Properties

Label 230.3.f.a.93.6
Level $230$
Weight $3$
Character 230.93
Analytic conductor $6.267$
Analytic rank $0$
Dimension $20$
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: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} - 439644 x^{11} + 460536 x^{10} - 1833716 x^{9} + 16970128 x^{8} + \cdots + 88804 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 93.6
Root \(0.608645 + 0.608645i\) of defining polynomial
Character \(\chi\) \(=\) 230.93
Dual form 230.3.f.a.47.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(0.608645 + 0.608645i) q^{3} -2.00000i q^{4} +(4.88434 - 1.06922i) q^{5} -1.21729 q^{6} +(3.48181 - 3.48181i) q^{7} +(2.00000 + 2.00000i) q^{8} -8.25910i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(0.608645 + 0.608645i) q^{3} -2.00000i q^{4} +(4.88434 - 1.06922i) q^{5} -1.21729 q^{6} +(3.48181 - 3.48181i) q^{7} +(2.00000 + 2.00000i) q^{8} -8.25910i q^{9} +(-3.81512 + 5.95356i) q^{10} -3.82644 q^{11} +(1.21729 - 1.21729i) q^{12} +(-13.1059 - 13.1059i) q^{13} +6.96363i q^{14} +(3.62360 + 2.32205i) q^{15} -4.00000 q^{16} +(15.9881 - 15.9881i) q^{17} +(8.25910 + 8.25910i) q^{18} +6.16230i q^{19} +(-2.13844 - 9.76868i) q^{20} +4.23838 q^{21} +(3.82644 - 3.82644i) q^{22} +(3.39116 + 3.39116i) q^{23} +2.43458i q^{24} +(22.7135 - 10.4449i) q^{25} +26.2118 q^{26} +(10.5047 - 10.5047i) q^{27} +(-6.96363 - 6.96363i) q^{28} +32.8492i q^{29} +(-5.94566 + 1.30155i) q^{30} +27.0235 q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.32894 - 2.32894i) q^{33} +31.9763i q^{34} +(13.2835 - 20.7292i) q^{35} -16.5182 q^{36} +(-20.0504 + 20.0504i) q^{37} +(-6.16230 - 6.16230i) q^{38} -15.9537i q^{39} +(11.9071 + 7.63024i) q^{40} +17.5188 q^{41} +(-4.23838 + 4.23838i) q^{42} +(26.6029 + 26.6029i) q^{43} +7.65288i q^{44} +(-8.83080 - 40.3403i) q^{45} -6.78233 q^{46} +(33.3658 - 33.3658i) q^{47} +(-2.43458 - 2.43458i) q^{48} +24.7540i q^{49} +(-12.2687 + 33.1584i) q^{50} +19.4622 q^{51} +(-26.2118 + 26.2118i) q^{52} +(-42.6629 - 42.6629i) q^{53} +21.0093i q^{54} +(-18.6896 + 4.09131i) q^{55} +13.9273 q^{56} +(-3.75065 + 3.75065i) q^{57} +(-32.8492 - 32.8492i) q^{58} +28.9195i q^{59} +(4.64411 - 7.24721i) q^{60} -3.95181 q^{61} +(-27.0235 + 27.0235i) q^{62} +(-28.7567 - 28.7567i) q^{63} +8.00000i q^{64} +(-78.0268 - 50.0006i) q^{65} +4.65789 q^{66} +(-69.4085 + 69.4085i) q^{67} +(-31.9763 - 31.9763i) q^{68} +4.12803i q^{69} +(7.44565 + 34.0127i) q^{70} +65.0625 q^{71} +(16.5182 - 16.5182i) q^{72} +(-52.2889 - 52.2889i) q^{73} -40.1008i q^{74} +(20.1817 + 7.46726i) q^{75} +12.3246 q^{76} +(-13.3230 + 13.3230i) q^{77} +(15.9537 + 15.9537i) q^{78} +62.2321i q^{79} +(-19.5374 + 4.27688i) q^{80} -61.5447 q^{81} +(-17.5188 + 17.5188i) q^{82} +(-95.2795 - 95.2795i) q^{83} -8.47675i q^{84} +(60.9967 - 95.1864i) q^{85} -53.2058 q^{86} +(-19.9935 + 19.9935i) q^{87} +(-7.65288 - 7.65288i) q^{88} +131.536i q^{89} +(49.1711 + 31.5095i) q^{90} -91.2647 q^{91} +(6.78233 - 6.78233i) q^{92} +(16.4477 + 16.4477i) q^{93} +66.7316i q^{94} +(6.58885 + 30.0988i) q^{95} +4.86916 q^{96} +(20.1747 - 20.1747i) q^{97} +(-24.7540 - 24.7540i) q^{98} +31.6030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) 0.608645 + 0.608645i 0.202882 + 0.202882i 0.801233 0.598352i \(-0.204177\pi\)
−0.598352 + 0.801233i \(0.704177\pi\)
\(4\) 2.00000i 0.500000i
\(5\) 4.88434 1.06922i 0.976868 0.213844i
\(6\) −1.21729 −0.202882
\(7\) 3.48181 3.48181i 0.497402 0.497402i −0.413226 0.910628i \(-0.635598\pi\)
0.910628 + 0.413226i \(0.135598\pi\)
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 8.25910i 0.917678i
\(10\) −3.81512 + 5.95356i −0.381512 + 0.595356i
\(11\) −3.82644 −0.347858 −0.173929 0.984758i \(-0.555646\pi\)
−0.173929 + 0.984758i \(0.555646\pi\)
\(12\) 1.21729 1.21729i 0.101441 0.101441i
\(13\) −13.1059 13.1059i −1.00815 1.00815i −0.999967 0.00818068i \(-0.997396\pi\)
−0.00818068 0.999967i \(-0.502604\pi\)
\(14\) 6.96363i 0.497402i
\(15\) 3.62360 + 2.32205i 0.241574 + 0.154804i
\(16\) −4.00000 −0.250000
\(17\) 15.9881 15.9881i 0.940479 0.940479i −0.0578462 0.998326i \(-0.518423\pi\)
0.998326 + 0.0578462i \(0.0184233\pi\)
\(18\) 8.25910 + 8.25910i 0.458839 + 0.458839i
\(19\) 6.16230i 0.324332i 0.986764 + 0.162166i \(0.0518479\pi\)
−0.986764 + 0.162166i \(0.948152\pi\)
\(20\) −2.13844 9.76868i −0.106922 0.488434i
\(21\) 4.23838 0.201827
\(22\) 3.82644 3.82644i 0.173929 0.173929i
\(23\) 3.39116 + 3.39116i 0.147442 + 0.147442i
\(24\) 2.43458i 0.101441i
\(25\) 22.7135 10.4449i 0.908541 0.417795i
\(26\) 26.2118 1.00815
\(27\) 10.5047 10.5047i 0.389062 0.389062i
\(28\) −6.96363 6.96363i −0.248701 0.248701i
\(29\) 32.8492i 1.13273i 0.824154 + 0.566366i \(0.191651\pi\)
−0.824154 + 0.566366i \(0.808349\pi\)
\(30\) −5.94566 + 1.30155i −0.198189 + 0.0433850i
\(31\) 27.0235 0.871725 0.435863 0.900013i \(-0.356443\pi\)
0.435863 + 0.900013i \(0.356443\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) −2.32894 2.32894i −0.0705741 0.0705741i
\(34\) 31.9763i 0.940479i
\(35\) 13.2835 20.7292i 0.379530 0.592262i
\(36\) −16.5182 −0.458839
\(37\) −20.0504 + 20.0504i −0.541903 + 0.541903i −0.924086 0.382184i \(-0.875172\pi\)
0.382184 + 0.924086i \(0.375172\pi\)
\(38\) −6.16230 6.16230i −0.162166 0.162166i
\(39\) 15.9537i 0.409069i
\(40\) 11.9071 + 7.63024i 0.297678 + 0.190756i
\(41\) 17.5188 0.427287 0.213643 0.976912i \(-0.431467\pi\)
0.213643 + 0.976912i \(0.431467\pi\)
\(42\) −4.23838 + 4.23838i −0.100914 + 0.100914i
\(43\) 26.6029 + 26.6029i 0.618672 + 0.618672i 0.945191 0.326519i \(-0.105876\pi\)
−0.326519 + 0.945191i \(0.605876\pi\)
\(44\) 7.65288i 0.173929i
\(45\) −8.83080 40.3403i −0.196240 0.896450i
\(46\) −6.78233 −0.147442
\(47\) 33.3658 33.3658i 0.709911 0.709911i −0.256605 0.966516i \(-0.582604\pi\)
0.966516 + 0.256605i \(0.0826040\pi\)
\(48\) −2.43458 2.43458i −0.0507204 0.0507204i
\(49\) 24.7540i 0.505183i
\(50\) −12.2687 + 33.1584i −0.245373 + 0.663168i
\(51\) 19.4622 0.381612
\(52\) −26.2118 + 26.2118i −0.504074 + 0.504074i
\(53\) −42.6629 42.6629i −0.804960 0.804960i 0.178906 0.983866i \(-0.442744\pi\)
−0.983866 + 0.178906i \(0.942744\pi\)
\(54\) 21.0093i 0.389062i
\(55\) −18.6896 + 4.09131i −0.339812 + 0.0743874i
\(56\) 13.9273 0.248701
\(57\) −3.75065 + 3.75065i −0.0658009 + 0.0658009i
\(58\) −32.8492 32.8492i −0.566366 0.566366i
\(59\) 28.9195i 0.490161i 0.969503 + 0.245080i \(0.0788143\pi\)
−0.969503 + 0.245080i \(0.921186\pi\)
\(60\) 4.64411 7.24721i 0.0774018 0.120787i
\(61\) −3.95181 −0.0647838 −0.0323919 0.999475i \(-0.510312\pi\)
−0.0323919 + 0.999475i \(0.510312\pi\)
\(62\) −27.0235 + 27.0235i −0.435863 + 0.435863i
\(63\) −28.7567 28.7567i −0.456455 0.456455i
\(64\) 8.00000i 0.125000i
\(65\) −78.0268 50.0006i −1.20041 0.769240i
