Properties

Label 300.3.c.e.151.6
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
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] = [300,3,Mod(151,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.151");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.4069419264.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 7x^{6} + 50x^{4} - 84x^{3} + 55x^{2} - 12x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.6
Root \(0.845613 - 0.488215i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.e.151.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.177680 + 1.99209i) q^{2} -1.73205i q^{3} +(-3.93686 + 0.707911i) q^{4} +(3.45040 - 0.307751i) q^{6} +1.19501i q^{7} +(-2.10973 - 7.71680i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(0.177680 + 1.99209i) q^{2} -1.73205i q^{3} +(-3.93686 + 0.707911i) q^{4} +(3.45040 - 0.307751i) q^{6} +1.19501i q^{7} +(-2.10973 - 7.71680i) q^{8} -3.00000 q^{9} -8.22072i q^{11} +(1.22614 + 6.81884i) q^{12} -11.1863 q^{13} +(-2.38058 + 0.212331i) q^{14} +(14.9977 - 5.57389i) q^{16} -20.9256 q^{17} +(-0.533041 - 5.97628i) q^{18} -27.9657i q^{19} +2.06983 q^{21} +(16.3764 - 1.46066i) q^{22} -9.48564i q^{23} +(-13.3659 + 3.65415i) q^{24} +(-1.98759 - 22.2842i) q^{26} +5.19615i q^{27} +(-0.845964 - 4.70460i) q^{28} +40.4205 q^{29} -55.3130i q^{31} +(13.7685 + 28.8865i) q^{32} -14.2387 q^{33} +(-3.71807 - 41.6858i) q^{34} +(11.8106 - 2.12373i) q^{36} -50.1890 q^{37} +(55.7102 - 4.96895i) q^{38} +19.3753i q^{39} -73.6361 q^{41} +(0.367767 + 4.12328i) q^{42} -19.0843i q^{43} +(5.81954 + 32.3638i) q^{44} +(18.8963 - 1.68541i) q^{46} +18.0598i q^{47} +(-9.65427 - 25.9768i) q^{48} +47.5719 q^{49} +36.2442i q^{51} +(44.0391 - 7.91894i) q^{52} +57.2212 q^{53} +(-10.3512 + 0.923254i) q^{54} +(9.22169 - 2.52115i) q^{56} -48.4380 q^{57} +(7.18193 + 80.5213i) q^{58} +60.6645i q^{59} -21.3518 q^{61} +(110.189 - 9.82804i) q^{62} -3.58504i q^{63} +(-55.0981 + 32.5607i) q^{64} +(-2.52994 - 28.3648i) q^{66} +9.68679i q^{67} +(82.3812 - 14.8135i) q^{68} -16.4296 q^{69} +68.6944i q^{71} +(6.32918 + 23.1504i) q^{72} -84.7825 q^{73} +(-8.91760 - 99.9811i) q^{74} +(19.7972 + 110.097i) q^{76} +9.82388 q^{77} +(-38.5974 + 3.44261i) q^{78} -23.2903i q^{79} +9.00000 q^{81} +(-13.0837 - 146.690i) q^{82} +93.2595i q^{83} +(-8.14861 + 1.46525i) q^{84} +(38.0177 - 3.39091i) q^{86} -70.0104i q^{87} +(-63.4377 + 17.3435i) q^{88} +62.9898 q^{89} -13.3678i q^{91} +(6.71499 + 37.3436i) q^{92} -95.8049 q^{93} +(-35.9767 + 3.20887i) q^{94} +(50.0328 - 23.8478i) q^{96} -91.3962 q^{97} +(8.45260 + 94.7677i) q^{98} +24.6622i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 8 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} - 8 q^{13} + 22 q^{14} + 40 q^{16} + 6 q^{18} + 24 q^{21} - 4 q^{22} - 36 q^{24} - 66 q^{26} - 104 q^{28} - 32 q^{29} - 112 q^{32} + 124 q^{34} + 24 q^{36} + 176 q^{37} + 170 q^{38} - 16 q^{41} - 54 q^{42} + 40 q^{44} - 76 q^{46} - 24 q^{48} + 16 q^{49} - 56 q^{52} + 304 q^{53} + 18 q^{54} - 172 q^{56} - 72 q^{57} + 12 q^{58} + 136 q^{61} + 238 q^{62} + 16 q^{64} - 108 q^{66} - 88 q^{68} - 96 q^{69} + 60 q^{72} - 240 q^{73} - 108 q^{74} + 120 q^{76} + 384 q^{77} - 150 q^{78} + 72 q^{81} - 320 q^{82} - 144 q^{84} + 214 q^{86} + 200 q^{88} + 128 q^{89} - 312 q^{92} - 72 q^{93} + 12 q^{94} + 96 q^{96} - 216 q^{97} - 60 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.177680 + 1.99209i 0.0888402 + 0.996046i
\(3\) 1.73205i 0.577350i
\(4\) −3.93686 + 0.707911i −0.984215 + 0.176978i
\(5\) 0 0
\(6\) 3.45040 0.307751i 0.575067 0.0512919i
\(7\) 1.19501i 0.170716i 0.996350 + 0.0853582i \(0.0272035\pi\)
−0.996350 + 0.0853582i \(0.972797\pi\)
\(8\) −2.10973 7.71680i −0.263716 0.964600i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 8.22072i 0.747338i −0.927562 0.373669i \(-0.878100\pi\)
0.927562 0.373669i \(-0.121900\pi\)
\(12\) 1.22614 + 6.81884i 0.102178 + 0.568237i
\(13\) −11.1863 −0.860488 −0.430244 0.902713i \(-0.641572\pi\)
−0.430244 + 0.902713i \(0.641572\pi\)
\(14\) −2.38058 + 0.212331i −0.170041 + 0.0151665i
\(15\) 0 0
\(16\) 14.9977 5.57389i 0.937358 0.348368i
\(17\) −20.9256 −1.23092 −0.615459 0.788169i \(-0.711030\pi\)
−0.615459 + 0.788169i \(0.711030\pi\)
\(18\) −0.533041 5.97628i −0.0296134 0.332015i
\(19\) 27.9657i 1.47188i −0.677048 0.735939i \(-0.736741\pi\)
0.677048 0.735939i \(-0.263259\pi\)
\(20\) 0 0
\(21\) 2.06983 0.0985631
\(22\) 16.3764 1.46066i 0.744383 0.0663937i
\(23\) 9.48564i 0.412419i −0.978508 0.206209i \(-0.933887\pi\)
0.978508 0.206209i \(-0.0661128\pi\)
\(24\) −13.3659 + 3.65415i −0.556912 + 0.152256i
\(25\) 0 0
\(26\) −1.98759 22.2842i −0.0764459 0.857085i
\(27\) 5.19615i 0.192450i
\(28\) −0.845964 4.70460i −0.0302130 0.168022i
\(29\) 40.4205 1.39381 0.696905 0.717163i \(-0.254560\pi\)
0.696905 + 0.717163i \(0.254560\pi\)
\(30\) 0 0
\(31\) 55.3130i 1.78429i −0.451748 0.892145i \(-0.649200\pi\)
0.451748 0.892145i \(-0.350800\pi\)
\(32\) 13.7685 + 28.8865i 0.430266 + 0.902702i
\(33\) −14.2387 −0.431476
\(34\) −3.71807 41.6858i −0.109355 1.22605i
\(35\) 0 0
\(36\) 11.8106 2.12373i 0.328072 0.0589926i
\(37\) −50.1890 −1.35646 −0.678230 0.734850i \(-0.737253\pi\)
−0.678230 + 0.734850i \(0.737253\pi\)
\(38\) 55.7102 4.96895i 1.46606 0.130762i
\(39\) 19.3753i 0.496803i
\(40\) 0 0
\(41\) −73.6361 −1.79600 −0.898001 0.439994i \(-0.854981\pi\)
−0.898001 + 0.439994i \(0.854981\pi\)
\(42\) 0.367767 + 4.12328i 0.00875637 + 0.0981734i
\(43\) 19.0843i 0.443822i −0.975067 0.221911i \(-0.928771\pi\)
0.975067 0.221911i \(-0.0712294\pi\)
\(44\) 5.81954 + 32.3638i 0.132262 + 0.735541i
\(45\) 0 0
\(46\) 18.8963 1.68541i 0.410788 0.0366394i
\(47\) 18.0598i 0.384251i 0.981370 + 0.192125i \(0.0615380\pi\)
−0.981370 + 0.192125i \(0.938462\pi\)
\(48\) −9.65427 25.9768i −0.201131 0.541184i
\(49\) 47.5719 0.970856
\(50\) 0 0
\(51\) 36.2442i 0.710671i
\(52\) 44.0391 7.91894i 0.846905 0.152287i
\(53\) 57.2212 1.07965 0.539823 0.841779i \(-0.318491\pi\)
0.539823 + 0.841779i \(0.318491\pi\)
\(54\) −10.3512 + 0.923254i −0.191689 + 0.0170973i
\(55\) 0 0
\(56\) 9.22169 2.52115i 0.164673 0.0450206i
\(57\) −48.4380 −0.849789
