2i 1.19510i 0.801832 + 0.597549i \(0.203859\pi\)
−0.801832 + 0.597549i \(0.796141\pi\)
\(180\) 6930.82 + 9343.97i 0.213914 + 0.288394i
\(181\) 38251.7i 1.16760i −0.811898 0.583800i \(-0.801565\pi\)
0.811898 0.583800i \(-0.198435\pi\)
\(182\) −32376.1 + 4322.65i −0.977421 + 0.130499i
\(183\) 60893.9i 1.81833i
\(184\) 40922.1 + 40922.1i 1.20871 + 1.20871i
\(185\) −20059.7 2974.35i −0.586113 0.0869059i
\(186\) 44840.6i 1.29612i
\(187\) 104.875 104.875i 0.00299909 0.00299909i
\(188\) −2869.69 + 2869.69i −0.0811931 + 0.0811931i
\(189\) −14358.7 + 14358.7i −0.401968 + 0.401968i
\(190\) −5867.49 + 4352.17i −0.162534 + 0.120559i
\(191\) 58381.3 1.60032 0.800160 0.599786i \(-0.204748\pi\)
0.800160 + 0.599786i \(0.204748\pi\)
\(192\) −40353.8 −1.09467
\(193\) 18900.7 + 18900.7i 0.507414 + 0.507414i 0.913732 0.406318i \(-0.133187\pi\)
−0.406318 + 0.913732i \(0.633187\pi\)
\(194\) 31664.8i 0.841344i
\(195\) −34470.1 35482.7i −0.906513 0.933141i
\(196\) −20306.6 −0.528597
\(197\) −41161.7 + 41161.7i −1.06062 + 1.06062i −0.0625830 + 0.998040i \(0.519934\pi\)
−0.998040 + 0.0625830i \(0.980066\pi\)
\(198\) 8143.32i 0.207717i
\(199\) 7371.87i 0.186154i 0.995659 + 0.0930768i \(0.0296702\pi\)
−0.995659 + 0.0930768i \(0.970330\pi\)
\(200\) −37168.5 + 19872.7i −0.929213 + 0.496817i
\(201\) 34639.0 + 34639.0i 0.857379 + 0.857379i
\(202\) 7721.62 + 7721.62i 0.189237 + 0.189237i
\(203\) 63031.1 + 63031.1i 1.52955 + 1.52955i
\(204\) −275.446 −0.00661876
\(205\) −9675.81 1434.68i −0.230239 0.0341388i
\(206\) −30586.6 + 30586.6i −0.720770 + 0.720770i
\(207\) 48138.8 1.12345
\(208\) 9119.67 1217.60i 0.210791 0.0281435i
\(209\) −5506.45 −0.126061
\(210\) 33704.3 + 45439.4i 0.764271 + 1.03037i
\(211\) −20922.5 −0.469946 −0.234973 0.972002i \(-0.575500\pi\)
−0.234973 + 0.972002i \(0.575500\pi\)
\(212\) 13326.9 0.296523
\(213\) 15733.5 15733.5i 0.346789 0.346789i
\(214\) 8546.19 + 8546.19i 0.186614 + 0.186614i
\(215\) 67075.4 49752.7i 1.45106 1.07632i
\(216\) 13905.7 13905.7i 0.298047 0.298047i
\(217\) 96076.8i 2.04032i
\(218\) −55961.0 −1.17753
\(219\) −13858.5 + 13858.5i −0.288954 + 0.288954i
\(220\) −10730.3 1591.04i −0.221700 0.0328726i
\(221\) 475.018 63.4215i 0.00972581 0.00129853i
\(222\) 26361.8i 0.534896i
\(223\) 34337.0 34337.0i 0.690483 0.690483i −0.271855 0.962338i \(-0.587637\pi\)
0.962338 + 0.271855i \(0.0876372\pi\)
\(224\) 64610.5 1.28768
\(225\) −10173.0 + 33550.3i −0.200948 + 0.662722i
\(226\) 36555.7 + 36555.7i 0.715712 + 0.715712i
\(227\) 37503.4 37503.4i 0.727812 0.727812i −0.242371 0.970184i \(-0.577925\pi\)
0.970184 + 0.242371i \(0.0779252\pi\)
\(228\) 7231.13 + 7231.13i 0.139103 + 0.139103i
\(229\) 5100.19 5100.19i 0.0972557 0.0972557i −0.656805 0.754061i \(-0.728092\pi\)
0.754061 + 0.656805i \(0.228092\pi\)
\(230\) −8734.23 + 58905.6i −0.165108 + 1.11353i
\(231\) 42643.4i 0.799149i
\(232\) −61042.5 61042.5i −1.13411 1.13411i
\(233\) 61062.0 1.12476 0.562379 0.826880i \(-0.309886\pi\)
0.562379 + 0.826880i \(0.309886\pi\)
\(234\) 15979.8 20904.3i 0.291837 0.381773i
\(235\) −12097.6 1793.78i −0.219061 0.0324813i
\(236\) −5322.49 5322.49i −0.0955633 0.0955633i
\(237\) 32925.8i 0.586192i
\(238\) −548.069 −0.00967568
\(239\) −14053.0 14053.0i −0.246021 0.246021i 0.573315 0.819335i \(-0.305657\pi\)
−0.819335 + 0.573315i \(0.805657\pi\)
\(240\) −9493.81 12799.3i −0.164823 0.222210i
\(241\) 18222.3 18222.3i 0.313739 0.313739i −0.532617 0.846356i \(-0.678792\pi\)
0.846356 + 0.532617i \(0.178792\pi\)
\(242\) −23366.2 23366.2i −0.398985 0.398985i
\(243\) 69557.8i 1.17797i
\(244\) 43145.1i 0.724690i
\(245\) −36456.2 49149.4i −0.607351 0.818816i
\(246\) 12715.6i 0.210120i
\(247\) −14135.4 10805.4i −0.231693 0.177112i
\(248\) 93045.7i 1.51284i
\(249\) −83581.6 83581.6i −1.34807 1.34807i
\(250\) −39208.4 18535.6i −0.627334 0.296570i
\(251\) 117416.i 1.86372i 0.362821 + 0.931859i \(0.381814\pi\)
−0.362821 + 0.931859i \(0.618186\pi\)
\(252\) 22913.1 22913.1i 0.360813 0.360813i
\(253\) −31738.9 + 31738.9i −0.495851 + 0.495851i
\(254\) 40823.3 40823.3i 0.632763 0.632763i
\(255\) −494.506 666.681i −0.00760486 0.0102527i
\(256\) −69798.4 −1.06504
\(257\) 66273.8 1.00340 0.501701 0.865041i \(-0.332708\pi\)
0.501701 + 0.865041i \(0.332708\pi\)
\(258\) 76765.8 + 76765.8i 1.15326 + 1.15326i
\(259\) 56483.6i 0.842021i
\(260\) −24423.1 25140.5i −0.361289 0.371901i
\(261\) −71807.5 −1.05412
\(262\) −13819.9 + 13819.9i −0.201328 + 0.201328i
\(263\) 20370.0i 0.294496i −0.989100 0.147248i \(-0.952958\pi\)
0.989100 0.147248i \(-0.0470415\pi\)
\(264\) 41298.0i 0.592545i
\(265\) 23925.7 + 32256.1i 0.340701 + 0.459324i
\(266\) 14388.1 + 14388.1i 0.203349 + 0.203349i
\(267\) −12083.0 12083.0i −0.169493 0.169493i
\(268\) 24542.7 + 24542.7i 0.341707 + 0.341707i
\(269\) −24183.0 −0.334199 −0.167099 0.985940i \(-0.553440\pi\)
−0.167099 + 0.985940i \(0.553440\pi\)
\(270\) 20016.6 + 2967.97i 0.274577 + 0.0407129i
\(271\) 45864.2 45864.2i 0.624504 0.624504i −0.322176 0.946680i \(-0.604414\pi\)
0.946680 + 0.322176i \(0.104414\pi\)
\(272\) 154.380 0.00208666
\(273\) −83679.9 + 109468.i −1.12278 + 1.46879i
\(274\) −60382.7 −0.804287
\(275\) −15413.1 28827.6i −0.203810 0.381192i
\(276\) 83359.7 1.09430
\(277\) −91774.5 −1.19609 −0.598043 0.801464i \(-0.704055\pi\)
−0.598043 + 0.801464i \(0.704055\pi\)
\(278\) −28422.9 + 28422.9i −0.367772 + 0.367772i
