Properties

Label 230.3.f.b.47.3
Level $230$
Weight $3$
Character 230.47
Analytic conductor $6.267$
Analytic rank $0$
Dimension $24$
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] = [230,3,Mod(47,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([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("230.47");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.3
Character \(\chi\) \(=\) 230.47
Dual form 230.3.f.b.93.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-2.98637 + 2.98637i) q^{3} +2.00000i q^{4} +(-3.91488 + 3.11026i) q^{5} -5.97274 q^{6} +(-3.94695 - 3.94695i) q^{7} +(-2.00000 + 2.00000i) q^{8} -8.83680i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-2.98637 + 2.98637i) q^{3} +2.00000i q^{4} +(-3.91488 + 3.11026i) q^{5} -5.97274 q^{6} +(-3.94695 - 3.94695i) q^{7} +(-2.00000 + 2.00000i) q^{8} -8.83680i q^{9} +(-7.02514 - 0.804611i) q^{10} +8.59939 q^{11} +(-5.97274 - 5.97274i) q^{12} +(2.89951 - 2.89951i) q^{13} -7.89389i q^{14} +(2.40286 - 20.9797i) q^{15} -4.00000 q^{16} +(-15.7131 - 15.7131i) q^{17} +(8.83680 - 8.83680i) q^{18} +12.0018i q^{19} +(-6.22053 - 7.82975i) q^{20} +23.5741 q^{21} +(8.59939 + 8.59939i) q^{22} +(-3.39116 + 3.39116i) q^{23} -11.9455i q^{24} +(5.65250 - 24.3526i) q^{25} +5.79903 q^{26} +(-0.487368 - 0.487368i) q^{27} +(7.89389 - 7.89389i) q^{28} +41.1195i q^{29} +(23.3825 - 18.5768i) q^{30} -19.8906 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-25.6809 + 25.6809i) q^{33} -31.4263i q^{34} +(27.7278 + 3.17576i) q^{35} +17.6736 q^{36} +(-40.5371 - 40.5371i) q^{37} +(-12.0018 + 12.0018i) q^{38} +17.3180i q^{39} +(1.60922 - 14.0503i) q^{40} -48.8398 q^{41} +(23.5741 + 23.5741i) q^{42} +(-29.7297 + 29.7297i) q^{43} +17.1988i q^{44} +(27.4848 + 34.5950i) q^{45} -6.78233 q^{46} +(5.79882 + 5.79882i) q^{47} +(11.9455 - 11.9455i) q^{48} -17.8432i q^{49} +(30.0051 - 18.7001i) q^{50} +93.8504 q^{51} +(5.79903 + 5.79903i) q^{52} +(-8.37708 + 8.37708i) q^{53} -0.974735i q^{54} +(-33.6655 + 26.7464i) q^{55} +15.7878 q^{56} +(-35.8418 - 35.8418i) q^{57} +(-41.1195 + 41.1195i) q^{58} +91.8342i q^{59} +(41.9593 + 4.80573i) q^{60} -6.02932 q^{61} +(-19.8906 - 19.8906i) q^{62} +(-34.8784 + 34.8784i) q^{63} -8.00000i q^{64} +(-2.33298 + 20.3695i) q^{65} -51.3619 q^{66} +(21.2877 + 21.2877i) q^{67} +(31.4263 - 31.4263i) q^{68} -20.2545i q^{69} +(24.5521 + 30.9036i) q^{70} +89.1373 q^{71} +(17.6736 + 17.6736i) q^{72} +(-80.4250 + 80.4250i) q^{73} -81.0743i q^{74} +(55.8454 + 89.6063i) q^{75} -24.0036 q^{76} +(-33.9413 - 33.9413i) q^{77} +(-17.3180 + 17.3180i) q^{78} +66.7607i q^{79} +(15.6595 - 12.4411i) q^{80} +82.4421 q^{81} +(-48.8398 - 48.8398i) q^{82} +(30.2065 - 30.2065i) q^{83} +47.1481i q^{84} +(110.387 + 12.6430i) q^{85} -59.4594 q^{86} +(-122.798 - 122.798i) q^{87} +(-17.1988 + 17.1988i) q^{88} -48.7863i q^{89} +(-7.11019 + 62.0798i) q^{90} -22.8884 q^{91} +(-6.78233 - 6.78233i) q^{92} +(59.4008 - 59.4008i) q^{93} +11.5976i q^{94} +(-37.3288 - 46.9855i) q^{95} +23.8910 q^{96} +(-40.6035 - 40.6035i) q^{97} +(17.8432 - 17.8432i) q^{98} -75.9911i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −2.98637 + 2.98637i −0.995456 + 0.995456i −0.999990 0.00453331i \(-0.998557\pi\)
0.00453331 + 0.999990i \(0.498557\pi\)
\(4\) 2.00000i 0.500000i
\(5\) −3.91488 + 3.11026i −0.782975 + 0.622053i
\(6\) −5.97274 −0.995456
\(7\) −3.94695 3.94695i −0.563849 0.563849i 0.366549 0.930399i \(-0.380539\pi\)
−0.930399 + 0.366549i \(0.880539\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 8.83680i 0.981867i
\(10\) −7.02514 0.804611i −0.702514 0.0804611i
\(11\) 8.59939 0.781763 0.390881 0.920441i \(-0.372170\pi\)
0.390881 + 0.920441i \(0.372170\pi\)
\(12\) −5.97274 5.97274i −0.497728 0.497728i
\(13\) 2.89951 2.89951i 0.223039 0.223039i −0.586738 0.809777i \(-0.699588\pi\)
0.809777 + 0.586738i \(0.199588\pi\)
\(14\) 7.89389i 0.563849i
\(15\) 2.40286 20.9797i 0.160191 1.39864i
\(16\) −4.00000 −0.250000
\(17\) −15.7131 15.7131i −0.924302 0.924302i 0.0730280 0.997330i \(-0.476734\pi\)
−0.997330 + 0.0730280i \(0.976734\pi\)
\(18\) 8.83680 8.83680i 0.490933 0.490933i
\(19\) 12.0018i 0.631674i 0.948814 + 0.315837i \(0.102285\pi\)
−0.948814 + 0.315837i \(0.897715\pi\)
\(20\) −6.22053 7.82975i −0.311026 0.391488i
\(21\) 23.5741 1.12257
\(22\) 8.59939 + 8.59939i 0.390881 + 0.390881i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 11.9455i 0.497728i
\(25\) 5.65250 24.3526i 0.226100 0.974104i
\(26\) 5.79903 0.223039
\(27\) −0.487368 0.487368i −0.0180507 0.0180507i
\(28\) 7.89389 7.89389i 0.281925 0.281925i
\(29\) 41.1195i 1.41791i 0.705253 + 0.708956i \(0.250834\pi\)
−0.705253 + 0.708956i \(0.749166\pi\)
\(30\) 23.3825 18.5768i 0.779418 0.619227i
\(31\) −19.8906 −0.641633 −0.320817 0.947141i \(-0.603957\pi\)
−0.320817 + 0.947141i \(0.603957\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −25.6809 + 25.6809i −0.778211 + 0.778211i
\(34\) 31.4263i 0.924302i
\(35\) 27.7278 + 3.17576i 0.792224 + 0.0907359i
\(36\) 17.6736 0.490933
\(37\) −40.5371 40.5371i −1.09560 1.09560i −0.994919 0.100680i \(-0.967898\pi\)
−0.100680 0.994919i \(-0.532102\pi\)
\(38\) −12.0018 + 12.0018i −0.315837 + 0.315837i
\(39\) 17.3180i 0.444052i
\(40\) 1.60922 14.0503i 0.0402305 0.351257i
\(41\) −48.8398 −1.19121 −0.595607 0.803276i \(-0.703088\pi\)
−0.595607 + 0.803276i \(0.703088\pi\)
\(42\) 23.5741 + 23.5741i 0.561287 + 0.561287i
\(43\) −29.7297 + 29.7297i −0.691388 + 0.691388i −0.962537 0.271149i \(-0.912596\pi\)
0.271149 + 0.962537i \(0.412596\pi\)
\(44\) 17.1988i 0.390881i
\(45\) 27.4848 + 34.5950i 0.610773 + 0.768777i
\(46\) −6.78233 −0.147442
\(47\) 5.79882 + 5.79882i 0.123379 + 0.123379i 0.766100 0.642721i \(-0.222195\pi\)
−0.642721 + 0.766100i \(0.722195\pi\)
\(48\) 11.9455 11.9455i 0.248864 0.248864i
\(49\) 17.8432i 0.364148i
\(50\) 30.0051 18.7001i 0.600102 0.374002i
\(51\) 93.8504 1.84020
\(52\) 5.79903 + 5.79903i 0.111520 + 0.111520i
\(53\) −8.37708 + 8.37708i −0.158058 + 0.158058i −0.781706 0.623648i \(-0.785650\pi\)
0.623648 + 0.781706i \(0.285650\pi\)
\(54\) 0.974735i 0.0180507i
\(55\) −33.6655 + 26.7464i −0.612101 + 0.486298i
\(56\) 15.7878 0.281925
\(57\) −35.8418 35.8418i −0.628804 0.628804i
\(58\) −41.1195 + 41.1195i −0.708956 + 0.708956i
\(59\) 91.8342i 1.55651i 0.627947 + 0.778256i \(0.283895\pi\)
−0.627947 + 0.778256i \(0.716105\pi\)
\(60\) 41.9593 + 4.80573i 0.699322 + 0.0800955i
\(61\) −6.02932 −0.0988413 −0.0494206 0.998778i \(-0.515737\pi\)
−0.0494206 + 0.998778i \(0.515737\pi\)
\(62\) −19.8906 19.8906i −0.320817 0.320817i
\(63\) −34.8784 + 34.8784i −0.553625 + 0.553625i
\(64\) 8.00000i 0.125000i
\(65\) −2.33298 + 20.3695i −0.0358920 + 0.313377i
\(66\) −51.3619 −0.778211
\(67\) 21.2877 + 21.2877i 0.317727 + 0.317727i 0.847893 0.530167i \(-0.177871\pi\)
−0.530167 + 0.847893i \(0.677871\pi\)
\(68\) 31.4263 31.4263i 0.462151 0.462151i
