Properties

Label 690.3.k.a.553.20
Level $690$
Weight $3$
Character 690.553
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [690,3,Mod(277,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.277");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (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: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 553.20
Character \(\chi\) \(=\) 690.553
Dual form 690.3.k.a.277.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(1.06006 - 4.88634i) q^{5} +2.44949 q^{6} +(6.77823 - 6.77823i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(1.06006 - 4.88634i) q^{5} +2.44949 q^{6} +(6.77823 - 6.77823i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-3.82628 - 5.94639i) q^{10} +6.48073 q^{11} +(2.44949 - 2.44949i) q^{12} +(7.70435 + 7.70435i) q^{13} -13.5565i q^{14} +(7.28281 - 4.68622i) q^{15} -4.00000 q^{16} +(0.781759 - 0.781759i) q^{17} +(3.00000 + 3.00000i) q^{18} +0.529087i q^{19} +(-9.77267 - 2.12011i) q^{20} +16.6032 q^{21} +(6.48073 - 6.48073i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-22.7526 - 10.3596i) q^{25} +15.4087 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-13.5565 - 13.5565i) q^{28} -22.8105i q^{29} +(2.59660 - 11.9690i) q^{30} -24.3355 q^{31} +(-4.00000 + 4.00000i) q^{32} +(7.93724 + 7.93724i) q^{33} -1.56352i q^{34} +(-25.9354 - 40.3060i) q^{35} +6.00000 q^{36} +(6.38099 - 6.38099i) q^{37} +(0.529087 + 0.529087i) q^{38} +18.8717i q^{39} +(-11.8928 + 7.65256i) q^{40} +16.5189 q^{41} +(16.6032 - 16.6032i) q^{42} +(11.3582 + 11.3582i) q^{43} -12.9615i q^{44} +(14.6590 + 3.18017i) q^{45} -6.78233 q^{46} +(-19.1854 + 19.1854i) q^{47} +(-4.89898 - 4.89898i) q^{48} -42.8889i q^{49} +(-33.1121 + 12.3930i) q^{50} +1.91491 q^{51} +(15.4087 - 15.4087i) q^{52} +(-7.76688 - 7.76688i) q^{53} +7.34847i q^{54} +(6.86994 - 31.6670i) q^{55} -27.1129 q^{56} +(-0.647996 + 0.647996i) q^{57} +(-22.8105 - 22.8105i) q^{58} -62.7613i q^{59} +(-9.37243 - 14.5656i) q^{60} +37.8465 q^{61} +(-24.3355 + 24.3355i) q^{62} +(20.3347 + 20.3347i) q^{63} +8.00000i q^{64} +(45.8131 - 29.4790i) q^{65} +15.8745 q^{66} +(-23.8308 + 23.8308i) q^{67} +(-1.56352 - 1.56352i) q^{68} -8.30662i q^{69} +(-66.2415 - 14.3706i) q^{70} +82.9169 q^{71} +(6.00000 - 6.00000i) q^{72} +(32.9265 + 32.9265i) q^{73} -12.7620i q^{74} +(-15.1782 - 40.5539i) q^{75} +1.05817 q^{76} +(43.9279 - 43.9279i) q^{77} +(18.8717 + 18.8717i) q^{78} +55.5424i q^{79} +(-4.24022 + 19.5453i) q^{80} -9.00000 q^{81} +(16.5189 - 16.5189i) q^{82} +(-53.8067 - 53.8067i) q^{83} -33.2064i q^{84} +(-2.99123 - 4.64864i) q^{85} +22.7164 q^{86} +(27.9371 - 27.9371i) q^{87} +(-12.9615 - 12.9615i) q^{88} -9.20780i q^{89} +(17.8392 - 11.4788i) q^{90} +104.444 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-29.8048 - 29.8048i) q^{93} +38.3707i q^{94} +(2.58529 + 0.560862i) q^{95} -9.79796 q^{96} +(79.6850 - 79.6850i) q^{97} +(-42.8889 - 42.8889i) q^{98} +19.4422i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 1.06006 4.88634i 0.212011 0.977267i
\(6\) 2.44949 0.408248
\(7\) 6.77823 6.77823i 0.968319 0.968319i −0.0311941 0.999513i \(-0.509931\pi\)
0.999513 + 0.0311941i \(0.00993100\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −3.82628 5.94639i −0.382628 0.594639i
\(11\) 6.48073 0.589157 0.294579 0.955627i \(-0.404821\pi\)
0.294579 + 0.955627i \(0.404821\pi\)
\(12\) 2.44949 2.44949i 0.204124 0.204124i
\(13\) 7.70435 + 7.70435i 0.592642 + 0.592642i 0.938344 0.345702i \(-0.112359\pi\)
−0.345702 + 0.938344i \(0.612359\pi\)
\(14\) 13.5565i 0.968319i
\(15\) 7.28281 4.68622i 0.485521 0.312414i
\(16\) −4.00000 −0.250000
\(17\) 0.781759 0.781759i 0.0459858 0.0459858i −0.683740 0.729726i \(-0.739648\pi\)
0.729726 + 0.683740i \(0.239648\pi\)
\(18\) 3.00000 + 3.00000i 0.166667 + 0.166667i
\(19\) 0.529087i 0.0278467i 0.999903 + 0.0139233i \(0.00443208\pi\)
−0.999903 + 0.0139233i \(0.995568\pi\)
\(20\) −9.77267 2.12011i −0.488634 0.106006i
\(21\) 16.6032 0.790629
\(22\) 6.48073 6.48073i 0.294579 0.294579i
\(23\) −3.39116 3.39116i −0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −22.7526 10.3596i −0.910102 0.414383i
\(26\) 15.4087 0.592642
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) −13.5565 13.5565i −0.484160 0.484160i
\(29\) 22.8105i 0.786570i −0.919417 0.393285i \(-0.871338\pi\)
0.919417 0.393285i \(-0.128662\pi\)
\(30\) 2.59660 11.9690i 0.0865532 0.398968i
\(31\) −24.3355 −0.785017 −0.392508 0.919748i \(-0.628393\pi\)
−0.392508 + 0.919748i \(0.628393\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) 7.93724 + 7.93724i 0.240522 + 0.240522i
\(34\) 1.56352i 0.0459858i
\(35\) −25.9354 40.3060i −0.741012 1.15160i
\(36\) 6.00000 0.166667
\(37\) 6.38099 6.38099i 0.172459 0.172459i −0.615600 0.788059i \(-0.711086\pi\)
0.788059 + 0.615600i \(0.211086\pi\)
\(38\) 0.529087 + 0.529087i 0.0139233 + 0.0139233i
\(39\) 18.8717i 0.483890i
\(40\) −11.8928 + 7.65256i −0.297320 + 0.191314i
\(41\) 16.5189 0.402899 0.201450 0.979499i \(-0.435435\pi\)
0.201450 + 0.979499i \(0.435435\pi\)
\(42\) 16.6032 16.6032i 0.395315 0.395315i
\(43\) 11.3582 + 11.3582i 0.264144 + 0.264144i 0.826735 0.562591i \(-0.190195\pi\)
−0.562591 + 0.826735i \(0.690195\pi\)
\(44\) 12.9615i 0.294579i
\(45\) 14.6590 + 3.18017i 0.325756 + 0.0706704i
\(46\) −6.78233 −0.147442
\(47\) −19.1854 + 19.1854i −0.408199 + 0.408199i −0.881110 0.472911i \(-0.843203\pi\)
0.472911 + 0.881110i \(0.343203\pi\)
\(48\) −4.89898 4.89898i −0.102062 0.102062i
\(49\) 42.8889i 0.875284i
\(50\) −33.1121 + 12.3930i −0.662243 + 0.247860i
\(51\) 1.91491 0.0375473
\(52\) 15.4087 15.4087i 0.296321 0.296321i
\(53\) −7.76688 7.76688i −0.146545 0.146545i 0.630028 0.776573i \(-0.283043\pi\)
−0.776573 + 0.630028i \(0.783043\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 6.86994 31.6670i 0.124908 0.575764i
\(56\) −27.1129 −0.484160
\(57\) −0.647996 + 0.647996i −0.0113684 + 0.0113684i
\(58\) −22.8105 22.8105i −0.393285 0.393285i
\(59\) 62.7613i 1.06375i −0.846822 0.531876i \(-0.821487\pi\)
0.846822 0.531876i \(-0.178513\pi\)
\(60\) −9.37243 14.5656i −0.156207 0.242760i
\(61\) 37.8465 0.620435 0.310218 0.950666i \(-0.399598\pi\)
0.310218 + 0.950666i \(0.399598\pi\)
\(62\) −24.3355 + 24.3355i −0.392508 + 0.392508i
\(63\) 20.3347 + 20.3347i 0.322773 + 0.322773i
\(64\) 8.00000i 0.125000i
\(65\) 45.8131 29.4790i 0.704817 0.453523i
\(66\) 15.8745 0.240522
\(67\) −23.8308 + 23.8308i −0.355683 + 0.355683i −0.862219 0.506536i \(-0.830926\pi\)
0.506536 + 0.862219i \(0.330926\pi\)
\(68\) −1.56352 1.56352i −0.0229929 0.0229929i
\(69\) 8.30662i 0.120386i
\(70\) −66.2415 14.3706i −0.946307 0.205295i
\(71\) 82.9169 1.16784 0.583922 0.811810i \(-0.301517\pi\)
0.583922 + 0.811810i \(0.301517\pi\)
\(72\) 6.00000 6.00000i 0.0833333 0.0833333i
\(73\) 32.9265 + 32.9265i 0.451048 + 0.451048i 0.895702 0.444654i \(-0.146674\pi\)