\(58\) 7.18193 + 80.5213i 0.123826 + 1.38830i
\(59\) 60.6645i 1.02821i 0.857727 + 0.514106i \(0.171876\pi\)
−0.857727 + 0.514106i \(0.828124\pi\)
\(60\) 0 0
\(61\) −21.3518 −0.350030 −0.175015 0.984566i \(-0.555997\pi\)
−0.175015 + 0.984566i \(0.555997\pi\)
\(62\) 110.189 9.82804i 1.77724 0.158517i
\(63\) 3.58504i 0.0569054i
\(64\) −55.0981 + 32.5607i −0.860908 + 0.508761i
\(65\) 0 0
\(66\) −2.52994 28.3648i −0.0383324 0.429770i
\(67\) 9.68679i 0.144579i 0.997384 + 0.0722895i \(0.0230305\pi\)
−0.997384 + 0.0722895i \(0.976969\pi\)
\(68\) 82.3812 14.8135i 1.21149 0.217845i
\(69\) −16.4296 −0.238110
\(70\) 0 0
\(71\) 68.6944i 0.967527i 0.875199 + 0.483763i \(0.160730\pi\)
−0.875199 + 0.483763i \(0.839270\pi\)
\(72\) 6.32918 + 23.1504i 0.0879053 + 0.321533i
\(73\) −84.7825 −1.16140 −0.580702 0.814116i \(-0.697222\pi\)
−0.580702 + 0.814116i \(0.697222\pi\)
\(74\) −8.91760 99.9811i −0.120508 1.35110i
\(75\) 0 0
\(76\) 19.7972 + 110.097i 0.260490 + 1.44864i
\(77\) 9.82388 0.127583
\(78\) −38.5974 + 3.44261i −0.494839 + 0.0441361i
\(79\) 23.2903i 0.294814i −0.989076 0.147407i \(-0.952907\pi\)
0.989076 0.147407i \(-0.0470928\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −13.0837 146.690i −0.159557 1.78890i
\(83\) 93.2595i 1.12361i 0.827270 + 0.561804i \(0.189893\pi\)
−0.827270 + 0.561804i \(0.810107\pi\)
\(84\) −8.14861 + 1.46525i −0.0970073 + 0.0174435i
\(85\) 0 0
\(86\) 38.0177 3.39091i 0.442067 0.0394292i
\(87\) 70.0104i 0.804717i
\(88\) −63.4377 + 17.3435i −0.720883 + 0.197085i
\(89\) 62.9898 0.707750 0.353875 0.935293i \(-0.384864\pi\)
0.353875 + 0.935293i \(0.384864\pi\)
\(90\) 0 0
\(91\) 13.3678i 0.146899i
\(92\) 6.71499 + 37.3436i 0.0729890 + 0.405909i
\(93\) −95.8049 −1.03016
\(94\) −35.9767 + 3.20887i −0.382731 + 0.0341369i
\(95\) 0 0
\(96\) 50.0328 23.8478i 0.521175 0.248414i
\(97\) −91.3962 −0.942229 −0.471115 0.882072i \(-0.656148\pi\)
−0.471115 + 0.882072i \(0.656148\pi\)
\(98\) 8.45260 + 94.7677i 0.0862510 + 0.967017i
\(99\) 24.6622i 0.249113i
\(100\) 0 0
\(101\) −29.9780 −0.296811 −0.148406 0.988927i \(-0.547414\pi\)
−0.148406 + 0.988927i \(0.547414\pi\)
\(102\) −72.2019 + 6.43989i −0.707861 + 0.0631362i
\(103\) 88.7485i 0.861636i −0.902439 0.430818i \(-0.858225\pi\)
0.902439 0.430818i \(-0.141775\pi\)
\(104\) 23.6001 + 86.3228i 0.226924 + 0.830027i
\(105\) 0 0
\(106\) 10.1671 + 113.990i 0.0959159 + 1.07538i
\(107\) 162.922i 1.52263i −0.648381 0.761316i \(-0.724553\pi\)
0.648381 0.761316i \(-0.275447\pi\)
\(108\) −3.67841 20.4565i −0.0340594 0.189412i
\(109\) −103.352 −0.948182 −0.474091 0.880476i \(-0.657223\pi\)
−0.474091 + 0.880476i \(0.657223\pi\)
\(110\) 0 0
\(111\) 86.9299i 0.783152i
\(112\) 6.66088 + 17.9225i 0.0594722 + 0.160022i
\(113\) 31.2691 0.276717 0.138359 0.990382i \(-0.455817\pi\)
0.138359 + 0.990382i \(0.455817\pi\)
\(114\) −8.60647 96.4929i −0.0754954 0.846429i
\(115\) 0 0
\(116\) −159.130 + 28.6141i −1.37181 + 0.246673i
\(117\) 33.5590 0.286829
\(118\) −120.849 + 10.7789i −1.02415 + 0.0913465i
\(119\) 25.0064i 0.210138i
\(120\) 0 0
\(121\) 53.4198 0.441486
\(122\) −3.79380 42.5348i −0.0310967 0.348646i
\(123\) 127.541i 1.03692i
\(124\) 39.1567 + 217.760i 0.315780 + 1.75613i
\(125\) 0 0
\(126\) 7.14174 0.636992i 0.0566804 0.00505549i
\(127\) 178.474i 1.40531i 0.711531 + 0.702655i \(0.248002\pi\)
−0.711531 + 0.702655i \(0.751998\pi\)
\(128\) −74.6537 103.975i −0.583232 0.812305i
\(129\) −33.0550 −0.256240
\(130\) 0 0
\(131\) 153.743i 1.17361i 0.809727 + 0.586806i \(0.199615\pi\)
−0.809727 + 0.586806i \(0.800385\pi\)
\(132\) 56.0558 10.0797i 0.424665 0.0763617i
\(133\) 33.4194 0.251274
\(134\) −19.2970 + 1.72115i −0.144007 + 0.0128444i
\(135\) 0 0
\(136\) 44.1473 + 161.479i 0.324613 + 1.18734i
\(137\) 52.9928 0.386809 0.193405 0.981119i \(-0.438047\pi\)
0.193405 + 0.981119i \(0.438047\pi\)
\(138\) −2.91922 32.7293i −0.0211537 0.237169i
\(139\) 21.8420i 0.157137i 0.996909 + 0.0785684i \(0.0250349\pi\)
−0.996909 + 0.0785684i \(0.974965\pi\)
\(140\) 0 0
\(141\) 31.2804 0.221847
\(142\) −136.846 + 12.2056i −0.963701 + 0.0859552i
\(143\) 91.9598i 0.643076i
\(144\) −44.9932 + 16.7217i −0.312453 + 0.116123i
\(145\) 0 0
\(146\) −15.0642 168.895i −0.103179 1.15681i
\(147\) 82.3970i 0.560524i
\(148\) 197.587 35.5294i 1.33505 0.240063i
\(149\) −3.12940 −0.0210027 −0.0105013 0.999945i \(-0.503343\pi\)
−0.0105013 + 0.999945i \(0.503343\pi\)
\(150\) 0 0
\(151\) 296.461i 1.96332i −0.190646 0.981659i \(-0.561058\pi\)
0.190646 0.981659i \(-0.438942\pi\)
\(152\) −215.806 + 58.9999i −1.41977 + 0.388157i
\(153\) 62.7769 0.410306
\(154\) 1.74551 + 19.5701i 0.0113345 + 0.127078i
\(155\) 0 0
\(156\) −13.7160 76.2779i −0.0879231 0.488961i
\(157\) 265.686 1.69227 0.846133 0.532972i \(-0.178925\pi\)
0.846133 + 0.532972i \(0.178925\pi\)
\(158\) 46.3965 4.13824i 0.293649 0.0261914i
\(159\) 99.1101i 0.623334i
\(160\) 0 0
\(161\) 11.3355 0.0704067
\(162\) 1.59912 + 17.9288i 0.00987113 + 0.110672i
\(163\) 205.531i 1.26093i −0.776218 0.630465i \(-0.782864\pi\)
0.776218 0.630465i \(-0.217136\pi\)
\(164\) 289.895 52.1278i 1.76765 0.317852i
\(165\) 0 0
\(166\) −185.781 + 16.5704i −1.11917 + 0.0998215i
\(167\) 11.6359i 0.0696763i 0.999393 + 0.0348381i \(0.0110916\pi\)
−0.999393 + 0.0348381i \(0.988908\pi\)
\(168\) −4.36677 15.9724i −0.0259927 0.0950740i
\(169\) −43.8657 −0.259560
\(170\) 0 0
\(171\) 83.8970i 0.490626i
\(172\) 13.5100 + 75.1323i 0.0785466 + 0.436816i
\(173\) 106.062 0.613077 0.306538 0.951858i \(-0.400829\pi\)
0.306538 + 0.951858i \(0.400829\pi\)
\(174\) 139.467 12.4395i 0.801535 0.0714912i
\(175\) 0 0
\(176\) −45.8214 123.292i −0.260349 0.700523i
\(177\) 105.074 0.593639
\(178\) 11.1920 + 125.481i 0.0628766 + 0.704951i
\(179\) 43.3304i 0.242069i −0.992648 0.121035i \(-0.961379\pi\)
0.992648 0.121035i \(-0.0386212\pi\)
\(180\) 0 0
\(181\) 203.614 1.12494 0.562469 0.826819i \(-0.309852\pi\)
0.562469 + 0.826819i \(0.309852\pi\)
\(182\) 26.6300 2.37520i 0.146319 0.0130506i
\(183\) 36.9824i 0.202090i
\(184\) −73.1988 + 20.0121i −0.397819 + 0.108761i
\(185\) 0 0
\(186\) −17.0227 190.852i −0.0915197 1.02609i
\(187\) 172.024i 0.919913i