\(279\) −54727.3 54727.3i −0.703065 0.703065i
\(280\) 69937.6 + 94288.2i 0.892062 + 1.20266i
\(281\) 4584.41 4584.41i 0.0580591 0.0580591i −0.677481 0.735540i \(-0.736928\pi\)
0.735540 + 0.677481i \(0.236928\pi\)
\(282\) 15898.3i 0.199918i
\(283\) −104879. −1.30953 −0.654766 0.755832i \(-0.727233\pi\)
−0.654766 + 0.755832i \(0.727233\pi\)
\(284\) 11147.6 11147.6i 0.138212 0.138212i
\(285\) −4520.01 + 30484.0i −0.0556481 + 0.375303i
\(286\) 3246.85 + 24318.4i 0.0396944 + 0.297306i
\(287\) 27244.9i 0.330767i
\(288\) −36803.4 + 36803.4i −0.443714 + 0.443714i
\(289\) −83513.0 −0.999904
\(290\) 13028.6 87868.0i 0.154918 1.04480i
\(291\) 94452.2 + 94452.2i 1.11539 + 1.11539i
\(292\) −9819.19 + 9819.19i −0.115162 + 0.115162i
\(293\) −110200. 110200.i −1.28365 1.28365i −0.938574 0.345078i \(-0.887852\pi\)
−0.345078 0.938574i \(-0.612148\pi\)
\(294\) 56250.1 56250.1i 0.650771 0.650771i
\(295\) 3326.97 22437.8i 0.0382300 0.257832i
\(296\) 54701.6i 0.624334i
\(297\) 10785.2 + 10785.2i 0.122268 + 0.122268i
\(298\) 47683.6 0.536954
\(299\) −143757. + 19193.6i −1.60801 + 0.214691i
\(300\) −17616.1 + 58097.4i −0.195734 + 0.645527i
\(301\) −164481. 164481.i −1.81544 1.81544i
\(302\) 26540.8i 0.291005i
\(303\) 46065.3 0.501751
\(304\) −4052.84 4052.84i −0.0438543 0.0438543i
\(305\) 104427. 77458.1i 1.12257 0.832659i
\(306\) 312.191 312.191i 0.00333409 0.00333409i
\(307\) 86941.0 + 86941.0i 0.922461 + 0.922461i 0.997203 0.0747419i \(-0.0238133\pi\)
−0.0747419 + 0.997203i \(0.523813\pi\)
\(308\) 30214.1i 0.318499i
\(309\) 182472.i 1.91108i
\(310\) 76897.2 57038.0i 0.800179 0.593527i
\(311\) 97359.6i 1.00660i 0.864111 + 0.503301i \(0.167881\pi\)
−0.864111 + 0.503301i \(0.832119\pi\)
\(312\) 81039.9 106014.i 0.832511 1.08907i
\(313\) 43692.2i 0.445979i 0.974821 + 0.222990i \(0.0715816\pi\)
−0.974821 + 0.222990i \(0.928418\pi\)
\(314\) 24068.7 + 24068.7i 0.244114 + 0.244114i
\(315\) 96593.7 + 14322.4i 0.973482 + 0.144343i
\(316\) 23328.9i 0.233626i
\(317\) 72240.4 72240.4i 0.718889 0.718889i −0.249489 0.968378i \(-0.580263\pi\)
0.968378 + 0.249489i \(0.0802626\pi\)
\(318\) −36916.1 + 36916.1i −0.365058 + 0.365058i
\(319\) 47344.1 47344.1i 0.465248 0.465248i
\(320\) −51330.7 69202.8i −0.501276 0.675809i
\(321\) 50984.4 0.494798
\(322\) 165865. 1.59972
\(323\) −211.101 211.101i −0.00202342 0.00202342i
\(324\) 66020.0i 0.628906i
\(325\) 17002.8 104248.i 0.160973 0.986959i
\(326\) −8054.74 −0.0757908
\(327\) −166925. + 166925.i −1.56108 + 1.56108i
\(328\) 26385.4i 0.245254i
\(329\) 34064.2i 0.314707i
\(330\) 34130.6 25316.1i 0.313412 0.232471i
\(331\) −86768.0 86768.0i −0.791961 0.791961i 0.189852 0.981813i \(-0.439199\pi\)
−0.981813 + 0.189852i \(0.939199\pi\)
\(332\) −59220.1 59220.1i −0.537270 0.537270i
\(333\) −32174.2 32174.2i −0.290148 0.290148i
\(334\) −82686.7 −0.741213
\(335\) −15341.1 + 103464.i −0.136699 + 0.921932i
\(336\) −31386.2 + 31386.2i −0.278010 + 0.278010i
\(337\) −3730.58 −0.0328486 −0.0164243 0.999865i \(-0.505228\pi\)
−0.0164243 + 0.999865i \(0.505228\pi\)
\(338\) −39385.7 + 68798.1i −0.344751 + 0.602203i
\(339\) 218082. 1.89767
\(340\) −350.372 472.363i −0.00303090 0.00408619i
\(341\) 72165.6 0.620614
\(342\) −16391.5 −0.140142
\(343\) −2302.68 + 2302.68i −0.0195725 + 0.0195725i
\(344\) 159292. + 159292.i 1.34610 + 1.34610i
\(345\) 149655. + 201761.i 1.25734 + 1.69512i
\(346\) 12225.5 12225.5i 0.102121 0.102121i
\(347\) 34660.7i 0.287858i 0.989588 + 0.143929i \(0.0459737\pi\)
−0.989588 + 0.143929i \(0.954026\pi\)
\(348\) −124346. −1.02677
\(349\) −7412.49 + 7412.49i −0.0608574 + 0.0608574i −0.736880 0.676023i \(-0.763702\pi\)
0.676023 + 0.736880i \(0.263702\pi\)
\(350\) −35051.6 + 115599.i −0.286136 + 0.943668i
\(351\) 6522.14 + 48850.0i 0.0529391 + 0.396507i
\(352\) 48530.5i 0.391678i
\(353\) 95189.5 95189.5i 0.763906 0.763906i −0.213120 0.977026i \(-0.568363\pi\)
0.977026 + 0.213120i \(0.0683626\pi\)
\(354\) 29487.0 0.235301
\(355\) 46994.6 + 6968.12i 0.372899 + 0.0552916i
\(356\) −8561.14 8561.14i −0.0675509 0.0675509i
\(357\) −1634.82 + 1634.82i −0.0128273 + 0.0128273i
\(358\) −75154.3 75154.3i −0.586392 0.586392i
\(359\) 74820.5 74820.5i 0.580539 0.580539i −0.354512 0.935051i \(-0.615353\pi\)
0.935051 + 0.354512i \(0.115353\pi\)
\(360\) −93546.3 13870.6i −0.721808 0.107026i
\(361\) 119237.i 0.914950i
\(362\) 75075.0 + 75075.0i 0.572899 + 0.572899i
\(363\) −139397. −1.05789
\(364\) −59289.7 + 77561.2i −0.447483 + 0.585385i
\(365\) −41394.3 6137.75i −0.310710 0.0460705i
\(366\) 119514. + 119514.i 0.892186 + 0.892186i
\(367\) 77746.8i 0.577232i 0.957445 + 0.288616i \(0.0931951\pi\)
−0.957445 + 0.288616i \(0.906805\pi\)
\(368\) −46720.7 −0.344996
\(369\) −15519.2 15519.2i −0.113977 0.113977i
\(370\) 45207.9 33532.7i 0.330226 0.244943i
\(371\) 79097.6 79097.6i 0.574666 0.574666i
\(372\) −94768.6 94768.6i −0.684823 0.684823i
\(373\) 228528.i 1.64257i −0.570522 0.821283i \(-0.693259\pi\)
0.570522 0.821283i \(-0.306741\pi\)
\(374\) 411.667i 0.00294309i
\(375\) −172243. + 61664.3i −1.22484 + 0.438502i
\(376\) 32989.5i 0.233346i
\(377\) 214439. 28630.6i 1.50876 0.201441i
\(378\) 56362.4i 0.394462i
\(379\) 104576. + 104576.i 0.728039 + 0.728039i 0.970229 0.242190i \(-0.0778656\pi\)
−0.242190 + 0.970229i \(0.577866\pi\)
\(380\) −3202.56 + 21598.8i −0.0221784 + 0.149576i
\(381\) 243542.i 1.67773i