−0.444654 + 0.895702i \(0.646674\pi\)
\(74\) 12.7620i 0.172459i
\(75\) −15.1782 40.5539i −0.202377 0.540719i
\(76\) 1.05817 0.0139233
\(77\) 43.9279 43.9279i 0.570492 0.570492i
\(78\) 18.8717 + 18.8717i 0.241945 + 0.241945i
\(79\) 55.5424i 0.703069i 0.936175 + 0.351534i \(0.114340\pi\)
−0.936175 + 0.351534i \(0.885660\pi\)
\(80\) −4.24022 + 19.5453i −0.0530028 + 0.244317i
\(81\) −9.00000 −0.111111
\(82\) 16.5189 16.5189i 0.201450 0.201450i
\(83\) −53.8067 53.8067i −0.648274 0.648274i 0.304302 0.952576i \(-0.401577\pi\)
−0.952576 + 0.304302i \(0.901577\pi\)
\(84\) 33.2064i 0.395315i
\(85\) −2.99123 4.64864i −0.0351909 0.0546899i
\(86\) 22.7164 0.264144
\(87\) 27.9371 27.9371i 0.321116 0.321116i
\(88\) −12.9615 12.9615i −0.147289 0.147289i
\(89\) 9.20780i 0.103458i −0.998661 0.0517292i \(-0.983527\pi\)
0.998661 0.0517292i \(-0.0164733\pi\)
\(90\) 17.8392 11.4788i 0.198213 0.127543i
\(91\) 104.444 1.14773
\(92\) −6.78233 + 6.78233i −0.0737210 + 0.0737210i
\(93\) −29.8048 29.8048i −0.320482 0.320482i
\(94\) 38.3707i 0.408199i
\(95\) 2.58529 + 0.560862i 0.0272136 + 0.00590381i
\(96\) −9.79796 −0.102062
\(97\) 79.6850 79.6850i 0.821495 0.821495i −0.164828 0.986322i \(-0.552707\pi\)
0.986322 + 0.164828i \(0.0527068\pi\)
\(98\) −42.8889 42.8889i −0.437642 0.437642i
\(99\) 19.4422i 0.196386i
\(100\) −20.7192 + 45.5051i −0.207192 + 0.455051i
\(101\) −139.733 −1.38350 −0.691749 0.722138i \(-0.743160\pi\)
−0.691749 + 0.722138i \(0.743160\pi\)
\(102\) 1.91491 1.91491i 0.0187736 0.0187736i
\(103\) 98.3312 + 98.3312i 0.954672 + 0.954672i 0.999016 0.0443444i \(-0.0141199\pi\)
−0.0443444 + 0.999016i \(0.514120\pi\)
\(104\) 30.8174i 0.296321i
\(105\) 17.6003 81.1289i 0.167622 0.772656i
\(106\) −15.5338 −0.146545
\(107\) −11.4279 + 11.4279i −0.106803 + 0.106803i −0.758489 0.651686i \(-0.774062\pi\)
0.651686 + 0.758489i \(0.274062\pi\)
\(108\) 7.34847 + 7.34847i 0.0680414 + 0.0680414i
\(109\) 79.8261i 0.732350i 0.930546 + 0.366175i \(0.119333\pi\)
−0.930546 + 0.366175i \(0.880667\pi\)
\(110\) −24.7971 38.5370i −0.225428 0.350336i
\(111\) 15.6302 0.140812
\(112\) −27.1129 + 27.1129i −0.242080 + 0.242080i
\(113\) 80.7359 + 80.7359i 0.714477 + 0.714477i 0.967468 0.252992i \(-0.0814145\pi\)
−0.252992 + 0.967468i \(0.581415\pi\)
\(114\) 1.29599i 0.0113684i
\(115\) −20.1652 + 12.9755i −0.175350 + 0.112831i
\(116\) −45.6211 −0.393285
\(117\) −23.1130 + 23.1130i −0.197547 + 0.197547i
\(118\) −62.7613 62.7613i −0.531876 0.531876i
\(119\) 10.5979i 0.0890579i
\(120\) −23.9381 5.19319i −0.199484 0.0432766i
\(121\) −79.0002 −0.652894
\(122\) 37.8465 37.8465i 0.310218 0.310218i
\(123\) 20.2314 + 20.2314i 0.164483 + 0.164483i
\(124\) 48.6710i 0.392508i
\(125\) −74.7394 + 100.195i −0.597915 + 0.801559i
\(126\) 40.6694 0.322773
\(127\) −130.755 + 130.755i −1.02957 + 1.02957i −0.0300209 + 0.999549i \(0.509557\pi\)
−0.999549 + 0.0300209i \(0.990443\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 27.8218i 0.215673i
\(130\) 16.3341 75.2921i 0.125647 0.579170i
\(131\) 38.3122 0.292459 0.146230 0.989251i \(-0.453286\pi\)
0.146230 + 0.989251i \(0.453286\pi\)
\(132\) 15.8745 15.8745i 0.120261 0.120261i
\(133\) 3.58627 + 3.58627i 0.0269645 + 0.0269645i
\(134\) 47.6616i 0.355683i
\(135\) 14.0587 + 21.8484i 0.104138 + 0.161840i
\(136\) −3.12703 −0.0229929
\(137\) −43.2358 + 43.2358i −0.315589 + 0.315589i −0.847070 0.531481i \(-0.821636\pi\)
0.531481 + 0.847070i \(0.321636\pi\)
\(138\) −8.30662 8.30662i −0.0601929 0.0601929i
\(139\) 113.502i 0.816562i 0.912856 + 0.408281i \(0.133872\pi\)
−0.912856 + 0.408281i \(0.866128\pi\)
\(140\) −80.6121 + 51.8708i −0.575801 + 0.370506i
\(141\) −46.9944 −0.333293
\(142\) 82.9169 82.9169i 0.583922 0.583922i
\(143\) 49.9298 + 49.9298i 0.349159 + 0.349159i
\(144\) 12.0000i 0.0833333i
\(145\) −111.460 24.1805i −0.768690 0.166762i
\(146\) 65.8530 0.451048
\(147\) 52.5280 52.5280i 0.357333 0.357333i
\(148\) −12.7620 12.7620i −0.0862295 0.0862295i
\(149\) 80.8820i 0.542832i 0.962462 + 0.271416i \(0.0874920\pi\)
−0.962462 + 0.271416i \(0.912508\pi\)
\(150\) −55.7322 25.3757i −0.371548 0.169171i
\(151\) −54.8655 −0.363348 −0.181674 0.983359i \(-0.558152\pi\)
−0.181674 + 0.983359i \(0.558152\pi\)
\(152\) 1.05817 1.05817i 0.00696167 0.00696167i
\(153\) 2.34528 + 2.34528i 0.0153286 + 0.0153286i
\(154\) 87.8558i 0.570492i
\(155\) −25.7970 + 118.912i −0.166432 + 0.767171i
\(156\) 37.7434 0.241945
\(157\) −143.794 + 143.794i −0.915885 + 0.915885i −0.996727 0.0808422i \(-0.974239\pi\)
0.0808422 + 0.996727i \(0.474239\pi\)
\(158\) 55.5424 + 55.5424i 0.351534 + 0.351534i
\(159\) 19.0249i 0.119653i
\(160\) 15.3051 + 23.7856i 0.0956570 + 0.148660i
\(161\) −45.9722 −0.285542
\(162\) −9.00000 + 9.00000i −0.0555556 + 0.0555556i
\(163\) 108.194 + 108.194i 0.663769 + 0.663769i 0.956266 0.292497i \(-0.0944862\pi\)
−0.292497 + 0.956266i \(0.594486\pi\)
\(164\) 33.0377i 0.201450i
\(165\) 47.1979 30.3701i 0.286048 0.184061i
\(166\) −107.613 −0.648274
\(167\) 178.168 178.168i 1.06688 1.06688i 0.0692787 0.997597i \(-0.477930\pi\)
0.997597 0.0692787i \(-0.0220698\pi\)
\(168\) −33.2064 33.2064i −0.197657 0.197657i
\(169\) 50.2860i 0.297550i
\(170\) −7.63987 1.65742i −0.0449404 0.00974951i
\(171\) −1.58726 −0.00928222
\(172\) 22.7164 22.7164i 0.132072 0.132072i
\(173\) −12.0550 12.0550i −0.0696822 0.0696822i 0.671407 0.741089i \(-0.265690\pi\)
−0.741089 + 0.671407i \(0.765690\pi\)
\(174\) 55.8742i 0.321116i
\(175\) −224.442 + 84.0025i −1.28253 + 0.480014i
\(176\) −25.9229 −0.147289
\(177\) 76.8666 76.8666i 0.434275 0.434275i
\(178\) −9.20780 9.20780i −0.0517292 0.0517292i
\(179\) 47.2728i 0.264094i −0.991243 0.132047i \(-0.957845\pi\)
0.991243 0.132047i \(-0.0421550\pi\)
\(180\) 6.36034 29.3180i 0.0353352 0.162878i
\(181\) −47.4383 −0.262090 −0.131045 0.991376i \(-0.541833\pi\)
−0.131045 + 0.991376i \(0.541833\pi\)
\(182\) 104.444 104.444i 0.573867 0.573867i
\(183\) 46.3524 + 46.3524i 0.253292 + 0.253292i
\(184\) 13.5647i 0.0737210i
\(185\) −24.4154 37.9438i −0.131975 0.205102i
\(186\) −59.6096 −0.320482
\(187\) 5.06637 5.06637i 0.0270929 0.0270929i
\(188\) 38.3707 + 38.3707i 0.204100 + 0.204100i
\(189\) 49.8097i 0.263543i
\(190\) 3.14616 2.02443i 0.0165587 0.0106549i
\(191\) 126.903 0.664416 0.332208 0.943206i \(-0.392206\pi\)
0.332208 + 0.943206i \(0.392206\pi\)
\(192\) −9.79796 + 9.79796i −0.0510310 + 0.0510310i
\(193\) −148.959 148.959i −0.771811 0.771811i 0.206612 0.978423i \(-0.433756\pi\)
−0.978423 + 0.206612i \(0.933756\pi\)
\(194\) 159.370i 0.821495i
\(195\) 92.2136 + 20.0051i 0.472890 + 0.102590i
\(196\) −85.7779 −0.437642
\(197\) 10.2081 10.2081i 0.0518175 0.0518175i −0.680723 0.732541i \(-0.738334\pi\)
0.732541 + 0.680723i \(0.238334\pi\)
\(198\) 19.4422 + 19.4422i 0.0981929 + 0.0981929i
\(199\) 365.840i 1.83839i 0.393803 + 0.919195i \(0.371159\pi\)
−0.393803 + 0.919195i \(0.628841\pi\)