\(188\) −12.7847 71.0988i −0.0680038 0.378185i
\(189\) −6.20948 −0.0328544
\(190\) 0 0
\(191\) 251.536i 1.31694i −0.752606 0.658471i \(-0.771204\pi\)
0.752606 0.658471i \(-0.228796\pi\)
\(192\) 56.3968 + 95.4327i 0.293733 + 0.497045i
\(193\) 281.811 1.46016 0.730081 0.683360i \(-0.239482\pi\)
0.730081 + 0.683360i \(0.239482\pi\)
\(194\) −16.2393 182.070i −0.0837078 0.938503i
\(195\) 0 0
\(196\) −187.284 + 33.6767i −0.955531 + 0.171820i
\(197\) 243.485 1.23596 0.617982 0.786193i \(-0.287951\pi\)
0.617982 + 0.786193i \(0.287951\pi\)
\(198\) −49.1293 + 4.38198i −0.248128 + 0.0221312i
\(199\) 121.958i 0.612853i −0.951894 0.306427i \(-0.900867\pi\)
0.951894 0.306427i \(-0.0991335\pi\)
\(200\) 0 0
\(201\) 16.7780 0.0834727
\(202\) −5.32649 59.7188i −0.0263688 0.295638i
\(203\) 48.3031i 0.237946i
\(204\) −25.6577 142.688i −0.125773 0.699453i
\(205\) 0 0
\(206\) 176.795 15.7689i 0.858229 0.0765479i
\(207\) 28.4569i 0.137473i
\(208\) −167.770 + 62.3515i −0.806585 + 0.299767i
\(209\) −229.898 −1.09999
\(210\) 0 0
\(211\) 132.543i 0.628168i −0.949395 0.314084i \(-0.898303\pi\)
0.949395 0.314084i \(-0.101697\pi\)
\(212\) −225.272 + 40.5076i −1.06260 + 0.191073i
\(213\) 118.982 0.558602
\(214\) 324.555 28.9480i 1.51661 0.135271i
\(215\) 0 0
\(216\) 40.0977 10.9625i 0.185637 0.0507521i
\(217\) 66.0998 0.304608
\(218\) −18.3636 205.886i −0.0842366 0.944433i
\(219\) 146.848i 0.670537i
\(220\) 0 0
\(221\) 234.081 1.05919
\(222\) −173.172 + 15.4457i −0.780056 + 0.0695754i
\(223\) 225.442i 1.01095i −0.862841 0.505475i \(-0.831317\pi\)
0.862841 0.505475i \(-0.168683\pi\)
\(224\) −34.5198 + 16.4536i −0.154106 + 0.0734534i
\(225\) 0 0
\(226\) 5.55590 + 62.2908i 0.0245836 + 0.275623i
\(227\) 108.080i 0.476124i 0.971250 + 0.238062i \(0.0765122\pi\)
−0.971250 + 0.238062i \(0.923488\pi\)
\(228\) 190.693 34.2898i 0.836375 0.150394i
\(229\) −57.3495 −0.250435 −0.125217 0.992129i \(-0.539963\pi\)
−0.125217 + 0.992129i \(0.539963\pi\)
\(230\) 0 0
\(231\) 17.0155i 0.0736600i
\(232\) −85.2762 311.917i −0.367570 1.34447i
\(233\) −285.320 −1.22455 −0.612274 0.790646i \(-0.709745\pi\)
−0.612274 + 0.790646i \(0.709745\pi\)
\(234\) 5.96278 + 66.8527i 0.0254820 + 0.285695i
\(235\) 0 0
\(236\) −42.9451 238.828i −0.181971 1.01198i
\(237\) −40.3400 −0.170211
\(238\) 49.8151 4.44315i 0.209307 0.0186687i
\(239\) 77.2471i 0.323210i 0.986856 + 0.161605i \(0.0516670\pi\)
−0.986856 + 0.161605i \(0.948333\pi\)
\(240\) 0 0
\(241\) −130.557 −0.541732 −0.270866 0.962617i \(-0.587310\pi\)
−0.270866 + 0.962617i \(0.587310\pi\)
\(242\) 9.49164 + 106.417i 0.0392217 + 0.439740i
\(243\) 15.5885i 0.0641500i
\(244\) 84.0591 15.1152i 0.344504 0.0619475i
\(245\) 0 0
\(246\) −254.074 + 22.6616i −1.03282 + 0.0921203i
\(247\) 312.834i 1.26653i
\(248\) −426.840 + 116.695i −1.72113 + 0.470546i
\(249\) 161.530 0.648715
\(250\) 0 0
\(251\) 437.197i 1.74182i 0.491441 + 0.870911i \(0.336470\pi\)
−0.491441 + 0.870911i \(0.663530\pi\)
\(252\) 2.53789 + 14.1138i 0.0100710 + 0.0560072i
\(253\) −77.9788 −0.308216
\(254\) −355.537 + 31.7114i −1.39975 + 0.124848i
\(255\) 0 0
\(256\) 193.863 167.191i 0.757279 0.653091i
\(257\) −74.3682 −0.289370 −0.144685 0.989478i \(-0.546217\pi\)
−0.144685 + 0.989478i \(0.546217\pi\)
\(258\) −5.87323 65.8486i −0.0227644 0.255227i
\(259\) 59.9766i 0.231570i
\(260\) 0 0
\(261\) −121.261 −0.464603
\(262\) −306.271 + 27.3172i −1.16897 + 0.104264i
\(263\) 458.790i 1.74445i −0.489105 0.872225i \(-0.662676\pi\)
0.489105 0.872225i \(-0.337324\pi\)
\(264\) 30.0398 + 109.877i 0.113787 + 0.416202i
\(265\) 0 0
\(266\) 5.93797 + 66.5745i 0.0223232 + 0.250280i
\(267\) 109.101i 0.408620i
\(268\) −6.85739 38.1355i −0.0255873 0.142297i
\(269\) −320.405 −1.19110 −0.595549 0.803319i \(-0.703065\pi\)
−0.595549 + 0.803319i \(0.703065\pi\)
\(270\) 0 0
\(271\) 359.059i 1.32494i −0.749088 0.662470i \(-0.769508\pi\)
0.749088 0.662470i \(-0.230492\pi\)
\(272\) −313.837 + 116.637i −1.15381 + 0.428813i
\(273\) −23.1538 −0.0848124
\(274\) 9.41579 + 105.567i 0.0343642 + 0.385280i
\(275\) 0 0
\(276\) 64.6810 11.6307i 0.234352 0.0421402i
\(277\) −138.027 −0.498293 −0.249147 0.968466i \(-0.580150\pi\)
−0.249147 + 0.968466i \(0.580150\pi\)
\(278\) −43.5113 + 3.88090i −0.156516 + 0.0139601i
\(279\) 165.939i 0.594764i
\(280\) 0 0
\(281\) 462.504 1.64592 0.822960 0.568099i \(-0.192321\pi\)
0.822960 + 0.568099i \(0.192321\pi\)
\(282\) 5.55792 + 62.3135i 0.0197089 + 0.220970i
\(283\) 323.973i 1.14478i 0.819981 + 0.572391i \(0.193984\pi\)
−0.819981 + 0.572391i \(0.806016\pi\)
\(284\) −48.6295 270.440i −0.171231 0.952254i
\(285\) 0 0
\(286\) −183.192 + 16.3394i −0.640533 + 0.0571309i
\(287\) 87.9962i 0.306607i
\(288\) −41.3055 86.6594i −0.143422 0.300901i
\(289\) 148.882 0.515161
\(290\) 0 0
\(291\) 158.303i 0.543996i
\(292\) 333.777 60.0185i 1.14307 0.205543i
\(293\) −150.416 −0.513365 −0.256683 0.966496i \(-0.582629\pi\)
−0.256683 + 0.966496i \(0.582629\pi\)
\(294\) 164.142 14.6403i 0.558308 0.0497970i
\(295\) 0 0
\(296\) 105.885 + 387.299i 0.357720 + 1.30844i
\(297\) 42.7161 0.143825
\(298\) −0.556033 6.23406i −0.00186588 0.0209196i
\(299\) 106.110i 0.354882i
\(300\) 0 0
\(301\) 22.8060 0.0757676
\(302\) 590.577 52.6753i 1.95555 0.174421i
\(303\) 51.9233i 0.171364i
\(304\) −155.878 419.421i −0.512755 1.37968i
\(305\) 0 0
\(306\) 11.1542 + 125.057i 0.0364517 + 0.408684i
\(307\) 563.915i 1.83686i −0.395587 0.918428i \(-0.629459\pi\)
0.395587 0.918428i \(-0.370541\pi\)
\(308\) −38.6752 + 6.95443i −0.125569 + 0.0225793i
\(309\) −153.717 −0.497466
\(310\) 0 0
\(311\) 40.0214i 0.128686i 0.997928 + 0.0643431i \(0.0204952\pi\)
−0.997928 + 0.0643431i \(0.979505\pi\)
\(312\) 149.515 40.8766i 0.479216 0.131015i
\(313\) −1.82657 −0.00583568 −0.00291784 0.999996i \(-0.500929\pi\)
−0.00291784 + 0.999996i \(0.500929\pi\)
\(314\) 47.2071 + 529.270i 0.150341 + 1.68557i
\(315\) 0 0
\(316\) 16.4875 + 91.6908i 0.0521756 + 0.290161i
\(317\) −246.416 −0.777338 −0.388669 0.921378i \(-0.627065\pi\)
−0.388669 + 0.921378i \(0.627065\pi\)
\(318\) 197.436 17.6099i 0.620869 0.0553771i
\(319\) 332.286i 1.04165i
\(320\) 0 0
\(321\) −282.189 −0.879092
\(322\) 2.01409 + 22.5813i 0.00625494 + 0.0701283i