\(66\) 4.65789 0.0705741
\(67\) −69.4085 + 69.4085i −1.03595 + 1.03595i −0.0366182 + 0.999329i \(0.511659\pi\)
−0.999329 + 0.0366182i \(0.988341\pi\)
\(68\) −31.9763 31.9763i −0.470240 0.470240i
\(69\) 4.12803i 0.0598265i
\(70\) 7.44565 + 34.0127i 0.106366 + 0.485896i
\(71\) 65.0625 0.916373 0.458186 0.888856i \(-0.348499\pi\)
0.458186 + 0.888856i \(0.348499\pi\)
\(72\) 16.5182 16.5182i 0.229420 0.229420i
\(73\) −52.2889 52.2889i −0.716286 0.716286i 0.251557 0.967843i \(-0.419057\pi\)
−0.967843 + 0.251557i \(0.919057\pi\)
\(74\) 40.1008i 0.541903i
\(75\) 20.1817 + 7.46726i 0.269089 + 0.0995635i
\(76\) 12.3246 0.162166
\(77\) −13.3230 + 13.3230i −0.173025 + 0.173025i
\(78\) 15.9537 + 15.9537i 0.204535 + 0.204535i
\(79\) 62.2321i 0.787749i 0.919164 + 0.393874i \(0.128865\pi\)
−0.919164 + 0.393874i \(0.871135\pi\)
\(80\) −19.5374 + 4.27688i −0.244217 + 0.0534610i
\(81\) −61.5447 −0.759811
\(82\) −17.5188 + 17.5188i −0.213643 + 0.213643i
\(83\) −95.2795 95.2795i −1.14795 1.14795i −0.986956 0.160989i \(-0.948532\pi\)
−0.160989 0.986956i \(-0.551468\pi\)
\(84\) 8.47675i 0.100914i
\(85\) 60.9967 95.1864i 0.717608 1.11984i
\(86\) −53.2058 −0.618672
\(87\) −19.9935 + 19.9935i −0.229810 + 0.229810i
\(88\) −7.65288 7.65288i −0.0869646 0.0869646i
\(89\) 131.536i 1.47793i 0.673744 + 0.738964i \(0.264685\pi\)
−0.673744 + 0.738964i \(0.735315\pi\)
\(90\) 49.1711 + 31.5095i 0.546345 + 0.350105i
\(91\) −91.2647 −1.00291
\(92\) 6.78233 6.78233i 0.0737210 0.0737210i
\(93\) 16.4477 + 16.4477i 0.176857 + 0.176857i
\(94\) 66.7316i 0.709911i
\(95\) 6.58885 + 30.0988i 0.0693564 + 0.316829i
\(96\) 4.86916 0.0507204
\(97\) 20.1747 20.1747i 0.207986 0.207986i −0.595425 0.803411i \(-0.703016\pi\)
0.803411 + 0.595425i \(0.203016\pi\)
\(98\) −24.7540 24.7540i −0.252591 0.252591i
\(99\) 31.6030i 0.319222i
\(100\) −20.8897 45.4271i −0.208897 0.454271i
\(101\) −21.2449 −0.210345 −0.105173 0.994454i \(-0.533540\pi\)
−0.105173 + 0.994454i \(0.533540\pi\)
\(102\) −19.4622 + 19.4622i −0.190806 + 0.190806i
\(103\) 111.237 + 111.237i 1.07997 + 1.07997i 0.996511 + 0.0834631i \(0.0265981\pi\)
0.0834631 + 0.996511i \(0.473402\pi\)
\(104\) 52.4237i 0.504074i
\(105\) 20.7017 4.53176i 0.197159 0.0431596i
\(106\) 85.3257 0.804960
\(107\) 44.1284 44.1284i 0.412415 0.412415i −0.470164 0.882579i \(-0.655805\pi\)
0.882579 + 0.470164i \(0.155805\pi\)
\(108\) −21.0093 21.0093i −0.194531 0.194531i
\(109\) 56.9538i 0.522512i 0.965270 + 0.261256i \(0.0841367\pi\)
−0.965270 + 0.261256i \(0.915863\pi\)
\(110\) 14.5983 22.7809i 0.132712 0.207100i
\(111\) −24.4071 −0.219884
\(112\) −13.9273 + 13.9273i −0.124350 + 0.124350i
\(113\) −15.3107 15.3107i −0.135493 0.135493i 0.636107 0.771601i \(-0.280544\pi\)
−0.771601 + 0.636107i \(0.780544\pi\)
\(114\) 7.50130i 0.0658009i
\(115\) 20.1895 + 12.9377i 0.175561 + 0.112502i
\(116\) 65.6984 0.566366
\(117\) −108.243 + 108.243i −0.925155 + 0.925155i
\(118\) −28.9195 28.9195i −0.245080 0.245080i
\(119\) 111.335i 0.935592i
\(120\) 2.60310 + 11.8913i 0.0216925 + 0.0990943i
\(121\) −106.358 −0.878995
\(122\) 3.95181 3.95181i 0.0323919 0.0323919i
\(123\) 10.6627 + 10.6627i 0.0866886 + 0.0866886i
\(124\) 54.0470i 0.435863i
\(125\) 99.7728 75.3020i 0.798182 0.602416i
\(126\) 57.5133 0.456455
\(127\) −121.636 + 121.636i −0.957760 + 0.957760i −0.999143 0.0413833i \(-0.986824\pi\)
0.0413833 + 0.999143i \(0.486824\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 32.3834i 0.251034i
\(130\) 128.027 28.0262i 0.984827 0.215586i
\(131\) 70.2174 0.536011 0.268005 0.963417i \(-0.413635\pi\)
0.268005 + 0.963417i \(0.413635\pi\)
\(132\) −4.65789 + 4.65789i −0.0352870 + 0.0352870i
\(133\) 21.4560 + 21.4560i 0.161323 + 0.161323i
\(134\) 138.817i 1.03595i
\(135\) 40.0765 62.5401i 0.296863 0.463260i
\(136\) 63.9526 0.470240
\(137\) 90.3324 90.3324i 0.659360 0.659360i −0.295868 0.955229i \(-0.595609\pi\)
0.955229 + 0.295868i \(0.0956090\pi\)
\(138\) −4.12803 4.12803i −0.0299133 0.0299133i
\(139\) 35.1379i 0.252791i 0.991980 + 0.126395i \(0.0403408\pi\)
−0.991980 + 0.126395i \(0.959659\pi\)
\(140\) −41.4584 26.5671i −0.296131 0.189765i
\(141\) 40.6159 0.288056
\(142\) −65.0625 + 65.0625i −0.458186 + 0.458186i
\(143\) 50.1490 + 50.1490i 0.350692 + 0.350692i
\(144\) 33.0364i 0.229420i
\(145\) 35.1230 + 160.447i 0.242228 + 1.10653i
\(146\) 104.578 0.716286
\(147\) −15.0664 + 15.0664i −0.102492 + 0.102492i
\(148\) 40.1008 + 40.1008i 0.270951 + 0.270951i
\(149\) 82.9264i 0.556553i −0.960501 0.278277i \(-0.910237\pi\)
0.960501 0.278277i \(-0.0897632\pi\)
\(150\) −27.6490 + 12.7144i −0.184326 + 0.0847629i
\(151\) 256.123 1.69618 0.848088 0.529856i \(-0.177754\pi\)
0.848088 + 0.529856i \(0.177754\pi\)
\(152\) −12.3246 + 12.3246i −0.0810829 + 0.0810829i
\(153\) −132.048 132.048i −0.863057 0.863057i
\(154\) 26.6459i 0.173025i
\(155\) 131.992 28.8941i 0.851561 0.186413i
\(156\) −31.9074 −0.204535
\(157\) 114.268 114.268i 0.727821 0.727821i −0.242364 0.970185i \(-0.577923\pi\)
0.970185 + 0.242364i \(0.0779228\pi\)
\(158\) −62.2321 62.2321i −0.393874 0.393874i
\(159\) 51.9331i 0.326623i
\(160\) 15.2605 23.8142i 0.0953780 0.148839i
\(161\) 23.6148 0.146676
\(162\) 61.5447 61.5447i 0.379906 0.379906i
\(163\) 200.462 + 200.462i 1.22983 + 1.22983i 0.964028 + 0.265802i \(0.0856368\pi\)
0.265802 + 0.964028i \(0.414363\pi\)
\(164\) 35.0375i 0.213643i
\(165\) −13.8655 8.88520i −0.0840334 0.0538497i
\(166\) 190.559 1.14795
\(167\) 1.21328 1.21328i 0.00726515 0.00726515i −0.703465 0.710730i \(-0.748365\pi\)
0.710730 + 0.703465i \(0.248365\pi\)
\(168\) 8.47675 + 8.47675i 0.0504569 + 0.0504569i
\(169\) 174.530i 1.03272i
\(170\) 34.1897 + 156.183i 0.201116 + 0.918724i
\(171\) 50.8951 0.297632
\(172\) 53.2058 53.2058i 0.309336 0.309336i
\(173\) −186.625 186.625i −1.07876 1.07876i −0.996621 0.0821339i \(-0.973826\pi\)
−0.0821339 0.996621i \(-0.526174\pi\)
\(174\) 39.9870i 0.229810i
\(175\) 42.7172 115.451i 0.244098 0.659722i
\(176\) 15.3058 0.0869646
\(177\) −17.6017 + 17.6017i −0.0994446 + 0.0994446i
\(178\) −131.536 131.536i −0.738964 0.738964i
\(179\) 156.890i 0.876479i −0.898858 0.438240i \(-0.855602\pi\)
0.898858 0.438240i \(-0.144398\pi\)
\(180\) −80.6805 + 17.6616i −0.448225 + 0.0981200i
\(181\) −110.482 −0.610396 −0.305198 0.952289i \(-0.598723\pi\)
−0.305198 + 0.952289i \(0.598723\pi\)
\(182\) 91.2647 91.2647i 0.501454 0.501454i
\(183\) −2.40525 2.40525i −0.0131434 0.0131434i
\(184\) 13.5647i 0.0737210i
\(185\) −76.4947 + 119.371i −0.413485 + 0.645250i
\(186\) −32.8954 −0.176857
\(187\) −61.1777 + 61.1777i −0.327154 + 0.327154i
\(188\) −66.7316 66.7316i −0.354955 0.354955i
\(189\) 73.1506i 0.387040i
\(190\) −36.6876 23.5099i −0.193093 0.123736i
\(191\) −101.977 −0.533913 −0.266956 0.963709i \(-0.586018\pi\)