\(200\) 24.7860 + 66.2243i 0.123930 + 0.331121i
\(201\) −58.3732 −0.290414
\(202\) −139.733 + 139.733i −0.691749 + 0.691749i
\(203\) −154.615 154.615i −0.761651 0.761651i
\(204\) 3.82982i 0.0187736i
\(205\) 17.5109 80.7167i 0.0854192 0.393740i
\(206\) 196.662 0.954672
\(207\) 10.1735 10.1735i 0.0491473 0.0491473i
\(208\) −30.8174 30.8174i −0.148161 0.148161i
\(209\) 3.42887i 0.0164061i
\(210\) −63.5286 98.7292i −0.302517 0.470139i
\(211\) 52.5021 0.248825 0.124413 0.992231i \(-0.460295\pi\)
0.124413 + 0.992231i \(0.460295\pi\)
\(212\) −15.5338 + 15.5338i −0.0732724 + 0.0732724i
\(213\) 101.552 + 101.552i 0.476770 + 0.476770i
\(214\) 22.8558i 0.106803i
\(215\) 67.5403 43.4596i 0.314141 0.202138i
\(216\) 14.6969 0.0680414
\(217\) −164.952 + 164.952i −0.760147 + 0.760147i
\(218\) 79.8261 + 79.8261i 0.366175 + 0.366175i
\(219\) 80.6531i 0.368279i
\(220\) −63.3340 13.7399i −0.287882 0.0624540i
\(221\) 12.0459 0.0545063
\(222\) 15.6302 15.6302i 0.0704061 0.0704061i
\(223\) −20.5666 20.5666i −0.0922271 0.0922271i 0.659488 0.751715i \(-0.270773\pi\)
−0.751715 + 0.659488i \(0.770773\pi\)
\(224\) 54.2259i 0.242080i
\(225\) 31.0787 68.2577i 0.138128 0.303367i
\(226\) 161.472 0.714477
\(227\) 233.250 233.250i 1.02753 1.02753i 0.0279229 0.999610i \(-0.491111\pi\)
0.999610 0.0279229i \(-0.00888930\pi\)
\(228\) 1.29599 + 1.29599i 0.00568418 + 0.00568418i
\(229\) 407.228i 1.77829i 0.457629 + 0.889143i \(0.348699\pi\)
−0.457629 + 0.889143i \(0.651301\pi\)
\(230\) −7.18965 + 33.1407i −0.0312594 + 0.144090i
\(231\) 107.601 0.465805
\(232\) −45.6211 + 45.6211i −0.196643 + 0.196643i
\(233\) 67.8138 + 67.8138i 0.291046 + 0.291046i 0.837494 0.546447i \(-0.184020\pi\)
−0.546447 + 0.837494i \(0.684020\pi\)
\(234\) 46.2261i 0.197547i
\(235\) 73.4086 + 114.084i 0.312377 + 0.485463i
\(236\) −125.523 −0.531876
\(237\) −68.0253 + 68.0253i −0.287027 + 0.287027i
\(238\) −10.5979 10.5979i −0.0445289 0.0445289i
\(239\) 126.104i 0.527630i 0.964573 + 0.263815i \(0.0849808\pi\)
−0.964573 + 0.263815i \(0.915019\pi\)
\(240\) −29.1313 + 18.7449i −0.121380 + 0.0781036i
\(241\) 169.295 0.702467 0.351234 0.936288i \(-0.385762\pi\)
0.351234 + 0.936288i \(0.385762\pi\)
\(242\) −79.0002 + 79.0002i −0.326447 + 0.326447i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 75.6931i 0.310218i
\(245\) −209.570 45.4647i −0.855387 0.185570i
\(246\) 40.4628 0.164483
\(247\) −4.07627 + 4.07627i −0.0165031 + 0.0165031i
\(248\) 48.6710 + 48.6710i 0.196254 + 0.196254i
\(249\) 131.799i 0.529313i
\(250\) 25.4555 + 174.934i 0.101822 + 0.699737i
\(251\) 352.257 1.40341 0.701707 0.712466i \(-0.252422\pi\)
0.701707 + 0.712466i \(0.252422\pi\)
\(252\) 40.6694 40.6694i 0.161387 0.161387i
\(253\) −21.9772 21.9772i −0.0868665 0.0868665i
\(254\) 261.511i 1.02957i
\(255\) 2.02991 9.35689i 0.00796044 0.0366937i
\(256\) 16.0000 0.0625000
\(257\) 36.1183 36.1183i 0.140538 0.140538i −0.633338 0.773876i \(-0.718316\pi\)
0.773876 + 0.633338i \(0.218316\pi\)
\(258\) 27.8218 + 27.8218i 0.107836 + 0.107836i
\(259\) 86.5037i 0.333991i
\(260\) −58.9580 91.6262i −0.226762 0.352408i
\(261\) 68.4316 0.262190
\(262\) 38.3122 38.3122i 0.146230 0.146230i
\(263\) −217.636 217.636i −0.827513 0.827513i 0.159660 0.987172i \(-0.448960\pi\)
−0.987172 + 0.159660i \(0.948960\pi\)
\(264\) 31.7490i 0.120261i
\(265\) −46.1849 + 29.7182i −0.174283 + 0.112144i
\(266\) 7.17255 0.0269645
\(267\) 11.2772 11.2772i 0.0422367 0.0422367i
\(268\) 47.6616 + 47.6616i 0.177842 + 0.177842i
\(269\) 525.831i 1.95476i 0.211488 + 0.977381i \(0.432169\pi\)
−0.211488 + 0.977381i \(0.567831\pi\)
\(270\) 35.9071 + 7.78979i 0.132989 + 0.0288511i
\(271\) 518.661 1.91388 0.956939 0.290289i \(-0.0937514\pi\)
0.956939 + 0.290289i \(0.0937514\pi\)
\(272\) −3.12703 + 3.12703i −0.0114965 + 0.0114965i
\(273\) 127.917 + 127.917i 0.468560 + 0.468560i
\(274\) 86.4715i 0.315589i
\(275\) −147.453 67.1376i −0.536193 0.244137i
\(276\) −16.6132 −0.0601929
\(277\) −223.617 + 223.617i −0.807281 + 0.807281i −0.984222 0.176940i \(-0.943380\pi\)
0.176940 + 0.984222i \(0.443380\pi\)
\(278\) 113.502 + 113.502i 0.408281 + 0.408281i
\(279\) 73.0066i 0.261672i
\(280\) −28.7412 + 132.483i −0.102647 + 0.473153i
\(281\) 425.954 1.51585 0.757926 0.652341i \(-0.226213\pi\)
0.757926 + 0.652341i \(0.226213\pi\)
\(282\) −46.9944 + 46.9944i −0.166647 + 0.166647i
\(283\) 30.5658 + 30.5658i 0.108006 + 0.108006i 0.759045 0.651038i \(-0.225666\pi\)
−0.651038 + 0.759045i \(0.725666\pi\)
\(284\) 165.834i 0.583922i
\(285\) 2.47941 + 3.85324i 0.00869970 + 0.0135201i
\(286\) 99.8596 0.349159
\(287\) 111.969 111.969i 0.390135 0.390135i
\(288\) −12.0000 12.0000i −0.0416667 0.0416667i
\(289\) 287.778i 0.995771i
\(290\) −135.640 + 87.2795i −0.467726 + 0.300964i
\(291\) 195.188 0.670748
\(292\) 65.8530 65.8530i 0.225524 0.225524i
\(293\) −237.549 237.549i −0.810749 0.810749i 0.173997 0.984746i \(-0.444332\pi\)
−0.984746 + 0.173997i \(0.944332\pi\)
\(294\) 105.056i 0.357333i
\(295\) −306.673 66.5305i −1.03957 0.225527i
\(296\) −25.5239 −0.0862295
\(297\) −23.8117 + 23.8117i −0.0801741 + 0.0801741i
\(298\) 80.8820 + 80.8820i 0.271416 + 0.271416i
\(299\) 52.2534i 0.174761i
\(300\) −81.1079 + 30.3565i −0.270360 + 0.101188i
\(301\) 153.977 0.511552
\(302\) −54.8655 + 54.8655i −0.181674 + 0.181674i
\(303\) −171.138 171.138i −0.564811 0.564811i
\(304\) 2.11635i 0.00696167i
\(305\) 40.1195 184.931i 0.131539 0.606331i
\(306\) 4.69055 0.0153286
\(307\) −237.912 + 237.912i −0.774959 + 0.774959i −0.978969 0.204010i \(-0.934602\pi\)
0.204010 + 0.978969i \(0.434602\pi\)
\(308\) −87.8558 87.8558i −0.285246 0.285246i
\(309\) 240.861i 0.779486i
\(310\) 93.1145 + 144.709i 0.300369 + 0.466802i
\(311\) −81.3114 −0.261452 −0.130726 0.991419i \(-0.541731\pi\)
−0.130726 + 0.991419i \(0.541731\pi\)
\(312\) 37.7434 37.7434i 0.120973 0.120973i
\(313\) −327.200 327.200i −1.04537 1.04537i −0.998921 0.0464467i \(-0.985210\pi\)
−0.0464467 0.998921i \(-0.514790\pi\)
\(314\) 287.588i 0.915885i
\(315\) 120.918 77.8063i 0.383867 0.247004i
\(316\) 111.085 0.351534
\(317\) 274.470 274.470i 0.865837 0.865837i −0.126171 0.992008i \(-0.540269\pi\)
0.992008 + 0.126171i \(0.0402690\pi\)
\(318\) −19.0249 19.0249i −0.0598267 0.0598267i
\(319\) 147.829i 0.463414i
\(320\) 39.0907 + 8.48045i 0.122158 + 0.0265014i
\(321\) −27.9925 −0.0872040
\(322\) −45.9722 + 45.9722i −0.142771 + 0.142771i
\(323\) 0.413618 + 0.413618i 0.00128055 + 0.00128055i
\(324\) 18.0000i 0.0555556i
\(325\) −95.4798 255.108i −0.293784 0.784946i
\(326\) 216.389 0.663769
\(327\) −97.7666 + 97.7666i −0.298981 + 0.298981i
\(328\) −33.0377 33.0377i −0.100725 0.100725i
\(329\) 260.086i 0.790535i
\(330\) 16.8278 77.5680i 0.0509934 0.235055i
\(331\) 209.454 0.632791 0.316396 0.948627i \(-0.397527\pi\)
0.316396 + 0.948627i \(0.397527\pi\)
\(332\) −107.613 + 107.613i −0.324137 + 0.324137i
\(333\) 19.1430 + 19.1430i 0.0574864 + 0.0574864i