\(323\) 585.199i 1.81176i
\(324\) −35.4317 + 6.37120i −0.109357 + 0.0196642i
\(325\) 0 0
\(326\) 409.438 36.5189i 1.25594 0.112021i
\(327\) 179.011i 0.547433i
\(328\) 155.352 + 568.235i 0.473634 + 1.73242i
\(329\) −21.5817 −0.0655978
\(330\) 0 0
\(331\) 417.672i 1.26185i 0.775844 + 0.630925i \(0.217325\pi\)
−0.775844 + 0.630925i \(0.782675\pi\)
\(332\) −66.0194 367.149i −0.198854 1.10587i
\(333\) 150.567 0.452153
\(334\) −23.1798 + 2.06748i −0.0694007 + 0.00619005i
\(335\) 0 0
\(336\) 31.0427 11.5370i 0.0923889 0.0343363i
\(337\) 317.379 0.941779 0.470889 0.882192i \(-0.343933\pi\)
0.470889 + 0.882192i \(0.343933\pi\)
\(338\) −7.79408 87.3845i −0.0230594 0.258534i
\(339\) 54.1596i 0.159763i
\(340\) 0 0
\(341\) −454.713 −1.33347
\(342\) −167.131 + 14.9068i −0.488686 + 0.0435873i
\(343\) 115.405i 0.336457i
\(344\) −147.270 + 40.2627i −0.428110 + 0.117043i
\(345\) 0 0
\(346\) 18.8452 + 211.286i 0.0544659 + 0.610653i
\(347\) 222.581i 0.641443i −0.947174 0.320721i \(-0.896075\pi\)
0.947174 0.320721i \(-0.103925\pi\)
\(348\) 49.5611 + 275.621i 0.142417 + 0.792014i
\(349\) 560.812 1.60691 0.803455 0.595366i \(-0.202993\pi\)
0.803455 + 0.595366i \(0.202993\pi\)
\(350\) 0 0
\(351\) 58.1259i 0.165601i
\(352\) 237.468 113.187i 0.674624 0.321554i
\(353\) −304.856 −0.863616 −0.431808 0.901966i \(-0.642124\pi\)
−0.431808 + 0.901966i \(0.642124\pi\)
\(354\) 18.6696 + 209.317i 0.0527390 + 0.591291i
\(355\) 0 0
\(356\) −247.982 + 44.5911i −0.696578 + 0.125256i
\(357\) −43.3124 −0.121323
\(358\) 86.3181 7.69896i 0.241112 0.0215055i
\(359\) 105.860i 0.294874i −0.989071 0.147437i \(-0.952898\pi\)
0.989071 0.147437i \(-0.0471023\pi\)
\(360\) 0 0
\(361\) −421.079 −1.16642
\(362\) 36.1782 + 405.617i 0.0999396 + 1.12049i
\(363\) 92.5257i 0.254892i
\(364\) 9.46324 + 52.6273i 0.0259979 + 0.144581i
\(365\) 0 0
\(366\) −73.6724 + 6.57105i −0.201291 + 0.0179537i
\(367\) 360.200i 0.981470i −0.871309 0.490735i \(-0.836728\pi\)
0.871309 0.490735i \(-0.163272\pi\)
\(368\) −52.8719 142.263i −0.143674 0.386584i
\(369\) 220.908 0.598667
\(370\) 0 0
\(371\) 68.3802i 0.184313i
\(372\) 377.171 67.8214i 1.01390 0.182316i
\(373\) 135.489 0.363242 0.181621 0.983369i \(-0.441866\pi\)
0.181621 + 0.983369i \(0.441866\pi\)
\(374\) −342.687 + 30.5652i −0.916275 + 0.0817252i
\(375\) 0 0
\(376\) 139.364 38.1012i 0.370648 0.101333i
\(377\) −452.158 −1.19936
\(378\) −1.10330 12.3698i −0.00291879 0.0327245i
\(379\) 310.686i 0.819753i 0.912141 + 0.409876i \(0.134428\pi\)
−0.912141 + 0.409876i \(0.865572\pi\)
\(380\) 0 0
\(381\) 309.126 0.811356
\(382\) 501.083 44.6930i 1.31173 0.116997i
\(383\) 121.981i 0.318487i −0.987239 0.159244i \(-0.949094\pi\)
0.987239 0.159244i \(-0.0509056\pi\)
\(384\) −180.090 + 129.304i −0.468985 + 0.336729i
\(385\) 0 0
\(386\) 50.0723 + 561.394i 0.129721 + 1.45439i
\(387\) 57.2530i 0.147941i
\(388\) 359.814 64.7004i 0.927356 0.166754i
\(389\) 544.266 1.39914 0.699570 0.714564i \(-0.253375\pi\)
0.699570 + 0.714564i \(0.253375\pi\)
\(390\) 0 0
\(391\) 198.493i 0.507654i
\(392\) −100.364 367.103i −0.256030 0.936488i
\(393\) 266.291 0.677586
\(394\) 43.2625 + 485.044i 0.109803 + 1.23108i
\(395\) 0 0
\(396\) −17.4586 97.0915i −0.0440874 0.245180i
\(397\) −504.528 −1.27085 −0.635425 0.772162i \(-0.719175\pi\)
−0.635425 + 0.772162i \(0.719175\pi\)
\(398\) 242.951 21.6695i 0.610430 0.0544460i
\(399\) 57.8841i 0.145073i
\(400\) 0 0
\(401\) −278.018 −0.693312 −0.346656 0.937992i \(-0.612683\pi\)
−0.346656 + 0.937992i \(0.612683\pi\)
\(402\) 2.98112 + 33.4233i 0.00741573 + 0.0831426i
\(403\) 618.750i 1.53536i
\(404\) 118.019 21.2217i 0.292126 0.0525290i
\(405\) 0 0
\(406\) −96.2242 + 8.58251i −0.237005 + 0.0211392i
\(407\) 412.590i 1.01373i
\(408\) 279.690 76.4654i 0.685514 0.187415i
\(409\) −296.549 −0.725059 −0.362530 0.931972i \(-0.618087\pi\)
−0.362530 + 0.931972i \(0.618087\pi\)
\(410\) 0 0
\(411\) 91.7863i 0.223324i
\(412\) 62.8261 + 349.390i 0.152490 + 0.848035i
\(413\) −72.4950 −0.175533
\(414\) −56.6888 + 5.05623i −0.136929 + 0.0122131i
\(415\) 0 0
\(416\) −154.019 323.134i −0.370239 0.776764i
\(417\) 37.8315 0.0907230
\(418\) −40.8483 457.978i −0.0977233 1.09564i
\(419\) 315.615i 0.753258i 0.926364 + 0.376629i \(0.122917\pi\)
−0.926364 + 0.376629i \(0.877083\pi\)
\(420\) 0 0
\(421\) −360.355 −0.855951 −0.427975 0.903790i \(-0.640773\pi\)
−0.427975 + 0.903790i \(0.640773\pi\)
\(422\) 264.039 23.5504i 0.625684 0.0558066i
\(423\) 54.1793i 0.128084i
\(424\) −120.721 441.565i −0.284720 1.04143i
\(425\) 0 0
\(426\) 21.1408 + 237.023i 0.0496263 + 0.556393i
\(427\) 25.5157i 0.0597558i
\(428\) 115.334 + 641.400i 0.269472 + 1.49860i
\(429\) 159.279 0.371280
\(430\) 0 0
\(431\) 523.617i 1.21489i −0.794362 0.607445i \(-0.792195\pi\)
0.794362 0.607445i \(-0.207805\pi\)
\(432\) 28.9628 + 77.9305i 0.0670435 + 0.180395i
\(433\) 21.5381 0.0497415 0.0248707 0.999691i \(-0.492083\pi\)
0.0248707 + 0.999691i \(0.492083\pi\)
\(434\) 11.7446 + 131.677i 0.0270614 + 0.303403i
\(435\) 0 0
\(436\) 406.882 73.1639i 0.933215 0.167807i
\(437\) −265.272 −0.607030
\(438\) −292.534 + 26.0919i −0.667886 + 0.0595706i
\(439\) 247.777i 0.564412i 0.959354 + 0.282206i \(0.0910662\pi\)
−0.959354 + 0.282206i \(0.908934\pi\)
\(440\) 0 0
\(441\) −142.716 −0.323619
\(442\) 41.5916 + 466.311i 0.0940987 + 1.05500i
\(443\) 584.775i 1.32003i −0.751251 0.660017i \(-0.770549\pi\)
0.751251 0.660017i \(-0.229451\pi\)
\(444\) −61.5386 342.231i −0.138601 0.770790i
\(445\) 0 0
\(446\) 449.101 40.0566i 1.00695 0.0898130i
\(447\) 5.42028i 0.0121259i
\(448\) −38.9105 65.8430i −0.0868538 0.146971i
\(449\) 152.093 0.338738 0.169369 0.985553i \(-0.445827\pi\)
0.169369 + 0.985553i \(0.445827\pi\)
\(450\) 0 0
\(451\) 605.342i 1.34222i
\(452\) −123.102 + 22.1357i −0.272349 + 0.0489728i
\(453\) −513.485 −1.13352
\(454\) −215.306 + 19.2037i −0.474242 + 0.0422990i
\(455\) 0 0
\(456\) 102.191 + 373.786i 0.224103 + 0.819707i
\(457\) −602.441 −1.31825 −0.659126 0.752033i \(-0.729074\pi\)
−0.659126 + 0.752033i \(0.729074\pi\)
\(458\) −10.1899 114.246i −0.0222487 0.249444i
\(459\) 108.733i 0.236890i
\(460\) 0 0