\(382\) −114582. + 114582.i −0.785219 + 0.785219i
\(383\) −188674. + 188674.i −1.28622 + 1.28622i −0.349152 + 0.937066i \(0.613530\pi\)
−0.937066 + 0.349152i \(0.886470\pi\)
\(384\) −43713.6 + 43713.6i −0.296452 + 0.296452i
\(385\) −73129.3 + 54243.1i −0.493367 + 0.365951i
\(386\) −74191.0 −0.497939
\(387\) 187383. 1.25115
\(388\) 66922.2 + 66922.2i 0.444536 + 0.444536i
\(389\) 19213.2i 0.126970i −0.997983 0.0634849i \(-0.979779\pi\)
0.997983 0.0634849i \(-0.0202215\pi\)
\(390\) 137293. + 1987.29i 0.902651 + 0.0130657i
\(391\) −2433.55 −0.0159179
\(392\) 116721. 116721.i 0.759584 0.759584i
\(393\) 82446.4i 0.533810i
\(394\) 161572.i 1.04082i
\(395\) −56464.6 + 41882.2i −0.361894 + 0.268433i
\(396\) −17210.5 17210.5i −0.109750 0.109750i
\(397\) −124954. 124954.i −0.792808 0.792808i 0.189142 0.981950i \(-0.439430\pi\)
−0.981950 + 0.189142i \(0.939430\pi\)
\(398\) −14468.4 14468.4i −0.0913388 0.0913388i
\(399\) 85836.0 0.539168
\(400\) 9873.31 32561.9i 0.0617082 0.203512i
\(401\) 59134.8 59134.8i 0.367752 0.367752i −0.498905 0.866657i \(-0.666264\pi\)
0.866657 + 0.498905i \(0.166264\pi\)
\(402\) −135969. −0.841369
\(403\) 185253. + 141612.i 1.14066 + 0.871946i
\(404\) 32638.6 0.199972
\(405\) 159793. 118525.i 0.974197 0.722604i
\(406\) −247417. −1.50099
\(407\) 42426.2 0.256121
\(408\) 1583.24 1583.24i 0.00951103 0.00951103i
\(409\) 75924.7 + 75924.7i 0.453875 + 0.453875i 0.896639 0.442763i \(-0.146002\pi\)
−0.442763 + 0.896639i \(0.646002\pi\)
\(410\) 21806.1 16174.5i 0.129721 0.0962195i
\(411\) −180114. + 180114.i −1.06626 + 1.06626i
\(412\) 129287.i 0.761658i
\(413\) −63179.9 −0.370407
\(414\) −94479.9 + 94479.9i −0.551238 + 0.551238i
\(415\) 37017.1 249652.i 0.214935 1.44957i
\(416\) 95232.3 124580.i 0.550298 0.719884i
\(417\) 169564.i 0.975126i
\(418\) 10807.3 10807.3i 0.0618534 0.0618534i
\(419\) −115602. −0.658473 −0.329236 0.944248i \(-0.606791\pi\)
−0.329236 + 0.944248i \(0.606791\pi\)
\(420\) 167267. + 24801.5i 0.948224 + 0.140598i
\(421\) −54540.6 54540.6i −0.307720 0.307720i 0.536305 0.844024i \(-0.319820\pi\)
−0.844024 + 0.536305i \(0.819820\pi\)
\(422\) 41063.6 41063.6i 0.230586 0.230586i
\(423\) −19403.7 19403.7i −0.108443 0.108443i
\(424\) −76602.1 + 76602.1i −0.426098 + 0.426098i
\(425\) 514.273 1696.06i 0.00284719 0.00938995i
\(426\) 61758.7i 0.340313i
\(427\) −256074. 256074.i −1.40446 1.40446i
\(428\) 36124.0 0.197201
\(429\) 82223.8 + 62854.0i 0.446769 + 0.341522i
\(430\) −33998.5 + 229293.i −0.183875 + 1.24009i
\(431\) 134785. + 134785.i 0.725583 + 0.725583i 0.969736 0.244154i \(-0.0785102\pi\)
−0.244154 + 0.969736i \(0.578510\pi\)
\(432\) 15876.1i 0.0850700i
\(433\) −42349.4 −0.225877 −0.112938 0.993602i \(-0.536026\pi\)
−0.112938 + 0.993602i \(0.536026\pi\)
\(434\) −188566. 188566.i −1.00111 1.00111i
\(435\) −223237. 300962.i −1.17974 1.59050i
\(436\) −118271. + 118271.i −0.622165 + 0.622165i
\(437\) 63886.6 + 63886.6i 0.334539 + 0.334539i
\(438\) 54399.1i 0.283559i
\(439\) 293456.i 1.52270i −0.648342 0.761350i \(-0.724537\pi\)
0.648342 0.761350i \(-0.275463\pi\)
\(440\) 70822.1 52531.8i 0.365817 0.271342i
\(441\) 137305.i 0.706006i
\(442\) −807.823 + 1056.77i −0.00413496 + 0.00540925i
\(443\) 239583.i 1.22081i 0.792088 + 0.610406i \(0.208994\pi\)
−0.792088 + 0.610406i \(0.791006\pi\)
\(444\) −55714.5 55714.5i −0.282619 0.282619i
\(445\) 5351.37 36090.8i 0.0270237 0.182254i
\(446\) 134783.i 0.677590i
\(447\) 142234. 142234.i 0.711851 0.711851i
\(448\) −169698. + 169698.i −0.845512 + 0.845512i
\(449\) −195773. + 195773.i −0.971091 + 0.971091i −0.999594 0.0285030i \(-0.990926\pi\)
0.0285030 + 0.999594i \(0.490926\pi\)
\(450\) −45881.6 85813.7i −0.226576 0.423772i
\(451\) 20464.3 0.100611
\(452\) 154518. 0.756312
\(453\) −79167.9 79167.9i −0.385791 0.385791i
\(454\) 147213.i 0.714222i
\(455\) −294169. 4258.04i −1.42093 0.0205677i
\(456\) −83128.0 −0.399777
\(457\) −87988.1 + 87988.1i −0.421300 + 0.421300i −0.885651 0.464351i \(-0.846288\pi\)
0.464351 + 0.885651i \(0.346288\pi\)
\(458\) 20019.8i 0.0954397i
\(459\) 826.942i 0.00392509i
\(460\) 106035. + 142954.i 0.501110 + 0.675585i
\(461\) 56098.7 + 56098.7i 0.263968 + 0.263968i 0.826664 0.562696i \(-0.190236\pi\)
−0.562696 + 0.826664i \(0.690236\pi\)
\(462\) −83694.3 83694.3i −0.392113 0.392113i
\(463\) −21715.3 21715.3i −0.101299 0.101299i 0.654641 0.755940i \(-0.272820\pi\)
−0.755940 + 0.654641i \(0.772820\pi\)
\(464\) 69692.1 0.323704
\(465\) 59237.7 399512.i 0.273963 1.84767i
\(466\) −119844. + 119844.i −0.551878 + 0.551878i
\(467\) −114586. −0.525409 −0.262705 0.964876i \(-0.584614\pi\)
−0.262705 + 0.964876i \(0.584614\pi\)
\(468\) −10407.8 77953.0i −0.0475190 0.355911i
\(469\) 291331. 1.32447
\(470\) 27264.1 20222.9i 0.123423 0.0915479i
\(471\) 143588. 0.647256
\(472\) 61186.6 0.274645
\(473\) −123545. + 123545.i −0.552210 + 0.552210i
\(474\) −64622.0 64622.0i −0.287623 0.287623i
\(475\) −58026.6 + 31024.8i −0.257182 + 0.137506i
\(476\) −1158.32 + 1158.32i −0.00511228 + 0.00511228i
\(477\) 90111.1i 0.396042i
\(478\) 55162.2 0.241427
\(479\) 258343. 258343.i 1.12597 1.12597i 0.135142 0.990826i \(-0.456851\pi\)
0.990826 0.135142i \(-0.0431492\pi\)
\(480\) −268667. 39836.6i −1.16609 0.172902i
\(481\) 108910. + 83253.7i 0.470737 + 0.359843i
\(482\) 71528.0i 0.307880i
\(483\) 494754. 494754.i 2.12078 2.12078i