\(334\) 356.337i 1.06688i
\(335\) 91.1832 + 141.707i 0.272189 + 0.423006i
\(336\) −66.4129 −0.197657
\(337\) −267.075 + 267.075i −0.792506 + 0.792506i −0.981901 0.189395i \(-0.939347\pi\)
0.189395 + 0.981901i \(0.439347\pi\)
\(338\) −50.2860 50.2860i −0.148775 0.148775i
\(339\) 197.762i 0.583368i
\(340\) −9.29729 + 5.98246i −0.0273450 + 0.0175955i
\(341\) −157.712 −0.462498
\(342\) −1.58726 + 1.58726i −0.00464111 + 0.00464111i
\(343\) 41.4222 + 41.4222i 0.120765 + 0.120765i
\(344\) 45.4328i 0.132072i
\(345\) −40.5890 8.80549i −0.117649 0.0255232i
\(346\) −24.1100 −0.0696822
\(347\) 302.377 302.377i 0.871403 0.871403i −0.121222 0.992625i \(-0.538681\pi\)
0.992625 + 0.121222i \(0.0386813\pi\)
\(348\) −55.8742 55.8742i −0.160558 0.160558i
\(349\) 38.7883i 0.111141i 0.998455 + 0.0555706i \(0.0176978\pi\)
−0.998455 + 0.0555706i \(0.982302\pi\)
\(350\) −140.439 + 308.444i −0.401255 + 0.881270i
\(351\) −56.6152 −0.161297
\(352\) −25.9229 + 25.9229i −0.0736446 + 0.0736446i
\(353\) 228.425 + 228.425i 0.647096 + 0.647096i 0.952290 0.305194i \(-0.0987213\pi\)
−0.305194 + 0.952290i \(0.598721\pi\)
\(354\) 153.733i 0.434275i
\(355\) 87.8966 405.160i 0.247596 1.14130i
\(356\) −18.4156 −0.0517292
\(357\) 12.9797 12.9797i 0.0363577 0.0363577i
\(358\) −47.2728 47.2728i −0.132047 0.132047i
\(359\) 572.493i 1.59469i −0.603525 0.797344i \(-0.706238\pi\)
0.603525 0.797344i \(-0.293762\pi\)
\(360\) −22.9577 35.6784i −0.0637713 0.0991065i
\(361\) 360.720 0.999225
\(362\) −47.4383 + 47.4383i −0.131045 + 0.131045i
\(363\) −96.7550 96.7550i −0.266543 0.266543i
\(364\) 208.888i 0.573867i
\(365\) 195.794 125.986i 0.536421 0.345167i
\(366\) 92.7047 0.253292
\(367\) −156.250 + 156.250i −0.425750 + 0.425750i −0.887178 0.461428i \(-0.847337\pi\)
0.461428 + 0.887178i \(0.347337\pi\)
\(368\) 13.5647 + 13.5647i 0.0368605 + 0.0368605i
\(369\) 49.5566i 0.134300i
\(370\) −62.3593 13.5284i −0.168539 0.0365633i
\(371\) −105.291 −0.283804
\(372\) −59.6096 + 59.6096i −0.160241 + 0.160241i
\(373\) 14.7884 + 14.7884i 0.0396472 + 0.0396472i 0.726652 0.687005i \(-0.241075\pi\)
−0.687005 + 0.726652i \(0.741075\pi\)
\(374\) 10.1327i 0.0270929i
\(375\) −214.250 + 31.1765i −0.571333 + 0.0831374i
\(376\) 76.7415 0.204100
\(377\) 175.740 175.740i 0.466155 0.466155i
\(378\) 49.8097 + 49.8097i 0.131772 + 0.131772i
\(379\) 39.4302i 0.104038i −0.998646 0.0520188i \(-0.983434\pi\)
0.998646 0.0520188i \(-0.0165656\pi\)
\(380\) 1.12172 5.17059i 0.00295190 0.0136068i
\(381\) −320.284 −0.840640
\(382\) 126.903 126.903i 0.332208 0.332208i
\(383\) −262.977 262.977i −0.686624 0.686624i 0.274860 0.961484i \(-0.411368\pi\)
−0.961484 + 0.274860i \(0.911368\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −168.080 261.213i −0.436573 0.678474i
\(386\) −297.919 −0.771811
\(387\) −34.0746 + 34.0746i −0.0880480 + 0.0880480i
\(388\) −159.370 159.370i −0.410747 0.410747i
\(389\) 412.312i 1.05993i 0.848021 + 0.529963i \(0.177794\pi\)
−0.848021 + 0.529963i \(0.822206\pi\)
\(390\) 112.219 72.2085i 0.287740 0.185150i
\(391\) −5.30215 −0.0135605
\(392\) −85.7779 + 85.7779i −0.218821 + 0.218821i
\(393\) 46.9226 + 46.9226i 0.119396 + 0.119396i
\(394\) 20.4161i 0.0518175i
\(395\) 271.399 + 58.8781i 0.687086 + 0.149058i
\(396\) 38.8844 0.0981929
\(397\) 79.4123 79.4123i 0.200031 0.200031i −0.599982 0.800013i \(-0.704826\pi\)
0.800013 + 0.599982i \(0.204826\pi\)
\(398\) 365.840 + 365.840i 0.919195 + 0.919195i
\(399\) 8.78454i 0.0220164i
\(400\) 91.0102 + 41.4383i 0.227526 + 0.103596i
\(401\) −604.333 −1.50706 −0.753532 0.657411i \(-0.771651\pi\)
−0.753532 + 0.657411i \(0.771651\pi\)
\(402\) −58.3732 + 58.3732i −0.145207 + 0.145207i
\(403\) −187.489 187.489i −0.465234 0.465234i
\(404\) 279.467i 0.691749i
\(405\) −9.54051 + 43.9770i −0.0235568 + 0.108585i
\(406\) −309.230 −0.761651
\(407\) 41.3534 41.3534i 0.101606 0.101606i
\(408\) −3.82982 3.82982i −0.00938681 0.00938681i
\(409\) 31.8712i 0.0779247i 0.999241 + 0.0389624i \(0.0124052\pi\)
−0.999241 + 0.0389624i \(0.987595\pi\)
\(410\) −63.2058 98.2277i −0.154161 0.239580i
\(411\) −105.906 −0.257678
\(412\) 196.662 196.662i 0.477336 0.477336i
\(413\) −425.411 425.411i −1.03005 1.03005i
\(414\) 20.3470i 0.0491473i
\(415\) −319.956 + 205.880i −0.770978 + 0.496095i
\(416\) −61.6348 −0.148161
\(417\) −139.011 + 139.011i −0.333360 + 0.333360i
\(418\) 3.42887 + 3.42887i 0.00820303 + 0.00820303i
\(419\) 542.434i 1.29459i 0.762239 + 0.647296i \(0.224100\pi\)
−0.762239 + 0.647296i \(0.775900\pi\)
\(420\) −162.258 35.2007i −0.386328 0.0838112i
\(421\) −377.783 −0.897347 −0.448673 0.893696i \(-0.648103\pi\)
−0.448673 + 0.893696i \(0.648103\pi\)
\(422\) 52.5021 52.5021i 0.124413 0.124413i
\(423\) −57.5561 57.5561i −0.136066 0.136066i
\(424\) 31.0675i 0.0732724i
\(425\) −25.8857 + 9.68832i −0.0609075 + 0.0227960i
\(426\) 203.104 0.476770
\(427\) 256.533 256.533i 0.600779 0.600779i
\(428\) 22.8558 + 22.8558i 0.0534013 + 0.0534013i
\(429\) 122.303i 0.285087i
\(430\) 24.0807 111.000i 0.0560015 0.258139i
\(431\) −380.401 −0.882600 −0.441300 0.897360i \(-0.645483\pi\)
−0.441300 + 0.897360i \(0.645483\pi\)
\(432\) 14.6969 14.6969i 0.0340207 0.0340207i
\(433\) −520.972 520.972i −1.20317 1.20317i −0.973197 0.229972i \(-0.926137\pi\)
−0.229972 0.973197i \(-0.573863\pi\)
\(434\) 329.904i 0.760147i
\(435\) −106.895 166.125i −0.245736 0.381896i
\(436\) 159.652 0.366175
\(437\) 1.79422 1.79422i 0.00410577 0.00410577i
\(438\) 80.6531 + 80.6531i 0.184139 + 0.184139i
\(439\) 62.4039i 0.142150i 0.997471 + 0.0710750i \(0.0226430\pi\)
−0.997471 + 0.0710750i \(0.977357\pi\)
\(440\) −77.0739 + 49.5942i −0.175168 + 0.112714i
\(441\) 128.667 0.291761
\(442\) 12.0459 12.0459i 0.0272531 0.0272531i
\(443\) 3.05050 + 3.05050i 0.00688601 + 0.00688601i 0.710541 0.703655i \(-0.248450\pi\)
−0.703655 + 0.710541i \(0.748450\pi\)
\(444\) 31.2603i 0.0704061i
\(445\) −44.9924 9.76079i −0.101107 0.0219344i
\(446\) −41.1333 −0.0922271
\(447\) −99.0598 + 99.0598i −0.221610 + 0.221610i
\(448\) 54.2259 + 54.2259i 0.121040 + 0.121040i
\(449\) 122.374i 0.272547i −0.990671 0.136274i \(-0.956487\pi\)
0.990671 0.136274i \(-0.0435127\pi\)
\(450\) −37.1789 99.3364i −0.0826199 0.220748i
\(451\) 107.054 0.237371
\(452\) 161.472 161.472i 0.357238 0.357238i
\(453\) −67.1963 67.1963i −0.148336 0.148336i
\(454\) 466.500i 1.02753i
\(455\) 110.716 510.347i 0.243332 1.12164i
\(456\) 2.59198 0.00568418
\(457\) 191.581 191.581i 0.419213 0.419213i −0.465719 0.884933i \(-0.654204\pi\)
0.884933 + 0.465719i \(0.154204\pi\)
\(458\) 407.228 + 407.228i 0.889143 + 0.889143i
\(459\) 5.74473i 0.0125158i
\(460\) 25.9511 + 40.3304i 0.0564154 + 0.0876748i
\(461\) −69.9790 −0.151798 −0.0758992 0.997115i \(-0.524183\pi\)
−0.0758992 + 0.997115i \(0.524183\pi\)
\(462\) 107.601 107.601i 0.232902 0.232902i
\(463\) −506.603 506.603i −1.09417 1.09417i −0.995078 0.0990971i \(-0.968405\pi\)