\(461\) −504.912 −1.09525 −0.547626 0.836723i \(-0.684468\pi\)
−0.547626 + 0.836723i \(0.684468\pi\)
\(462\) 33.8964 3.02331i 0.0733687 0.00654397i
\(463\) 504.560i 1.08976i −0.838513 0.544881i \(-0.816575\pi\)
0.838513 0.544881i \(-0.183425\pi\)
\(464\) 606.215 225.300i 1.30650 0.485559i
\(465\) 0 0
\(466\) −50.6957 568.383i −0.108789 1.21971i
\(467\) 751.418i 1.60903i −0.593931 0.804516i \(-0.702425\pi\)
0.593931 0.804516i \(-0.297575\pi\)
\(468\) −132.117 + 23.7568i −0.282302 + 0.0507624i
\(469\) −11.5759 −0.0246820
\(470\) 0 0
\(471\) 460.181i 0.977030i
\(472\) 468.136 127.986i 0.991814 0.271156i
\(473\) −156.887 −0.331685
\(474\) −7.16763 80.3611i −0.0151216 0.169538i
\(475\) 0 0
\(476\) 17.7023 + 98.4468i 0.0371898 + 0.206821i
\(477\) −171.664 −0.359882
\(478\) −153.883 + 13.7253i −0.321932 + 0.0287140i
\(479\) 581.401i 1.21378i −0.794786 0.606890i \(-0.792417\pi\)
0.794786 0.606890i \(-0.207583\pi\)
\(480\) 0 0
\(481\) 561.431 1.16722
\(482\) −23.1975 260.082i −0.0481276 0.539590i
\(483\) 19.6336i 0.0406493i
\(484\) −210.306 + 37.8164i −0.434517 + 0.0781331i
\(485\) 0 0
\(486\) 31.0536 2.76976i 0.0638964 0.00569910i
\(487\) 557.489i 1.14474i 0.819995 + 0.572371i \(0.193976\pi\)
−0.819995 + 0.572371i \(0.806024\pi\)
\(488\) 45.0465 + 164.768i 0.0923084 + 0.337639i
\(489\) −355.991 −0.727998
\(490\) 0 0
\(491\) 26.2032i 0.0533670i 0.999644 + 0.0266835i \(0.00849463\pi\)
−0.999644 + 0.0266835i \(0.991505\pi\)
\(492\) −90.2880 502.113i −0.183512 1.02055i
\(493\) −845.824 −1.71567
\(494\) −623.193 + 55.5844i −1.26152 + 0.112519i
\(495\) 0 0
\(496\) −308.309 829.569i −0.621590 1.67252i
\(497\) −82.0908 −0.165173
\(498\) 28.7007 + 321.783i 0.0576320 + 0.646150i
\(499\) 444.615i 0.891011i 0.895279 + 0.445506i \(0.146976\pi\)
−0.895279 + 0.445506i \(0.853024\pi\)
\(500\) 0 0
\(501\) 20.1540 0.0402276
\(502\) −870.937 + 77.6814i −1.73493 + 0.154744i
\(503\) 216.819i 0.431052i 0.976498 + 0.215526i \(0.0691466\pi\)
−0.976498 + 0.215526i \(0.930853\pi\)
\(504\) −27.6651 + 7.56346i −0.0548910 + 0.0150069i
\(505\) 0 0
\(506\) −13.8553 155.341i −0.0273820 0.306998i
\(507\) 75.9777i 0.149857i
\(508\) −126.344 702.628i −0.248708 1.38313i
\(509\) 202.830 0.398488 0.199244 0.979950i \(-0.436151\pi\)
0.199244 + 0.979950i \(0.436151\pi\)
\(510\) 0 0
\(511\) 101.316i 0.198271i
\(512\) 367.506 + 356.487i 0.717786 + 0.696264i
\(513\) 145.314 0.283263
\(514\) −13.2138 148.148i −0.0257077 0.288226i
\(515\) 0 0
\(516\) 130.133 23.4000i 0.252196 0.0453489i
\(517\) 148.464 0.287165
\(518\) 119.479 10.6567i 0.230654 0.0205727i
\(519\) 183.705i 0.353960i
\(520\) 0 0
\(521\) 769.410 1.47679 0.738397 0.674366i \(-0.235583\pi\)
0.738397 + 0.674366i \(0.235583\pi\)
\(522\) −21.5458 241.564i −0.0412754 0.462766i
\(523\) 38.9898i 0.0745502i 0.999305 + 0.0372751i \(0.0118678\pi\)
−0.999305 + 0.0372751i \(0.988132\pi\)
\(524\) −108.837 605.266i −0.207703 1.15509i
\(525\) 0 0
\(526\) 913.953 81.5180i 1.73755 0.154977i
\(527\) 1157.46i 2.19632i
\(528\) −213.548 + 79.3650i −0.404447 + 0.150313i
\(529\) 439.023 0.829911
\(530\) 0 0
\(531\) 181.994i 0.342737i
\(532\) −131.567 + 23.6579i −0.247307 + 0.0444698i
\(533\) 823.718 1.54544
\(534\) 217.340 19.3852i 0.407004 0.0363018i
\(535\) 0 0
\(536\) 74.7510 20.4365i 0.139461 0.0381277i
\(537\) −75.0504 −0.139759
\(538\) −56.9297 638.277i −0.105817 1.18639i
\(539\) 391.076i 0.725558i
\(540\) 0 0
\(541\) −32.0904 −0.0593168 −0.0296584 0.999560i \(-0.509442\pi\)
−0.0296584 + 0.999560i \(0.509442\pi\)
\(542\) 715.278 63.7977i 1.31970 0.117708i
\(543\) 352.669i 0.649483i
\(544\) −288.115 604.467i −0.529622 1.11115i
\(545\) 0 0
\(546\) −4.11397 46.1245i −0.00753475 0.0844770i
\(547\) 254.839i 0.465885i −0.972491 0.232942i \(-0.925165\pi\)
0.972491 0.232942i \(-0.0748354\pi\)
\(548\) −208.625 + 37.5142i −0.380703 + 0.0684566i
\(549\) 64.0554 0.116677
\(550\) 0 0
\(551\) 1130.39i 2.05152i
\(552\) 34.6620 + 126.784i 0.0627934 + 0.229681i
\(553\) 27.8323 0.0503296
\(554\) −24.5247 274.963i −0.0442685 0.496323i
\(555\) 0 0
\(556\) −15.4622 85.9890i −0.0278097 0.154656i
\(557\) 577.439 1.03670 0.518348 0.855170i \(-0.326547\pi\)
0.518348 + 0.855170i \(0.326547\pi\)
\(558\) −330.566 + 29.4841i −0.592412 + 0.0528389i
\(559\) 213.484i 0.381903i
\(560\) 0 0
\(561\) 297.954 0.531112
\(562\) 82.1778 + 921.350i 0.146224 + 1.63941i
\(563\) 367.058i 0.651967i −0.945375 0.325984i \(-0.894305\pi\)
0.945375 0.325984i \(-0.105695\pi\)
\(564\) −123.147 + 22.1438i −0.218345 + 0.0392620i
\(565\) 0 0
\(566\) −645.384 + 57.5636i −1.14025 + 0.101703i
\(567\) 10.7551i 0.0189685i
\(568\) 530.101 144.926i 0.933277 0.255152i
\(569\) −522.006 −0.917410 −0.458705 0.888589i \(-0.651687\pi\)
−0.458705 + 0.888589i \(0.651687\pi\)
\(570\) 0 0
\(571\) 832.421i 1.45783i 0.684604 + 0.728915i \(0.259975\pi\)
−0.684604 + 0.728915i \(0.740025\pi\)
\(572\) −65.0994 362.033i −0.113810 0.632925i
\(573\) −435.673 −0.760337
\(574\) 175.296 15.6352i 0.305394 0.0272390i
\(575\) 0 0
\(576\) 165.294 97.6821i 0.286969 0.169587i
\(577\) 427.659 0.741177 0.370588 0.928797i \(-0.379156\pi\)
0.370588 + 0.928797i \(0.379156\pi\)
\(578\) 26.4533 + 296.586i 0.0457670 + 0.513124i
\(579\) 488.112i 0.843025i
\(580\) 0 0
\(581\) −111.446 −0.191818
\(582\) −315.354 + 28.1273i −0.541845 + 0.0483287i
\(583\) 470.400i 0.806861i
\(584\) 178.868 + 654.250i 0.306281 + 1.12029i
\(585\) 0 0
\(586\) −26.7260 299.642i −0.0456074 0.511335i
\(587\) 586.262i 0.998743i 0.866388 + 0.499372i \(0.166436\pi\)
−0.866388 + 0.499372i \(0.833564\pi\)
\(588\) 58.3298 + 324.385i 0.0992003 + 0.551676i
\(589\) −1546.87 −2.62626
\(590\) 0 0
\(591\) 421.728i 0.713584i
\(592\) −752.721 + 279.748i −1.27149 + 0.472548i
\(593\) 518.375 0.874156 0.437078 0.899424i \(-0.356013\pi\)
0.437078 + 0.899424i \(0.356013\pi\)
\(594\) 7.58981 + 85.0944i 0.0127775 + 0.143257i
\(595\) 0 0
\(596\) 12.3200 2.21534i 0.0206712 0.00371701i
\(597\) −211.237 −0.353831
\(598\) −211.380 + 18.8536i −0.353478 + 0.0315277i
\(599\) 405.480i 0.676928i 0.940979 + 0.338464i \(0.109907\pi\)
−0.940979 + 0.338464i \(0.890093\pi\)
\(600\) 0 0
\(601\) −350.551 −0.583279 −0.291640 0.956528i \(-0.594201\pi\)