\(484\) −98766.8 −0.421619
\(485\) −41831.5 + 282121.i −0.177836 + 1.19937i
\(486\) 136518. + 136518.i 0.577986 + 0.577986i
\(487\) −7983.76 + 7983.76i −0.0336628 + 0.0336628i −0.723738 0.690075i \(-0.757577\pi\)
0.690075 + 0.723738i \(0.257577\pi\)
\(488\) 247995. + 247995.i 1.04137 + 1.04137i
\(489\) −24026.3 + 24026.3i −0.100478 + 0.100478i
\(490\) 168014. + 24912.4i 0.699769 + 0.103758i
\(491\) 16818.2i 0.0697618i 0.999391 + 0.0348809i \(0.0111052\pi\)
−0.999391 + 0.0348809i \(0.988895\pi\)
\(492\) −26873.9 26873.9i −0.111020 0.111020i
\(493\) 3630.07 0.0149355
\(494\) 48950.1 6535.51i 0.200586 0.0267809i
\(495\) 10757.9 72553.8i 0.0439054 0.296108i
\(496\) 53115.0 + 53115.0i 0.215901 + 0.215901i
\(497\) 132326.i 0.535714i
\(498\) 328084. 1.32290
\(499\) −280657. 280657.i −1.12713 1.12713i −0.990641 0.136492i \(-0.956417\pi\)
−0.136492 0.990641i \(-0.543583\pi\)
\(500\) −122039. + 43691.0i −0.488158 + 0.174764i
\(501\) −246644. + 246644.i −0.982642 + 0.982642i
\(502\) −230447. 230447.i −0.914459 0.914459i
\(503\) 314884.i 1.24456i −0.782797 0.622278i \(-0.786207\pi\)
0.782797 0.622278i \(-0.213793\pi\)
\(504\) 263405.i 1.03696i
\(505\) 58595.8 + 78997.5i 0.229765 + 0.309764i
\(506\) 124585.i 0.486592i
\(507\) 87733.4 + 322699.i 0.341310 + 1.25540i
\(508\) 172556.i 0.668658i
\(509\) −177611. 177611.i −0.685544 0.685544i 0.275700 0.961244i \(-0.411090\pi\)
−0.961244 + 0.275700i \(0.911090\pi\)
\(510\) 2279.01 + 337.920i 0.00876205 + 0.00129919i
\(511\) 116557.i 0.446372i
\(512\) 77255.5 77255.5i 0.294706 0.294706i
\(513\) 21709.2 21709.2i 0.0824916 0.0824916i
\(514\) −130073. + 130073.i −0.492334 + 0.492334i
\(515\) −312922. + 232107.i −1.17983 + 0.875134i
\(516\) 324482. 1.21868
\(517\) 25586.4 0.0957258
\(518\) −110858. 110858.i −0.413149 0.413149i
\(519\) 72934.3i 0.270768i
\(520\) 284888. + 4123.70i 1.05358 + 0.0152504i
\(521\) 336979. 1.24144 0.620722 0.784031i \(-0.286840\pi\)
0.620722 + 0.784031i \(0.286840\pi\)
\(522\) 140933. 140933.i 0.517217 0.517217i
\(523\) 82275.6i 0.300793i −0.988626 0.150396i \(-0.951945\pi\)
0.988626 0.150396i \(-0.0480550\pi\)
\(524\) 58415.7i 0.212749i
\(525\) 240264. + 449373.i 0.871705 + 1.63038i
\(526\) 39979.2 + 39979.2i 0.144498 + 0.144498i
\(527\) 2766.61 + 2766.61i 0.00996156 + 0.00996156i
\(528\) 23574.9 + 23574.9i 0.0845634 + 0.0845634i
\(529\) 456637. 1.63177
\(530\) −110265. 16349.6i −0.392543 0.0582044i
\(531\) 35988.5 35988.5i 0.127636 0.127636i
\(532\) 60817.4 0.214884
\(533\) 52532.9 + 40157.5i 0.184917 + 0.141355i
\(534\) 47429.4 0.166328
\(535\) 64853.1 + 87433.4i 0.226581 + 0.305471i
\(536\) −282140. −0.982052
\(537\) −448352. −1.55479
\(538\) 47462.8 47462.8i 0.163979 0.163979i
\(539\) 90527.8 + 90527.8i 0.311605 + 0.311605i
\(540\) 48577.0 36031.6i 0.166588 0.123565i
\(541\) 185136. 185136.i 0.632551 0.632551i −0.316156 0.948707i \(-0.602392\pi\)
0.948707 + 0.316156i \(0.102392\pi\)
\(542\) 180031.i 0.612843i
\(543\) 447878. 1.51901
\(544\) 1860.52 1860.52i 0.00628688 0.00628688i
\(545\) −498591. 73928.6i −1.67861 0.248897i
\(546\) −50612.7 379082.i −0.169775 1.27159i
\(547\) 463547.i 1.54924i 0.632426 + 0.774621i \(0.282059\pi\)
−0.632426 + 0.774621i \(0.717941\pi\)
\(548\) −127616. + 127616.i −0.424956 + 0.424956i
\(549\) 291730. 0.967912
\(550\) 86829.3 + 26328.1i 0.287039 + 0.0870350i
\(551\) −95298.1 95298.1i −0.313892 0.313892i
\(552\) −479145. + 479145.i −1.57249 + 1.57249i
\(553\) 138461. + 138461.i 0.452770 + 0.452770i
\(554\) 180122. 180122.i 0.586876 0.586876i
\(555\) 34825.8 234873.i 0.113062 0.762514i
\(556\) 120141.i 0.388634i
\(557\) 196769. + 196769.i 0.634228 + 0.634228i 0.949126 0.314897i \(-0.101970\pi\)
−0.314897 + 0.949126i \(0.601970\pi\)
\(558\) 214822. 0.689937
\(559\) −559583. + 74712.0i −1.79077 + 0.239093i
\(560\) −93748.1 13900.5i −0.298942 0.0443256i
\(561\) 1227.95 + 1227.95i 0.00390172 + 0.00390172i
\(562\) 17995.2i 0.0569750i
\(563\) 167590. 0.528725 0.264363 0.964423i \(-0.414838\pi\)
0.264363 + 0.964423i \(0.414838\pi\)
\(564\) −33600.4 33600.4i −0.105630 0.105630i
\(565\) 277404. + 373990.i 0.868993 + 1.17155i
\(566\) 205841. 205841.i 0.642540 0.642540i
\(567\) −391840. 391840.i −1.21883 1.21883i
\(568\) 128151.i 0.397216i
\(569\) 212375.i 0.655962i 0.944684 + 0.327981i \(0.106368\pi\)
−0.944684 + 0.327981i \(0.893632\pi\)
\(570\) −50958.3 68700.8i −0.156843 0.211452i
\(571\) 352407.i 1.08087i 0.841387 + 0.540433i \(0.181739\pi\)
−0.841387 + 0.540433i \(0.818261\pi\)
\(572\) 58258.0 + 44533.9i 0.178059 + 0.136113i
\(573\) 683570.i 2.08197i
\(574\) −53472.4 53472.4i −0.162295 0.162295i
\(575\) −155637. + 513287.i −0.470736 + 1.55248i
\(576\) 193326.i 0.582701i
\(577\) 339319. 339319.i 1.01919 1.01919i 0.0193799 0.999812i \(-0.493831\pi\)
0.999812 0.0193799i \(-0.00616920\pi\)
\(578\) 163907. 163907.i 0.490617 0.490617i
\(579\) −221302. + 221302.i −0.660129 + 0.660129i
\(580\) −158170. 213241.i −0.470183 0.633890i
\(581\) −702963. −2.08248
\(582\) −370754. −1.09456
\(583\) −59412.1 59412.1i −0.174798 0.174798i
\(584\) 112880.i 0.330972i
\(585\) 169990. 165139.i 0.496720 0.482545i
\(586\) 432570. 1.25968
\(587\) 151834. 151834.i 0.440649 0.440649i −0.451581 0.892230i \(-0.649140\pi\)
0.892230 + 0.451581i \(0.149140\pi\)
\(588\) 237764.i 0.687688i
\(589\) 145261.i 0.418714i
\(590\) 37508.0 + 50567.4i 0.107751 + 0.145267i