−0.266956 + 0.963709i \(0.586018\pi\)
\(192\) −4.86916 + 4.86916i −0.0253602 + 0.0253602i
\(193\) 213.999 + 213.999i 1.10880 + 1.10880i 0.993308 + 0.115497i \(0.0368461\pi\)
0.115497 + 0.993308i \(0.463154\pi\)
\(194\) 40.3493i 0.207986i
\(195\) −17.0580 77.9233i −0.0874770 0.399606i
\(196\) 49.5079 0.252591
\(197\) −187.001 + 187.001i −0.949243 + 0.949243i −0.998773 0.0495299i \(-0.984228\pi\)
0.0495299 + 0.998773i \(0.484228\pi\)
\(198\) −31.6030 31.6030i −0.159611 0.159611i
\(199\) 365.937i 1.83888i 0.393229 + 0.919441i \(0.371358\pi\)
−0.393229 + 0.919441i \(0.628642\pi\)
\(200\) 66.3168 + 24.5373i 0.331584 + 0.122687i
\(201\) −84.4902 −0.420349
\(202\) 21.2449 21.2449i 0.105173 0.105173i
\(203\) 114.375 + 114.375i 0.563423 + 0.563423i
\(204\) 38.9244i 0.190806i
\(205\) 85.5675 18.7314i 0.417403 0.0913727i
\(206\) −222.475 −1.07997
\(207\) 28.0080 28.0080i 0.135304 0.135304i
\(208\) 52.4237 + 52.4237i 0.252037 + 0.252037i
\(209\) 23.5797i 0.112821i
\(210\) −16.1699 + 25.2334i −0.0769996 + 0.120159i
\(211\) −269.478 −1.27715 −0.638575 0.769560i \(-0.720476\pi\)
−0.638575 + 0.769560i \(0.720476\pi\)
\(212\) −85.3257 + 85.3257i −0.402480 + 0.402480i
\(213\) 39.5999 + 39.5999i 0.185915 + 0.185915i
\(214\) 88.2569i 0.412415i
\(215\) 158.382 + 101.493i 0.736660 + 0.472062i
\(216\) 42.0187 0.194531
\(217\) 94.0907 94.0907i 0.433598 0.433598i
\(218\) −56.9538 56.9538i −0.261256 0.261256i
\(219\) 63.6507i 0.290642i
\(220\) 8.18262 + 37.3793i 0.0371937 + 0.169906i
\(221\) −419.079 −1.89628
\(222\) 24.4071 24.4071i 0.109942 0.109942i
\(223\) −182.711 182.711i −0.819333 0.819333i 0.166678 0.986011i \(-0.446696\pi\)
−0.986011 + 0.166678i \(0.946696\pi\)
\(224\) 27.8545i 0.124350i
\(225\) −86.2652 187.593i −0.383401 0.833749i
\(226\) 30.6214 0.135493
\(227\) 71.0092 71.0092i 0.312816 0.312816i −0.533184 0.846000i \(-0.679005\pi\)
0.846000 + 0.533184i \(0.179005\pi\)
\(228\) 7.50130 + 7.50130i 0.0329005 + 0.0329005i
\(229\) 97.6089i 0.426240i −0.977026 0.213120i \(-0.931638\pi\)
0.977026 0.213120i \(-0.0683625\pi\)
\(230\) −33.1272 + 7.25180i −0.144031 + 0.0315296i
\(231\) −16.2179 −0.0702074
\(232\) −65.6984 + 65.6984i −0.283183 + 0.283183i
\(233\) −93.7032 93.7032i −0.402160 0.402160i 0.476834 0.878993i \(-0.341784\pi\)
−0.878993 + 0.476834i \(0.841784\pi\)
\(234\) 216.486i 0.925155i
\(235\) 127.295 198.645i 0.541679 0.845299i
\(236\) 57.8390 0.245080
\(237\) −37.8773 + 37.8773i −0.159820 + 0.159820i
\(238\) 111.335 + 111.335i 0.467796 + 0.467796i
\(239\) 229.877i 0.961826i 0.876768 + 0.480913i \(0.159695\pi\)
−0.876768 + 0.480913i \(0.840305\pi\)
\(240\) −14.4944 9.28821i −0.0603934 0.0387009i
\(241\) −410.897 −1.70497 −0.852484 0.522753i \(-0.824905\pi\)
−0.852484 + 0.522753i \(0.824905\pi\)
\(242\) 106.358 106.358i 0.439497 0.439497i
\(243\) −132.001 132.001i −0.543213 0.543213i
\(244\) 7.90362i 0.0323919i
\(245\) 26.4674 + 120.907i 0.108030 + 0.493497i
\(246\) −21.3254 −0.0866886
\(247\) 80.7626 80.7626i 0.326974 0.326974i
\(248\) 54.0470 + 54.0470i 0.217931 + 0.217931i
\(249\) 115.983i 0.465794i
\(250\) −24.4707 + 175.075i −0.0978828 + 0.700299i
\(251\) 220.598 0.878875 0.439437 0.898273i \(-0.355178\pi\)
0.439437 + 0.898273i \(0.355178\pi\)
\(252\) −57.5133 + 57.5133i −0.228227 + 0.228227i
\(253\) −12.9761 12.9761i −0.0512889 0.0512889i
\(254\) 243.271i 0.957760i
\(255\) 95.0600 20.8094i 0.372784 0.0816054i
\(256\) 16.0000 0.0625000
\(257\) 222.012 222.012i 0.863860 0.863860i −0.127924 0.991784i \(-0.540831\pi\)
0.991784 + 0.127924i \(0.0408313\pi\)
\(258\) −32.3834 32.3834i −0.125517 0.125517i
\(259\) 139.623i 0.539087i
\(260\) −100.001 + 156.054i −0.384620 + 0.600206i
\(261\) 271.305 1.03948
\(262\) −70.2174 + 70.2174i −0.268005 + 0.268005i
\(263\) 273.600 + 273.600i 1.04030 + 1.04030i 0.999153 + 0.0411516i \(0.0131027\pi\)
0.0411516 + 0.999153i \(0.486897\pi\)
\(264\) 9.31578i 0.0352870i
\(265\) −253.996 162.764i −0.958475 0.614203i
\(266\) −42.9120 −0.161323
\(267\) −80.0585 + 80.0585i −0.299845 + 0.299845i
\(268\) 138.817 + 138.817i 0.517974 + 0.517974i
\(269\) 306.939i 1.14104i 0.821285 + 0.570518i \(0.193258\pi\)
−0.821285 + 0.570518i \(0.806742\pi\)
\(270\) 22.4636 + 102.617i 0.0831985 + 0.380062i
\(271\) −423.942 −1.56436 −0.782181 0.623051i \(-0.785893\pi\)
−0.782181 + 0.623051i \(0.785893\pi\)
\(272\) −63.9526 + 63.9526i −0.235120 + 0.235120i
\(273\) −55.5478 55.5478i −0.203472 0.203472i
\(274\) 180.665i 0.659360i
\(275\) −86.9120 + 39.9667i −0.316044 + 0.145333i
\(276\) 8.25606 0.0299133
\(277\) −123.494 + 123.494i −0.445828 + 0.445828i −0.893965 0.448137i \(-0.852088\pi\)
0.448137 + 0.893965i \(0.352088\pi\)
\(278\) −35.1379 35.1379i −0.126395 0.126395i
\(279\) 223.190i 0.799963i
\(280\) 68.0254 14.8913i 0.242948 0.0531832i
\(281\) 99.1668 0.352907 0.176453 0.984309i \(-0.443537\pi\)
0.176453 + 0.984309i \(0.443537\pi\)
\(282\) −40.6159 + 40.6159i −0.144028 + 0.144028i
\(283\) 200.417 + 200.417i 0.708186 + 0.708186i 0.966154 0.257968i \(-0.0830528\pi\)
−0.257968 + 0.966154i \(0.583053\pi\)
\(284\) 130.125i 0.458186i
\(285\) −14.3092 + 22.3297i −0.0502077 + 0.0783499i
\(286\) −100.298 −0.350692
\(287\) 60.9970 60.9970i 0.212533 0.212533i
\(288\) −33.0364 33.0364i −0.114710 0.114710i
\(289\) 222.242i 0.769003i
\(290\) −195.570 125.324i −0.674379 0.432151i
\(291\) 24.5584 0.0843932
\(292\) −104.578 + 104.578i −0.358143 + 0.358143i
\(293\) 147.035 + 147.035i 0.501826 + 0.501826i 0.912005 0.410179i \(-0.134534\pi\)
−0.410179 + 0.912005i \(0.634534\pi\)
\(294\) 30.1327i 0.102492i
\(295\) 30.9213 + 141.253i 0.104818 + 0.478822i
\(296\) −80.2016 −0.270951
\(297\) −40.1955 + 40.1955i −0.135338 + 0.135338i
\(298\) 82.9264 + 82.9264i 0.278277 + 0.278277i
\(299\) 88.8886i 0.297286i
\(300\) 14.9345 40.3634i 0.0497818 0.134545i
\(301\) 185.253 0.615457
\(302\) −256.123 + 256.123i −0.848088 + 0.848088i
\(303\) −12.9306 12.9306i −0.0426752 0.0426752i
\(304\) 24.6492i 0.0810829i
\(305\) −19.3020 + 4.22536i −0.0632852 + 0.0138536i
\(306\) 264.096 0.863057
\(307\) 170.158 170.158i 0.554262 0.554262i −0.373406 0.927668i \(-0.621810\pi\)
0.927668 + 0.373406i \(0.121810\pi\)
\(308\) 26.6459 + 26.6459i 0.0865127 + 0.0865127i
\(309\) 135.408i 0.438214i
\(310\) −103.098 + 160.886i −0.332574 + 0.518987i
\(311\) 86.2595 0.277362 0.138681 0.990337i \(-0.455714\pi\)
0.138681 + 0.990337i \(0.455714\pi\)
\(312\) 31.9074 31.9074i 0.102267 0.102267i
\(313\) −352.517 352.517i −1.12625 1.12625i −0.990781 0.135472i \(-0.956745\pi\)
−0.135472 0.990781i \(-0.543255\pi\)
\(314\) 228.536i 0.727821i
\(315\) −171.204 109.710i −0.543506 0.348286i
\(316\) 124.464 0.393874
\(317\) −79.7816 + 79.7816i −0.251677 + 0.251677i −0.821658 0.569981i \(-0.806951\pi\)