\(69\) 20.2545i 0.293544i
\(70\) 24.5521 + 30.9036i 0.350744 + 0.441480i
\(71\) 89.1373 1.25545 0.627727 0.778433i \(-0.283985\pi\)
0.627727 + 0.778433i \(0.283985\pi\)
\(72\) 17.6736 + 17.6736i 0.245467 + 0.245467i
\(73\) −80.4250 + 80.4250i −1.10171 + 1.10171i −0.107509 + 0.994204i \(0.534287\pi\)
−0.994204 + 0.107509i \(0.965713\pi\)
\(74\) 81.0743i 1.09560i
\(75\) 55.8454 + 89.6063i 0.744605 + 1.19475i
\(76\) −24.0036 −0.315837
\(77\) −33.9413 33.9413i −0.440796 0.440796i
\(78\) −17.3180 + 17.3180i −0.222026 + 0.222026i
\(79\) 66.7607i 0.845072i 0.906346 + 0.422536i \(0.138860\pi\)
−0.906346 + 0.422536i \(0.861140\pi\)
\(80\) 15.6595 12.4411i 0.195744 0.155513i
\(81\) 82.4421 1.01780
\(82\) −48.8398 48.8398i −0.595607 0.595607i
\(83\) 30.2065 30.2065i 0.363934 0.363934i −0.501325 0.865259i \(-0.667154\pi\)
0.865259 + 0.501325i \(0.167154\pi\)
\(84\) 47.1481i 0.561287i
\(85\) 110.387 + 12.6430i 1.29867 + 0.148741i
\(86\) −59.4594 −0.691388
\(87\) −122.798 122.798i −1.41147 1.41147i
\(88\) −17.1988 + 17.1988i −0.195441 + 0.195441i
\(89\) 48.7863i 0.548161i −0.961707 0.274081i \(-0.911627\pi\)
0.961707 0.274081i \(-0.0883735\pi\)
\(90\) −7.11019 + 62.0798i −0.0790021 + 0.689775i
\(91\) −22.8884 −0.251521
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 59.4008 59.4008i 0.638718 0.638718i
\(94\) 11.5976i 0.123379i
\(95\) −37.3288 46.9855i −0.392934 0.494585i
\(96\) 23.8910 0.248864
\(97\) −40.6035 40.6035i −0.418593 0.418593i 0.466126 0.884718i \(-0.345649\pi\)
−0.884718 + 0.466126i \(0.845649\pi\)
\(98\) 17.8432 17.8432i 0.182074 0.182074i
\(99\) 75.9911i 0.767587i
\(100\) 48.7052 + 11.3050i 0.487052 + 0.113050i
\(101\) −58.6599 −0.580791 −0.290396 0.956907i \(-0.593787\pi\)
−0.290396 + 0.956907i \(0.593787\pi\)
\(102\) 93.8504 + 93.8504i 0.920102 + 0.920102i
\(103\) −31.9173 + 31.9173i −0.309876 + 0.309876i −0.844861 0.534985i \(-0.820317\pi\)
0.534985 + 0.844861i \(0.320317\pi\)
\(104\) 11.5981i 0.111520i
\(105\) −92.2896 + 73.3216i −0.878948 + 0.698301i
\(106\) −16.7542 −0.158058
\(107\) 69.1476 + 69.1476i 0.646239 + 0.646239i 0.952082 0.305843i \(-0.0989382\pi\)
−0.305843 + 0.952082i \(0.598938\pi\)
\(108\) 0.974735 0.974735i 0.00902533 0.00902533i
\(109\) 209.433i 1.92141i −0.277577 0.960703i \(-0.589531\pi\)
0.277577 0.960703i \(-0.410469\pi\)
\(110\) −60.4119 6.91916i −0.549199 0.0629015i
\(111\) 242.118 2.18124
\(112\) 15.7878 + 15.7878i 0.140962 + 0.140962i
\(113\) −49.5439 + 49.5439i −0.438441 + 0.438441i −0.891487 0.453046i \(-0.850337\pi\)
0.453046 + 0.891487i \(0.350337\pi\)
\(114\) 71.6836i 0.628804i
\(115\) 2.72857 23.8234i 0.0237267 0.207160i
\(116\) −82.2389 −0.708956
\(117\) −25.6224 25.6224i −0.218995 0.218995i
\(118\) −91.8342 + 91.8342i −0.778256 + 0.778256i
\(119\) 124.038i 1.04233i
\(120\) 37.1536 + 46.7651i 0.309613 + 0.389709i
\(121\) −47.0505 −0.388847
\(122\) −6.02932 6.02932i −0.0494206 0.0494206i
\(123\) 145.854 145.854i 1.18580 1.18580i
\(124\) 39.7813i 0.320817i
\(125\) 53.6142 + 112.918i 0.428914 + 0.903346i
\(126\) −69.7568 −0.553625
\(127\) 50.2129 + 50.2129i 0.395377 + 0.395377i 0.876599 0.481222i \(-0.159807\pi\)
−0.481222 + 0.876599i \(0.659807\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 177.568i 1.37649i
\(130\) −22.7025 + 18.0365i −0.174634 + 0.138742i
\(131\) −76.6729 −0.585289 −0.292645 0.956221i \(-0.594535\pi\)
−0.292645 + 0.956221i \(0.594535\pi\)
\(132\) −51.3619 51.3619i −0.389105 0.389105i
\(133\) 47.3704 47.3704i 0.356169 0.356169i
\(134\) 42.5754i 0.317727i
\(135\) 3.42383 + 0.392141i 0.0253617 + 0.00290475i
\(136\) 62.8525 0.462151
\(137\) 188.464 + 188.464i 1.37565 + 1.37565i 0.851831 + 0.523817i \(0.175492\pi\)
0.523817 + 0.851831i \(0.324508\pi\)
\(138\) 20.2545 20.2545i 0.146772 0.146772i
\(139\) 182.679i 1.31424i 0.753786 + 0.657120i \(0.228226\pi\)
−0.753786 + 0.657120i \(0.771774\pi\)
\(140\) −6.35151 + 55.4557i −0.0453679 + 0.396112i
\(141\) −34.6348 −0.245637
\(142\) 89.1373 + 89.1373i 0.627727 + 0.627727i
\(143\) 24.9340 24.9340i 0.174364 0.174364i
\(144\) 35.3472i 0.245467i
\(145\) −127.892 160.978i −0.882016 1.11019i
\(146\) −160.850 −1.10171
\(147\) 53.2865 + 53.2865i 0.362493 + 0.362493i
\(148\) 81.0743 81.0743i 0.547799 0.547799i
\(149\) 228.292i 1.53216i −0.642744 0.766081i \(-0.722204\pi\)
0.642744 0.766081i \(-0.277796\pi\)
\(150\) −33.7609 + 145.452i −0.225073 + 0.969678i
\(151\) −87.2770 −0.577994 −0.288997 0.957330i \(-0.593322\pi\)
−0.288997 + 0.957330i \(0.593322\pi\)
\(152\) −24.0036 24.0036i −0.157918 0.157918i
\(153\) −138.854 + 138.854i −0.907541 + 0.907541i
\(154\) 67.8826i 0.440796i
\(155\) 77.8693 61.8651i 0.502383 0.399130i
\(156\) −34.6361 −0.222026
\(157\) −179.098 179.098i −1.14075 1.14075i −0.988313 0.152440i \(-0.951287\pi\)
−0.152440 0.988313i \(-0.548713\pi\)
\(158\) −66.7607 + 66.7607i −0.422536 + 0.422536i
\(159\) 50.0341i 0.314680i
\(160\) 28.1006 + 3.21844i 0.175629 + 0.0201153i
\(161\) 26.7695 0.166270
\(162\) 82.4421 + 82.4421i 0.508902 + 0.508902i
\(163\) −2.08145 + 2.08145i −0.0127697 + 0.0127697i −0.713463 0.700693i \(-0.752874\pi\)
0.700693 + 0.713463i \(0.252874\pi\)
\(164\) 97.6796i 0.595607i
\(165\) 20.6632 180.412i 0.125231 1.09341i
\(166\) 60.4131 0.363934
\(167\) −19.6858 19.6858i −0.117879 0.117879i 0.645707 0.763586i \(-0.276563\pi\)
−0.763586 + 0.645707i \(0.776563\pi\)
\(168\) −47.1481 + 47.1481i −0.280644 + 0.280644i
\(169\) 152.186i 0.900507i
\(170\) 97.7440 + 123.030i 0.574965 + 0.723705i
\(171\) 106.058 0.620219
\(172\) −59.4594 59.4594i −0.345694 0.345694i
\(173\) 14.1760 14.1760i 0.0819422 0.0819422i −0.664948 0.746890i \(-0.731546\pi\)
0.746890 + 0.664948i \(0.231546\pi\)
\(174\) 245.596i 1.41147i
\(175\) −118.429 + 73.8083i −0.676734 + 0.421762i
\(176\) −34.3976 −0.195441
\(177\) −274.251 274.251i −1.54944 1.54944i
\(178\) 48.7863 48.7863i 0.274081 0.274081i
\(179\) 292.614i 1.63472i −0.576130 0.817358i \(-0.695438\pi\)
0.576130 0.817358i \(-0.304562\pi\)
\(180\) −69.1900 + 54.9696i −0.384389 + 0.305387i
\(181\) 78.0441 0.431183 0.215591 0.976484i \(-0.430832\pi\)
0.215591 + 0.976484i \(0.430832\pi\)
\(182\) −22.8884 22.8884i −0.125761 0.125761i
\(183\) 18.0058 18.0058i 0.0983922 0.0983922i
\(184\) 13.5647i 0.0737210i
\(185\) 284.779 + 32.6166i 1.53935 + 0.176306i
\(186\) 118.802 0.638718
\(187\) −135.123 135.123i −0.722585 0.722585i
\(188\) −11.5976 + 11.5976i −0.0616896 + 0.0616896i
\(189\) 3.84723i 0.0203557i
\(190\) 9.65678 84.3143i 0.0508251 0.443760i
\(191\) −69.6705 −0.364767 −0.182384 0.983227i \(-0.558381\pi\)
−0.182384 + 0.983227i \(0.558381\pi\)
\(192\) 23.8910 + 23.8910i 0.124432 + 0.124432i
\(193\) −235.374 + 235.374i −1.21956 + 1.21956i −0.251769 + 0.967787i \(0.581012\pi\)
−0.967787 + 0.251769i \(0.918988\pi\)
\(194\) 81.2070i 0.418593i
\(195\) −53.8637 67.7980i −0.276224 0.347682i