\(591\) −481951. 481951.i −1.37984 1.37984i
\(592\) 31226.3 + 31226.3i 0.0891000 + 0.0891000i
\(593\) −91914.9 91914.9i −0.261383 0.261383i 0.564233 0.825616i \(-0.309172\pi\)
−0.825616 + 0.564233i \(0.809172\pi\)
\(594\) −42335.1 −0.119985
\(595\) −4883.08 724.039i −0.0137930 0.00204516i
\(596\) 100777. 100777.i 0.283707 0.283707i
\(597\) −86315.1 −0.242180
\(598\) 244476. 319816.i 0.683649 0.894331i
\(599\) −90700.3 −0.252787 −0.126394 0.991980i \(-0.540340\pi\)
−0.126394 + 0.991980i \(0.540340\pi\)
\(600\) −232684. 435196.i −0.646343 1.20888i
\(601\) 125558. 0.347613 0.173806 0.984780i \(-0.444393\pi\)
0.173806 + 0.984780i \(0.444393\pi\)
\(602\) 645638. 1.78154
\(603\) −165948. + 165948.i −0.456391 + 0.456391i
\(604\) −56092.8 56092.8i −0.153756 0.153756i
\(605\) −177315. 239052.i −0.484434 0.653103i
\(606\) −90410.3 + 90410.3i −0.246191 + 0.246191i
\(607\) 247009.i 0.670403i −0.942147 0.335201i \(-0.891196\pi\)
0.942147 0.335201i \(-0.108804\pi\)
\(608\) −97686.1 −0.264256
\(609\) −738013. + 738013.i −1.98989 + 1.98989i
\(610\) −52930.9 + 356978.i −0.142249 + 0.959360i
\(611\) 65681.7 + 50208.8i 0.175939 + 0.134492i
\(612\) 1319.60i 0.00352323i
\(613\) −134125. + 134125.i −0.356933 + 0.356933i −0.862681 0.505748i \(-0.831217\pi\)
0.505748 + 0.862681i \(0.331217\pi\)
\(614\) −341271. −0.905237
\(615\) 16798.3 113291.i 0.0444134 0.299534i
\(616\) −173668. 173668.i −0.457677 0.457677i
\(617\) 346776. 346776.i 0.910916 0.910916i −0.0854281 0.996344i \(-0.527226\pi\)
0.996344 + 0.0854281i \(0.0272258\pi\)
\(618\) −358130. 358130.i −0.937699 0.937699i
\(619\) 524188. 524188.i 1.36806 1.36806i 0.504860 0.863201i \(-0.331544\pi\)
0.863201 0.504860i \(-0.168456\pi\)
\(620\) 41971.6 283066.i 0.109187 0.736384i
\(621\) 250262.i 0.648950i
\(622\) −191083. 191083.i −0.493903 0.493903i
\(623\) −101624. −0.261830
\(624\) 14256.5 + 106780.i 0.0366138 + 0.274233i
\(625\) −324845. 216942.i −0.831602 0.555372i
\(626\) −85752.6 85752.6i −0.218826 0.218826i
\(627\) 64473.5i 0.164001i
\(628\) 101736. 0.257963
\(629\) 1626.49 + 1626.49i 0.00411103 + 0.00411103i
\(630\) −217690. + 161470.i −0.548476 + 0.406828i
\(631\) 222687. 222687.i 0.559288 0.559288i −0.369817 0.929105i \(-0.620580\pi\)
0.929105 + 0.369817i \(0.120580\pi\)
\(632\) −134093. 134093.i −0.335716 0.335716i
\(633\) 244975.i 0.611385i
\(634\) 283566.i 0.705465i
\(635\) 417650. 309789.i 1.03577 0.768279i
\(636\) 156041.i 0.385767i
\(637\) 54745.2 + 410034.i 0.134917 + 1.01051i
\(638\) 185840.i 0.456561i
\(639\) 75375.6 + 75375.6i 0.184599 + 0.184599i
\(640\) −130569. 19360.1i −0.318772 0.0472659i
\(641\) 59224.2i 0.144140i 0.997400 + 0.0720698i \(0.0229604\pi\)
−0.997400 + 0.0720698i \(0.977040\pi\)
\(642\) −100065. + 100065.i −0.242779 + 0.242779i
\(643\) 314696. 314696.i 0.761147 0.761147i −0.215383 0.976530i \(-0.569100\pi\)
0.976530 + 0.215383i \(0.0690999\pi\)
\(644\) 350548. 350548.i 0.845232 0.845232i
\(645\) 582540. + 785366.i 1.40025 + 1.88779i
\(646\) 828.637 0.00198564
\(647\) −88056.1 −0.210354 −0.105177 0.994454i \(-0.533541\pi\)
−0.105177 + 0.994454i \(0.533541\pi\)
\(648\) 379478. + 379478.i 0.903725 + 0.903725i
\(649\) 47455.9i 0.112668i
\(650\) 171231. + 237973.i 0.405281 + 0.563249i
\(651\) −1.12494e6 −2.65440
\(652\) −17023.3 + 17023.3i −0.0400451 + 0.0400451i
\(653\) 261310.i 0.612815i 0.951900 + 0.306407i \(0.0991270\pi\)
−0.951900 + 0.306407i \(0.900873\pi\)
\(654\) 655231.i 1.53193i
\(655\) −141387. + 104873.i −0.329555 + 0.244445i
\(656\) 15062.0 + 15062.0i 0.0350007 + 0.0350007i
\(657\) −66393.3 66393.3i −0.153813 0.153813i
\(658\) −66856.3 66856.3i −0.154415 0.154415i
\(659\) −805533. −1.85487 −0.927433 0.373990i \(-0.877989\pi\)
−0.927433 + 0.373990i \(0.877989\pi\)
\(660\) 18629.0 125638.i 0.0427662 0.288425i
\(661\) 209700. 209700.i 0.479949 0.479949i −0.425167 0.905115i \(-0.639784\pi\)
0.905115 + 0.425167i \(0.139784\pi\)
\(662\) 340591. 0.777173
\(663\) 742.584 + 5561.85i 0.00168935 + 0.0126530i
\(664\) 680785. 1.54409
\(665\) 109185. + 147200.i 0.246899 + 0.332863i
\(666\) 126294. 0.284730
\(667\) −1.09859e6 −2.46935
\(668\) −174755. + 174755.i −0.391630 + 0.391630i
\(669\) 402042. + 402042.i 0.898296 + 0.898296i
\(670\) −172954. 233173.i −0.385285 0.519432i
\(671\) −192343. + 192343.i −0.427200 + 0.427200i
\(672\) 756506.i 1.67523i
\(673\) 583650. 1.28861 0.644306 0.764768i \(-0.277146\pi\)
0.644306 + 0.764768i \(0.277146\pi\)
\(674\) 7321.85 7321.85i 0.0161176 0.0161176i
\(675\) 174420. + 52886.9i 0.382814 + 0.116075i
\(676\) 62161.7 + 228642.i 0.136028 + 0.500336i
\(677\) 313672.i 0.684382i −0.939630 0.342191i \(-0.888831\pi\)
0.939630 0.342191i \(-0.111169\pi\)
\(678\) −428020. + 428020.i −0.931118 + 0.931118i
\(679\) 794390. 1.72304
\(680\) 4729.02 + 701.196i 0.0102271 + 0.00151643i
\(681\) 439117. + 439117.i 0.946861 + 0.946861i
\(682\) −141636. + 141636.i −0.304513 + 0.304513i
\(683\) 224062. + 224062.i 0.480317 + 0.480317i 0.905233 0.424916i \(-0.139696\pi\)
−0.424916 + 0.905233i \(0.639696\pi\)
\(684\) −34642.8 + 34642.8i −0.0740458 + 0.0740458i
\(685\) −537986. 79769.9i −1.14654 0.170004i
\(686\) 9038.74i 0.0192070i
\(687\) 59716.6 + 59716.6i 0.126527 + 0.126527i
\(688\) −181863. −0.384208
\(689\) −35928.4 269099.i −0.0756833 0.566858i
\(690\) −689709. 102267.i −1.44866 0.214801i