0.569981 + 0.821658i \(0.306951\pi\)
\(318\) 51.9331 + 51.9331i 0.163312 + 0.163312i
\(319\) 125.696i 0.394030i
\(320\) 8.55376 + 39.0747i 0.0267305 + 0.122108i
\(321\) 53.7171 0.167343
\(322\) −23.6148 + 23.6148i −0.0733379 + 0.0733379i
\(323\) 98.5237 + 98.5237i 0.305027 + 0.305027i
\(324\) 123.089i 0.379906i
\(325\) −434.571 160.792i −1.33714 0.494745i
\(326\) −400.924 −1.22983
\(327\) −34.6646 + 34.6646i −0.106008 + 0.106008i
\(328\) 35.0375 + 35.0375i 0.106822 + 0.106822i
\(329\) 232.347i 0.706222i
\(330\) 22.7507 4.98031i 0.0689415 0.0150918i
\(331\) −123.045 −0.371738 −0.185869 0.982575i \(-0.559510\pi\)
−0.185869 + 0.982575i \(0.559510\pi\)
\(332\) −190.559 + 190.559i −0.573973 + 0.573973i
\(333\) 165.598 + 165.598i 0.497292 + 0.497292i
\(334\) 2.42656i 0.00726515i
\(335\) −264.802 + 413.228i −0.790453 + 1.23351i
\(336\) −16.9535 −0.0504569
\(337\) 329.255 329.255i 0.977018 0.977018i −0.0227234 0.999742i \(-0.507234\pi\)
0.999742 + 0.0227234i \(0.00723371\pi\)
\(338\) −174.530 174.530i −0.516361 0.516361i
\(339\) 18.6376i 0.0549781i
\(340\) −190.373 121.993i −0.559920 0.358804i
\(341\) −103.404 −0.303237
\(342\) −50.8951 + 50.8951i −0.148816 + 0.148816i
\(343\) 256.797 + 256.797i 0.748681 + 0.748681i
\(344\) 106.412i 0.309336i
\(345\) 4.41377 + 20.1627i 0.0127935 + 0.0584426i
\(346\) 373.249 1.07876
\(347\) 78.9165 78.9165i 0.227425 0.227425i −0.584191 0.811616i \(-0.698588\pi\)
0.811616 + 0.584191i \(0.198588\pi\)
\(348\) 39.9870 + 39.9870i 0.114905 + 0.114905i
\(349\) 209.184i 0.599381i −0.954037 0.299690i \(-0.903117\pi\)
0.954037 0.299690i \(-0.0968834\pi\)
\(350\) 72.7342 + 158.169i 0.207812 + 0.451910i
\(351\) −275.346 −0.784463
\(352\) −15.3058 + 15.3058i −0.0434823 + 0.0434823i
\(353\) 181.293 + 181.293i 0.513578 + 0.513578i 0.915621 0.402043i \(-0.131700\pi\)
−0.402043 + 0.915621i \(0.631700\pi\)
\(354\) 35.2034i 0.0994446i
\(355\) 317.787 69.5661i 0.895175 0.195961i
\(356\) 263.071 0.738964
\(357\) 67.7638 67.7638i 0.189815 0.189815i
\(358\) 156.890 + 156.890i 0.438240 + 0.438240i
\(359\) 701.621i 1.95438i −0.212378 0.977188i \(-0.568121\pi\)
0.212378 0.977188i \(-0.431879\pi\)
\(360\) 63.0189 98.3421i 0.175053 0.273173i
\(361\) 323.026 0.894809
\(362\) 110.482 110.482i 0.305198 0.305198i
\(363\) −64.7345 64.7345i −0.178332 0.178332i
\(364\) 182.529i 0.501454i
\(365\) −311.305 199.488i −0.852890 0.546543i
\(366\) 4.81050 0.0131434
\(367\) 159.383 159.383i 0.434287 0.434287i −0.455797 0.890084i \(-0.650646\pi\)
0.890084 + 0.455797i \(0.150646\pi\)
\(368\) −13.5647 13.5647i −0.0368605 0.0368605i
\(369\) 144.689i 0.392112i
\(370\) −42.8766 195.866i −0.115883 0.529367i
\(371\) −297.088 −0.800777
\(372\) 32.8954 32.8954i 0.0884285 0.0884285i
\(373\) 267.254 + 267.254i 0.716499 + 0.716499i 0.967886 0.251388i \(-0.0808870\pi\)
−0.251388 + 0.967886i \(0.580887\pi\)
\(374\) 122.355i 0.327154i
\(375\) 106.558 + 14.8940i 0.284156 + 0.0397173i
\(376\) 133.463 0.354955
\(377\) 430.519 430.519i 1.14196 1.14196i
\(378\) 73.1506 + 73.1506i 0.193520 + 0.193520i
\(379\) 204.998i 0.540893i 0.962735 + 0.270446i \(0.0871713\pi\)
−0.962735 + 0.270446i \(0.912829\pi\)
\(380\) 60.1975 13.1777i 0.158415 0.0346782i
\(381\) −148.066 −0.388624
\(382\) 101.977 101.977i 0.266956 0.266956i
\(383\) 463.802 + 463.802i 1.21097 + 1.21097i 0.970707 + 0.240265i \(0.0772344\pi\)
0.240265 + 0.970707i \(0.422766\pi\)
\(384\) 9.73832i 0.0253602i
\(385\) −50.8287 + 79.3190i −0.132022 + 0.206023i
\(386\) −427.999 −1.10880
\(387\) 219.716 219.716i 0.567742 0.567742i
\(388\) −40.3493 40.3493i −0.103993 0.103993i
\(389\) 507.724i 1.30520i 0.757701 + 0.652602i \(0.226322\pi\)
−0.757701 + 0.652602i \(0.773678\pi\)
\(390\) 94.9813 + 60.8652i 0.243542 + 0.156065i
\(391\) 108.437 0.277332
\(392\) −49.5079 + 49.5079i −0.126296 + 0.126296i
\(393\) 42.7375 + 42.7375i 0.108747 + 0.108747i
\(394\) 374.002i 0.949243i
\(395\) 66.5399 + 303.963i 0.168455 + 0.769526i
\(396\) 63.2059 0.159611
\(397\) −41.7475 + 41.7475i −0.105157 + 0.105157i −0.757728 0.652571i \(-0.773691\pi\)
0.652571 + 0.757728i \(0.273691\pi\)
\(398\) −365.937 365.937i −0.919441 0.919441i
\(399\) 26.1181i 0.0654590i
\(400\) −90.8541 + 41.7795i −0.227135 + 0.104449i
\(401\) 662.900 1.65312 0.826558 0.562851i \(-0.190296\pi\)
0.826558 + 0.562851i \(0.190296\pi\)
\(402\) 84.4902 84.4902i 0.210175 0.210175i
\(403\) −354.168 354.168i −0.878828 0.878828i
\(404\) 42.4898i 0.105173i
\(405\) −300.605 + 65.8048i −0.742235 + 0.162481i
\(406\) −228.750 −0.563423
\(407\) 76.7217 76.7217i 0.188505 0.188505i
\(408\) 38.9244 + 38.9244i 0.0954030 + 0.0954030i
\(409\) 4.51129i 0.0110300i 0.999985 + 0.00551502i \(0.00175550\pi\)
−0.999985 + 0.00551502i \(0.998245\pi\)
\(410\) −66.8361 + 104.299i −0.163015 + 0.254388i
\(411\) 109.961 0.267544
\(412\) 222.475 222.475i 0.539987 0.539987i
\(413\) 100.692 + 100.692i 0.243807 + 0.243807i
\(414\) 56.0160i 0.135304i
\(415\) −567.252 363.503i −1.36687 0.875910i
\(416\) −104.847 −0.252037
\(417\) −21.3865 + 21.3865i −0.0512866 + 0.0512866i
\(418\) 23.5797 + 23.5797i 0.0564107 + 0.0564107i
\(419\) 239.199i 0.570880i 0.958397 + 0.285440i \(0.0921397\pi\)
−0.958397 + 0.285440i \(0.907860\pi\)
\(420\) −9.06351 41.4033i −0.0215798 0.0985794i
\(421\) 222.759 0.529119 0.264559 0.964369i \(-0.414773\pi\)
0.264559 + 0.964369i \(0.414773\pi\)
\(422\) 269.478 269.478i 0.638575 0.638575i
\(423\) −275.572 275.572i −0.651470 0.651470i
\(424\) 170.651i 0.402480i
\(425\) 196.153 530.141i 0.461537 1.24739i
\(426\) −79.1999 −0.185915
\(427\) −13.7595 + 13.7595i −0.0322236 + 0.0322236i
\(428\) −88.2569 88.2569i −0.206208 0.206208i
\(429\) 61.0459i 0.142298i
\(430\) −259.875 + 56.8887i −0.604361 + 0.132299i
\(431\) −708.039 −1.64278 −0.821391 0.570366i \(-0.806801\pi\)
−0.821391 + 0.570366i \(0.806801\pi\)
\(432\) −42.0187 + 42.0187i −0.0972654 + 0.0972654i
\(433\) −179.204 179.204i −0.413866 0.413866i 0.469217 0.883083i \(-0.344536\pi\)
−0.883083 + 0.469217i \(0.844536\pi\)
\(434\) 188.181i 0.433598i
\(435\) −76.2776 + 119.033i −0.175351 + 0.273638i
\(436\) 113.908 0.261256
\(437\) −20.8974 + 20.8974i −0.0478201 + 0.0478201i
\(438\) 63.6507 + 63.6507i 0.145321 + 0.145321i
\(439\) 574.258i 1.30810i −0.756449 0.654052i \(-0.773068\pi\)
0.756449 0.654052i \(-0.226932\pi\)
\(440\) −45.5619 29.1967i −0.103550 0.0663560i
\(441\) 204.445 0.463595
\(442\) 419.079 419.079i 0.948142 0.948142i
\(443\) −83.8605 83.8605i −0.189301 0.189301i 0.606093 0.795394i \(-0.292736\pi\)
−0.795394 + 0.606093i \(0.792736\pi\)
\(444\) 48.8143i 0.109942i
\(445\) 140.641 + 642.465i 0.316046 + 1.44374i
\(446\) 365.422 0.819333
\(447\) 50.4727 50.4727i 0.112914 0.112914i
\(448\) 27.8545 + 27.8545i 0.0621752 + 0.0621752i