\(196\) 35.6865 0.182074
\(197\) 137.287 + 137.287i 0.696887 + 0.696887i 0.963738 0.266851i \(-0.0859832\pi\)
−0.266851 + 0.963738i \(0.585983\pi\)
\(198\) 75.9911 75.9911i 0.383793 0.383793i
\(199\) 221.293i 1.11202i −0.831174 0.556012i \(-0.812331\pi\)
0.831174 0.556012i \(-0.187669\pi\)
\(200\) 37.4002 + 60.0102i 0.187001 + 0.300051i
\(201\) −127.146 −0.632566
\(202\) −58.6599 58.6599i −0.290396 0.290396i
\(203\) 162.296 162.296i 0.799489 0.799489i
\(204\) 187.701i 0.920102i
\(205\) 191.202 151.905i 0.932691 0.740998i
\(206\) −63.8345 −0.309876
\(207\) 29.9671 + 29.9671i 0.144768 + 0.144768i
\(208\) −11.5981 + 11.5981i −0.0557599 + 0.0557599i
\(209\) 103.208i 0.493819i
\(210\) −165.611 18.9680i −0.788625 0.0903236i
\(211\) 206.938 0.980749 0.490374 0.871512i \(-0.336860\pi\)
0.490374 + 0.871512i \(0.336860\pi\)
\(212\) −16.7542 16.7542i −0.0790290 0.0790290i
\(213\) −266.197 + 266.197i −1.24975 + 1.24975i
\(214\) 138.295i 0.646239i
\(215\) 23.9208 208.855i 0.111260 0.971420i
\(216\) 1.94947 0.00902533
\(217\) 78.5072 + 78.5072i 0.361784 + 0.361784i
\(218\) 209.433 209.433i 0.960703 0.960703i
\(219\) 480.358i 2.19341i
\(220\) −53.4928 67.3311i −0.243149 0.306050i
\(221\) −91.1209 −0.412312
\(222\) 242.118 + 242.118i 1.09062 + 1.09062i
\(223\) −146.489 + 146.489i −0.656901 + 0.656901i −0.954646 0.297745i \(-0.903766\pi\)
0.297745 + 0.954646i \(0.403766\pi\)
\(224\) 31.5756i 0.140962i
\(225\) −215.199 49.9501i −0.956441 0.222000i
\(226\) −99.0877 −0.438441
\(227\) 116.497 + 116.497i 0.513202 + 0.513202i 0.915506 0.402304i \(-0.131791\pi\)
−0.402304 + 0.915506i \(0.631791\pi\)
\(228\) 71.6836 71.6836i 0.314402 0.314402i
\(229\) 398.498i 1.74017i 0.492905 + 0.870083i \(0.335935\pi\)
−0.492905 + 0.870083i \(0.664065\pi\)
\(230\) 26.5520 21.0948i 0.115443 0.0917167i
\(231\) 202.723 0.877587
\(232\) −82.2389 82.2389i −0.354478 0.354478i
\(233\) −133.851 + 133.851i −0.574470 + 0.574470i −0.933374 0.358904i \(-0.883150\pi\)
0.358904 + 0.933374i \(0.383150\pi\)
\(234\) 51.2449i 0.218995i
\(235\) −40.7375 4.66579i −0.173351 0.0198544i
\(236\) −183.668 −0.778256
\(237\) −199.372 199.372i −0.841233 0.841233i
\(238\) −124.038 + 124.038i −0.521167 + 0.521167i
\(239\) 206.404i 0.863615i 0.901966 + 0.431808i \(0.142124\pi\)
−0.901966 + 0.431808i \(0.857876\pi\)
\(240\) −9.61146 + 83.9187i −0.0400477 + 0.349661i
\(241\) −92.8472 −0.385258 −0.192629 0.981272i \(-0.561701\pi\)
−0.192629 + 0.981272i \(0.561701\pi\)
\(242\) −47.0505 47.0505i −0.194424 0.194424i
\(243\) −241.816 + 241.816i −0.995129 + 0.995129i
\(244\) 12.0586i 0.0494206i
\(245\) 55.4972 + 69.8541i 0.226519 + 0.285119i
\(246\) 291.707 1.18580
\(247\) 34.7994 + 34.7994i 0.140888 + 0.140888i
\(248\) 39.7813 39.7813i 0.160408 0.160408i
\(249\) 180.416i 0.724561i
\(250\) −59.3040 + 166.532i −0.237216 + 0.666130i
\(251\) 427.161 1.70184 0.850918 0.525298i \(-0.176046\pi\)
0.850918 + 0.525298i \(0.176046\pi\)
\(252\) −69.7568 69.7568i −0.276813 0.276813i
\(253\) −29.1619 + 29.1619i −0.115265 + 0.115265i
\(254\) 100.426i 0.395377i
\(255\) −367.413 + 291.900i −1.44083 + 1.14470i
\(256\) 16.0000 0.0625000
\(257\) 209.203 + 209.203i 0.814019 + 0.814019i 0.985234 0.171214i \(-0.0547691\pi\)
−0.171214 + 0.985234i \(0.554769\pi\)
\(258\) 177.568 177.568i 0.688247 0.688247i
\(259\) 319.996i 1.23551i
\(260\) −40.7390 4.66596i −0.156688 0.0179460i
\(261\) 363.364 1.39220
\(262\) −76.6729 76.6729i −0.292645 0.292645i
\(263\) 86.9091 86.9091i 0.330453 0.330453i −0.522305 0.852758i \(-0.674928\pi\)
0.852758 + 0.522305i \(0.174928\pi\)
\(264\) 102.724i 0.389105i
\(265\) 6.74029 58.8501i 0.0254350 0.222076i
\(266\) 94.7409 0.356169
\(267\) 145.694 + 145.694i 0.545670 + 0.545670i
\(268\) −42.5754 + 42.5754i −0.158863 + 0.158863i
\(269\) 324.191i 1.20517i 0.798054 + 0.602586i \(0.205863\pi\)
−0.798054 + 0.602586i \(0.794137\pi\)
\(270\) 3.03168 + 3.81597i 0.0112285 + 0.0141332i
\(271\) −374.518 −1.38199 −0.690993 0.722862i \(-0.742826\pi\)
−0.690993 + 0.722862i \(0.742826\pi\)
\(272\) 62.8525 + 62.8525i 0.231075 + 0.231075i
\(273\) 68.3533 68.3533i 0.250379 0.250379i
\(274\) 376.928i 1.37565i
\(275\) 48.6081 209.417i 0.176757 0.761518i
\(276\) 40.5091 0.146772
\(277\) 51.1306 + 51.1306i 0.184587 + 0.184587i 0.793351 0.608764i \(-0.208334\pi\)
−0.608764 + 0.793351i \(0.708334\pi\)
\(278\) −182.679 + 182.679i −0.657120 + 0.657120i
\(279\) 175.770i 0.629998i
\(280\) −61.8072 + 49.1042i −0.220740 + 0.175372i
\(281\) 398.890 1.41954 0.709769 0.704434i \(-0.248799\pi\)
0.709769 + 0.704434i \(0.248799\pi\)
\(282\) −34.6348 34.6348i −0.122819 0.122819i
\(283\) −23.1698 + 23.1698i −0.0818720 + 0.0818720i −0.746857 0.664985i \(-0.768438\pi\)
0.664985 + 0.746857i \(0.268438\pi\)
\(284\) 178.275i 0.627727i
\(285\) 251.794 + 28.8387i 0.883487 + 0.101188i
\(286\) 49.8681 0.174364
\(287\) 192.768 + 192.768i 0.671665 + 0.671665i
\(288\) −35.3472 + 35.3472i −0.122733 + 0.122733i
\(289\) 204.805i 0.708668i
\(290\) 33.0852 288.870i 0.114087 0.996103i
\(291\) 242.514 0.833381
\(292\) −160.850 160.850i −0.550856 0.550856i
\(293\) −60.7766 + 60.7766i −0.207429 + 0.207429i −0.803174 0.595745i \(-0.796857\pi\)
0.595745 + 0.803174i \(0.296857\pi\)
\(294\) 106.573i 0.362493i
\(295\) −285.629 359.520i −0.968233 1.21871i
\(296\) 162.149 0.547799
\(297\) −4.19106 4.19106i −0.0141113 0.0141113i
\(298\) 228.292 228.292i 0.766081 0.766081i
\(299\) 19.6655i 0.0657708i
\(300\) −179.213 + 111.691i −0.597375 + 0.372303i
\(301\) 234.683 0.779678
\(302\) −87.2770 87.2770i −0.288997 0.288997i
\(303\) 175.180 175.180i 0.578152 0.578152i
\(304\) 48.0072i 0.157918i
\(305\) 23.6040 18.7528i 0.0773903 0.0614845i
\(306\) −277.708 −0.907541
\(307\) 265.540 + 265.540i 0.864951 + 0.864951i 0.991908 0.126957i \(-0.0405210\pi\)
−0.126957 + 0.991908i \(0.540521\pi\)
\(308\) 67.8826 67.8826i 0.220398 0.220398i
\(309\) 190.633i 0.616937i
\(310\) 139.734 + 16.0042i 0.450756 + 0.0516265i
\(311\) −421.810 −1.35630 −0.678150 0.734923i \(-0.737218\pi\)
−0.678150 + 0.734923i \(0.737218\pi\)
\(312\) −34.6361 34.6361i −0.111013 0.111013i
\(313\) 129.271 129.271i 0.413008 0.413008i −0.469777 0.882785i \(-0.655666\pi\)
0.882785 + 0.469777i \(0.155666\pi\)
\(314\) 358.196i 1.14075i
\(315\) 28.0635 245.026i 0.0890905 0.777859i
\(316\) −133.521 −0.422536
\(317\) −268.224 268.224i −0.846131 0.846131i 0.143517 0.989648i \(-0.454159\pi\)
−0.989648 + 0.143517i \(0.954159\pi\)
\(318\) 50.0341 50.0341i 0.157340 0.157340i
\(319\) 353.602i 1.10847i
\(320\) 24.8821 + 31.3190i 0.0777566 + 0.0978719i
\(321\) −413.001 −1.28661
\(322\) 26.7695 + 26.7695i 0.0831351 + 0.0831351i
\(323\) 188.586 188.586i 0.583857 0.583857i
\(324\) 164.884i 0.508902i
\(325\) −54.2212 87.0002i −0.166834 0.267693i
\(326\) −4.16291 −0.0127697
\(327\) 625.445 + 625.445i 1.91268 + 1.91268i
\(328\) 97.6796 97.6796i 0.297804 0.297804i