\(691\) 162862. + 162862.i 0.341086 + 0.341086i 0.856775 0.515690i \(-0.172464\pi\)
−0.515690 + 0.856775i \(0.672464\pi\)
\(692\) 51676.1i 0.107914i
\(693\) −204295. −0.425394
\(694\) −68027.0 68027.0i −0.141242 0.141242i
\(695\) −290785. + 215688.i −0.602009 + 0.446536i
\(696\) 714729. 714729.i 1.47544 1.47544i
\(697\) 784.540 + 784.540i 0.00161492 + 0.00161492i
\(698\) 29096.3i 0.0597210i
\(699\) 714957.i 1.46327i
\(700\) 170234. + 318394.i 0.347416 + 0.649784i
\(701\) 692713.i 1.40967i 0.709371 + 0.704835i \(0.248979\pi\)
−0.709371 + 0.704835i \(0.751021\pi\)
\(702\) −108676. 83075.0i −0.220527 0.168576i
\(703\) 85398.8i 0.172799i
\(704\) 127464. + 127464.i 0.257183 + 0.257183i
\(705\) 21002.8 141648.i 0.0422571 0.284991i
\(706\) 373648.i 0.749642i
\(707\) 193716. 193716.i 0.387549 0.387549i
\(708\) 62319.5 62319.5i 0.124325 0.124325i
\(709\) 383095. 383095.i 0.762103 0.762103i −0.214599 0.976702i \(-0.568845\pi\)
0.976702 + 0.214599i \(0.0688445\pi\)
\(710\) −105910. + 78558.1i −0.210098 + 0.155838i
\(711\) −157741. −0.312036
\(712\) 98417.5 0.194139
\(713\) −837275. 837275.i −1.64698 1.64698i
\(714\) 6417.18i 0.0125877i
\(715\) −3198.31 + 220957.i −0.00625617 + 0.432211i
\(716\) −317671. −0.619657
\(717\) 164542. 164542.i 0.320065 0.320065i
\(718\) 293694.i 0.569699i
\(719\) 166519.i 0.322112i −0.986945 0.161056i \(-0.948510\pi\)
0.986945 0.161056i \(-0.0514900\pi\)
\(720\) 61318.8 45482.8i 0.118285 0.0877368i
\(721\) 767340. + 767340.i 1.47610 + 1.47610i
\(722\) 234021. + 234021.i 0.448933 + 0.448933i
\(723\) 213359. + 213359.i 0.408164 + 0.408164i
\(724\) 317335. 0.605398
\(725\) 232160. 765658.i 0.441684 1.45666i
\(726\) 273588. 273588.i 0.519067 0.519067i
\(727\) 552802. 1.04593 0.522963 0.852355i \(-0.324827\pi\)
0.522963 + 0.852355i \(0.324827\pi\)
\(728\) −105023. 786609.i −0.198163 1.48421i
\(729\) 169827. 0.319560
\(730\) 93289.1 69196.5i 0.175059 0.129849i
\(731\) −9472.73 −0.0177272
\(732\) 505174. 0.942798
\(733\) 340941. 340941.i 0.634558 0.634558i −0.314650 0.949208i \(-0.601887\pi\)
0.949208 + 0.314650i \(0.101887\pi\)
\(734\) −152590. 152590.i −0.283227 0.283227i
\(735\) 575477. 426856.i 1.06525 0.790144i
\(736\) −563057. + 563057.i −1.03943 + 1.03943i
\(737\) 218825.i 0.402868i
\(738\) 60917.8 0.111849
\(739\) −684691. + 684691.i −1.25373 + 1.25373i −0.299701 + 0.954033i \(0.596887\pi\)
−0.954033 + 0.299701i \(0.903113\pi\)
\(740\) 24675.1 166415.i 0.0450605 0.303898i
\(741\) 126518. 165507.i 0.230417 0.301425i
\(742\) 310483.i 0.563936i
\(743\) 86076.8 86076.8i 0.155922 0.155922i −0.624835 0.780757i \(-0.714834\pi\)
0.780757 + 0.624835i \(0.214834\pi\)
\(744\) 1.08945e6 1.96816
\(745\) 424842. + 62993.5i 0.765447 + 0.113497i
\(746\) 448523. + 448523.i 0.805947 + 0.805947i
\(747\) 400422. 400422.i 0.717590 0.717590i
\(748\) 870.041 + 870.041i 0.00155502 + 0.00155502i
\(749\) 214402. 214402.i 0.382178 0.382178i
\(750\) 217028. 459080.i 0.385828 0.816142i
\(751\) 142453.i 0.252575i −0.991994 0.126288i \(-0.959694\pi\)
0.991994 0.126288i \(-0.0403062\pi\)
\(752\) 18832.0 + 18832.0i 0.0333013 + 0.0333013i
\(753\) −1.37479e6 −2.42464
\(754\) −364678. + 477062.i −0.641456 + 0.839136i
\(755\) 35062.3 236468.i 0.0615101 0.414838i
\(756\) −119119. 119119.i −0.208420 0.208420i
\(757\) 564032.i 0.984266i −0.870520 0.492133i \(-0.836217\pi\)
0.870520 0.492133i \(-0.163783\pi\)
\(758\) −410494. −0.714445
\(759\) −371622. 371622.i −0.645086 0.645086i
\(760\) −105740. 142556.i −0.183068 0.246808i
\(761\) −472994. + 472994.i −0.816744 + 0.816744i −0.985635 0.168891i \(-0.945981\pi\)
0.168891 + 0.985635i \(0.445981\pi\)
\(762\) 477988. + 477988.i 0.823204 + 0.823204i
\(763\) 1.40392e6i 2.41153i
\(764\) 484329.i 0.829763i
\(765\) 3193.93 2369.07i 0.00545760 0.00404814i
\(766\) 740604.i 1.26220i
\(767\) −93123.6 + 121822.i −0.158296 + 0.207078i
\(768\) 817250.i 1.38558i
\(769\) −682483. 682483.i −1.15409 1.15409i −0.985725 0.168363i \(-0.946152\pi\)
−0.168363 0.985725i \(-0.553848\pi\)
\(770\) 37067.0 249988.i 0.0625181 0.421636i
\(771\) 775980.i 1.30539i
\(772\) −156799. + 156799.i −0.263093 + 0.263093i
\(773\) −235511. + 235511.i −0.394141 + 0.394141i −0.876161 0.482019i \(-0.839903\pi\)
0.482019 + 0.876161i \(0.339903\pi\)
\(774\) −367768. + 367768.i −0.613892 + 0.613892i
\(775\) 760475. 406599.i 1.26614 0.676960i
\(776\) −769328. −1.27758
\(777\) −661350. −1.09544
\(778\) 37708.9 + 37708.9i 0.0622995 + 0.0622995i
\(779\) 41192.2i 0.0678797i
\(780\) 294363. 285963.i 0.483832 0.470025i
\(781\) −99393.3 −0.162950
\(782\) 4776.22 4776.22i 0.00781036 0.00781036i
\(783\) 373309.i 0.608899i
\(784\) 133260.i 0.216804i
\(785\) 182646. + 246239.i 0.296395 + 0.399593i
\(786\) −161814. 161814.i −0.261921 0.261921i
\(787\) −499795. 499795.i −0.806942 0.806942i 0.177227 0.984170i \(-0.443287\pi\)
−0.984170 + 0.177227i \(0.943287\pi\)
\(788\) −341476. 341476.i −0.549931 0.549931i
\(789\) 238506. 0.383130
\(790\) 28620.2 193021.i 0.0458583 0.309279i
\(791\) 917089. 917089.i 1.46575 1.46575i
\(792\) 197850. 0.315417
\(793\) −871194. + 116316.i −1.38538 + 0.184967i
\(794\) 490482. 0.778005
\(795\) −377677. + 280139.i −0.597566 + 0.443241i
\(796\) −61156.8 −0.0965203
\(797\) 446000. 0.702131 0.351065 0.936351i \(-0.385820\pi\)
0.351065 + 0.936351i \(0.385820\pi\)
\(798\) −168467. + 168467.i −0.264550 + 0.264550i