−0.291640 + 0.956528i \(0.594201\pi\)
\(602\) 4.05219 + 45.4317i 0.00673121 + 0.0754680i
\(603\) 29.0604i 0.0481930i
\(604\) 209.868 + 1167.13i 0.347464 + 1.93233i
\(605\) 0 0
\(606\) −103.436 + 9.22576i −0.170687 + 0.0152240i
\(607\) 737.786i 1.21546i −0.794143 0.607731i \(-0.792080\pi\)
0.794143 0.607731i \(-0.207920\pi\)
\(608\) 807.829 385.046i 1.32867 0.633299i
\(609\) 83.6634 0.137378
\(610\) 0 0
\(611\) 202.023i 0.330643i
\(612\) −247.144 + 44.4404i −0.403830 + 0.0726151i
\(613\) 345.495 0.563614 0.281807 0.959471i \(-0.409066\pi\)
0.281807 + 0.959471i \(0.409066\pi\)
\(614\) 1123.37 100.197i 1.82959 0.163187i
\(615\) 0 0
\(616\) −20.7257 75.8090i −0.0336456 0.123066i
\(617\) 862.171 1.39736 0.698680 0.715434i \(-0.253771\pi\)
0.698680 + 0.715434i \(0.253771\pi\)
\(618\) −27.3125 306.218i −0.0441950 0.495499i
\(619\) 469.363i 0.758260i 0.925343 + 0.379130i \(0.123777\pi\)
−0.925343 + 0.379130i \(0.876223\pi\)
\(620\) 0 0
\(621\) 49.2888 0.0793701
\(622\) −79.7264 + 7.11102i −0.128177 + 0.0114325i
\(623\) 75.2737i 0.120824i
\(624\) 107.996 + 290.586i 0.173070 + 0.465682i
\(625\) 0 0
\(626\) −0.324545 3.63869i −0.000518443 0.00581260i
\(627\) 398.195i 0.635080i
\(628\) −1045.97 + 188.082i −1.66555 + 0.299494i
\(629\) 1050.24 1.66969
\(630\) 0 0
\(631\) 323.243i 0.512271i 0.966641 + 0.256136i \(0.0824494\pi\)
−0.966641 + 0.256136i \(0.917551\pi\)
\(632\) −179.727 + 49.1362i −0.284378 + 0.0777472i
\(633\) −229.572 −0.362673
\(634\) −43.7833 490.883i −0.0690588 0.774264i
\(635\) 0 0
\(636\) 70.1611 + 390.183i 0.110316 + 0.613495i
\(637\) −532.156 −0.835410
\(638\) 661.943 59.0406i 1.03753 0.0925402i
\(639\) 206.083i 0.322509i
\(640\) 0 0
\(641\) −44.1100 −0.0688144 −0.0344072 0.999408i \(-0.510954\pi\)
−0.0344072 + 0.999408i \(0.510954\pi\)
\(642\) −50.1394 562.146i −0.0780987 0.875616i
\(643\) 934.204i 1.45288i 0.687228 + 0.726442i \(0.258827\pi\)
−0.687228 + 0.726442i \(0.741173\pi\)
\(644\) −44.6262 + 8.02451i −0.0692953 + 0.0124604i
\(645\) 0 0
\(646\) −1165.77 + 103.978i −1.80460 + 0.160957i
\(647\) 481.023i 0.743467i −0.928339 0.371734i \(-0.878763\pi\)
0.928339 0.371734i \(-0.121237\pi\)
\(648\) −18.9875 69.4512i −0.0293018 0.107178i
\(649\) 498.706 0.768422
\(650\) 0 0
\(651\) 114.488i 0.175865i
\(652\) 145.498 + 809.148i 0.223156 + 1.24103i
\(653\) 1131.38 1.73259 0.866293 0.499536i \(-0.166496\pi\)
0.866293 + 0.499536i \(0.166496\pi\)
\(654\) −356.606 + 31.8067i −0.545268 + 0.0486340i
\(655\) 0 0
\(656\) −1104.37 + 410.440i −1.68350 + 0.625670i
\(657\) 254.348 0.387135
\(658\) −3.83464 42.9927i −0.00582772 0.0653385i
\(659\) 154.348i 0.234215i −0.993119 0.117107i \(-0.962638\pi\)
0.993119 0.117107i \(-0.0373622\pi\)
\(660\) 0 0
\(661\) 795.115 1.20290 0.601448 0.798912i \(-0.294591\pi\)
0.601448 + 0.798912i \(0.294591\pi\)
\(662\) −832.042 + 74.2122i −1.25686 + 0.112103i
\(663\) 405.441i 0.611524i
\(664\) 719.665 196.752i 1.08383 0.296313i
\(665\) 0 0
\(666\) 26.7528 + 299.943i 0.0401694 + 0.450365i
\(667\) 383.414i 0.574834i
\(668\) −8.23721 45.8090i −0.0123311 0.0685764i
\(669\) −390.477 −0.583672
\(670\) 0 0
\(671\) 175.527i 0.261591i
\(672\) 28.4984 + 59.7900i 0.0424083 + 0.0889732i
\(673\) 197.215 0.293039 0.146520 0.989208i \(-0.453193\pi\)
0.146520 + 0.989208i \(0.453193\pi\)
\(674\) 56.3921 + 632.249i 0.0836678 + 0.938055i
\(675\) 0 0
\(676\) 172.693 31.0530i 0.255463 0.0459364i
\(677\) 530.367 0.783408 0.391704 0.920091i \(-0.371886\pi\)
0.391704 + 0.920091i \(0.371886\pi\)
\(678\) 107.891 9.62309i 0.159131 0.0141934i
\(679\) 109.220i 0.160854i
\(680\) 0 0
\(681\) 187.200 0.274891
\(682\) −80.7935 905.830i −0.118466 1.32820i
\(683\) 797.231i 1.16725i 0.812024 + 0.583625i \(0.198366\pi\)
−0.812024 + 0.583625i \(0.801634\pi\)
\(684\) −59.3916 330.291i −0.0868299 0.482881i
\(685\) 0 0
\(686\) −229.897 + 20.5052i −0.335127 + 0.0298909i
\(687\) 99.3323i 0.144588i
\(688\) −106.374 286.221i −0.154613 0.416020i
\(689\) −640.096 −0.929022
\(690\) 0 0
\(691\) 498.569i 0.721518i 0.932659 + 0.360759i \(0.117482\pi\)
−0.932659 + 0.360759i \(0.882518\pi\)
\(692\) −417.552 + 75.0827i −0.603399 + 0.108501i
\(693\) −29.4716 −0.0425276
\(694\) 443.401 39.5482i 0.638906 0.0569859i
\(695\) 0 0
\(696\) −540.256 + 147.703i −0.776230 + 0.212217i
\(697\) 1540.88 2.21073
\(698\) 99.6452 + 1117.19i 0.142758 + 1.60056i
\(699\) 494.188i 0.706993i
\(700\) 0 0
\(701\) −455.939 −0.650412 −0.325206 0.945643i \(-0.605434\pi\)
−0.325206 + 0.945643i \(0.605434\pi\)
\(702\) 115.792 10.3278i 0.164946 0.0147120i
\(703\) 1403.57i 1.99654i
\(704\) 267.672 + 452.946i 0.380216 + 0.643389i
\(705\) 0 0
\(706\) −54.1670 607.302i −0.0767238 0.860201i
\(707\) 35.8241i 0.0506706i
\(708\) −413.662 + 74.3831i −0.584268 + 0.105061i
\(709\) −44.4190 −0.0626502 −0.0313251 0.999509i \(-0.509973\pi\)
−0.0313251 + 0.999509i \(0.509973\pi\)
\(710\) 0 0
\(711\) 69.8710i 0.0982715i
\(712\) −132.891 486.080i −0.186645 0.682696i
\(713\) −524.679 −0.735875
\(714\) −7.69576 86.2823i −0.0107784 0.120843i
\(715\) 0 0
\(716\) 30.6741 + 170.586i 0.0428409 + 0.238248i
\(717\) 133.796 0.186605
\(718\) 210.882 18.8092i 0.293708 0.0261966i
\(719\) 1349.94i 1.87752i −0.344566 0.938762i \(-0.611974\pi\)
0.344566 0.938762i \(-0.388026\pi\)
\(720\) 0 0
\(721\) 106.056 0.147095
\(722\) −74.8174 838.827i −0.103625 1.16181i
\(723\) 226.132i 0.312769i
\(724\) −801.599 + 144.140i −1.10718 + 0.199089i
\(725\) 0 0
\(726\) 184.320 16.4400i 0.253884 0.0226446i
\(727\) 191.470i 0.263370i −0.991292 0.131685i \(-0.957961\pi\)
0.991292 0.131685i \(-0.0420387\pi\)
\(728\) −103.157 + 28.2025i −0.141699 + 0.0387397i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 399.351i 0.546308i
\(732\) −26.1803 145.595i −0.0357654 0.198900i
\(733\) −358.832 −0.489539 −0.244769 0.969581i \(-0.578712\pi\)
−0.244769 + 0.969581i \(0.578712\pi\)
\(734\) 717.551 64.0004i 0.977589 0.0871940i
\(735\) 0 0
\(736\) 274.007 130.603i 0.372291 0.177450i
\(737\) 79.6324 0.108049
\(738\) 39.2510 + 440.069i 0.0531857 + 0.596300i
\(739\) 756.311i 1.02342i −0.859157 0.511712i \(-0.829011\pi\)
0.859157 0.511712i \(-0.170989\pi\)
\(740\) 0 0