\(329\) 45.7752i 0.139134i
\(330\) 201.075 159.749i 0.609320 0.484088i
\(331\) −234.830 −0.709455 −0.354727 0.934970i \(-0.615426\pi\)
−0.354727 + 0.934970i \(0.615426\pi\)
\(332\) 60.4131 + 60.4131i 0.181967 + 0.181967i
\(333\) −358.219 + 358.219i −1.07573 + 1.07573i
\(334\) 39.3716i 0.117879i
\(335\) −149.549 17.1283i −0.446415 0.0511292i
\(336\) −94.2963 −0.280644
\(337\) 183.913 + 183.913i 0.545737 + 0.545737i 0.925205 0.379468i \(-0.123893\pi\)
−0.379468 + 0.925205i \(0.623893\pi\)
\(338\) −152.186 + 152.186i −0.450253 + 0.450253i
\(339\) 295.912i 0.872898i
\(340\) −25.2859 + 220.774i −0.0743703 + 0.649335i
\(341\) −171.047 −0.501605
\(342\) 106.058 + 106.058i 0.310110 + 0.310110i
\(343\) −263.827 + 263.827i −0.769174 + 0.769174i
\(344\) 118.919i 0.345694i
\(345\) 62.9970 + 79.2940i 0.182600 + 0.229838i
\(346\) 28.3520 0.0819422
\(347\) −50.3871 50.3871i −0.145208 0.145208i 0.630766 0.775973i \(-0.282741\pi\)
−0.775973 + 0.630766i \(0.782741\pi\)
\(348\) 245.596 245.596i 0.705735 0.705735i
\(349\) 344.711i 0.987711i −0.869544 0.493855i \(-0.835587\pi\)
0.869544 0.493855i \(-0.164413\pi\)
\(350\) −192.237 44.6203i −0.549248 0.127486i
\(351\) −2.82626 −0.00805202
\(352\) −34.3976 34.3976i −0.0977203 0.0977203i
\(353\) 462.680 462.680i 1.31071 1.31071i 0.389814 0.920894i \(-0.372539\pi\)
0.920894 0.389814i \(-0.127461\pi\)
\(354\) 548.502i 1.54944i
\(355\) −348.961 + 277.241i −0.982990 + 0.780959i
\(356\) 97.5727 0.274081
\(357\) −370.423 370.423i −1.03760 1.03760i
\(358\) 292.614 292.614i 0.817358 0.817358i
\(359\) 408.460i 1.13777i 0.822417 + 0.568886i \(0.192625\pi\)
−0.822417 + 0.568886i \(0.807375\pi\)
\(360\) −124.160 14.2204i −0.344888 0.0395010i
\(361\) 216.957 0.600988
\(362\) 78.0441 + 78.0441i 0.215591 + 0.215591i
\(363\) 140.510 140.510i 0.387081 0.387081i
\(364\) 45.7769i 0.125761i
\(365\) 64.7109 564.997i 0.177290 1.54794i
\(366\) 36.0115 0.0983922
\(367\) −460.907 460.907i −1.25588 1.25588i −0.953043 0.302836i \(-0.902067\pi\)
−0.302836 0.953043i \(-0.597933\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 431.588i 1.16961i
\(370\) 252.163 + 317.396i 0.681520 + 0.857826i
\(371\) 66.1277 0.178242
\(372\) 118.802 + 118.802i 0.319359 + 0.319359i
\(373\) 267.027 267.027i 0.715889 0.715889i −0.251871 0.967761i \(-0.581046\pi\)
0.967761 + 0.251871i \(0.0810460\pi\)
\(374\) 270.247i 0.722585i
\(375\) −497.327 177.104i −1.32621 0.472276i
\(376\) −23.1953 −0.0616896
\(377\) 119.226 + 119.226i 0.316250 + 0.316250i
\(378\) −3.84723 + 3.84723i −0.0101778 + 0.0101778i
\(379\) 257.246i 0.678749i 0.940651 + 0.339374i \(0.110215\pi\)
−0.940651 + 0.339374i \(0.889785\pi\)
\(380\) 93.9711 74.6575i 0.247292 0.196467i
\(381\) −299.909 −0.787161
\(382\) −69.6705 69.6705i −0.182384 0.182384i
\(383\) 102.313 102.313i 0.267136 0.267136i −0.560809 0.827945i \(-0.689510\pi\)
0.827945 + 0.560809i \(0.189510\pi\)
\(384\) 47.7819i 0.124432i
\(385\) 238.443 + 27.3096i 0.619331 + 0.0709339i
\(386\) −470.749 −1.21956
\(387\) 262.715 + 262.715i 0.678851 + 0.678851i
\(388\) 81.2070 81.2070i 0.209296 0.209296i
\(389\) 13.5885i 0.0349319i 0.999847 + 0.0174660i \(0.00555987\pi\)
−0.999847 + 0.0174660i \(0.994440\pi\)
\(390\) 13.9343 121.662i 0.0357289 0.311953i
\(391\) 106.572 0.272562
\(392\) 35.6865 + 35.6865i 0.0910369 + 0.0910369i
\(393\) 228.974 228.974i 0.582630 0.582630i
\(394\) 274.573i 0.696887i
\(395\) −207.644 261.360i −0.525680 0.661671i
\(396\) 151.982 0.383793
\(397\) −444.867 444.867i −1.12057 1.12057i −0.991655 0.128918i \(-0.958850\pi\)
−0.128918 0.991655i \(-0.541150\pi\)
\(398\) 221.293 221.293i 0.556012 0.556012i
\(399\) 282.931i 0.709101i
\(400\) −22.6100 + 97.4104i −0.0565250 + 0.243526i
\(401\) −496.549 −1.23828 −0.619139 0.785281i \(-0.712518\pi\)
−0.619139 + 0.785281i \(0.712518\pi\)
\(402\) −127.146 127.146i −0.316283 0.316283i
\(403\) −57.6731 + 57.6731i −0.143110 + 0.143110i
\(404\) 117.320i 0.290396i
\(405\) −322.751 + 256.417i −0.796915 + 0.633128i
\(406\) 324.592 0.799489
\(407\) −348.595 348.595i −0.856498 0.856498i
\(408\) −187.701 + 187.701i −0.460051 + 0.460051i
\(409\) 504.901i 1.23448i 0.786776 + 0.617238i \(0.211748\pi\)
−0.786776 + 0.617238i \(0.788252\pi\)
\(410\) 343.106 + 39.2970i 0.836845 + 0.0958464i
\(411\) −1125.64 −2.73880
\(412\) −63.8345 63.8345i −0.154938 0.154938i
\(413\) 362.465 362.465i 0.877638 0.877638i
\(414\) 59.9341i 0.144768i
\(415\) −24.3045 + 212.205i −0.0585651 + 0.511338i
\(416\) −23.1961 −0.0557599
\(417\) −545.548 545.548i −1.30827 1.30827i
\(418\) −103.208 + 103.208i −0.246909 + 0.246909i
\(419\) 496.330i 1.18456i 0.805733 + 0.592280i \(0.201772\pi\)
−0.805733 + 0.592280i \(0.798228\pi\)
\(420\) −146.643 184.579i −0.349151 0.439474i
\(421\) −217.991 −0.517793 −0.258897 0.965905i \(-0.583359\pi\)
−0.258897 + 0.965905i \(0.583359\pi\)
\(422\) 206.938 + 206.938i 0.490374 + 0.490374i
\(423\) 51.2430 51.2430i 0.121142 0.121142i
\(424\) 33.5083i 0.0790290i
\(425\) −471.474 + 293.837i −1.10935 + 0.691381i
\(426\) −532.394 −1.24975
\(427\) 23.7974 + 23.7974i 0.0557316 + 0.0557316i
\(428\) −138.295 + 138.295i −0.323120 + 0.323120i
\(429\) 148.925i 0.347143i
\(430\) 232.776 184.934i 0.541340 0.430080i
\(431\) −194.670 −0.451670 −0.225835 0.974166i \(-0.572511\pi\)
−0.225835 + 0.974166i \(0.572511\pi\)
\(432\) 1.94947 + 1.94947i 0.00451266 + 0.00451266i
\(433\) −83.0439 + 83.0439i −0.191787 + 0.191787i −0.796468 0.604681i \(-0.793301\pi\)
0.604681 + 0.796468i \(0.293301\pi\)
\(434\) 157.014i 0.361784i
\(435\) 862.672 + 98.8045i 1.98315 + 0.227137i
\(436\) 418.867 0.960703
\(437\) −40.7001 40.7001i −0.0931352 0.0931352i
\(438\) 480.358 480.358i 1.09671 1.09671i
\(439\) 651.478i 1.48400i −0.670397 0.742002i \(-0.733876\pi\)
0.670397 0.742002i \(-0.266124\pi\)
\(440\) 13.8383 120.824i 0.0314507 0.274600i
\(441\) −157.677 −0.357545
\(442\) −91.1209 91.1209i −0.206156 0.206156i
\(443\) 32.9886 32.9886i 0.0744663 0.0744663i −0.668893 0.743359i \(-0.733231\pi\)
0.743359 + 0.668893i \(0.233231\pi\)
\(444\) 484.236i 1.09062i
\(445\) 151.738 + 190.992i 0.340985 + 0.429196i
\(446\) −292.978 −0.656901
\(447\) 681.765 + 681.765i 1.52520 + 1.52520i
\(448\) −31.5756 + 31.5756i −0.0704812 + 0.0704812i
\(449\) 528.035i 1.17603i −0.808852 0.588013i \(-0.799911\pi\)
0.808852 0.588013i \(-0.200089\pi\)
\(450\) −165.249 265.149i −0.367220 0.589220i
\(451\) −419.992 −0.931247
\(452\) −99.0877 99.0877i −0.219221 0.219221i
\(453\) 260.641 260.641i 0.575368 0.575368i
\(454\) 232.994i 0.513202i
\(455\) 89.6054 71.1891i 0.196935 0.156460i
\(456\) 143.367 0.314402
\(457\) −299.231 299.231i −0.654773 0.654773i 0.299365 0.954139i \(-0.403225\pi\)
−0.954139 + 0.299365i \(0.903225\pi\)
\(458\) −398.498 + 398.498i −0.870083 + 0.870083i
\(459\) 15.3161i 0.0333685i
\(460\) 47.6468 + 5.45714i 0.103580 + 0.0118633i
\(461\) 482.726 1.04713 0.523564 0.851986i \(-0.324602\pi\)