\(799\) 980.909 + 980.909i 0.00153651 + 0.00153651i
\(800\) −273433. 511411.i −0.427239 0.799079i
\(801\) 57886.9 57886.9i 0.0902225 0.0902225i
\(802\) 232122.i 0.360885i
\(803\) 87548.8 0.135775
\(804\) −287364. + 287364.i −0.444549 + 0.444549i
\(805\) 1.47779e6 + 219120.i 2.28045 + 0.338135i
\(806\) −641523. + 85652.1i −0.987511 + 0.131846i
\(807\) 283151.i 0.434782i
\(808\) −187604. + 187604.i −0.287356 + 0.287356i
\(809\) 235436. 0.359729 0.179865 0.983691i \(-0.442434\pi\)
0.179865 + 0.983691i \(0.442434\pi\)
\(810\) −80994.0 + 546242.i −0.123448 + 0.832559i
\(811\) −75024.6 75024.6i −0.114068 0.114068i 0.647769 0.761837i \(-0.275702\pi\)
−0.761837 + 0.647769i \(0.775702\pi\)
\(812\) −522904. + 522904.i −0.793067 + 0.793067i
\(813\) 537011. + 537011.i 0.812460 + 0.812460i
\(814\) −83267.9 + 83267.9i −0.125669 + 0.125669i
\(815\) −71764.6 10640.9i −0.108043 0.0160200i
\(816\) 1807.59i 0.00271468i
\(817\) 248682. + 248682.i 0.372563 + 0.372563i
\(818\) −298028. −0.445400
\(819\) −524437. 400893.i −0.781853 0.597668i
\(820\) 11902.1 80270.2i 0.0177009 0.119379i
\(821\) −167606. 167606.i −0.248659 0.248659i 0.571761 0.820420i \(-0.306260\pi\)
−0.820420 + 0.571761i \(0.806260\pi\)
\(822\) 707003.i 1.04635i
\(823\) −258606. −0.381803 −0.190901 0.981609i \(-0.561141\pi\)
−0.190901 + 0.981609i \(0.561141\pi\)
\(824\) −743131. 743131.i −1.09449 1.09449i
\(825\) 337534. 180468.i 0.495918 0.265150i
\(826\) 124000. 124000.i 0.181745 0.181745i
\(827\) 622523. + 622523.i 0.910216 + 0.910216i 0.996289 0.0860730i \(-0.0274318\pi\)
−0.0860730 + 0.996289i \(0.527432\pi\)
\(828\) 399358.i 0.582508i
\(829\) 599629.i 0.872517i 0.899821 + 0.436258i \(0.143697\pi\)
−0.899821 + 0.436258i \(0.856303\pi\)
\(830\) 417328. + 562632.i 0.605789 + 0.816710i
\(831\) 1.07456e6i 1.55607i
\(832\) 77081.6 + 577331.i 0.111354 + 0.834024i
\(833\) 6941.14i 0.0100032i
\(834\) −332795. 332795.i −0.478459 0.478459i
\(835\) −736706. 109235.i −1.05663 0.156671i
\(836\) 45681.4i 0.0653622i
\(837\) −284513. + 284513.i −0.406118 + 0.406118i
\(838\) 226887. 226887.i 0.323089 0.323089i
\(839\) −706041. + 706041.i −1.00301 + 1.00301i −0.00301619 + 0.999995i \(0.500960\pi\)
−0.999995 + 0.00301619i \(0.999040\pi\)
\(840\) −1.10399e6 + 818879.i −1.56462 + 1.16054i
\(841\) 931452. 1.31695
\(842\) 214089. 0.301974
\(843\) 53677.5 + 53677.5i 0.0755331 + 0.0755331i
\(844\) 173572.i 0.243666i
\(845\) −441799. + 560933.i −0.618744 + 0.785592i
\(846\) 76165.4 0.106418
\(847\) −586198. + 586198.i −0.817104 + 0.817104i
\(848\) 87456.5i 0.121619i
\(849\) 1.22800e6i 1.70366i
\(850\) 2319.44 + 4338.12i 0.00321030 + 0.00600432i
\(851\) −492234. 492234.i −0.679693 0.679693i
\(852\) 130524. + 130524.i 0.179809 + 0.179809i
\(853\) −423516. 423516.i −0.582065 0.582065i 0.353405 0.935470i \(-0.385024\pi\)
−0.935470 + 0.353405i \(0.885024\pi\)
\(854\) 1.00517e6 1.37824
\(855\) −146042. 21654.4i −0.199777 0.0296220i
\(856\) −207638. + 207638.i −0.283374 + 0.283374i
\(857\) 881968. 1.20086 0.600428 0.799679i \(-0.294997\pi\)
0.600428 + 0.799679i \(0.294997\pi\)
\(858\) −284738. + 38016.4i −0.386786 + 0.0516412i
\(859\) −793616. −1.07553 −0.537767 0.843093i \(-0.680732\pi\)
−0.537767 + 0.843093i \(0.680732\pi\)
\(860\) 412747. + 556455.i 0.558067 + 0.752373i
\(861\) −319003. −0.430317
\(862\) −529073. −0.712034
\(863\) −137937. + 137937.i −0.185208 + 0.185208i −0.793621 0.608413i \(-0.791807\pi\)
0.608413 + 0.793621i \(0.291807\pi\)
\(864\) 191332. + 191332.i 0.256307 + 0.256307i
\(865\) 125075. 92773.7i 0.167163 0.123992i
\(866\) 83117.3 83117.3i 0.110830 0.110830i
\(867\) 977829.i 1.30084i
\(868\) −797050. −1.05790
\(869\) 104001. 104001.i 0.137721 0.137721i
\(870\) 1.02882e6 + 152549.i 1.35926 + 0.201544i
\(871\) 429405. 561736.i 0.566019 0.740451i
\(872\) 1.35963e6i 1.78808i
\(873\) −452500. + 452500.i −0.593732 + 0.593732i
\(874\) −250775. −0.328293
\(875\) −465011. + 983639.i −0.607362 + 1.28475i
\(876\) −114970. 114970.i −0.149822 0.149822i
\(877\) 498804. 498804.i 0.648531 0.648531i −0.304107 0.952638i \(-0.598358\pi\)
0.952638 + 0.304107i \(0.0983580\pi\)
\(878\) 575953. + 575953.i 0.747133 + 0.747133i
\(879\) 1.29030e6 1.29030e6i 1.66999 1.66999i
\(880\) −10441.0 + 70416.4i −0.0134827 + 0.0909303i
\(881\) 702325.i 0.904870i −0.891797 0.452435i \(-0.850556\pi\)
0.891797 0.452435i \(-0.149444\pi\)
\(882\) 269482. + 269482.i 0.346412 + 0.346412i
\(883\) 42952.3 0.0550890 0.0275445 0.999621i \(-0.491231\pi\)
0.0275445 + 0.999621i \(0.491231\pi\)
\(884\) 526.143 + 3940.74i 0.000673285 + 0.00504282i
\(885\) 262718. + 38954.5i 0.335431 + 0.0497361i
\(886\) −470219. 470219.i −0.599009 0.599009i
\(887\) 653556.i 0.830683i 0.909666 + 0.415342i \(0.136338\pi\)
−0.909666 + 0.415342i \(0.863662\pi\)
\(888\) 640485. 0.812238
\(889\) −1.02415e6 1.02415e6i −1.29587 1.29587i
\(890\) 60331.0 + 81336.8i 0.0761659 + 0.102685i
\(891\) −294320. + 294320.i −0.370736 + 0.370736i
\(892\) 284859. + 284859.i 0.358014 + 0.358014i
\(893\) 51502.4i 0.0645840i
\(894\) 558314.i 0.698559i
\(895\) −570311. 768880.i −0.711977 0.959870i
\(896\) 367653.i 0.457954i
\(897\) −224732. 1.68321e6i −0.279306 2.09196i
\(898\) 768469.i 0.952958i
\(899\) 1.24894e6 + 1.24894e6i 1.54534 + 1.54534i
\(900\) −278332. 84394.9i −0.343620 0.104191i
\(901\) 4555.37i 0.00561143i