\(449\) 139.847i 0.311464i 0.987799 + 0.155732i \(0.0497736\pi\)
−0.987799 + 0.155732i \(0.950226\pi\)
\(450\) 273.859 + 101.328i 0.608575 + 0.225174i
\(451\) −67.0345 −0.148635
\(452\) −30.6214 + 30.6214i −0.0677465 + 0.0677465i
\(453\) 155.888 + 155.888i 0.344123 + 0.344123i
\(454\) 142.018i 0.312816i
\(455\) −445.768 + 97.5820i −0.979709 + 0.214466i
\(456\) −15.0026 −0.0329005
\(457\) 55.0666 55.0666i 0.120496 0.120496i −0.644288 0.764783i \(-0.722846\pi\)
0.764783 + 0.644288i \(0.222846\pi\)
\(458\) 97.6089 + 97.6089i 0.213120 + 0.213120i
\(459\) 335.900i 0.731809i
\(460\) 25.8754 40.3790i 0.0562509 0.0877804i
\(461\) 833.889 1.80887 0.904434 0.426613i \(-0.140293\pi\)
0.904434 + 0.426613i \(0.140293\pi\)
\(462\) 16.2179 16.2179i 0.0351037 0.0351037i
\(463\) −25.0740 25.0740i −0.0541555 0.0541555i 0.679510 0.733666i \(-0.262192\pi\)
−0.733666 + 0.679510i \(0.762192\pi\)
\(464\) 131.397i 0.283183i
\(465\) 97.9224 + 62.7500i 0.210586 + 0.134946i
\(466\) 187.406 0.402160
\(467\) 5.39172 5.39172i 0.0115454 0.0115454i −0.701310 0.712856i \(-0.747401\pi\)
0.712856 + 0.701310i \(0.247401\pi\)
\(468\) 216.486 + 216.486i 0.462577 + 0.462577i
\(469\) 483.335i 1.03056i
\(470\) 71.3508 + 325.940i 0.151810 + 0.693489i
\(471\) 139.097 0.295323
\(472\) −57.8390 + 57.8390i −0.122540 + 0.122540i
\(473\) −101.794 101.794i −0.215210 0.215210i
\(474\) 75.7546i 0.159820i
\(475\) 64.3644 + 139.968i 0.135504 + 0.294669i
\(476\) −222.671 −0.467796
\(477\) −352.357 + 352.357i −0.738694 + 0.738694i
\(478\) −229.877 229.877i −0.480913 0.480913i
\(479\) 272.405i 0.568695i 0.958721 + 0.284348i \(0.0917770\pi\)
−0.958721 + 0.284348i \(0.908223\pi\)
\(480\) 23.7826 5.20620i 0.0495471 0.0108463i
\(481\) 525.558 1.09264
\(482\) 410.897 410.897i 0.852484 0.852484i
\(483\) 14.3730 + 14.3730i 0.0297578 + 0.0297578i
\(484\) 212.717i 0.439497i
\(485\) 76.9688 120.111i 0.158698 0.247652i
\(486\) 264.002 0.543213
\(487\) −343.544 + 343.544i −0.705428 + 0.705428i −0.965570 0.260142i \(-0.916231\pi\)
0.260142 + 0.965570i \(0.416231\pi\)
\(488\) −7.90362 7.90362i −0.0161959 0.0161959i
\(489\) 244.021i 0.499020i
\(490\) −147.374 94.4393i −0.300763 0.192733i
\(491\) −490.578 −0.999140 −0.499570 0.866273i \(-0.666509\pi\)
−0.499570 + 0.866273i \(0.666509\pi\)
\(492\) 21.3254 21.3254i 0.0433443 0.0433443i
\(493\) 525.198 + 525.198i 1.06531 + 1.06531i
\(494\) 161.525i 0.326974i
\(495\) 33.7905 + 154.360i 0.0682637 + 0.311838i
\(496\) −108.094 −0.217931
\(497\) 226.535 226.535i 0.455806 0.455806i
\(498\) 115.983 + 115.983i 0.232897 + 0.232897i
\(499\) 668.332i 1.33934i −0.742657 0.669672i \(-0.766435\pi\)
0.742657 0.669672i \(-0.233565\pi\)
\(500\) −150.604 199.546i −0.301208 0.399091i
\(501\) 1.47691 0.00294793
\(502\) −220.598 + 220.598i −0.439437 + 0.439437i
\(503\) 139.902 + 139.902i 0.278135 + 0.278135i 0.832364 0.554229i \(-0.186987\pi\)
−0.554229 + 0.832364i \(0.686987\pi\)
\(504\) 115.027i 0.228227i
\(505\) −103.767 + 22.7155i −0.205480 + 0.0449811i
\(506\) 25.9522 0.0512889
\(507\) −106.227 + 106.227i −0.209520 + 0.209520i
\(508\) 243.271 + 243.271i 0.478880 + 0.478880i
\(509\) 428.803i 0.842442i 0.906958 + 0.421221i \(0.138398\pi\)
−0.906958 + 0.421221i \(0.861602\pi\)
\(510\) −74.2506 + 115.869i −0.145589 + 0.227195i
\(511\) −364.120 −0.712564
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) 64.7329 + 64.7329i 0.126185 + 0.126185i
\(514\) 444.024i 0.863860i
\(515\) 662.258 + 424.384i 1.28594 + 0.824046i
\(516\) 64.7669 0.125517
\(517\) −127.672 + 127.672i −0.246948 + 0.246948i
\(518\) −139.623 139.623i −0.269543 0.269543i
\(519\) 227.176i 0.437719i
\(520\) −56.0524 256.055i −0.107793 0.492413i
\(521\) 432.637 0.830398 0.415199 0.909731i \(-0.363712\pi\)
0.415199 + 0.909731i \(0.363712\pi\)
\(522\) −271.305 + 271.305i −0.519742 + 0.519742i
\(523\) −240.769 240.769i −0.460361 0.460361i 0.438413 0.898774i \(-0.355541\pi\)
−0.898774 + 0.438413i \(0.855541\pi\)
\(524\) 140.435i 0.268005i
\(525\) 96.2685 44.2693i 0.183369 0.0843224i
\(526\) −547.200 −1.04030
\(527\) 432.056 432.056i 0.819840 0.819840i
\(528\) 9.31578 + 9.31578i 0.0176435 + 0.0176435i
\(529\) 23.0000i 0.0434783i
\(530\) 416.760 91.2320i 0.786339 0.172136i
\(531\) 238.849 0.449810
\(532\) 42.9120 42.9120i 0.0806616 0.0806616i
\(533\) −229.599 229.599i −0.430768 0.430768i
\(534\) 160.117i 0.299845i
\(535\) 168.355 262.721i 0.314683 0.491068i
\(536\) −277.634 −0.517974
\(537\) 95.4902 95.4902i 0.177822 0.177822i
\(538\) −306.939 306.939i −0.570518 0.570518i
\(539\) 94.7195i 0.175732i
\(540\) −125.080 80.1531i −0.231630 0.148432i
\(541\) −914.332 −1.69008 −0.845039 0.534705i \(-0.820423\pi\)
−0.845039 + 0.534705i \(0.820423\pi\)
\(542\) 423.942 423.942i 0.782181 0.782181i
\(543\) −67.2441 67.2441i −0.123838 0.123838i
\(544\) 127.905i 0.235120i
\(545\) 60.8961 + 278.182i 0.111736 + 0.510425i
\(546\) 111.096 0.203472
\(547\) −636.733 + 636.733i −1.16405 + 1.16405i −0.180465 + 0.983581i \(0.557760\pi\)
−0.983581 + 0.180465i \(0.942240\pi\)
\(548\) −180.665 180.665i −0.329680 0.329680i
\(549\) 32.6384i 0.0594507i
\(550\) 46.9453 126.879i 0.0853552 0.230689i
\(551\) −202.427 −0.367381
\(552\) −8.25606 + 8.25606i −0.0149566 + 0.0149566i
\(553\) 216.681 + 216.681i 0.391828 + 0.391828i
\(554\) 246.989i 0.445828i
\(555\) −119.213 + 26.0966i −0.214798 + 0.0470209i
\(556\) 70.2758 0.126395
\(557\) −414.033 + 414.033i −0.743326 + 0.743326i −0.973217 0.229890i \(-0.926163\pi\)
0.229890 + 0.973217i \(0.426163\pi\)
\(558\) 223.190 + 223.190i 0.399982 + 0.399982i
\(559\) 697.311i 1.24743i
\(560\) −53.1341 + 82.9167i −0.0948824 + 0.148066i
\(561\) −74.4710 −0.132747
\(562\) −99.1668 + 99.1668i −0.176453 + 0.176453i
\(563\) −324.082 324.082i −0.575634 0.575634i 0.358063 0.933697i \(-0.383437\pi\)
−0.933697 + 0.358063i \(0.883437\pi\)
\(564\) 81.2317i 0.144028i
\(565\) −91.1533 58.4122i −0.161333 0.103384i
\(566\) −400.833 −0.708186
\(567\) −214.287 + 214.287i −0.377932 + 0.377932i
\(568\) 130.125 + 130.125i 0.229093 + 0.229093i
\(569\) 521.104i 0.915824i −0.888998 0.457912i \(-0.848598\pi\)
0.888998 0.457912i \(-0.151402\pi\)
\(570\) −8.02054 36.6389i −0.0140711 0.0642788i
\(571\) −308.824 −0.540847 −0.270423 0.962741i \(-0.587164\pi\)
−0.270423 + 0.962741i \(0.587164\pi\)
\(572\) 100.298 100.298i 0.175346 0.175346i
\(573\) −62.0680 62.0680i −0.108321 0.108321i
\(574\) 121.994i 0.212533i
\(575\) 112.446 + 41.6051i 0.195558 + 0.0723567i
\(576\) 66.0728 0.114710
\(577\) −243.906 + 243.906i −0.422714 + 0.422714i −0.886137 0.463423i \(-0.846621\pi\)
0.463423 + 0.886137i \(0.346621\pi\)
\(578\) 222.242 + 222.242i 0.384501 + 0.384501i
\(579\) 260.499i 0.449912i
\(580\) 320.893 70.2461i 0.553265 0.121114i
\(581\) −663.491 −1.14198