0.523564 + 0.851986i \(0.324602\pi\)
\(462\) 202.723 + 202.723i 0.438794 + 0.438794i
\(463\) 342.679 342.679i 0.740128 0.740128i −0.232474 0.972603i \(-0.574682\pi\)
0.972603 + 0.232474i \(0.0746821\pi\)
\(464\) 164.478i 0.354478i
\(465\) −47.7945 + 417.299i −0.102784 + 0.897417i
\(466\) −267.703 −0.574470
\(467\) 513.486 + 513.486i 1.09954 + 1.09954i 0.994464 + 0.105077i \(0.0335088\pi\)
0.105077 + 0.994464i \(0.466491\pi\)
\(468\) 51.2449 51.2449i 0.109498 0.109498i
\(469\) 168.043i 0.358300i
\(470\) −36.0717 45.4033i −0.0767483 0.0966028i
\(471\) 1069.71 2.27114
\(472\) −183.668 183.668i −0.389128 0.389128i
\(473\) −255.657 + 255.657i −0.540501 + 0.540501i
\(474\) 398.744i 0.841233i
\(475\) 292.275 + 67.8402i 0.615316 + 0.142822i
\(476\) −248.076 −0.521167
\(477\) 74.0266 + 74.0266i 0.155192 + 0.155192i
\(478\) −206.404 + 206.404i −0.431808 + 0.431808i
\(479\) 303.049i 0.632671i −0.948647 0.316335i \(-0.897548\pi\)
0.948647 0.316335i \(-0.102452\pi\)
\(480\) −93.5301 + 74.3072i −0.194854 + 0.154807i
\(481\) −235.076 −0.488723
\(482\) −92.8472 92.8472i −0.192629 0.192629i
\(483\) −79.9436 + 79.9436i −0.165515 + 0.165515i
\(484\) 94.1010i 0.194424i
\(485\) 285.245 + 32.6700i 0.588134 + 0.0673608i
\(486\) −483.633 −0.995129
\(487\) −269.987 269.987i −0.554388 0.554388i 0.373316 0.927704i \(-0.378221\pi\)
−0.927704 + 0.373316i \(0.878221\pi\)
\(488\) 12.0586 12.0586i 0.0247103 0.0247103i
\(489\) 12.4320i 0.0254233i
\(490\) −14.3569 + 125.351i −0.0292997 + 0.255819i
\(491\) −788.957 −1.60684 −0.803418 0.595415i \(-0.796988\pi\)
−0.803418 + 0.595415i \(0.796988\pi\)
\(492\) 291.707 + 291.707i 0.592901 + 0.592901i
\(493\) 646.115 646.115i 1.31058 1.31058i
\(494\) 69.5988i 0.140888i
\(495\) 236.352 + 297.496i 0.477480 + 0.601001i
\(496\) 79.5625 0.160408
\(497\) −351.820 351.820i −0.707887 0.707887i
\(498\) −180.416 + 180.416i −0.362281 + 0.362281i
\(499\) 811.329i 1.62591i −0.582326 0.812955i \(-0.697857\pi\)
0.582326 0.812955i \(-0.302143\pi\)
\(500\) −225.836 + 107.228i −0.451673 + 0.214457i
\(501\) 117.578 0.234687
\(502\) 427.161 + 427.161i 0.850918 + 0.850918i
\(503\) 690.146 690.146i 1.37206 1.37206i 0.514675 0.857385i \(-0.327912\pi\)
0.857385 0.514675i \(-0.172088\pi\)
\(504\) 139.514i 0.276813i
\(505\) 229.646 182.448i 0.454745 0.361283i
\(506\) −58.3239 −0.115265
\(507\) −454.483 454.483i −0.896415 0.896415i
\(508\) −100.426 + 100.426i −0.197689 + 0.197689i
\(509\) 282.285i 0.554588i 0.960785 + 0.277294i \(0.0894377\pi\)
−0.960785 + 0.277294i \(0.910562\pi\)
\(510\) −659.312 75.5131i −1.29277 0.148065i
\(511\) 634.867 1.24240
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 5.84929 5.84929i 0.0114021 0.0114021i
\(514\) 418.406i 0.814019i
\(515\) 25.6810 224.223i 0.0498660 0.435385i
\(516\) 355.135 0.688247
\(517\) 49.8663 + 49.8663i 0.0964532 + 0.0964532i
\(518\) −319.996 + 319.996i −0.617753 + 0.617753i
\(519\) 84.6695i 0.163140i
\(520\) −36.0730 45.4049i −0.0693712 0.0873172i
\(521\) 89.0529 0.170927 0.0854634 0.996341i \(-0.472763\pi\)
0.0854634 + 0.996341i \(0.472763\pi\)
\(522\) 363.364 + 363.364i 0.696101 + 0.696101i
\(523\) 126.934 126.934i 0.242703 0.242703i −0.575265 0.817967i \(-0.695101\pi\)
0.817967 + 0.575265i \(0.195101\pi\)
\(524\) 153.346i 0.292645i
\(525\) 133.253 574.090i 0.253814 1.09350i
\(526\) 173.818 0.330453
\(527\) 312.544 + 312.544i 0.593063 + 0.593063i
\(528\) 102.724 102.724i 0.194553 0.194553i
\(529\) 23.0000i 0.0434783i
\(530\) 65.5904 52.1099i 0.123756 0.0983205i
\(531\) 811.521 1.52829
\(532\) 94.7409 + 94.7409i 0.178084 + 0.178084i
\(533\) −141.612 + 141.612i −0.265688 + 0.265688i
\(534\) 291.388i 0.545670i
\(535\) −485.772 55.6369i −0.907984 0.103994i
\(536\) −85.1507 −0.158863
\(537\) 873.854 + 873.854i 1.62729 + 1.62729i
\(538\) −324.191 + 324.191i −0.602586 + 0.602586i
\(539\) 153.441i 0.284677i
\(540\) −0.784282 + 6.84765i −0.00145237 + 0.0126808i
\(541\) 190.762 0.352609 0.176305 0.984336i \(-0.443586\pi\)
0.176305 + 0.984336i \(0.443586\pi\)
\(542\) −374.518 374.518i −0.690993 0.690993i
\(543\) −233.068 + 233.068i −0.429224 + 0.429224i
\(544\) 125.705i 0.231075i
\(545\) 651.393 + 819.906i 1.19522 + 1.50441i
\(546\) 136.707 0.250379
\(547\) 409.164 + 409.164i 0.748015 + 0.748015i 0.974106 0.226091i \(-0.0725947\pi\)
−0.226091 + 0.974106i \(0.572595\pi\)
\(548\) −376.928 + 376.928i −0.687824 + 0.687824i
\(549\) 53.2799i 0.0970490i
\(550\) 258.026 160.809i 0.469137 0.292381i
\(551\) −493.507 −0.895658
\(552\) 40.5091 + 40.5091i 0.0733860 + 0.0733860i
\(553\) 263.501 263.501i 0.476494 0.476494i
\(554\) 102.261i 0.184587i
\(555\) −947.861 + 753.050i −1.70786 + 1.35685i
\(556\) −365.359 −0.657120
\(557\) 490.274 + 490.274i 0.880205 + 0.880205i 0.993555 0.113351i \(-0.0361583\pi\)
−0.113351 + 0.993555i \(0.536158\pi\)
\(558\) −175.770 + 175.770i −0.314999 + 0.314999i
\(559\) 172.403i 0.308414i
\(560\) −110.911 12.7030i −0.198056 0.0226840i
\(561\) 807.056 1.43860
\(562\) 398.890 + 398.890i 0.709769 + 0.709769i
\(563\) −624.598 + 624.598i −1.10941 + 1.10941i −0.116182 + 0.993228i \(0.537066\pi\)
−0.993228 + 0.116182i \(0.962934\pi\)
\(564\) 69.2696i 0.122819i
\(565\) 39.8635 348.053i 0.0705549 0.616022i
\(566\) −46.3395 −0.0818720
\(567\) −325.395 325.395i −0.573888 0.573888i
\(568\) −178.275 + 178.275i −0.313864 + 0.313864i
\(569\) 646.904i 1.13691i −0.822713 0.568457i \(-0.807541\pi\)
0.822713 0.568457i \(-0.192459\pi\)
\(570\) 222.955 + 280.632i 0.391149 + 0.492338i
\(571\) −320.656 −0.561569 −0.280785 0.959771i \(-0.590595\pi\)
−0.280785 + 0.959771i \(0.590595\pi\)
\(572\) 49.8681 + 49.8681i 0.0871820 + 0.0871820i
\(573\) 208.062 208.062i 0.363110 0.363110i
\(574\) 385.536i 0.671665i
\(575\) 63.4151 + 101.752i 0.110287 + 0.176960i
\(576\) −70.6944 −0.122733
\(577\) −45.0178 45.0178i −0.0780204 0.0780204i 0.667020 0.745040i \(-0.267570\pi\)
−0.745040 + 0.667020i \(0.767570\pi\)
\(578\) −204.805 + 204.805i −0.354334 + 0.354334i
\(579\) 1405.83i 2.42803i
\(580\) 321.955 255.785i 0.555095 0.441008i
\(581\) −238.447 −0.410408
\(582\) 242.514 + 242.514i 0.416691 + 0.416691i
\(583\) −72.0377 + 72.0377i −0.123564 + 0.123564i
\(584\) 321.700i 0.550856i
\(585\) 180.001 + 20.6161i 0.307694 + 0.0352412i
\(586\) −121.553 −0.207429
\(587\) −154.614 154.614i −0.263397 0.263397i 0.563036 0.826433i \(-0.309633\pi\)
−0.826433 + 0.563036i \(0.809633\pi\)
\(588\) −106.573 + 106.573i −0.181247 + 0.181247i
\(589\) 238.723i 0.405303i
\(590\) 73.8908 645.148i 0.125239 1.09347i
\(591\) −819.978 −1.38744
\(592\) 162.149 + 162.149i 0.273900 + 0.273900i
\(593\) −488.246 + 488.246i −0.823349 + 0.823349i −0.986587 0.163238i \(-0.947806\pi\)
0.163238 + 0.986587i \(0.447806\pi\)
\(594\) 8.38213i 0.0141113i
\(595\) −385.790 485.592i −0.648387 0.816122i
\(596\) 456.585 0.766081
\(597\) 660.862 + 660.862i 1.10697 + 1.10697i