\(902\) −40164.3 + 40164.3i −0.0493660 + 0.0493660i
\(903\) 1.92586e6 1.92586e6i 2.36183 2.36183i
\(904\) −888156. + 888156.i −1.08681 + 1.08681i
\(905\) 569709. + 768068.i 0.695594 + 0.937783i
\(906\) 310758. 0.378588
\(907\) −906967. −1.10250 −0.551248 0.834341i \(-0.685848\pi\)
−0.551248 + 0.834341i \(0.685848\pi\)
\(908\) 311127. + 311127.i 0.377369 + 0.377369i
\(909\) 220689.i 0.267087i
\(910\) 585709. 568995.i 0.707293 0.687109i
\(911\) 722252. 0.870266 0.435133 0.900366i \(-0.356701\pi\)
0.435133 + 0.900366i \(0.356701\pi\)
\(912\) 47453.5 47453.5i 0.0570530 0.0570530i
\(913\) 528012.i 0.633435i
\(914\) 345381.i 0.413433i
\(915\) 906934. + 1.22271e6i 1.08326 + 1.46043i
\(916\) 42311.0 + 42311.0i 0.0504269 + 0.0504269i
\(917\) 346707. + 346707.i 0.412310 + 0.412310i
\(918\) −1623.00 1623.00i −0.00192590 0.00192590i
\(919\) 494776. 0.585838 0.292919 0.956137i \(-0.405373\pi\)
0.292919 + 0.956137i \(0.405373\pi\)
\(920\) −1.43117e6 212207.i −1.69089 0.250717i
\(921\) −1.01797e6 + 1.01797e6i −1.20009 + 1.20009i
\(922\) −220205. −0.259039
\(923\) −255148. 195041.i −0.299494 0.228941i
\(924\) −353768. −0.414357
\(925\) 447084. 239040.i 0.522523 0.279375i
\(926\) 85239.4 0.0994074
\(927\) −874184. −1.01729
\(928\) 839899. 839899.i 0.975284 0.975284i
\(929\) −462963. 462963.i −0.536432 0.536432i 0.386047 0.922479i \(-0.373840\pi\)
−0.922479 + 0.386047i \(0.873840\pi\)
\(930\) 667841. + 900367.i 0.772160 + 1.04101i
\(931\) 182222. 182222.i 0.210233 0.210233i
\(932\) 506568.i 0.583185i
\(933\) −1.13996e6 −1.30956
\(934\) 224893. 224893.i 0.257799 0.257799i
\(935\) −543.843 + 3667.80i −0.000622085 + 0.00419548i
\(936\) 507891. + 388245.i 0.579721 + 0.443153i
\(937\) 337190.i 0.384057i 0.981389 + 0.192029i \(0.0615066\pi\)
−0.981389 + 0.192029i \(0.938493\pi\)
\(938\) −571782. + 571782.i −0.649867 + 0.649867i
\(939\) −511579. −0.580205
\(940\) 14881.1 100362.i 0.0168415 0.113583i
\(941\) −192025. 192025.i −0.216859 0.216859i 0.590314 0.807174i \(-0.299004\pi\)
−0.807174 + 0.590314i \(0.799004\pi\)
\(942\) −281814. + 281814.i −0.317585 + 0.317585i
\(943\) −237429. 237429.i −0.267000 0.267000i
\(944\) −34928.3 + 34928.3i −0.0391952 + 0.0391952i
\(945\) 74458.8 502167.i 0.0833782 0.562321i
\(946\) 484954.i 0.541899i
\(947\) 23050.0 + 23050.0i 0.0257023 + 0.0257023i 0.719841 0.694139i \(-0.244215\pi\)
−0.694139 + 0.719841i \(0.744215\pi\)
\(948\) −273152. −0.303939
\(949\) 224742. + 171799.i 0.249547 + 0.190760i
\(950\) 52995.3 174777.i 0.0587205 0.193659i
\(951\) 845842. + 845842.i 0.935251 + 0.935251i
\(952\) 13315.9i 0.0146925i
\(953\) −1.32264e6 −1.45632 −0.728159 0.685409i \(-0.759624\pi\)
−0.728159 + 0.685409i \(0.759624\pi\)
\(954\) −176857. 176857.i −0.194324 0.194324i
\(955\) −1.17226e6 + 869512.i −1.28533 + 0.953387i
\(956\) 116583. 116583.i 0.127561 0.127561i
\(957\) 554339. + 554339.i 0.605273 + 0.605273i
\(958\) 1.01408e6i 1.10494i
\(959\) 1.51485e6i 1.64714i
\(960\) 810276. 601016.i 0.879205 0.652144i
\(961\) 980212.i 1.06139i
\(962\) −377151. + 50354.9i −0.407536 + 0.0544116i
\(963\) 244255.i 0.263385i
\(964\) 151171. + 151171.i 0.162673 + 0.162673i
\(965\) −661013. 98011.7i −0.709831 0.105250i
\(966\) 1.94206e6i 2.08118i
\(967\) 367434. 367434.i 0.392940 0.392940i −0.482794 0.875734i \(-0.660378\pi\)
0.875734 + 0.482794i \(0.160378\pi\)
\(968\) 567704. 567704.i 0.605859 0.605859i
\(969\) 2471.72 2471.72i 0.00263240 0.00263240i
\(970\) −471606. 635808.i −0.501228 0.675744i
\(971\) 976368. 1.03556 0.517780 0.855514i \(-0.326759\pi\)
0.517780 + 0.855514i \(0.326759\pi\)
\(972\) 577049. 0.610774
\(973\) 713057. + 713057.i 0.753180 + 0.753180i
\(974\) 31338.8i 0.0330342i
\(975\) 1.22060e6 + 199080.i 1.28400 + 0.209421i
\(976\) −283135. −0.297231
\(977\) −326605. + 326605.i −0.342164 + 0.342164i −0.857180 0.515016i \(-0.827786\pi\)
0.515016 + 0.857180i \(0.327786\pi\)
\(978\) 94310.6i 0.0986014i
\(979\) 76331.9i 0.0796418i
\(980\) 407742. 302440.i 0.424555 0.314910i
\(981\) −799700. 799700.i −0.830977 0.830977i
\(982\) −33008.4 33008.4i −0.0342296 0.0342296i
\(983\) 517424. + 517424.i 0.535476 + 0.535476i 0.922197 0.386721i \(-0.126392\pi\)
−0.386721 + 0.922197i \(0.626392\pi\)
\(984\) 308939. 0.319067
\(985\) 213449. 1.43955e6i 0.219999 1.48373i
\(986\) −7124.57 + 7124.57i −0.00732833 + 0.00732833i
\(987\) −398848. −0.409424
\(988\) 89641.4 117266.i 0.0918322 0.120132i
\(989\) 2.86678e6 2.93091
\(990\) 121284. + 163512.i 0.123747 + 0.166832i
\(991\) −1.03885e6 −1.05781 −0.528904 0.848681i \(-0.677397\pi\)
−0.528904 + 0.848681i \(0.677397\pi\)
\(992\) 1.28024e6 1.30097
\(993\) 1.01594e6 1.01594e6i 1.03032 1.03032i
\(994\) 259711. + 259711.i 0.262855 + 0.262855i
\(995\) −109794. 148022.i −0.110901 0.149513i
\(996\) 693391. 693391.i 0.698971 0.698971i
\(997\) 1.68107e6i 1.69121i −0.533812 0.845603i \(-0.679241\pi\)
0.533812 0.845603i \(-0.320759\pi\)
\(998\) 1.10167e6 1.10609
\(999\) −167266. + 167266.i −0.167601 + 0.167601i
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 65.5.g.a.34.10 52
5.4 even 2 inner 65.5.g.a.34.17 yes 52
13.5 odd 4 inner 65.5.g.a.44.17 yes 52
65.44 odd 4 inner 65.5.g.a.44.10 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.5.g.a.34.10 52 1.1 even 1 trivial
65.5.g.a.34.17 yes 52 5.4 even 2 inner
65.5.g.a.44.10 yes 52 65.44 odd 4 inner
65.5.g.a.44.17 yes 52 13.5 odd 4 inner