−0.0990971 0.995078i \(-0.531595\pi\)
\(464\) 91.2422i 0.196643i
\(465\) −177.231 + 114.042i −0.381142 + 0.245251i
\(466\) 135.628 0.291046
\(467\) 361.691 361.691i 0.774498 0.774498i −0.204391 0.978889i \(-0.565521\pi\)
0.978889 + 0.204391i \(0.0655215\pi\)
\(468\) 46.2261 + 46.2261i 0.0987737 + 0.0987737i
\(469\) 323.061i 0.688830i
\(470\) 187.492 + 40.6751i 0.398920 + 0.0865429i
\(471\) −352.222 −0.747817
\(472\) −125.523 + 125.523i −0.265938 + 0.265938i
\(473\) 73.6094 + 73.6094i 0.155622 + 0.155622i
\(474\) 136.051i 0.287027i
\(475\) 5.48112 12.0381i 0.0115392 0.0253433i
\(476\) −21.1958 −0.0445289
\(477\) 23.3006 23.3006i 0.0488483 0.0488483i
\(478\) 126.104 + 126.104i 0.263815 + 0.263815i
\(479\) 472.746i 0.986945i −0.869762 0.493472i \(-0.835727\pi\)
0.869762 0.493472i \(-0.164273\pi\)
\(480\) −10.3864 + 47.8761i −0.0216383 + 0.0997419i
\(481\) 98.3227 0.204413
\(482\) 169.295 169.295i 0.351234 0.351234i
\(483\) −56.3042 56.3042i −0.116572 0.116572i
\(484\) 158.000i 0.326447i
\(485\) −304.897 473.838i −0.628654 0.976986i
\(486\) −22.0454 −0.0453609
\(487\) −245.070 + 245.070i −0.503224 + 0.503224i −0.912438 0.409214i \(-0.865803\pi\)
0.409214 + 0.912438i \(0.365803\pi\)
\(488\) −75.6931 75.6931i −0.155109 0.155109i
\(489\) 265.021i 0.541965i
\(490\) −255.034 + 164.105i −0.520478 + 0.334908i
\(491\) −89.9842 −0.183267 −0.0916336 0.995793i \(-0.529209\pi\)
−0.0916336 + 0.995793i \(0.529209\pi\)
\(492\) 40.4628 40.4628i 0.0822415 0.0822415i
\(493\) −17.8323 17.8323i −0.0361711 0.0361711i
\(494\) 8.15254i 0.0165031i
\(495\) 95.0011 + 20.6098i 0.191921 + 0.0416360i
\(496\) 97.3421 0.196254
\(497\) 562.030 562.030i 1.13085 1.13085i
\(498\) −131.799 131.799i −0.264657 0.264657i
\(499\) 823.542i 1.65038i −0.564852 0.825192i \(-0.691067\pi\)
0.564852 0.825192i \(-0.308933\pi\)
\(500\) 200.390 + 149.479i 0.400780 + 0.298958i
\(501\) 436.421 0.871101
\(502\) 352.257 352.257i 0.701707 0.701707i
\(503\) −141.332 141.332i −0.280978 0.280978i 0.552521 0.833499i \(-0.313666\pi\)
−0.833499 + 0.552521i \(0.813666\pi\)
\(504\) 81.3388i 0.161387i
\(505\) −148.125 + 682.784i −0.293317 + 1.35205i
\(506\) −43.9544 −0.0868665
\(507\) 61.5875 61.5875i 0.121474 0.121474i
\(508\) 261.511 + 261.511i 0.514785 + 0.514785i
\(509\) 565.134i 1.11028i 0.831756 + 0.555141i \(0.187336\pi\)
−0.831756 + 0.555141i \(0.812664\pi\)
\(510\) −7.32698 11.3868i −0.0143666 0.0223271i
\(511\) 446.367 0.873517
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) −1.94399 1.94399i −0.00378945 0.00378945i
\(514\) 72.2366i 0.140538i
\(515\) 584.716 376.243i 1.13537 0.730568i
\(516\) 55.6436 0.107836
\(517\) −124.335 + 124.335i −0.240494 + 0.240494i
\(518\) −86.5037 86.5037i −0.166995 0.166995i
\(519\) 29.5286i 0.0568953i
\(520\) −150.584 32.6682i −0.289585 0.0628234i
\(521\) −355.537 −0.682413 −0.341206 0.939988i \(-0.610835\pi\)
−0.341206 + 0.939988i \(0.610835\pi\)
\(522\) 68.4316 68.4316i 0.131095 0.131095i
\(523\) −325.412 325.412i −0.622204 0.622204i 0.323891 0.946094i \(-0.395009\pi\)
−0.946094 + 0.323891i \(0.895009\pi\)
\(524\) 76.6244i 0.146230i
\(525\) −377.766 172.002i −0.719554 0.327624i
\(526\) −435.272 −0.827513
\(527\) −19.0245 + 19.0245i −0.0360996 + 0.0360996i
\(528\) −31.7490 31.7490i −0.0601306 0.0601306i
\(529\) 23.0000i 0.0434783i
\(530\) −16.4666 + 75.9031i −0.0310691 + 0.143213i
\(531\) 188.284 0.354584
\(532\) 7.17255 7.17255i 0.0134822 0.0134822i
\(533\) 127.267 + 127.267i 0.238775 + 0.238775i
\(534\) 22.5544i 0.0422367i
\(535\) 43.7263 + 67.9546i 0.0817313 + 0.127018i
\(536\) 95.3231 0.177842
\(537\) 57.8971 57.8971i 0.107816 0.107816i
\(538\) 525.831 + 525.831i 0.977381 + 0.977381i
\(539\) 277.952i 0.515680i
\(540\) 43.6969 28.1173i 0.0809202 0.0520691i
\(541\) 862.324 1.59394 0.796972 0.604016i \(-0.206434\pi\)
0.796972 + 0.604016i \(0.206434\pi\)
\(542\) 518.661 518.661i 0.956939 0.956939i
\(543\) −58.0998 58.0998i −0.106998 0.106998i
\(544\) 6.25407i 0.0114965i
\(545\) 390.057 + 84.6202i 0.715701 + 0.155266i
\(546\) 255.834 0.468560
\(547\) 530.824 530.824i 0.970429 0.970429i −0.0291465 0.999575i \(-0.509279\pi\)
0.999575 + 0.0291465i \(0.00927895\pi\)
\(548\) 86.4715 + 86.4715i 0.157795 + 0.157795i
\(549\) 113.540i 0.206812i
\(550\) −214.591 + 80.3155i −0.390165 + 0.146028i
\(551\) 12.0688 0.0219034
\(552\) −16.6132 + 16.6132i −0.0300965 + 0.0300965i
\(553\) 376.480 + 376.480i 0.680795 + 0.680795i
\(554\) 447.234i 0.807281i
\(555\) 16.5688 76.3742i 0.0298538 0.137611i
\(556\) 227.004 0.408281
\(557\) 82.0074 82.0074i 0.147230 0.147230i −0.629649 0.776880i \(-0.716801\pi\)
0.776880 + 0.629649i \(0.216801\pi\)
\(558\) −73.0066 73.0066i −0.130836 0.130836i
\(559\) 175.015i 0.313086i
\(560\) 103.742 + 161.224i 0.185253 + 0.287900i
\(561\) 12.4100 0.0221212
\(562\) 425.954 425.954i 0.757926 0.757926i
\(563\) −467.229 467.229i −0.829892 0.829892i 0.157610 0.987501i \(-0.449621\pi\)
−0.987501 + 0.157610i \(0.949621\pi\)
\(564\) 93.9887i 0.166647i
\(565\) 480.087 308.918i 0.849712 0.546758i
\(566\) 61.1315 0.108006
\(567\) −61.0041 + 61.0041i −0.107591 + 0.107591i
\(568\) −165.834 165.834i −0.291961 0.291961i
\(569\) 571.773i 1.00487i 0.864614 + 0.502437i \(0.167563\pi\)
−0.864614 + 0.502437i \(0.832437\pi\)
\(570\) 6.33265 + 1.37382i 0.0111099 + 0.00241022i
\(571\) 303.885 0.532197 0.266099 0.963946i \(-0.414265\pi\)
0.266099 + 0.963946i \(0.414265\pi\)
\(572\) 99.8596 99.8596i 0.174580 0.174580i
\(573\) 155.424 + 155.424i 0.271247 + 0.271247i
\(574\) 223.938i 0.390135i
\(575\) 42.0266 + 112.289i 0.0730898 + 0.195285i
\(576\) −24.0000 −0.0416667
\(577\) 334.483 334.483i 0.579693 0.579693i −0.355126 0.934819i \(-0.615562\pi\)
0.934819 + 0.355126i \(0.115562\pi\)
\(578\) 287.778 + 287.778i 0.497885 + 0.497885i
\(579\) 364.875i 0.630181i
\(580\) −48.3609 + 222.920i −0.0833809 + 0.384345i
\(581\) −729.429 −1.25547
\(582\) 195.188 195.188i 0.335374 0.335374i
\(583\) −50.3350 50.3350i −0.0863379 0.0863379i
\(584\) 131.706i 0.225524i
\(585\) 88.4370 + 137.439i 0.151174 + 0.234939i
\(586\) −475.099 −0.810749
\(587\) 102.989 102.989i 0.175450 0.175450i −0.613919 0.789369i \(-0.710408\pi\)
0.789369 + 0.613919i \(0.210408\pi\)
\(588\) −105.056 105.056i −0.178667 0.178667i
\(589\) 12.8756i 0.0218601i
\(590\) −373.204 + 240.142i −0.632548 + 0.407021i
\(591\) 25.0045 0.0423088
\(592\) −25.5239 + 25.5239i −0.0431148 + 0.0431148i
\(593\) −798.294 798.294i −1.34620 1.34620i −0.889752 0.456444i \(-0.849123\pi\)
−0.456444 0.889752i \(-0.650877\pi\)
\(594\) 47.6234i 0.0801741i
\(595\) −51.7848 11.2344i −0.0870333 0.0188813i
\(596\) 161.764 0.271416
\(597\) −448.060 + 448.060i −0.750520 + 0.750520i
\(598\) −52.2534 52.2534i −0.0873803 0.0873803i
\(599\) 176.987i 0.295471i −0.989027 0.147736i \(-0.952802\pi\)
0.989027 0.147736i \(-0.0471984\pi\)
\(600\) −50.7514 + 111.464i −0.0845856 + 0.185774i