\(598\) −19.6655 + 19.6655i −0.0328854 + 0.0328854i
\(599\) 313.455i 0.523297i 0.965163 + 0.261649i \(0.0842661\pi\)
−0.965163 + 0.261649i \(0.915734\pi\)
\(600\) −290.903 67.5219i −0.484839 0.112536i
\(601\) 785.232 1.30654 0.653271 0.757124i \(-0.273396\pi\)
0.653271 + 0.757124i \(0.273396\pi\)
\(602\) 234.683 + 234.683i 0.389839 + 0.389839i
\(603\) 188.115 188.115i 0.311965 0.311965i
\(604\) 174.554i 0.288997i
\(605\) 184.197 146.340i 0.304458 0.241884i
\(606\) 350.360 0.578152
\(607\) −586.527 586.527i −0.966271 0.966271i 0.0331784 0.999449i \(-0.489437\pi\)
−0.999449 + 0.0331784i \(0.989437\pi\)
\(608\) 48.0072 48.0072i 0.0789592 0.0789592i
\(609\) 969.353i 1.59171i
\(610\) 42.3568 + 4.85126i 0.0694374 + 0.00795288i
\(611\) 33.6275 0.0550368
\(612\) −277.708 277.708i −0.453771 0.453771i
\(613\) 67.0740 67.0740i 0.109419 0.109419i −0.650277 0.759697i \(-0.725347\pi\)
0.759697 + 0.650277i \(0.225347\pi\)
\(614\) 531.080i 0.864951i
\(615\) −117.355 + 1024.64i −0.190822 + 1.66608i
\(616\) 135.765 0.220398
\(617\) −264.729 264.729i −0.429058 0.429058i 0.459250 0.888307i \(-0.348118\pi\)
−0.888307 + 0.459250i \(0.848118\pi\)
\(618\) 190.633 190.633i 0.308468 0.308468i
\(619\) 116.113i 0.187581i 0.995592 + 0.0937907i \(0.0298985\pi\)
−0.995592 + 0.0937907i \(0.970102\pi\)
\(620\) 123.730 + 155.739i 0.199565 + 0.251191i
\(621\) 3.30549 0.00532285
\(622\) −421.810 421.810i −0.678150 0.678150i
\(623\) −192.557 + 192.557i −0.309080 + 0.309080i
\(624\) 69.2721i 0.111013i
\(625\) −561.098 275.306i −0.897757 0.440490i
\(626\) 258.543 0.413008
\(627\) −308.218 308.218i −0.491575 0.491575i
\(628\) 358.196 358.196i 0.570376 0.570376i
\(629\) 1273.93i 2.02533i
\(630\) 273.089 216.962i 0.433475 0.344384i
\(631\) 1195.53 1.89466 0.947331 0.320255i \(-0.103769\pi\)
0.947331 + 0.320255i \(0.103769\pi\)
\(632\) −133.521 133.521i −0.211268 0.211268i
\(633\) −617.993 + 617.993i −0.976293 + 0.976293i
\(634\) 536.447i 0.846131i
\(635\) −352.753 40.4018i −0.555516 0.0636249i
\(636\) 100.068 0.157340
\(637\) −51.7367 51.7367i −0.0812193 0.0812193i
\(638\) −353.602 + 353.602i −0.554235 + 0.554235i
\(639\) 787.689i 1.23269i
\(640\) −6.43689 + 56.2011i −0.0100576 + 0.0878143i
\(641\) −799.813 −1.24776 −0.623879 0.781521i \(-0.714444\pi\)
−0.623879 + 0.781521i \(0.714444\pi\)
\(642\) −413.001 413.001i −0.643303 0.643303i
\(643\) −873.735 + 873.735i −1.35884 + 1.35884i −0.483495 + 0.875347i \(0.660633\pi\)
−0.875347 + 0.483495i \(0.839367\pi\)
\(644\) 53.5390i 0.0831351i
\(645\) 552.283 + 695.155i 0.856252 + 1.07776i
\(646\) 377.172 0.583857
\(647\) −332.571 332.571i −0.514019 0.514019i 0.401736 0.915756i \(-0.368407\pi\)
−0.915756 + 0.401736i \(0.868407\pi\)
\(648\) −164.884 + 164.884i −0.254451 + 0.254451i
\(649\) 789.718i 1.21682i
\(650\) 32.7790 141.221i 0.0504293 0.217264i
\(651\) −468.903 −0.720281
\(652\) −4.16291 4.16291i −0.00638483 0.00638483i
\(653\) −372.410 + 372.410i −0.570307 + 0.570307i −0.932214 0.361907i \(-0.882126\pi\)
0.361907 + 0.932214i \(0.382126\pi\)
\(654\) 1250.89i 1.91268i
\(655\) 300.165 238.473i 0.458267 0.364081i
\(656\) 195.359 0.297804
\(657\) 710.700 + 710.700i 1.08174 + 1.08174i
\(658\) 45.7752 45.7752i 0.0695672 0.0695672i
\(659\) 348.049i 0.528147i 0.964503 + 0.264074i \(0.0850662\pi\)
−0.964503 + 0.264074i \(0.914934\pi\)
\(660\) 360.825 + 41.3263i 0.546704 + 0.0626157i
\(661\) 577.080 0.873040 0.436520 0.899694i \(-0.356211\pi\)
0.436520 + 0.899694i \(0.356211\pi\)
\(662\) −234.830 234.830i −0.354727 0.354727i
\(663\) 272.121 272.121i 0.410438 0.410438i
\(664\) 120.826i 0.181967i
\(665\) −38.1148 + 332.784i −0.0573154 + 0.500427i
\(666\) −716.438 −1.07573
\(667\) −139.443 139.443i −0.209060 0.209060i
\(668\) 39.3716 39.3716i 0.0589395 0.0589395i
\(669\) 874.940i 1.30783i
\(670\) −132.421 166.677i −0.197643 0.248772i
\(671\) −51.8485 −0.0772704
\(672\) −94.2963 94.2963i −0.140322 0.140322i
\(673\) 766.103 766.103i 1.13834 1.13834i 0.149593 0.988748i \(-0.452204\pi\)
0.988748 0.149593i \(-0.0477964\pi\)
\(674\) 367.827i 0.545737i
\(675\) −14.6235 + 9.11382i −0.0216645 + 0.0135020i
\(676\) −304.371 −0.450253
\(677\) −85.8895 85.8895i −0.126868 0.126868i 0.640822 0.767690i \(-0.278594\pi\)
−0.767690 + 0.640822i \(0.778594\pi\)
\(678\) 295.912 295.912i 0.436449 0.436449i
\(679\) 320.519i 0.472046i
\(680\) −246.060 + 195.488i −0.361853 + 0.287482i
\(681\) −695.805 −1.02174
\(682\) −171.047 171.047i −0.250802 0.250802i
\(683\) −789.547 + 789.547i −1.15600 + 1.15600i −0.170671 + 0.985328i \(0.554594\pi\)
−0.985328 + 0.170671i \(0.945406\pi\)
\(684\) 212.115i 0.310110i
\(685\) −1323.98 151.640i −1.93282 0.221372i
\(686\) −527.653 −0.769174
\(687\) −1190.06 1190.06i −1.73226 1.73226i
\(688\) 118.919 118.919i 0.172847 0.172847i
\(689\) 48.5789i 0.0705064i
\(690\) −16.2970 + 142.291i −0.0236189 + 0.206219i
\(691\) −61.5184 −0.0890281 −0.0445140 0.999009i \(-0.514174\pi\)
−0.0445140 + 0.999009i \(0.514174\pi\)
\(692\) 28.3520 + 28.3520i 0.0409711 + 0.0409711i
\(693\) −299.933 + 299.933i −0.432803 + 0.432803i
\(694\) 100.774i 0.145208i
\(695\) −568.181 715.167i −0.817527 1.02902i
\(696\) 491.191 0.705735
\(697\) 767.426 + 767.426i 1.10104 + 1.10104i
\(698\) 344.711 344.711i 0.493855 0.493855i
\(699\) 799.460i 1.14372i
\(700\) −147.617 236.857i −0.210881 0.338367i
\(701\) 304.128 0.433849 0.216925 0.976188i \(-0.430397\pi\)
0.216925 + 0.976188i \(0.430397\pi\)
\(702\) −2.82626 2.82626i −0.00402601 0.00402601i
\(703\) 486.519 486.519i 0.692061 0.692061i
\(704\) 68.7951i 0.0977203i
\(705\) 135.591 107.723i 0.192328 0.152799i
\(706\) 925.359 1.31071
\(707\) 231.527 + 231.527i 0.327479 + 0.327479i
\(708\) 548.502 548.502i 0.774720 0.774720i
\(709\) 548.324i 0.773376i 0.922210 + 0.386688i \(0.126381\pi\)
−0.922210 + 0.386688i \(0.873619\pi\)
\(710\) −626.202 71.7208i −0.881975 0.101015i
\(711\) 589.951 0.829749
\(712\) 97.5727 + 97.5727i 0.137040 + 0.137040i
\(713\) 67.4524 67.4524i 0.0946037 0.0946037i
\(714\) 740.845i 1.03760i
\(715\) −20.0622 + 175.165i −0.0280590 + 0.244986i
\(716\) 585.228 0.817358
\(717\) −616.399 616.399i −0.859691 0.859691i
\(718\) −408.460 + 408.460i −0.568886 + 0.568886i
\(719\) 235.548i 0.327605i −0.986493 0.163802i \(-0.947624\pi\)
0.986493 0.163802i \(-0.0523759\pi\)
\(720\) −109.939 138.380i −0.152693 0.192194i
\(721\) 251.951 0.349447
\(722\) 216.957 + 216.957i 0.300494 + 0.300494i
\(723\) 277.276 277.276i 0.383508 0.383508i
\(724\) 156.088i 0.215591i
\(725\) 1001.37 + 232.428i 1.38119 + 0.320590i
\(726\) 281.020 0.387081
\(727\) −125.017 125.017i −0.171963 0.171963i 0.615878 0.787841i \(-0.288801\pi\)
−0.787841 + 0.615878i \(0.788801\pi\)
\(728\) 45.7769 45.7769i 0.0628803 0.0628803i
\(729\) 702.327i 0.963411i
\(730\) 629.708 500.286i 0.862614 0.685324i
\(731\) 934.293 1.27810
\(732\) 36.0115 + 36.0115i 0.0491961 + 0.0491961i