\(582\) −24.5584 + 24.5584i −0.0421966 + 0.0421966i
\(583\) 163.247 + 163.247i 0.280012 + 0.280012i
\(584\) 209.155i 0.358143i
\(585\) −412.960 + 644.432i −0.705915 + 1.10159i
\(586\) −294.070 −0.501826
\(587\) −153.926 + 153.926i −0.262226 + 0.262226i −0.825958 0.563732i \(-0.809365\pi\)
0.563732 + 0.825958i \(0.309365\pi\)
\(588\) 30.1327 + 30.1327i 0.0512461 + 0.0512461i
\(589\) 166.527i 0.282728i
\(590\) −172.174 110.331i −0.291820 0.187002i
\(591\) −227.634 −0.385168
\(592\) 80.2016 80.2016i 0.135476 0.135476i
\(593\) −506.955 506.955i −0.854899 0.854899i 0.135832 0.990732i \(-0.456629\pi\)
−0.990732 + 0.135832i \(0.956629\pi\)
\(594\) 80.3910i 0.135338i
\(595\) −119.042 543.800i −0.200071 0.913950i
\(596\) −165.853 −0.278277
\(597\) −222.726 + 222.726i −0.373075 + 0.373075i
\(598\) 88.8886 + 88.8886i 0.148643 + 0.148643i
\(599\) 884.769i 1.47708i 0.674211 + 0.738539i \(0.264484\pi\)
−0.674211 + 0.738539i \(0.735516\pi\)
\(600\) 25.4289 + 55.2979i 0.0423814 + 0.0921632i
\(601\) −142.836 −0.237664 −0.118832 0.992914i \(-0.537915\pi\)
−0.118832 + 0.992914i \(0.537915\pi\)
\(602\) −185.253 + 185.253i −0.307729 + 0.307729i
\(603\) 573.252 + 573.252i 0.950666 + 0.950666i
\(604\) 512.245i 0.848088i
\(605\) −519.490 + 113.720i −0.858662 + 0.187968i
\(606\) 25.8612 0.0426752
\(607\) −560.960 + 560.960i −0.924152 + 0.924152i −0.997320 0.0731676i \(-0.976689\pi\)
0.0731676 + 0.997320i \(0.476689\pi\)
\(608\) 24.6492 + 24.6492i 0.0405414 + 0.0405414i
\(609\) 139.227i 0.228616i
\(610\) 15.0766 23.5273i 0.0247158 0.0385694i
\(611\) −874.579 −1.43139
\(612\) −264.096 + 264.096i −0.431529 + 0.431529i
\(613\) −240.604 240.604i −0.392502 0.392502i 0.483076 0.875578i \(-0.339519\pi\)
−0.875578 + 0.483076i \(0.839519\pi\)
\(614\) 340.317i 0.554262i
\(615\) 63.4810 + 40.6795i 0.103221 + 0.0661455i
\(616\) −53.2918 −0.0865127
\(617\) 634.877 634.877i 1.02897 1.02897i 0.0294068 0.999568i \(-0.490638\pi\)
0.999568 0.0294068i \(-0.00936183\pi\)
\(618\) −135.408 135.408i −0.219107 0.219107i
\(619\) 339.323i 0.548179i 0.961704 + 0.274089i \(0.0883764\pi\)
−0.961704 + 0.274089i \(0.911624\pi\)
\(620\) −57.7881 263.984i −0.0932066 0.425780i
\(621\) 71.2461 0.114728
\(622\) −86.2595 + 86.2595i −0.138681 + 0.138681i
\(623\) 457.983 + 457.983i 0.735125 + 0.735125i
\(624\) 63.8148i 0.102267i
\(625\) 406.810 474.480i 0.650895 0.759168i
\(626\) 705.035 1.12625
\(627\) 14.3517 14.3517i 0.0228894 0.0228894i
\(628\) −228.536 228.536i −0.363911 0.363911i
\(629\) 641.137i 1.01930i
\(630\) 280.915 61.4944i 0.445896 0.0976101i
\(631\) 913.051 1.44699 0.723495 0.690329i \(-0.242534\pi\)
0.723495 + 0.690329i \(0.242534\pi\)
\(632\) −124.464 + 124.464i −0.196937 + 0.196937i
\(633\) −164.017 164.017i −0.259110 0.259110i
\(634\) 159.563i 0.251677i
\(635\) −464.054 + 724.164i −0.730794 + 1.14042i
\(636\) −103.866 −0.163312
\(637\) 324.423 324.423i 0.509298 0.509298i
\(638\) 125.696 + 125.696i 0.197015 + 0.197015i
\(639\) 537.358i 0.840935i
\(640\) −47.6285 30.5210i −0.0744195 0.0476890i
\(641\) 799.743 1.24765 0.623824 0.781565i \(-0.285578\pi\)
0.623824 + 0.781565i \(0.285578\pi\)
\(642\) −53.7171 + 53.7171i −0.0836715 + 0.0836715i
\(643\) −362.899 362.899i −0.564385 0.564385i 0.366165 0.930550i \(-0.380670\pi\)
−0.930550 + 0.366165i \(0.880670\pi\)
\(644\) 47.2296i 0.0733379i
\(645\) 34.6250 + 158.172i 0.0536822 + 0.245227i
\(646\) −197.047 −0.305027
\(647\) −735.285 + 735.285i −1.13645 + 1.13645i −0.147372 + 0.989081i \(0.547081\pi\)
−0.989081 + 0.147372i \(0.952919\pi\)
\(648\) −123.089 123.089i −0.189953 0.189953i
\(649\) 110.659i 0.170506i
\(650\) 595.363 273.779i 0.915944 0.421199i
\(651\) 114.536 0.175938
\(652\) 400.924 400.924i 0.614915 0.614915i
\(653\) −633.952 633.952i −0.970831 0.970831i 0.0287558 0.999586i \(-0.490845\pi\)
−0.999586 + 0.0287558i \(0.990845\pi\)
\(654\) 69.3293i 0.106008i
\(655\) 342.966 75.0779i 0.523612 0.114623i
\(656\) −70.0750 −0.106822
\(657\) −431.859 + 431.859i −0.657320 + 0.657320i
\(658\) 232.347 + 232.347i 0.353111 + 0.353111i
\(659\) 378.146i 0.573817i −0.957958 0.286909i \(-0.907372\pi\)
0.957958 0.286909i \(-0.0926276\pi\)
\(660\) −17.7704 + 27.7310i −0.0269248 + 0.0420167i
\(661\) −417.405 −0.631476 −0.315738 0.948846i \(-0.602252\pi\)
−0.315738 + 0.948846i \(0.602252\pi\)
\(662\) 123.045 123.045i 0.185869 0.185869i
\(663\) −255.070 255.070i −0.384721 0.384721i
\(664\) 381.118i 0.573973i
\(665\) 127.739 + 81.8571i 0.192089 + 0.123093i
\(666\) −331.197 −0.497292
\(667\) −111.397 + 111.397i −0.167012 + 0.167012i
\(668\) −2.42656 2.42656i −0.00363257 0.00363257i
\(669\) 222.413i 0.332455i
\(670\) −148.426 678.029i −0.221531 1.01198i
\(671\) 15.1214 0.0225356
\(672\) 16.9535 16.9535i 0.0252284 0.0252284i
\(673\) −591.106 591.106i −0.878316 0.878316i 0.115045 0.993360i \(-0.463299\pi\)
−0.993360 + 0.115045i \(0.963299\pi\)
\(674\) 658.510i 0.977018i
\(675\) 128.878 348.318i 0.190931 0.516027i
\(676\) 349.060 0.516361
\(677\) 415.702 415.702i 0.614035 0.614035i −0.329960 0.943995i \(-0.607035\pi\)
0.943995 + 0.329960i \(0.107035\pi\)
\(678\) 18.6376 + 18.6376i 0.0274891 + 0.0274891i
\(679\) 140.489i 0.206906i
\(680\) 312.366 68.3794i 0.459362 0.100558i
\(681\) 86.4388 0.126929
\(682\) 103.404 103.404i 0.151618 0.151618i
\(683\) −286.643 286.643i −0.419682 0.419682i 0.465412 0.885094i \(-0.345906\pi\)
−0.885094 + 0.465412i \(0.845906\pi\)
\(684\) 101.790i 0.148816i
\(685\) 344.629 537.799i 0.503108 0.785108i
\(686\) −513.595 −0.748681
\(687\) 59.4091 59.4091i 0.0864762 0.0864762i
\(688\) −106.412 106.412i −0.154668 0.154668i
\(689\) 1118.27i 1.62304i
\(690\) −24.5765 15.7489i −0.0356181 0.0228245i
\(691\) 830.206 1.20146 0.600728 0.799453i \(-0.294877\pi\)
0.600728 + 0.799453i \(0.294877\pi\)
\(692\) −373.249 + 373.249i −0.539378 + 0.539378i
\(693\) 110.036 + 110.036i 0.158782 + 0.158782i
\(694\) 157.833i 0.227425i
\(695\) 37.5701 + 171.625i 0.0540577 + 0.246943i
\(696\) −79.9740 −0.114905
\(697\) 280.092 280.092i 0.401854 0.401854i
\(698\) 209.184 + 209.184i 0.299690 + 0.299690i
\(699\) 114.064i 0.163182i
\(700\) −230.903 85.4344i −0.329861 0.122049i
\(701\) 228.321 0.325708 0.162854 0.986650i \(-0.447930\pi\)
0.162854 + 0.986650i \(0.447930\pi\)
\(702\) 275.346 275.346i 0.392231 0.392231i
\(703\) −123.557 123.557i −0.175756 0.175756i
\(704\) 30.6115i 0.0434823i
\(705\) 198.382 43.4273i 0.281392 0.0615990i
\(706\) −362.586 −0.513578
\(707\) −73.9707 + 73.9707i −0.104626 + 0.104626i
\(708\) 35.2034 + 35.2034i 0.0497223 + 0.0497223i
\(709\) 701.099i 0.988856i 0.869219 + 0.494428i \(0.164622\pi\)
−0.869219 + 0.494428i \(0.835378\pi\)
\(710\) −248.221 + 387.353i −0.349607 + 0.545568i
\(711\) 513.982 0.722900
\(712\) −263.071 + 263.071i −0.369482 + 0.369482i