\(601\) −879.913 −1.46408 −0.732041 0.681261i \(-0.761432\pi\)
−0.732041 + 0.681261i \(0.761432\pi\)
\(602\) 153.977 153.977i 0.255776 0.255776i
\(603\) −71.4923 71.4923i −0.118561 0.118561i
\(604\) 109.731i 0.181674i
\(605\) −83.7446 + 386.021i −0.138421 + 0.638052i
\(606\) −342.275 −0.564811
\(607\) 80.2035 80.2035i 0.132131 0.132131i −0.637948 0.770079i \(-0.720217\pi\)
0.770079 + 0.637948i \(0.220217\pi\)
\(608\) −2.11635 2.11635i −0.00348083 0.00348083i
\(609\) 378.728i 0.621886i
\(610\) −144.811 225.050i −0.237396 0.368935i
\(611\) −295.622 −0.483832
\(612\) 4.69055 4.69055i 0.00766430 0.00766430i
\(613\) −619.641 619.641i −1.01083 1.01083i −0.999941 0.0108925i \(-0.996533\pi\)
−0.0108925 0.999941i \(-0.503467\pi\)
\(614\) 475.825i 0.774959i
\(615\) 120.304 77.4110i 0.195616 0.125872i
\(616\) −175.712 −0.285246
\(617\) −29.7434 + 29.7434i −0.0482065 + 0.0482065i −0.730799 0.682593i \(-0.760852\pi\)
0.682593 + 0.730799i \(0.260852\pi\)
\(618\) 240.861 + 240.861i 0.389743 + 0.389743i
\(619\) 220.508i 0.356233i −0.984009 0.178116i \(-0.943000\pi\)
0.984009 0.178116i \(-0.0570004\pi\)
\(620\) 237.823 + 51.5940i 0.383586 + 0.0832162i
\(621\) 24.9199 0.0401286
\(622\) −81.3114 + 81.3114i −0.130726 + 0.130726i
\(623\) −62.4127 62.4127i −0.100181 0.100181i
\(624\) 75.4869i 0.120973i
\(625\) 410.358 + 471.414i 0.656573 + 0.754262i
\(626\) −654.400 −1.04537
\(627\) −4.19949 + 4.19949i −0.00669775 + 0.00669775i
\(628\) 287.588 + 287.588i 0.457942 + 0.457942i
\(629\) 9.97678i 0.0158613i
\(630\) 43.1119 198.724i 0.0684315 0.315436i
\(631\) 716.316 1.13521 0.567604 0.823302i \(-0.307871\pi\)
0.567604 + 0.823302i \(0.307871\pi\)
\(632\) 111.085 111.085i 0.175767 0.175767i
\(633\) 64.3017 + 64.3017i 0.101582 + 0.101582i
\(634\) 548.941i 0.865837i
\(635\) 500.307 + 777.523i 0.787885 + 1.22445i
\(636\) −38.0498 −0.0598267
\(637\) 330.431 330.431i 0.518730 0.518730i
\(638\) −147.829 147.829i −0.231707 0.231707i
\(639\) 248.751i 0.389281i
\(640\) 47.5711 30.6102i 0.0743299 0.0478285i
\(641\) −969.601 −1.51264 −0.756319 0.654203i \(-0.773004\pi\)
−0.756319 + 0.654203i \(0.773004\pi\)
\(642\) −27.9925 + 27.9925i −0.0436020 + 0.0436020i
\(643\) 373.341 + 373.341i 0.580623 + 0.580623i 0.935075 0.354451i \(-0.115332\pi\)
−0.354451 + 0.935075i \(0.615332\pi\)
\(644\) 91.9445i 0.142771i
\(645\) 135.947 + 29.4927i 0.210770 + 0.0457250i
\(646\) 0.827236 0.00128055
\(647\) −695.075 + 695.075i −1.07430 + 1.07430i −0.0772961 + 0.997008i \(0.524629\pi\)
−0.997008 + 0.0772961i \(0.975371\pi\)
\(648\) 18.0000 + 18.0000i 0.0277778 + 0.0277778i
\(649\) 406.739i 0.626717i
\(650\) −350.587 159.628i −0.539365 0.245581i
\(651\) −404.048 −0.620657
\(652\) 216.389 216.389i 0.331885 0.331885i
\(653\) 42.2499 + 42.2499i 0.0647012 + 0.0647012i 0.738717 0.674016i \(-0.235432\pi\)
−0.674016 + 0.738717i \(0.735432\pi\)
\(654\) 195.533i 0.298981i
\(655\) 40.6131 187.206i 0.0620047 0.285811i
\(656\) −66.0755 −0.100725
\(657\) −98.7795 + 98.7795i −0.150349 + 0.150349i
\(658\) 260.086 + 260.086i 0.395267 + 0.395267i
\(659\) 961.226i 1.45861i 0.684187 + 0.729307i \(0.260157\pi\)
−0.684187 + 0.729307i \(0.739843\pi\)
\(660\) −60.7402 94.3959i −0.0920306 0.143024i
\(661\) 163.994 0.248100 0.124050 0.992276i \(-0.460412\pi\)
0.124050 + 0.992276i \(0.460412\pi\)
\(662\) 209.454 209.454i 0.316396 0.316396i
\(663\) 14.7531 + 14.7531i 0.0222521 + 0.0222521i
\(664\) 215.227i 0.324137i
\(665\) 21.3254 13.7221i 0.0320683 0.0206347i
\(666\) 38.2859 0.0574864
\(667\) −77.3543 + 77.3543i −0.115973 + 0.115973i
\(668\) −356.337 356.337i −0.533438 0.533438i
\(669\) 50.3778i 0.0753031i
\(670\) 232.890 + 50.5239i 0.347598 + 0.0754088i
\(671\) 245.273 0.365534
\(672\) −66.4129 + 66.4129i −0.0988287 + 0.0988287i
\(673\) 171.550 + 171.550i 0.254904 + 0.254904i 0.822978 0.568074i \(-0.192311\pi\)
−0.568074 + 0.822978i \(0.692311\pi\)
\(674\) 534.149i 0.792506i
\(675\) 121.662 45.5347i 0.180240 0.0674588i
\(676\) −100.572 −0.148775
\(677\) −164.860 + 164.860i −0.243516 + 0.243516i −0.818303 0.574787i \(-0.805085\pi\)
0.574787 + 0.818303i \(0.305085\pi\)
\(678\) 197.762 + 197.762i 0.291684 + 0.291684i
\(679\) 1080.25i 1.59094i
\(680\) −3.31483 + 15.2797i −0.00487475 + 0.0224702i
\(681\) 571.343 0.838977
\(682\) −157.712 + 157.712i −0.231249 + 0.231249i
\(683\) 16.9389 + 16.9389i 0.0248007 + 0.0248007i 0.719398 0.694598i \(-0.244418\pi\)
−0.694598 + 0.719398i \(0.744418\pi\)
\(684\) 3.17452i 0.00464111i
\(685\) 165.432 + 257.097i 0.241507 + 0.375324i
\(686\) 82.8445 0.120765
\(687\) −498.750 + 498.750i −0.725982 + 0.725982i
\(688\) −45.4328 45.4328i −0.0660360 0.0660360i
\(689\) 119.677i 0.173697i
\(690\) −49.3944 + 31.7835i −0.0715862 + 0.0460630i
\(691\) 1270.25 1.83828 0.919141 0.393928i \(-0.128884\pi\)
0.919141 + 0.393928i \(0.128884\pi\)
\(692\) −24.1100 + 24.1100i −0.0348411 + 0.0348411i
\(693\) 131.784 + 131.784i 0.190164 + 0.190164i
\(694\) 604.754i 0.871403i
\(695\) 554.609 + 120.319i 0.797999 + 0.173120i
\(696\) −111.748 −0.160558
\(697\) 12.9138 12.9138i 0.0185276 0.0185276i
\(698\) 38.7883 + 38.7883i 0.0555706 + 0.0555706i
\(699\) 166.109i 0.237638i
\(700\) 168.005 + 448.884i 0.240007 + 0.641263i
\(701\) −1394.68 −1.98956 −0.994781 0.102031i \(-0.967466\pi\)
−0.994781 + 0.102031i \(0.967466\pi\)
\(702\) −56.6152 + 56.6152i −0.0806484 + 0.0806484i
\(703\) 3.37609 + 3.37609i 0.00480241 + 0.00480241i
\(704\) 51.8458i 0.0736446i
\(705\) −49.8167 + 229.630i −0.0706620 + 0.325717i
\(706\) 456.850 0.647096
\(707\) −947.145 + 947.145i −1.33967 + 1.33967i
\(708\) −153.733 153.733i −0.217137 0.217137i
\(709\) 842.555i 1.18837i 0.804328 + 0.594185i \(0.202525\pi\)
−0.804328 + 0.594185i \(0.797475\pi\)
\(710\) −317.263 493.057i −0.446850 0.694446i
\(711\) −166.627 −0.234356
\(712\) −18.4156 + 18.4156i −0.0258646 + 0.0258646i
\(713\) 82.5258 + 82.5258i 0.115744 + 0.115744i
\(714\) 25.9594i 0.0363577i
\(715\) 296.902 191.045i 0.415248 0.267196i
\(716\) −94.5456 −0.132047
\(717\) −154.445 + 154.445i −0.215404 + 0.215404i
\(718\) −572.493 572.493i −0.797344 0.797344i
\(719\) 685.162i 0.952937i −0.879191 0.476469i \(-0.841917\pi\)
0.879191 0.476469i \(-0.158083\pi\)
\(720\) −58.6360 12.7207i −0.0814389 0.0176676i
\(721\) 1333.02 1.84885
\(722\) 360.720 360.720i 0.499612 0.499612i
\(723\) 207.343 + 207.343i 0.286781 + 0.286781i
\(724\) 94.8765i 0.131045i
\(725\) −236.308 + 518.998i −0.325942 + 0.715860i
\(726\) −193.510 −0.266543
\(727\) 752.841 752.841i 1.03554 1.03554i 0.0361997 0.999345i \(-0.488475\pi\)
0.999345 0.0361997i \(-0.0115252\pi\)
\(728\) −208.888 208.888i −0.286933 0.286933i
\(729\) 27.0000i 0.0370370i
\(730\) 69.8079 321.780i 0.0956272 0.440794i
\(731\) 17.7587 0.0242938
\(732\) 92.7047 92.7047i 0.126646 0.126646i
\(733\) −232.917 232.917i −0.317758 0.317758i 0.530148 0.847905i \(-0.322137\pi\)
−0.847905 + 0.530148i \(0.822137\pi\)