\(733\) 644.938 644.938i 0.879861 0.879861i −0.113659 0.993520i \(-0.536257\pi\)
0.993520 + 0.113659i \(0.0362570\pi\)
\(734\) 921.815i 1.25588i
\(735\) −374.345 42.8749i −0.509313 0.0583332i
\(736\) 27.1293 0.0368605
\(737\) 183.061 + 183.061i 0.248387 + 0.248387i
\(738\) −431.588 + 431.588i −0.584807 + 0.584807i
\(739\) 1162.01i 1.57241i −0.617966 0.786205i \(-0.712043\pi\)
0.617966 0.786205i \(-0.287957\pi\)
\(740\) −65.2332 + 569.558i −0.0881530 + 0.769673i
\(741\) −207.848 −0.280496
\(742\) 66.1277 + 66.1277i 0.0891209 + 0.0891209i
\(743\) 736.103 736.103i 0.990718 0.990718i −0.00923932 0.999957i \(-0.502941\pi\)
0.999957 + 0.00923932i \(0.00294101\pi\)
\(744\) 237.603i 0.319359i
\(745\) 710.049 + 893.736i 0.953086 + 1.19965i
\(746\) 534.053 0.715889
\(747\) −266.929 266.929i −0.357335 0.357335i
\(748\) 270.247 270.247i 0.361292 0.361292i
\(749\) 545.844i 0.728763i
\(750\) −320.224 674.431i −0.426965 0.899241i
\(751\) 793.620 1.05675 0.528375 0.849011i \(-0.322801\pi\)
0.528375 + 0.849011i \(0.322801\pi\)
\(752\) −23.1953 23.1953i −0.0308448 0.0308448i
\(753\) −1275.66 + 1275.66i −1.69410 + 1.69410i
\(754\) 238.453i 0.316250i
\(755\) 341.679 271.455i 0.452555 0.359543i
\(756\) −7.69445 −0.0101778
\(757\) −472.738 472.738i −0.624489 0.624489i 0.322187 0.946676i \(-0.395582\pi\)
−0.946676 + 0.322187i \(0.895582\pi\)
\(758\) −257.246 + 257.246i −0.339374 + 0.339374i
\(759\) 174.177i 0.229482i
\(760\) 168.629 + 19.3136i 0.221880 + 0.0254126i
\(761\) 17.0753 0.0224379 0.0112190 0.999937i \(-0.496429\pi\)
0.0112190 + 0.999937i \(0.496429\pi\)
\(762\) −299.909 299.909i −0.393581 0.393581i
\(763\) −826.622 + 826.622i −1.08338 + 1.08338i
\(764\) 139.341i 0.182384i
\(765\) 111.723 975.468i 0.146044 1.27512i
\(766\) 204.626 0.267136
\(767\) 266.275 + 266.275i 0.347164 + 0.347164i
\(768\) −47.7819 + 47.7819i −0.0622160 + 0.0622160i
\(769\) 1084.43i 1.41019i −0.709114 0.705094i \(-0.750905\pi\)
0.709114 0.705094i \(-0.249095\pi\)
\(770\) 211.133 + 265.752i 0.274199 + 0.345133i
\(771\) −1249.51 −1.62064
\(772\) −470.749 470.749i −0.609778 0.609778i
\(773\) 352.889 352.889i 0.456519 0.456519i −0.440992 0.897511i \(-0.645373\pi\)
0.897511 + 0.440992i \(0.145373\pi\)
\(774\) 525.431i 0.678851i
\(775\) −112.432 + 484.389i −0.145073 + 0.625017i
\(776\) 162.414 0.209296
\(777\) −955.626 955.626i −1.22989 1.22989i
\(778\) −13.5885 + 13.5885i −0.0174660 + 0.0174660i
\(779\) 586.165i 0.752459i
\(780\) 135.596 107.727i 0.173841 0.138112i
\(781\) 766.526 0.981467
\(782\) 106.572 + 106.572i 0.136281 + 0.136281i
\(783\) 20.0403 20.0403i 0.0255942 0.0255942i
\(784\) 71.3730i 0.0910369i
\(785\) 1258.19 + 144.104i 1.60279 + 0.183572i
\(786\) 457.947 0.582630
\(787\) 958.735 + 958.735i 1.21822 + 1.21822i 0.968256 + 0.249959i \(0.0804171\pi\)
0.249959 + 0.968256i \(0.419583\pi\)
\(788\) −274.573 + 274.573i −0.348443 + 0.348443i
\(789\) 519.085i 0.657903i
\(790\) 53.7164 469.003i 0.0679954 0.593675i
\(791\) 391.094 0.494430
\(792\) 151.982 + 151.982i 0.191897 + 0.191897i
\(793\) −17.4821 + 17.4821i −0.0220455 + 0.0220455i
\(794\) 889.735i 1.12057i
\(795\) 155.619 + 195.877i 0.195748 + 0.246386i
\(796\) 442.586 0.556012
\(797\) 575.899 + 575.899i 0.722583 + 0.722583i 0.969131 0.246547i \(-0.0792961\pi\)
−0.246547 + 0.969131i \(0.579296\pi\)
\(798\) −282.931 + 282.931i −0.354550 + 0.354550i
\(799\) 182.235i 0.228079i
\(800\) −120.020 + 74.8004i −0.150026 + 0.0935005i
\(801\) −431.115 −0.538221
\(802\) −496.549 496.549i −0.619139 0.619139i
\(803\) −691.606 + 691.606i −0.861278 + 0.861278i
\(804\) 254.291i 0.316283i
\(805\) −104.799 + 83.2602i −0.130185 + 0.103429i
\(806\) −115.346 −0.143110
\(807\) −968.155 968.155i −1.19970 1.19970i
\(808\) 117.320 117.320i 0.145198 0.145198i
\(809\) 694.940i 0.859011i 0.903064 + 0.429505i \(0.141312\pi\)
−0.903064 + 0.429505i \(0.858688\pi\)
\(810\) −579.168 66.3338i −0.715022 0.0818936i
\(811\) 700.473 0.863715 0.431857 0.901942i \(-0.357858\pi\)
0.431857 + 0.901942i \(0.357858\pi\)
\(812\) 324.592 + 324.592i 0.399744 + 0.399744i
\(813\) 1118.45 1118.45i 1.37571 1.37571i
\(814\) 697.189i 0.856498i
\(815\) 1.67476 14.6225i 0.00205492 0.0179417i
\(816\) −375.402 −0.460051
\(817\) −356.810 356.810i −0.436732 0.436732i
\(818\) −504.901 + 504.901i −0.617238 + 0.617238i
\(819\) 202.261i 0.246961i
\(820\) 303.809 + 382.403i 0.370499 + 0.466346i
\(821\) −803.333 −0.978481 −0.489240 0.872149i \(-0.662726\pi\)
−0.489240 + 0.872149i \(0.662726\pi\)
\(822\) −1125.64 1125.64i −1.36940 1.36940i
\(823\) −112.109 + 112.109i −0.136220 + 0.136220i −0.771929 0.635709i \(-0.780708\pi\)
0.635709 + 0.771929i \(0.280708\pi\)
\(824\) 127.669i 0.154938i
\(825\) 480.236 + 770.560i 0.582105 + 0.934012i
\(826\) 724.929 0.877638
\(827\) 132.725 + 132.725i 0.160490 + 0.160490i 0.782784 0.622294i \(-0.213799\pi\)
−0.622294 + 0.782784i \(0.713799\pi\)
\(828\) −59.9341 + 59.9341i −0.0723842 + 0.0723842i
\(829\) 901.283i 1.08719i 0.839347 + 0.543597i \(0.182938\pi\)
−0.839347 + 0.543597i \(0.817062\pi\)
\(830\) −236.510 + 187.901i −0.284951 + 0.226386i
\(831\) −305.390 −0.367497
\(832\) −23.1961 23.1961i −0.0278799 0.0278799i
\(833\) −280.373 + 280.373i −0.336582 + 0.336582i
\(834\) 1091.10i 1.30827i
\(835\) 138.296 + 15.8394i 0.165623 + 0.0189694i
\(836\) −206.416 −0.246909
\(837\) 9.69405 + 9.69405i 0.0115819 + 0.0115819i
\(838\) −496.330 + 496.330i −0.592280 + 0.592280i
\(839\) 590.121i 0.703363i −0.936120 0.351681i \(-0.885610\pi\)
0.936120 0.351681i \(-0.114390\pi\)
\(840\) 37.9359 331.222i 0.0451618 0.394312i
\(841\) −849.809 −1.01047
\(842\) −217.991 217.991i −0.258897 0.258897i
\(843\) −1191.23 + 1191.23i −1.41309 + 1.41309i
\(844\) 413.876i 0.490374i
\(845\) −473.338 595.788i −0.560163 0.705074i
\(846\) 102.486 0.121142
\(847\) 185.706 + 185.706i 0.219251 + 0.219251i
\(848\) 33.5083 33.5083i 0.0395145 0.0395145i
\(849\) 138.387i 0.163000i
\(850\) −765.311 177.637i −0.900366 0.208985i
\(851\) 274.936 0.323074
\(852\) −532.394 532.394i −0.624875 0.624875i
\(853\) 250.343 250.343i 0.293485 0.293485i −0.544970 0.838455i \(-0.683459\pi\)
0.838455 + 0.544970i \(0.183459\pi\)
\(854\) 47.5948i 0.0557316i
\(855\) −415.202 + 329.867i −0.485616 + 0.385809i
\(856\) −276.590 −0.323120
\(857\) 728.387 + 728.387i 0.849926 + 0.849926i 0.990124 0.140197i \(-0.0447737\pi\)
−0.140197 + 0.990124i \(0.544774\pi\)
\(858\) −148.925 + 148.925i −0.173572 + 0.173572i
\(859\) 285.323i 0.332157i −0.986113 0.166078i \(-0.946889\pi\)
0.986113 0.166078i \(-0.0531105\pi\)
\(860\) 417.711 + 47.8417i 0.485710 + 0.0556298i
\(861\) −1151.35 −1.33723
\(862\) −194.670 194.670i −0.225835 0.225835i
\(863\) −804.770 + 804.770i −0.932526 + 0.932526i −0.997863 0.0653374i \(-0.979188\pi\)
0.0653374 + 0.997863i \(0.479188\pi\)
\(864\) 3.89894i 0.00451266i
\(865\) −11.4062 + 99.5884i −0.0131863 + 0.115131i