\(713\) 91.6411 + 91.6411i 0.128529 + 0.128529i
\(714\) 135.528i 0.189815i
\(715\) 298.565 + 191.324i 0.417574 + 0.267587i
\(716\) −313.780 −0.438240
\(717\) −139.913 + 139.913i −0.195137 + 0.195137i
\(718\) 701.621 + 701.621i 0.977188 + 0.977188i
\(719\) 955.252i 1.32858i −0.747473 0.664292i \(-0.768733\pi\)
0.747473 0.664292i \(-0.231267\pi\)
\(720\) 35.3232 + 161.361i 0.0490600 + 0.224113i
\(721\) 774.615 1.07436
\(722\) −323.026 + 323.026i −0.447405 + 0.447405i
\(723\) −250.091 250.091i −0.345907 0.345907i
\(724\) 220.963i 0.305198i
\(725\) 343.106 + 746.122i 0.473249 + 1.02913i
\(726\) 129.469 0.178332
\(727\) −131.313 + 131.313i −0.180623 + 0.180623i −0.791627 0.611004i \(-0.790766\pi\)
0.611004 + 0.791627i \(0.290766\pi\)
\(728\) −182.529 182.529i −0.250727 0.250727i
\(729\) 393.219i 0.539395i
\(730\) 510.793 111.817i 0.699716 0.153173i
\(731\) 850.662 1.16370
\(732\) −4.81050 + 4.81050i −0.00657172 + 0.00657172i
\(733\) 590.972 + 590.972i 0.806237 + 0.806237i 0.984062 0.177825i \(-0.0569060\pi\)
−0.177825 + 0.984062i \(0.556906\pi\)
\(734\) 318.766i 0.434287i
\(735\) −57.4800 + 89.6985i −0.0782041 + 0.122039i
\(736\) 27.1293 0.0368605
\(737\) 265.588 265.588i 0.360363 0.360363i
\(738\) 144.689 + 144.689i 0.196056 + 0.196056i
\(739\) 764.194i 1.03409i −0.855958 0.517046i \(-0.827032\pi\)
0.855958 0.517046i \(-0.172968\pi\)
\(740\) 238.742 + 152.989i 0.322625 + 0.206742i
\(741\) 98.3114 0.132674
\(742\) 297.088 297.088i 0.400388 0.400388i
\(743\) −864.163 864.163i −1.16307 1.16307i −0.983799 0.179273i \(-0.942625\pi\)
−0.179273 0.983799i \(-0.557375\pi\)
\(744\) 65.7908i 0.0884285i
\(745\) −88.6666 405.041i −0.119016 0.543679i
\(746\) −534.508 −0.716499
\(747\) −786.923 + 786.923i −1.05344 + 1.05344i
\(748\) 122.355 + 122.355i 0.163577 + 0.163577i
\(749\) 307.294i 0.410272i
\(750\) −121.452 + 91.6644i −0.161936 + 0.122219i
\(751\) −285.420 −0.380053 −0.190027 0.981779i \(-0.560857\pi\)
−0.190027 + 0.981779i \(0.560857\pi\)
\(752\) −133.463 + 133.463i −0.177478 + 0.177478i
\(753\) 134.266 + 134.266i 0.178308 + 0.178308i
\(754\) 861.038i 1.14196i
\(755\) 1250.99 273.851i 1.65694 0.362717i
\(756\) −146.301 −0.193520
\(757\) 410.339 410.339i 0.542060 0.542060i −0.382072 0.924132i \(-0.624790\pi\)
0.924132 + 0.382072i \(0.124790\pi\)
\(758\) −204.998 204.998i −0.270446 0.270446i
\(759\) 15.7957i 0.0208112i
\(760\) −47.0198 + 73.3752i −0.0618682 + 0.0965463i
\(761\) 1360.01 1.78713 0.893565 0.448934i \(-0.148196\pi\)
0.893565 + 0.448934i \(0.148196\pi\)
\(762\) 148.066 148.066i 0.194312 0.194312i
\(763\) 198.302 + 198.302i 0.259898 + 0.259898i
\(764\) 203.955i 0.266956i
\(765\) −786.154 503.778i −1.02765 0.658533i
\(766\) −927.605 −1.21097
\(767\) 379.016 379.016i 0.494154 0.494154i
\(768\) 9.73832 + 9.73832i 0.0126801 + 0.0126801i
\(769\) 1442.78i 1.87618i −0.346393 0.938090i \(-0.612594\pi\)
0.346393 0.938090i \(-0.387406\pi\)
\(770\) −28.4903 130.148i −0.0370004 0.169023i
\(771\) 270.253 0.350523
\(772\) 427.999 427.999i 0.554402 0.554402i
\(773\) 176.154 + 176.154i 0.227883 + 0.227883i 0.811808 0.583925i \(-0.198484\pi\)
−0.583925 + 0.811808i \(0.698484\pi\)
\(774\) 439.432i 0.567742i
\(775\) 613.799 282.257i 0.791999 0.364202i
\(776\) 80.6987 0.103993
\(777\) −84.9811 + 84.9811i −0.109371 + 0.109371i
\(778\) −507.724 507.724i −0.652602 0.652602i
\(779\) 107.956i 0.138583i
\(780\) −155.847 + 34.1160i −0.199803 + 0.0437385i
\(781\) −248.958 −0.318768
\(782\) −108.437 + 108.437i −0.138666 + 0.138666i
\(783\) 345.070 + 345.070i 0.440702 + 0.440702i
\(784\) 99.0158i 0.126296i
\(785\) 435.946 680.301i 0.555345 0.866626i
\(786\) −85.4750 −0.108747
\(787\) −310.617 + 310.617i −0.394685 + 0.394685i −0.876354 0.481668i \(-0.840031\pi\)
0.481668 + 0.876354i \(0.340031\pi\)
\(788\) 374.002 + 374.002i 0.474621 + 0.474621i
\(789\) 333.051i 0.422117i
\(790\) −370.503 237.423i −0.468991 0.300535i
\(791\) −106.618 −0.134789
\(792\) −63.2059 + 63.2059i −0.0798055 + 0.0798055i
\(793\) 51.7921 + 51.7921i 0.0653116 + 0.0653116i
\(794\) 83.4949i 0.105157i
\(795\) −55.5279 253.659i −0.0698464 0.319068i
\(796\) 731.875 0.919441
\(797\) 446.213 446.213i 0.559866 0.559866i −0.369403 0.929269i \(-0.620438\pi\)
0.929269 + 0.369403i \(0.120438\pi\)
\(798\) −26.1181 26.1181i −0.0327295 0.0327295i
\(799\) 1066.92i 1.33531i
\(800\) 49.0747 132.634i 0.0613433 0.165792i
\(801\) 1086.37 1.35626
\(802\) −662.900 + 662.900i −0.826558 + 0.826558i
\(803\) 200.080 + 200.080i 0.249166 + 0.249166i
\(804\) 168.980i 0.210175i
\(805\) 115.343 25.2494i 0.143283 0.0313657i
\(806\) 708.335 0.878828
\(807\) −186.817 + 186.817i −0.231495 + 0.231495i
\(808\) −42.4898 42.4898i −0.0525864 0.0525864i
\(809\) 399.170i 0.493411i −0.969090 0.246706i \(-0.920652\pi\)
0.969090 0.246706i \(-0.0793481\pi\)
\(810\) 234.800 366.410i 0.289877 0.452358i
\(811\) −1016.76 −1.25371 −0.626855 0.779136i \(-0.715658\pi\)
−0.626855 + 0.779136i \(0.715658\pi\)
\(812\) 228.750 228.750i 0.281711 0.281711i
\(813\) −258.030 258.030i −0.317380 0.317380i
\(814\) 153.443i 0.188505i
\(815\) 1193.46 + 764.787i 1.46437 + 0.938389i
\(816\) −77.8488 −0.0954030
\(817\) −163.935 + 163.935i −0.200655 + 0.200655i
\(818\) −4.51129 4.51129i −0.00551502 0.00551502i
\(819\) 753.764i 0.920347i
\(820\) −37.4628 171.135i −0.0456864 0.208701i
\(821\) 231.396 0.281847 0.140923 0.990021i \(-0.454993\pi\)
0.140923 + 0.990021i \(0.454993\pi\)
\(822\) −109.961 + 109.961i −0.133772 + 0.133772i
\(823\) −298.923 298.923i −0.363211 0.363211i 0.501783 0.864994i \(-0.332678\pi\)
−0.864994 + 0.501783i \(0.832678\pi\)
\(824\) 444.949i 0.539987i
\(825\) −77.2241 28.5730i −0.0936049 0.0346340i
\(826\) −201.384 −0.243807
\(827\) 19.4139 19.4139i 0.0234750 0.0234750i −0.695272 0.718747i \(-0.744716\pi\)
0.718747 + 0.695272i \(0.244716\pi\)
\(828\) −56.0160 56.0160i −0.0676521 0.0676521i
\(829\) 626.889i 0.756199i 0.925765 + 0.378099i \(0.123422\pi\)
−0.925765 + 0.378099i \(0.876578\pi\)
\(830\) 930.755 203.749i 1.12139 0.245481i
\(831\) −150.329 −0.180901
\(832\) 104.847 104.847i 0.126018 0.126018i
\(833\) 395.770 + 395.770i 0.475114 + 0.475114i
\(834\) 42.7730i 0.0512866i
\(835\) 4.62880 7.22333i 0.00554348 0.00865069i
\(836\) −47.1594 −0.0564107
\(837\) 283.873 283.873i 0.339155 0.339155i
\(838\) −239.199 239.199i −0.285440 0.285440i
\(839\) 144.679i 0.172442i 0.996276 + 0.0862211i \(0.0274792\pi\)
−0.996276 + 0.0862211i \(0.972521\pi\)
\(840\) 50.4668 + 32.3398i 0.0600796 + 0.0384998i
\(841\) −238.071 −0.283081
\(842\) −222.759 + 222.759i −0.264559 + 0.264559i
\(843\) 60.3574 + 60.3574i 0.0715983 + 0.0715983i
\(844\) 538.957i 0.638575i
\(845\) 186.611 + 852.463i 0.220841 + 1.00883i
\(846\) 551.143 0.651470