\(734\) 312.501i 0.425750i
\(735\) −200.987 312.352i −0.273451 0.424969i
\(736\) 27.1293 0.0368605
\(737\) −154.441 + 154.441i −0.209553 + 0.209553i
\(738\) 49.5566 + 49.5566i 0.0671499 + 0.0671499i
\(739\) 135.488i 0.183339i 0.995789 + 0.0916696i \(0.0292204\pi\)
−0.995789 + 0.0916696i \(0.970780\pi\)
\(740\) −75.8877 + 48.8309i −0.102551 + 0.0659877i
\(741\) −9.98478 −0.0134747
\(742\) −105.291 + 105.291i −0.141902 + 0.141902i
\(743\) 726.590 + 726.590i 0.977914 + 0.977914i 0.999761 0.0218472i \(-0.00695474\pi\)
−0.0218472 + 0.999761i \(0.506955\pi\)
\(744\) 119.219i 0.160241i
\(745\) 395.217 + 85.7395i 0.530492 + 0.115087i
\(746\) 29.5768 0.0396472
\(747\) 161.420 161.420i 0.216091 0.216091i
\(748\) −10.1327 10.1327i −0.0135464 0.0135464i
\(749\) 154.922i 0.206838i
\(750\) −183.073 + 245.426i −0.244098 + 0.327235i
\(751\) −1008.88 −1.34339 −0.671694 0.740829i \(-0.734433\pi\)
−0.671694 + 0.740829i \(0.734433\pi\)
\(752\) 76.7415 76.7415i 0.102050 0.102050i
\(753\) 431.425 + 431.425i 0.572941 + 0.572941i
\(754\) 351.481i 0.466155i
\(755\) −58.1605 + 268.091i −0.0770338 + 0.355088i
\(756\) 99.6193 0.131772
\(757\) 570.746 570.746i 0.753958 0.753958i −0.221257 0.975215i \(-0.571016\pi\)
0.975215 + 0.221257i \(0.0710161\pi\)
\(758\) −39.4302 39.4302i −0.0520188 0.0520188i
\(759\) 53.8330i 0.0709262i
\(760\) −4.04887 6.29231i −0.00532746 0.00827936i
\(761\) −1183.62 −1.55535 −0.777675 0.628667i \(-0.783601\pi\)
−0.777675 + 0.628667i \(0.783601\pi\)
\(762\) −320.284 + 320.284i −0.420320 + 0.420320i
\(763\) 541.080 + 541.080i 0.709148 + 0.709148i
\(764\) 253.807i 0.332208i
\(765\) 13.9459 8.97368i 0.0182300 0.0117303i
\(766\) −525.954 −0.686624
\(767\) 483.535 483.535i 0.630424 0.630424i
\(768\) 19.5959 + 19.5959i 0.0255155 + 0.0255155i
\(769\) 363.068i 0.472130i 0.971737 + 0.236065i \(0.0758578\pi\)
−0.971737 + 0.236065i \(0.924142\pi\)
\(770\) −429.293 93.1321i −0.557523 0.120951i
\(771\) 88.4714 0.114749
\(772\) −297.919 + 297.919i −0.385905 + 0.385905i
\(773\) −1014.90 1014.90i −1.31293 1.31293i −0.919242 0.393693i \(-0.871197\pi\)
−0.393693 0.919242i \(-0.628803\pi\)
\(774\) 68.1492i 0.0880480i
\(775\) 553.695 + 252.106i 0.714446 + 0.325298i
\(776\) −318.740 −0.410747
\(777\) 105.945 105.945i 0.136351 0.136351i
\(778\) 412.312 + 412.312i 0.529963 + 0.529963i
\(779\) 8.73991i 0.0112194i
\(780\) 40.0102 184.427i 0.0512951 0.236445i
\(781\) 537.362 0.688044
\(782\) −5.30215 + 5.30215i −0.00678024 + 0.00678024i
\(783\) 83.8113 + 83.8113i 0.107039 + 0.107039i
\(784\) 171.556i 0.218821i
\(785\) 550.196 + 855.055i 0.700886 + 1.08924i
\(786\) 93.8453 0.119396
\(787\) −225.596 + 225.596i −0.286653 + 0.286653i −0.835755 0.549102i \(-0.814970\pi\)
0.549102 + 0.835755i \(0.314970\pi\)
\(788\) −20.4161 20.4161i −0.0259088 0.0259088i
\(789\) 533.097i 0.675661i
\(790\) 330.277 212.521i 0.418072 0.269014i
\(791\) 1094.49 1.38368
\(792\) 38.8844 38.8844i 0.0490964 0.0490964i
\(793\) 291.583 + 291.583i 0.367696 + 0.367696i
\(794\) 158.825i 0.200031i
\(795\) −92.9620 20.1674i −0.116933 0.0253679i
\(796\) 731.679 0.919195
\(797\) −991.681 + 991.681i −1.24427 + 1.24427i −0.286054 + 0.958213i \(0.592344\pi\)
−0.958213 + 0.286054i \(0.907656\pi\)
\(798\) 8.78454 + 8.78454i 0.0110082 + 0.0110082i
\(799\) 29.9967i 0.0375428i
\(800\) 132.449 49.5719i 0.165561 0.0619649i
\(801\) 27.6234 0.0344862
\(802\) −604.333 + 604.333i −0.753532 + 0.753532i
\(803\) 213.388 + 213.388i 0.265738 + 0.265738i
\(804\) 116.746i 0.145207i
\(805\) −48.7331 + 224.636i −0.0605381 + 0.279051i
\(806\) −374.979 −0.465234
\(807\) −644.009 + 644.009i −0.798028 + 0.798028i
\(808\) 279.467 + 279.467i 0.345875 + 0.345875i
\(809\) 846.880i 1.04682i −0.852080 0.523412i \(-0.824659\pi\)
0.852080 0.523412i \(-0.175341\pi\)
\(810\) 34.4365 + 53.5175i 0.0425142 + 0.0660710i
\(811\) −703.466 −0.867405 −0.433703 0.901056i \(-0.642793\pi\)
−0.433703 + 0.901056i \(0.642793\pi\)
\(812\) −309.230 + 309.230i −0.380826 + 0.380826i
\(813\) 635.227 + 635.227i 0.781337 + 0.781337i
\(814\) 82.7069i 0.101606i
\(815\) 643.366 413.982i 0.789406 0.507953i
\(816\) −7.65964 −0.00938681
\(817\) −6.00947 + 6.00947i −0.00735553 + 0.00735553i
\(818\) 31.8712 + 31.8712i 0.0389624 + 0.0389624i
\(819\) 313.331i 0.382578i
\(820\) −161.433 35.0219i −0.196870 0.0427096i
\(821\) −252.059 −0.307015 −0.153507 0.988147i \(-0.549057\pi\)
−0.153507 + 0.988147i \(0.549057\pi\)
\(822\) −105.906 + 105.906i −0.128839 + 0.128839i
\(823\) 511.780 + 511.780i 0.621847 + 0.621847i 0.946003 0.324156i \(-0.105080\pi\)
−0.324156 + 0.946003i \(0.605080\pi\)
\(824\) 393.325i 0.477336i
\(825\) −98.3660 262.819i −0.119232 0.318568i
\(826\) −850.822 −1.03005
\(827\) 169.581 169.581i 0.205055 0.205055i −0.597107 0.802162i \(-0.703683\pi\)
0.802162 + 0.597107i \(0.203683\pi\)
\(828\) −20.3470 20.3470i −0.0245737 0.0245737i
\(829\) 772.576i 0.931938i 0.884801 + 0.465969i \(0.154294\pi\)
−0.884801 + 0.465969i \(0.845706\pi\)
\(830\) −114.076 + 525.835i −0.137441 + 0.633537i
\(831\) −547.747 −0.659142
\(832\) −61.6348 + 61.6348i −0.0740803 + 0.0740803i
\(833\) −33.5288 33.5288i −0.0402507 0.0402507i
\(834\) 278.022i 0.333360i
\(835\) −681.722 1059.46i −0.816433 1.26881i
\(836\) 6.85773 0.00820303
\(837\) 89.4144 89.4144i 0.106827 0.106827i
\(838\) 542.434 + 542.434i 0.647296 + 0.647296i
\(839\) 252.116i 0.300496i −0.988648 0.150248i \(-0.951993\pi\)
0.988648 0.150248i \(-0.0480072\pi\)
\(840\) −197.458 + 127.057i −0.235070 + 0.151258i
\(841\) 320.679 0.381307
\(842\) −377.783 + 377.783i −0.448673 + 0.448673i
\(843\) 521.685 + 521.685i 0.618844 + 0.618844i
\(844\) 105.004i 0.124413i
\(845\) −245.714 53.3060i −0.290786 0.0630840i
\(846\) −115.112 −0.136066
\(847\) −535.482 + 535.482i −0.632210 + 0.632210i
\(848\) 31.0675 + 31.0675i 0.0366362 + 0.0366362i
\(849\) 74.8705i 0.0881867i
\(850\) −16.1974 + 35.5740i −0.0190557 + 0.0418518i
\(851\) −43.2780 −0.0508554
\(852\) 203.104 203.104i 0.238385 0.238385i
\(853\) −758.628 758.628i −0.889365 0.889365i 0.105097 0.994462i \(-0.466485\pi\)
−0.994462 + 0.105097i \(0.966485\pi\)
\(854\) 513.066i 0.600779i
\(855\) −1.68258 + 7.75588i −0.00196794 + 0.00907121i
\(856\) 45.7115 0.0534013
\(857\) −303.385 + 303.385i −0.354008 + 0.354008i −0.861598 0.507591i \(-0.830536\pi\)
0.507591 + 0.861598i \(0.330536\pi\)
\(858\) 122.303 + 122.303i 0.142544 + 0.142544i
\(859\) 1629.59i 1.89707i −0.316668 0.948536i \(-0.602564\pi\)
0.316668 0.948536i \(-0.397436\pi\)
\(860\) −86.9193 135.081i −0.101069 0.157070i
\(861\) 274.266 0.318544
\(862\) −380.401 + 380.401i −0.441300 + 0.441300i
\(863\) −545.327 545.327i −0.631896 0.631896i 0.316647 0.948543i \(-0.397443\pi\)
−0.948543 + 0.316647i \(0.897443\pi\)
\(864\) 29.3939i 0.0340207i
\(865\) −71.6839 + 46.1259i −0.0828715 + 0.0533247i
\(866\) −1041.94 −1.20317
\(867\) −352.454 + 352.454i −0.406522 + 0.406522i