\(866\) −166.088 −0.191787
\(867\) −611.623 611.623i −0.705448 0.705448i
\(868\) −157.014 + 157.014i −0.180892 + 0.180892i
\(869\) 574.101i 0.660646i
\(870\) 763.868 + 961.477i 0.878009 + 1.10515i
\(871\) 123.448 0.141731
\(872\) 418.867 + 418.867i 0.480352 + 0.480352i
\(873\) −358.805 + 358.805i −0.411002 + 0.411002i
\(874\) 81.4002i 0.0931352i
\(875\) 234.070 657.294i 0.267508 0.751193i
\(876\) 960.715 1.09671
\(877\) 469.300 + 469.300i 0.535120 + 0.535120i 0.922091 0.386972i \(-0.126479\pi\)
−0.386972 + 0.922091i \(0.626479\pi\)
\(878\) 651.478 651.478i 0.742002 0.742002i
\(879\) 363.003i 0.412973i
\(880\) 134.662 106.986i 0.153025 0.121574i
\(881\) −1625.01 −1.84451 −0.922254 0.386584i \(-0.873655\pi\)
−0.922254 + 0.386584i \(0.873655\pi\)
\(882\) −157.677 157.677i −0.178772 0.178772i
\(883\) −931.471 + 931.471i −1.05489 + 1.05489i −0.0564909 + 0.998403i \(0.517991\pi\)
−0.998403 + 0.0564909i \(0.982009\pi\)
\(884\) 182.242i 0.206156i
\(885\) 1926.65 + 220.665i 2.17701 + 0.249339i
\(886\) 65.9772 0.0744663
\(887\) 1221.10 + 1221.10i 1.37666 + 1.37666i 0.850193 + 0.526471i \(0.176485\pi\)
0.526471 + 0.850193i \(0.323515\pi\)
\(888\) −484.236 + 484.236i −0.545310 + 0.545310i
\(889\) 396.375i 0.445866i
\(890\) −39.2540 + 342.731i −0.0441056 + 0.385091i
\(891\) 708.952 0.795681
\(892\) −292.978 292.978i −0.328451 0.328451i
\(893\) −69.5962 + 69.5962i −0.0779353 + 0.0779353i
\(894\) 1363.53i 1.52520i
\(895\) 910.107 + 1145.55i 1.01688 + 1.27994i
\(896\) −63.1511 −0.0704812
\(897\) −58.7283 58.7283i −0.0654719 0.0654719i
\(898\) 528.035 528.035i 0.588013 0.588013i
\(899\) 817.892i 0.909779i
\(900\) 99.9001 430.398i 0.111000 0.478220i
\(901\) 263.260 0.292187
\(902\) −419.992 419.992i −0.465623 0.465623i
\(903\) −700.850 + 700.850i −0.776135 + 0.776135i
\(904\) 198.175i 0.219221i
\(905\) −305.533 + 242.738i −0.337605 + 0.268219i
\(906\) 521.283 0.575368
\(907\) 8.51812 + 8.51812i 0.00939153 + 0.00939153i 0.711787 0.702395i \(-0.247886\pi\)
−0.702395 + 0.711787i \(0.747886\pi\)
\(908\) −232.994 + 232.994i −0.256601 + 0.256601i
\(909\) 518.366i 0.570260i
\(910\) 160.795 + 18.4163i 0.176697 + 0.0202377i
\(911\) −1480.85 −1.62552 −0.812760 0.582599i \(-0.802036\pi\)
−0.812760 + 0.582599i \(0.802036\pi\)
\(912\) 143.367 + 143.367i 0.157201 + 0.157201i
\(913\) 259.758 259.758i 0.284510 0.284510i
\(914\) 598.463i 0.654773i
\(915\) −14.4876 + 126.493i −0.0158335 + 0.138244i
\(916\) −796.996 −0.870083
\(917\) 302.624 + 302.624i 0.330015 + 0.330015i
\(918\) −15.3161 + 15.3161i −0.0166843 + 0.0166843i
\(919\) 886.832i 0.964996i −0.875897 0.482498i \(-0.839729\pi\)
0.875897 0.482498i \(-0.160271\pi\)
\(920\) 42.1897 + 53.1040i 0.0458584 + 0.0577217i
\(921\) −1586.00 −1.72204
\(922\) 482.726 + 482.726i 0.523564 + 0.523564i
\(923\) 258.455 258.455i 0.280016 0.280016i
\(924\) 405.445i 0.438794i
\(925\) −1216.32 + 758.049i −1.31494 + 0.819512i
\(926\) 685.359 0.740128
\(927\) 282.047 + 282.047i 0.304257 + 0.304257i
\(928\) 164.478 164.478i 0.177239 0.177239i
\(929\) 435.730i 0.469031i −0.972112 0.234516i \(-0.924650\pi\)
0.972112 0.234516i \(-0.0753504\pi\)
\(930\) −465.093 + 369.504i −0.500100 + 0.397316i
\(931\) 214.151 0.230023
\(932\) −267.703 267.703i −0.287235 0.287235i
\(933\) 1259.68 1259.68i 1.35014 1.35014i
\(934\) 1026.97i 1.09954i
\(935\) 949.260 + 108.722i 1.01525 + 0.116280i
\(936\) 102.490 0.109498
\(937\) 642.646 + 642.646i 0.685854 + 0.685854i 0.961313 0.275459i \(-0.0888297\pi\)
−0.275459 + 0.961313i \(0.588830\pi\)
\(938\) 168.043 168.043i 0.179150 0.179150i
\(939\) 772.105i 0.822263i
\(940\) 9.33158 81.4750i 0.00992722 0.0866756i
\(941\) −615.461 −0.654050 −0.327025 0.945016i \(-0.606046\pi\)
−0.327025 + 0.945016i \(0.606046\pi\)
\(942\) 1069.71 + 1069.71i 1.13557 + 1.13557i
\(943\) 165.624 165.624i 0.175635 0.175635i
\(944\) 367.337i 0.389128i
\(945\) −11.9659 15.0614i −0.0126623 0.0159380i
\(946\) −511.314 −0.540501
\(947\) 870.854 + 870.854i 0.919593 + 0.919593i 0.997000 0.0774070i \(-0.0246641\pi\)
−0.0774070 + 0.997000i \(0.524664\pi\)
\(948\) 398.744 398.744i 0.420616 0.420616i
\(949\) 466.387i 0.491451i
\(950\) 224.435 + 360.115i 0.236247 + 0.379069i
\(951\) 1602.03 1.68457
\(952\) −248.076 248.076i −0.260584 0.260584i
\(953\) −45.2805 + 45.2805i −0.0475137 + 0.0475137i −0.730464 0.682951i \(-0.760696\pi\)
0.682951 + 0.730464i \(0.260696\pi\)
\(954\) 148.053i 0.155192i
\(955\) 272.751 216.694i 0.285604 0.226904i
\(956\) −412.808 −0.431808
\(957\) −1055.99 1055.99i −1.10343 1.10343i
\(958\) 303.049 303.049i 0.316335 0.316335i
\(959\) 1487.71i 1.55132i
\(960\) −167.837 19.2229i −0.174831 0.0200239i
\(961\) −565.363 −0.588307
\(962\) −235.076 235.076i −0.244362 0.244362i
\(963\) 611.044 611.044i 0.634521 0.634521i
\(964\) 185.694i 0.192629i
\(965\) 189.385 1653.54i 0.196254 1.71351i
\(966\) −159.887 −0.165515
\(967\) −16.9436 16.9436i −0.0175218 0.0175218i 0.698292 0.715813i \(-0.253944\pi\)
−0.715813 + 0.698292i \(0.753944\pi\)
\(968\) 94.1010 94.1010i 0.0972118 0.0972118i
\(969\) 1126.37i 1.16241i
\(970\) 252.575 + 317.915i 0.260387 + 0.327748i
\(971\) −477.035 −0.491282 −0.245641 0.969361i \(-0.578999\pi\)
−0.245641 + 0.969361i \(0.578999\pi\)
\(972\) −483.633 483.633i −0.497565 0.497565i
\(973\) 721.026 721.026i 0.741033 0.741033i
\(974\) 539.974i 0.554388i
\(975\) 421.739 + 97.8903i 0.432553 + 0.100400i
\(976\) 24.1173 0.0247103
\(977\) −1000.38 1000.38i −1.02393 1.02393i −0.999706 0.0242270i \(-0.992288\pi\)
−0.0242270 0.999706i \(-0.507712\pi\)
\(978\) 12.4320 12.4320i 0.0127116 0.0127116i
\(979\) 419.533i 0.428532i
\(980\) −139.708 + 110.994i −0.142559 + 0.113260i
\(981\) −1850.72 −1.88657
\(982\) −788.957 788.957i −0.803418 0.803418i
\(983\) −58.1099 + 58.1099i −0.0591149 + 0.0591149i −0.736046 0.676931i \(-0.763309\pi\)
0.676931 + 0.736046i \(0.263309\pi\)
\(984\) 583.414i 0.592901i
\(985\) −964.458 110.462i −0.979146 0.112145i
\(986\) 1292.23 1.31058
\(987\) 136.702 + 136.702i 0.138502 + 0.138502i
\(988\) −69.5988 + 69.5988i −0.0704441 + 0.0704441i
\(989\) 201.637i 0.203879i
\(990\) −61.1433 + 533.848i −0.0617609 + 0.539241i
\(991\) −637.010 −0.642795 −0.321398 0.946944i \(-0.604153\pi\)
−0.321398 + 0.946944i \(0.604153\pi\)
\(992\) 79.5625 + 79.5625i 0.0802041 + 0.0802041i
\(993\) 701.288 701.288i 0.706231 0.706231i
\(994\) 703.640i 0.707887i
\(995\) 688.280 + 866.334i 0.691738 + 0.870688i
\(996\) −360.832 −0.362281
\(997\) 192.918 + 192.918i 0.193498 + 0.193498i 0.797206 0.603708i \(-0.206311\pi\)
−0.603708 + 0.797206i \(0.706311\pi\)
\(998\) 811.329 811.329i 0.812955 0.812955i
\(999\) 39.5130i 0.0395525i
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 230.3.f.b.47.3 24
5.3 odd 4 inner 230.3.f.b.93.3 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.3.f.b.47.3 24 1.1 even 1 trivial
230.3.f.b.93.3 yes 24 5.3 odd 4 inner