\(741\) 541.844 0.731233
\(742\) −136.220 + 12.1498i −0.183584 + 0.0163744i
\(743\) 1148.65i 1.54596i −0.634432 0.772979i \(-0.718766\pi\)
0.634432 0.772979i \(-0.281234\pi\)
\(744\) 202.122 + 739.308i 0.271670 + 0.993693i
\(745\) 0 0
\(746\) 24.0738 + 269.907i 0.0322705 + 0.361805i
\(747\) 279.778i 0.374536i
\(748\) −121.777 677.233i −0.162804 0.905392i
\(749\) 194.694 0.259938
\(750\) 0 0
\(751\) 431.186i 0.574149i 0.957908 + 0.287074i \(0.0926827\pi\)
−0.957908 + 0.287074i \(0.907317\pi\)
\(752\) 100.663 + 270.856i 0.133861 + 0.360180i
\(753\) 757.248 1.00564
\(754\) −80.3395 900.739i −0.106551 1.19461i
\(755\) 0 0
\(756\) 24.4458 4.39576i 0.0323358 0.00581449i
\(757\) 645.657 0.852916 0.426458 0.904507i \(-0.359761\pi\)
0.426458 + 0.904507i \(0.359761\pi\)
\(758\) −618.916 + 55.2029i −0.816511 + 0.0728270i
\(759\) 135.063i 0.177949i
\(760\) 0 0
\(761\) −291.287 −0.382768 −0.191384 0.981515i \(-0.561298\pi\)
−0.191384 + 0.981515i \(0.561298\pi\)
\(762\) 54.9257 + 615.808i 0.0720810 + 0.808147i
\(763\) 123.507i 0.161870i
\(764\) 178.065 + 990.261i 0.233069 + 1.29615i
\(765\) 0 0
\(766\) 242.997 21.6736i 0.317228 0.0282945i
\(767\) 678.614i 0.884764i
\(768\) −289.584 335.781i −0.377063 0.437215i
\(769\) −724.076 −0.941582 −0.470791 0.882245i \(-0.656031\pi\)
−0.470791 + 0.882245i \(0.656031\pi\)
\(770\) 0 0
\(771\) 128.809i 0.167068i
\(772\) −1109.45 + 199.497i −1.43711 + 0.258416i
\(773\) 399.686 0.517058 0.258529 0.966003i \(-0.416762\pi\)
0.258529 + 0.966003i \(0.416762\pi\)
\(774\) −114.053 + 10.1727i −0.147356 + 0.0131431i
\(775\) 0 0
\(776\) 192.821 + 705.287i 0.248481 + 0.908875i
\(777\) −103.882 −0.133697
\(778\) 96.7053 + 1084.23i 0.124300 + 1.39361i
\(779\) 2059.28i 2.64349i
\(780\) 0 0
\(781\) 564.717 0.723070
\(782\) −395.416 + 35.2683i −0.505647 + 0.0451001i
\(783\) 210.031i 0.268239i
\(784\) 713.471 265.161i 0.910039 0.338215i
\(785\) 0 0
\(786\) 47.3147 + 530.476i 0.0601968 + 0.674906i
\(787\) 381.830i 0.485172i −0.970130 0.242586i \(-0.922004\pi\)
0.970130 0.242586i \(-0.0779957\pi\)
\(788\) −958.565 + 172.366i −1.21645 + 0.218738i
\(789\) −794.648 −1.00716
\(790\) 0 0
\(791\) 37.3670i 0.0472402i
\(792\) 190.313 52.0304i 0.240294 0.0656950i
\(793\) 238.849 0.301196
\(794\) −89.6446 1005.07i −0.112903 1.26583i
\(795\) 0 0
\(796\) 86.3353 + 480.131i 0.108461 + 0.603180i
\(797\) 18.3955 0.0230810 0.0115405 0.999933i \(-0.496326\pi\)
0.0115405 + 0.999933i \(0.496326\pi\)
\(798\) 115.310 10.2849i 0.144499 0.0128883i
\(799\) 377.912i 0.472981i
\(800\) 0 0
\(801\) −188.969 −0.235917
\(802\) −49.3983 553.837i −0.0615939 0.690570i
\(803\) 696.974i 0.867962i
\(804\) −66.0527 + 11.8773i −0.0821551 + 0.0147728i
\(805\) 0 0
\(806\) −1232.61 + 109.940i −1.52929 + 0.136402i
\(807\) 554.958i 0.687681i
\(808\) 63.2453 + 231.334i 0.0782739 + 0.286304i
\(809\) −992.161 −1.22640 −0.613202 0.789926i \(-0.710119\pi\)
−0.613202 + 0.789926i \(0.710119\pi\)
\(810\) 0 0
\(811\) 482.957i 0.595509i 0.954643 + 0.297754i \(0.0962376\pi\)
−0.954643 + 0.297754i \(0.903762\pi\)
\(812\) −34.1943 190.162i −0.0421112 0.234190i
\(813\) −621.908 −0.764955
\(814\) −821.917 + 73.3091i −1.00973 + 0.0900603i
\(815\) 0 0
\(816\) 202.022 + 543.581i 0.247575 + 0.666153i
\(817\) −533.706 −0.653251
\(818\) −52.6910 590.753i −0.0644144 0.722192i
\(819\) 40.1035i 0.0489665i
\(820\) 0 0
\(821\) 614.955 0.749031 0.374516 0.927221i \(-0.377809\pi\)
0.374516 + 0.927221i \(0.377809\pi\)
\(822\) 182.847 16.3086i 0.222441 0.0198402i
\(823\) 11.2878i 0.0137154i 0.999976 + 0.00685772i \(0.00218290\pi\)
−0.999976 + 0.00685772i \(0.997817\pi\)
\(824\) −684.855 + 187.235i −0.831135 + 0.227227i
\(825\) 0 0
\(826\) −12.8809 144.417i −0.0155943 0.174839i
\(827\) 449.125i 0.543078i 0.962427 + 0.271539i \(0.0875325\pi\)
−0.962427 + 0.271539i \(0.912467\pi\)
\(828\) −20.1450 112.031i −0.0243297 0.135303i
\(829\) 135.766 0.163771 0.0818855 0.996642i \(-0.473906\pi\)
0.0818855 + 0.996642i \(0.473906\pi\)
\(830\) 0 0
\(831\) 239.070i 0.287690i
\(832\) 616.346 364.235i 0.740801 0.437782i
\(833\) −995.472 −1.19504
\(834\) 6.72191 + 75.3638i 0.00805985 + 0.0903643i
\(835\) 0 0
\(836\) 905.076 162.747i 1.08263 0.194674i
\(837\) 287.415 0.343387
\(838\) −628.734 + 56.0786i −0.750280 + 0.0669196i
\(839\) 1509.47i 1.79913i 0.436789 + 0.899564i \(0.356116\pi\)
−0.436789 + 0.899564i \(0.643884\pi\)
\(840\) 0 0
\(841\) 792.817 0.942707
\(842\) −64.0280 717.861i −0.0760428 0.852566i
\(843\) 801.080i 0.950273i
\(844\) 93.8290 + 521.805i 0.111172 + 0.618252i
\(845\) 0 0
\(846\) 107.930 9.62660i 0.127577 0.0113790i
\(847\) 63.8374i 0.0753688i
\(848\) 858.188 318.945i 1.01201 0.376114i
\(849\) 561.138 0.660940
\(850\) 0 0
\(851\) 476.075i 0.559430i
\(852\) −468.416 + 84.2288i −0.549784 + 0.0988601i
\(853\) −909.826 −1.06662 −0.533310 0.845920i \(-0.679052\pi\)
−0.533310 + 0.845920i \(0.679052\pi\)
\(854\) 50.8297 4.53364i 0.0595195 0.00530872i
\(855\) 0 0
\(856\) −1257.23 + 343.720i −1.46873 + 0.401542i
\(857\) −505.304 −0.589620 −0.294810 0.955556i \(-0.595256\pi\)
−0.294810 + 0.955556i \(0.595256\pi\)
\(858\) 28.3008 + 317.298i 0.0329846 + 0.369812i
\(859\) 45.9728i 0.0535189i −0.999642 0.0267595i \(-0.991481\pi\)
0.999642 0.0267595i \(-0.00851882\pi\)
\(860\) 0 0
\(861\) −152.414 −0.177020
\(862\) 1043.09 93.0365i 1.21009 0.107931i
\(863\) 142.006i 0.164549i −0.996610 0.0822746i \(-0.973782\pi\)
0.996610 0.0822746i \(-0.0262185\pi\)
\(864\) −150.099 + 71.5433i −0.173725 + 0.0828047i
\(865\) 0 0
\(866\) 3.82689 + 42.9058i 0.00441904 + 0.0495448i
\(867\) 257.871i 0.297429i
\(868\) −260.226 + 46.7928i −0.299799 + 0.0539088i
\(869\) −191.463 −0.220326
\(870\) 0 0
\(871\) 108.360i 0.124408i
\(872\) 218.044 + 797.546i 0.250051 + 0.914617i
\(873\) 274.189 0.314076
\(874\) −47.1336 528.446i −0.0539287 0.604630i
\(875\) 0 0
\(876\) −103.955 578.119i −0.118670 0.659953i
\(877\) 549.975 0.627109 0.313555 0.949570i \(-0.398480\pi\)
0.313555 + 0.949570i \(0.398480\pi\)
\(878\) −493.594 + 44.0251i −0.562180 + 0.0501425i
\(879\) 260.528i 0.296391i
\(880\) 0 0
\(881\) 636.072 0.721989 0.360995 0.932568i \(-0.382437\pi\)
0.360995 + 0.932568i \(0.382437\pi\)