\(868\) 329.904 + 329.904i 0.380073 + 0.380073i
\(869\) 359.955i 0.414218i
\(870\) −273.020 59.2298i −0.313816 0.0680802i
\(871\) −367.201 −0.421586
\(872\) 159.652 159.652i 0.183087 0.183087i
\(873\) 239.055 + 239.055i 0.273832 + 0.273832i
\(874\) 3.58844i 0.00410577i
\(875\) 172.544 + 1185.75i 0.197193 + 1.35514i
\(876\) 161.306 0.184139
\(877\) −229.151 + 229.151i −0.261290 + 0.261290i −0.825578 0.564288i \(-0.809151\pi\)
0.564288 + 0.825578i \(0.309151\pi\)
\(878\) 62.4039 + 62.4039i 0.0710750 + 0.0710750i
\(879\) 581.875i 0.661974i
\(880\) −27.4797 + 126.668i −0.0312270 + 0.143941i
\(881\) −1029.46 −1.16851 −0.584254 0.811571i \(-0.698613\pi\)
−0.584254 + 0.811571i \(0.698613\pi\)
\(882\) 128.667 128.667i 0.145881 0.145881i
\(883\) 1211.81 + 1211.81i 1.37238 + 1.37238i 0.856906 + 0.515473i \(0.172384\pi\)
0.515473 + 0.856906i \(0.327616\pi\)
\(884\) 24.0918i 0.0272531i
\(885\) −294.113 457.079i −0.332331 0.516474i
\(886\) 6.10101 0.00688601
\(887\) 653.892 653.892i 0.737196 0.737196i −0.234839 0.972034i \(-0.575456\pi\)
0.972034 + 0.234839i \(0.0754562\pi\)
\(888\) −31.2603 31.2603i −0.0352031 0.0352031i
\(889\) 1772.58i 1.99391i
\(890\) −54.7532 + 35.2316i −0.0615205 + 0.0395861i
\(891\) −58.3266 −0.0654619
\(892\) −41.1333 + 41.1333i −0.0461136 + 0.0461136i
\(893\) −10.1507 10.1507i −0.0113670 0.0113670i
\(894\) 198.120i 0.221610i
\(895\) −230.991 50.1118i −0.258090 0.0559909i
\(896\) 108.452 0.121040
\(897\) 63.9971 63.9971i 0.0713457 0.0713457i
\(898\) −122.374 122.374i −0.136274 0.136274i
\(899\) 555.106i 0.617471i
\(900\) −136.515 62.1575i −0.151684 0.0690639i
\(901\) −12.1436 −0.0134780
\(902\) 107.054 107.054i 0.118685 0.118685i
\(903\) 188.583 + 188.583i 0.208840 + 0.208840i
\(904\) 322.943i 0.357238i
\(905\) −50.2872 + 231.799i −0.0555660 + 0.256132i
\(906\) −134.393 −0.148336
\(907\) −494.427 + 494.427i −0.545123 + 0.545123i −0.925026 0.379903i \(-0.875957\pi\)
0.379903 + 0.925026i \(0.375957\pi\)
\(908\) −466.500 466.500i −0.513767 0.513767i
\(909\) 419.200i 0.461166i
\(910\) −399.631 621.064i −0.439155 0.682488i
\(911\) 1357.22 1.48982 0.744909 0.667167i \(-0.232493\pi\)
0.744909 + 0.667167i \(0.232493\pi\)
\(912\) 2.59198 2.59198i 0.00284209 0.00284209i
\(913\) −348.707 348.707i −0.381935 0.381935i
\(914\) 383.161i 0.419213i
\(915\) 275.629 177.357i 0.301234 0.193833i
\(916\) 814.455 0.889143
\(917\) 259.689 259.689i 0.283194 0.283194i
\(918\) 5.74473 + 5.74473i 0.00625788 + 0.00625788i
\(919\) 34.5757i 0.0376232i 0.999823 + 0.0188116i \(0.00598828\pi\)
−0.999823 + 0.0188116i \(0.994012\pi\)
\(920\) 66.2815 + 14.3793i 0.0720451 + 0.0156297i
\(921\) −582.764 −0.632751
\(922\) −69.9790 + 69.9790i −0.0758992 + 0.0758992i
\(923\) 638.821 + 638.821i 0.692114 + 0.692114i
\(924\) 215.202i 0.232902i
\(925\) −211.288 + 79.0794i −0.228420 + 0.0854913i
\(926\) −1013.21 −1.09417
\(927\) −294.994 + 294.994i −0.318224 + 0.318224i
\(928\) 91.2422 + 91.2422i 0.0983213 + 0.0983213i
\(929\) 317.252i 0.341499i 0.985314 + 0.170749i \(0.0546189\pi\)
−0.985314 + 0.170749i \(0.945381\pi\)
\(930\) −63.1895 + 291.273i −0.0679457 + 0.313196i
\(931\) 22.6920 0.0243737
\(932\) 135.628 135.628i 0.145523 0.145523i
\(933\) −99.5858 99.5858i −0.106737 0.106737i
\(934\) 723.381i 0.774498i
\(935\) −19.3853 30.1266i −0.0207330 0.0322210i
\(936\) 92.4522 0.0987737
\(937\) −1061.58 + 1061.58i −1.13296 + 1.13296i −0.143279 + 0.989682i \(0.545765\pi\)
−0.989682 + 0.143279i \(0.954235\pi\)
\(938\) 323.061 + 323.061i 0.344415 + 0.344415i
\(939\) 801.473i 0.853539i
\(940\) 228.168 146.817i 0.242731 0.156189i
\(941\) 615.031 0.653593 0.326797 0.945095i \(-0.394031\pi\)
0.326797 + 0.945095i \(0.394031\pi\)
\(942\) −352.222 + 352.222i −0.373908 + 0.373908i
\(943\) −56.0182 56.0182i −0.0594042 0.0594042i
\(944\) 251.045i 0.265938i
\(945\) 243.387 + 52.8010i 0.257552 + 0.0558741i
\(946\) 147.219 0.155622
\(947\) −560.762 + 560.762i −0.592146 + 0.592146i −0.938211 0.346065i \(-0.887518\pi\)
0.346065 + 0.938211i \(0.387518\pi\)
\(948\) 136.051 + 136.051i 0.143513 + 0.143513i
\(949\) 507.354i 0.534620i
\(950\) −6.55696 17.5192i −0.00690206 0.0184413i
\(951\) 672.312 0.706953
\(952\) −21.1958 + 21.1958i −0.0222645 + 0.0222645i
\(953\) 576.041 + 576.041i 0.604450 + 0.604450i 0.941490 0.337040i \(-0.109426\pi\)
−0.337040 + 0.941490i \(0.609426\pi\)
\(954\) 46.6013i 0.0488483i
\(955\) 134.525 620.093i 0.140864 0.649312i
\(956\) 252.207 0.263815
\(957\) 181.053 181.053i 0.189188 0.189188i
\(958\) −472.746 472.746i −0.493472 0.493472i
\(959\) 586.124i 0.611183i
\(960\) 37.4897 + 58.2625i 0.0390518 + 0.0606901i
\(961\) −368.782 −0.383749
\(962\) 98.3227 98.3227i 0.102207 0.102207i
\(963\) −34.2836 34.2836i −0.0356009 0.0356009i
\(964\) 338.589i 0.351234i
\(965\) −885.772 + 569.961i −0.917898 + 0.590633i
\(966\) −112.608 −0.116572
\(967\) −1250.23 + 1250.23i −1.29290 + 1.29290i −0.359910 + 0.932987i \(0.617193\pi\)
−0.932987 + 0.359910i \(0.882807\pi\)
\(968\) 158.000 + 158.000i 0.163223 + 0.163223i
\(969\) 1.01315i 0.00104557i
\(970\) −778.735 168.941i −0.802820 0.174166i
\(971\) 1207.50 1.24357 0.621784 0.783189i \(-0.286408\pi\)
0.621784 + 0.783189i \(0.286408\pi\)
\(972\) −22.0454 + 22.0454i −0.0226805 + 0.0226805i
\(973\) 769.344 + 769.344i 0.790692 + 0.790692i
\(974\) 490.141i 0.503224i
\(975\) 195.503 429.380i 0.200516 0.440390i
\(976\) −151.386 −0.155109
\(977\) −873.381 + 873.381i −0.893942 + 0.893942i −0.994892 0.100950i \(-0.967812\pi\)
0.100950 + 0.994892i \(0.467812\pi\)
\(978\) 265.021 + 265.021i 0.270983 + 0.270983i
\(979\) 59.6733i 0.0609533i
\(980\) −90.9294 + 419.140i −0.0927851 + 0.427693i
\(981\) −239.478 −0.244117
\(982\) −89.9842 + 89.9842i −0.0916336 + 0.0916336i
\(983\) 1034.87 + 1034.87i 1.05277 + 1.05277i 0.998528 + 0.0542382i \(0.0172730\pi\)
0.0542382 + 0.998528i \(0.482727\pi\)
\(984\) 80.9256i 0.0822415i
\(985\) −39.0589 60.7011i −0.0396537 0.0616255i
\(986\) −35.6647 −0.0361711
\(987\) −318.539 + 318.539i −0.322734 + 0.322734i
\(988\) 8.15254 + 8.15254i 0.00825155 + 0.00825155i
\(989\) 77.0350i 0.0778918i
\(990\) 115.611 74.3912i 0.116779 0.0751427i
\(991\) −665.229 −0.671270 −0.335635 0.941992i \(-0.608951\pi\)
−0.335635 + 0.941992i \(0.608951\pi\)
\(992\) 97.3421 97.3421i 0.0981271 0.0981271i
\(993\) 256.528 + 256.528i 0.258336 + 0.258336i
\(994\) 1124.06i 1.13085i
\(995\) 1787.62 + 387.811i 1.79660 + 0.389759i
\(996\) −263.598 −0.264657
\(997\) 802.959 802.959i 0.805375 0.805375i −0.178555 0.983930i \(-0.557142\pi\)
0.983930 + 0.178555i \(0.0571423\pi\)
\(998\) −823.542 823.542i −0.825192 0.825192i
\(999\) 46.8905i 0.0469374i
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 690.3.k.a.553.20 yes 40
5.2 odd 4 inner 690.3.k.a.277.20 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.3.k.a.277.20 40 5.2 odd 4 inner
690.3.k.a.553.20 yes 40 1.1 even 1 trivial