\(882\) −25.3578 284.303i −0.0287503 0.322339i
\(883\) 689.661i 0.781043i −0.920594 0.390521i \(-0.872295\pi\)
0.920594 0.390521i \(-0.127705\pi\)
\(884\) −921.545 + 165.709i −1.04247 + 0.187453i
\(885\) 0 0
\(886\) 1164.93 103.903i 1.31481 0.117272i
\(887\) 1053.94i 1.18821i 0.804389 + 0.594103i \(0.202493\pi\)
−0.804389 + 0.594103i \(0.797507\pi\)
\(888\) 670.821 183.398i 0.755429 0.206530i
\(889\) −213.279 −0.239909
\(890\) 0 0
\(891\) 73.9865i 0.0830376i
\(892\) 159.593 + 887.533i 0.178916 + 0.994992i
\(893\) 505.054 0.565570
\(894\) −10.7977 + 0.963078i −0.0120780 + 0.00107727i
\(895\) 0 0
\(896\) 124.252 89.2123i 0.138674 0.0995673i
\(897\) 183.787 0.204891
\(898\) 27.0240 + 302.984i 0.0300936 + 0.337399i
\(899\) 2235.78i 2.48696i
\(900\) 0 0
\(901\) −1197.39 −1.32896
\(902\) −1205.90 + 107.557i −1.33691 + 0.119243i
\(903\) 39.5012i 0.0437444i
\(904\) −65.9691 241.297i −0.0729747 0.266922i
\(905\) 0 0
\(906\) −91.2363 1022.91i −0.100702 1.12904i
\(907\) 496.037i 0.546899i −0.961886 0.273449i \(-0.911835\pi\)
0.961886 0.273449i \(-0.0881646\pi\)
\(908\) −76.5112 425.497i −0.0842635 0.468609i
\(909\) 89.9339 0.0989372
\(910\) 0 0
\(911\) 336.684i 0.369577i 0.982778 + 0.184788i \(0.0591599\pi\)
−0.982778 + 0.184788i \(0.940840\pi\)
\(912\) −726.459 + 269.988i −0.796556 + 0.296039i
\(913\) 766.660 0.839715
\(914\) −107.042 1200.12i −0.117114 1.31304i
\(915\) 0 0
\(916\) 225.777 40.5984i 0.246481 0.0443214i
\(917\) −183.725 −0.200355
\(918\) 216.606 19.3197i 0.235954 0.0210454i
\(919\) 937.464i 1.02009i 0.860147 + 0.510046i \(0.170371\pi\)
−0.860147 + 0.510046i \(0.829629\pi\)
\(920\) 0 0
\(921\) −976.729 −1.06051
\(922\) −89.7129 1005.83i −0.0973025 1.09092i
\(923\) 768.439i 0.832545i
\(924\) 12.0454 + 66.9875i 0.0130362 + 0.0724973i
\(925\) 0 0
\(926\) 1005.13 89.6504i 1.08545 0.0968147i
\(927\) 266.246i 0.287212i
\(928\) 556.530 + 1167.61i 0.599709 + 1.25820i
\(929\) 858.647 0.924270 0.462135 0.886810i \(-0.347084\pi\)
0.462135 + 0.886810i \(0.347084\pi\)
\(930\) 0 0
\(931\) 1330.38i 1.42898i
\(932\) 1123.26 201.981i 1.20522 0.216718i
\(933\) 69.3191 0.0742971
\(934\) 1496.89 133.512i 1.60267 0.142947i
\(935\) 0 0
\(936\) −70.8004 258.968i −0.0756414 0.276676i
\(937\) −1276.09 −1.36189 −0.680943 0.732336i \(-0.738430\pi\)
−0.680943 + 0.732336i \(0.738430\pi\)
\(938\) −2.05680 23.0602i −0.00219275 0.0245844i
\(939\) 3.16371i 0.00336923i
\(940\) 0 0
\(941\) 536.218 0.569838 0.284919 0.958552i \(-0.408033\pi\)
0.284919 + 0.958552i \(0.408033\pi\)
\(942\) 916.723 81.7652i 0.973167 0.0867995i
\(943\) 698.485i 0.740705i
\(944\) 338.138 + 909.830i 0.358197 + 0.963803i
\(945\) 0 0
\(946\) −27.8757 312.533i −0.0294669 0.330373i
\(947\) 48.1723i 0.0508683i 0.999677 + 0.0254341i \(0.00809681\pi\)
−0.999677 + 0.0254341i \(0.991903\pi\)
\(948\) 158.813 28.5572i 0.167524 0.0301236i
\(949\) 948.407 0.999375
\(950\) 0 0
\(951\) 426.805i 0.448796i
\(952\) −192.970 + 52.7567i −0.202699 + 0.0554167i
\(953\) −1449.85 −1.52136 −0.760679 0.649129i \(-0.775134\pi\)
−0.760679 + 0.649129i \(0.775134\pi\)
\(954\) −30.5013 341.970i −0.0319720 0.358459i
\(955\) 0 0
\(956\) −54.6841 304.111i −0.0572009 0.318108i
\(957\) −575.536 −0.601396
\(958\) 1158.20 103.303i 1.20898 0.107832i
\(959\) 63.3272i 0.0660346i
\(960\) 0 0
\(961\) −2098.53 −2.18369
\(962\) 99.7553 + 1118.42i 0.103696 + 1.16260i
\(963\) 488.765i 0.507544i
\(964\) 513.986 92.4231i 0.533181 0.0958746i
\(965\) 0 0
\(966\) 39.1120 3.48851i 0.0404886 0.00361129i
\(967\) 1320.06i 1.36510i 0.730837 + 0.682552i \(0.239130\pi\)
−0.730837 + 0.682552i \(0.760870\pi\)
\(968\) −112.701 412.230i −0.116427 0.425857i
\(969\) 1013.59 1.04602
\(970\) 0 0
\(971\) 1269.58i 1.30749i −0.756713 0.653747i \(-0.773196\pi\)
0.756713 0.653747i \(-0.226804\pi\)
\(972\) 11.0352 + 61.3696i 0.0113531 + 0.0631374i
\(973\) −26.1015 −0.0268258
\(974\) −1110.57 + 99.0548i −1.14021 + 0.101699i
\(975\) 0 0
\(976\) −320.229 + 119.013i −0.328103 + 0.121939i
\(977\) −1262.18 −1.29190 −0.645948 0.763382i \(-0.723538\pi\)
−0.645948 + 0.763382i \(0.723538\pi\)
\(978\) −63.2526 709.167i −0.0646755 0.725119i
\(979\) 517.821i 0.528929i
\(980\) 0 0
\(981\) 310.055 0.316061
\(982\) −52.1992 + 4.65580i −0.0531560 + 0.00474114i
\(983\) 235.722i 0.239798i 0.992786 + 0.119899i \(0.0382571\pi\)
−0.992786 + 0.119899i \(0.961743\pi\)
\(984\) 984.212 269.077i 1.00022 0.273453i
\(985\) 0 0
\(986\) −150.286 1684.96i −0.152420 1.70888i
\(987\) 37.3806i 0.0378729i
\(988\) −221.458 1231.58i −0.224148 1.24654i
\(989\) −181.027 −0.183040
\(990\) 0 0
\(991\) 1601.53i 1.61607i −0.589135 0.808035i \(-0.700531\pi\)
0.589135 0.808035i \(-0.299469\pi\)
\(992\) 1597.80 761.578i 1.61068 0.767719i
\(993\) 723.430 0.728530
\(994\) −14.5859 163.532i −0.0146740 0.164520i
\(995\) 0 0
\(996\) −635.921 + 114.349i −0.638475 + 0.114808i
\(997\) −984.298 −0.987260 −0.493630 0.869672i \(-0.664330\pi\)
−0.493630 + 0.869672i \(0.664330\pi\)
\(998\) −885.713 + 78.9993i −0.887488 + 0.0791576i
\(999\) 260.790i 0.261051i
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 300.3.c.e.151.6 yes 8
3.2 odd 2 900.3.c.t.451.3 8
4.3 odd 2 inner 300.3.c.e.151.5 8
5.2 odd 4 300.3.f.c.199.2 16
5.3 odd 4 300.3.f.c.199.15 16
5.4 even 2 300.3.c.g.151.3 yes 8
12.11 even 2 900.3.c.t.451.4 8
15.2 even 4 900.3.f.h.199.15 16
15.8 even 4 900.3.f.h.199.2 16
15.14 odd 2 900.3.c.n.451.6 8
20.3 even 4 300.3.f.c.199.1 16
20.7 even 4 300.3.f.c.199.16 16
20.19 odd 2 300.3.c.g.151.4 yes 8
60.23 odd 4 900.3.f.h.199.16 16
60.47 odd 4 900.3.f.h.199.1 16
60.59 even 2 900.3.c.n.451.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.3.c.e.151.5 8 4.3 odd 2 inner
300.3.c.e.151.6 yes 8 1.1 even 1 trivial
300.3.c.g.151.3 yes 8 5.4 even 2
300.3.c.g.151.4 yes 8 20.19 odd 2
300.3.f.c.199.1 16 20.3 even 4
300.3.f.c.199.2 16 5.2 odd 4
300.3.f.c.199.15 16 5.3 odd 4
300.3.f.c.199.16 16 20.7 even 4
900.3.c.n.451.5 8 60.59 even 2
900.3.c.n.451.6 8 15.14 odd 2
900.3.c.t.451.3 8 3.2 odd 2
900.3.c.t.451.4 8 12.11 even 2
900.3.f.h.199.1 16 60.47 odd 4
900.3.f.h.199.2 16 15.8 even 4
900.3.f.h.199.15 16 15.2 even 4
900.3.f.h.199.16 16 60.23 odd 4