\(847\) −370.320 + 370.320i −0.437214 + 0.437214i
\(848\) 170.651 + 170.651i 0.201240 + 0.201240i
\(849\) 243.965i 0.287356i
\(850\) 333.988 + 726.295i 0.392927 + 0.854464i
\(851\) −135.988 −0.159798
\(852\) 79.1999 79.1999i 0.0929576 0.0929576i
\(853\) −47.8789 47.8789i −0.0561300 0.0561300i 0.678485 0.734615i \(-0.262637\pi\)
−0.734615 + 0.678485i \(0.762637\pi\)
\(854\) 27.5189i 0.0322236i
\(855\) 248.589 54.4180i 0.290747 0.0636468i
\(856\) 176.514 0.206208
\(857\) −3.82783 + 3.82783i −0.00446655 + 0.00446655i −0.709337 0.704870i \(-0.751005\pi\)
0.704870 + 0.709337i \(0.251005\pi\)
\(858\) −61.0459 61.0459i −0.0711490 0.0711490i
\(859\) 843.353i 0.981785i −0.871220 0.490892i \(-0.836671\pi\)
0.871220 0.490892i \(-0.163329\pi\)
\(860\) 202.986 316.764i 0.236031 0.368330i
\(861\) 74.2511 0.0862382
\(862\) 708.039 708.039i 0.821391 0.821391i
\(863\) −1167.76 1167.76i −1.35314 1.35314i −0.882121 0.471022i \(-0.843885\pi\)
−0.471022 0.882121i \(-0.656115\pi\)
\(864\) 84.0373i 0.0972654i
\(865\) −1111.08 711.995i −1.28449 0.823116i
\(866\) 358.408 0.413866
\(867\) 135.266 135.266i 0.156016 0.156016i
\(868\) −188.181 188.181i −0.216799 0.216799i
\(869\) 238.128i 0.274025i
\(870\) −42.7549 195.310i −0.0491436 0.224494i
\(871\) 1819.32 2.08878
\(872\) −113.908 + 113.908i −0.130628 + 0.130628i
\(873\) −166.625 166.625i −0.190864 0.190864i
\(874\) 41.7947i 0.0478201i
\(875\) 85.2025 609.578i 0.0973742 0.696660i
\(876\) −127.301 −0.145321
\(877\) 542.109 542.109i 0.618140 0.618140i −0.326914 0.945054i \(-0.606009\pi\)
0.945054 + 0.326914i \(0.106009\pi\)
\(878\) 574.258 + 574.258i 0.654052 + 0.654052i
\(879\) 178.984i 0.203622i
\(880\) 74.7586 16.3652i 0.0849529 0.0185969i
\(881\) −585.615 −0.664716 −0.332358 0.943153i \(-0.607844\pi\)
−0.332358 + 0.943153i \(0.607844\pi\)
\(882\) −204.445 + 204.445i −0.231798 + 0.231798i
\(883\) −224.300 224.300i −0.254020 0.254020i 0.568597 0.822616i \(-0.307487\pi\)
−0.822616 + 0.568597i \(0.807487\pi\)
\(884\) 838.157i 0.948142i
\(885\) −67.1526 + 104.793i −0.0758786 + 0.118410i
\(886\) 167.721 0.189301
\(887\) −644.816 + 644.816i −0.726963 + 0.726963i −0.970014 0.243051i \(-0.921852\pi\)
0.243051 + 0.970014i \(0.421852\pi\)
\(888\) −48.8143 48.8143i −0.0549710 0.0549710i
\(889\) 847.024i 0.952783i
\(890\) −783.105 501.824i −0.879894 0.563847i
\(891\) 235.497 0.264307
\(892\) −365.422 + 365.422i −0.409666 + 0.409666i
\(893\) 205.610 + 205.610i 0.230247 + 0.230247i
\(894\) 100.945i 0.112914i
\(895\) −167.750 766.303i −0.187430 0.856204i
\(896\) −55.7090 −0.0621752
\(897\) 54.1016 54.1016i 0.0603139 0.0603139i
\(898\) −139.847 139.847i −0.155732 0.155732i
\(899\) 887.701i 0.987431i
\(900\) −375.187 + 172.530i −0.416874 + 0.191701i
\(901\) −1364.20 −1.51410
\(902\) 67.0345 67.0345i 0.0743176 0.0743176i
\(903\) 112.753 + 112.753i 0.124865 + 0.124865i
\(904\) 61.2429i 0.0677465i
\(905\) −539.630 + 118.129i −0.596276 + 0.130530i
\(906\) −311.775 −0.344123
\(907\) 155.510 155.510i 0.171455 0.171455i −0.616163 0.787618i \(-0.711314\pi\)
0.787618 + 0.616163i \(0.211314\pi\)
\(908\) −142.018 142.018i −0.156408 0.156408i
\(909\) 175.464i 0.193029i
\(910\) 348.186 543.350i 0.382622 0.597088i
\(911\) 852.459 0.935740 0.467870 0.883797i \(-0.345021\pi\)
0.467870 + 0.883797i \(0.345021\pi\)
\(912\) 15.0026 15.0026i 0.0164502 0.0164502i
\(913\) 364.581 + 364.581i 0.399322 + 0.399322i
\(914\) 110.133i 0.120496i
\(915\) −14.3198 9.17631i −0.0156501 0.0100288i
\(916\) −195.218 −0.213120
\(917\) 244.484 244.484i 0.266613 0.266613i
\(918\) 335.900 + 335.900i 0.365904 + 0.365904i
\(919\) 648.546i 0.705708i −0.935678 0.352854i \(-0.885211\pi\)
0.935678 0.352854i \(-0.114789\pi\)
\(920\) 14.5036 + 66.2544i 0.0157648 + 0.0720157i
\(921\) 207.132 0.224899
\(922\) −833.889 + 833.889i −0.904434 + 0.904434i
\(923\) −852.703 852.703i −0.923839 0.923839i
\(924\) 32.4358i 0.0351037i
\(925\) −245.992 + 664.839i −0.265937 + 0.718745i
\(926\) 50.1480 0.0541555
\(927\) 918.720 918.720i 0.991068 0.991068i
\(928\) 131.397 + 131.397i 0.141591 + 0.141591i
\(929\) 1006.77i 1.08371i −0.840472 0.541855i \(-0.817722\pi\)
0.840472 0.541855i \(-0.182278\pi\)
\(930\) −160.672 + 35.1724i −0.172766 + 0.0378198i
\(931\) −152.541 −0.163847
\(932\) −187.406 + 187.406i −0.201080 + 0.201080i
\(933\) 52.5014 + 52.5014i 0.0562716 + 0.0562716i
\(934\) 10.7834i 0.0115454i
\(935\) −233.400 + 364.225i −0.249626 + 0.389546i
\(936\) −432.972 −0.462577
\(937\) −926.870 + 926.870i −0.989189 + 0.989189i −0.999942 0.0107534i \(-0.996577\pi\)
0.0107534 + 0.999942i \(0.496577\pi\)
\(938\) −483.335 483.335i −0.515282 0.515282i
\(939\) 429.116i 0.456992i
\(940\) −397.291 254.589i −0.422650 0.270839i
\(941\) −482.722 −0.512989 −0.256494 0.966546i \(-0.582567\pi\)
−0.256494 + 0.966546i \(0.582567\pi\)
\(942\) −139.097 + 139.097i −0.147662 + 0.147662i
\(943\) 59.4090 + 59.4090i 0.0630000 + 0.0630000i
\(944\) 115.678i 0.122540i
\(945\) −78.2141 357.292i −0.0827662 0.378087i
\(946\) 203.589 0.215210
\(947\) 97.7843 97.7843i 0.103257 0.103257i −0.653591 0.756848i \(-0.726738\pi\)
0.756848 + 0.653591i \(0.226738\pi\)
\(948\) 75.7546 + 75.7546i 0.0799099 + 0.0799099i
\(949\) 1370.59i 1.44424i
\(950\) −204.332 75.6032i −0.215086 0.0795823i
\(951\) −97.1174 −0.102121
\(952\) 222.671 222.671i 0.233898 0.233898i
\(953\) −1062.06 1062.06i −1.11444 1.11444i −0.992543 0.121895i \(-0.961103\pi\)
−0.121895 0.992543i \(-0.538897\pi\)
\(954\) 704.714i 0.738694i
\(955\) −498.092 + 109.036i −0.521562 + 0.114174i
\(956\) 459.753 0.480913
\(957\) 76.5040 76.5040i 0.0799415 0.0799415i
\(958\) −272.405 272.405i −0.284348 0.284348i
\(959\) 629.041i 0.655934i
\(960\) −18.5764 + 28.9888i −0.0193504 + 0.0301967i
\(961\) −230.731 −0.240095
\(962\) −525.558 + 525.558i −0.546318 + 0.546318i
\(963\) −364.461 364.461i −0.378465 0.378465i
\(964\) 821.795i 0.852484i
\(965\) 1274.06 + 816.433i 1.32027 + 0.846045i
\(966\) −28.7461 −0.0297578
\(967\) −1144.22 + 1144.22i −1.18327 + 1.18327i −0.204378 + 0.978892i \(0.565517\pi\)
−0.978892 + 0.204378i \(0.934483\pi\)
\(968\) −212.717 212.717i −0.219749 0.219749i
\(969\) 119.932i 0.123769i
\(970\) 43.1423 + 197.080i 0.0444766 + 0.203175i
\(971\) −950.040 −0.978414 −0.489207 0.872168i \(-0.662714\pi\)
−0.489207 + 0.872168i \(0.662714\pi\)
\(972\) −264.002 + 264.002i −0.271607 + 0.271607i
\(973\) 122.344 + 122.344i 0.125739 + 0.125739i
\(974\) 687.087i 0.705428i
\(975\) −166.634 362.365i −0.170907 0.371656i
\(976\) 15.8072 0.0161959
\(977\) −188.141 + 188.141i −0.192570 + 0.192570i −0.796806 0.604236i \(-0.793479\pi\)
0.604236 + 0.796806i \(0.293479\pi\)
\(978\) −244.021 244.021i −0.249510 0.249510i
\(979\) 503.314i 0.514110i
\(980\) 241.813 52.9348i 0.246748 0.0540151i
\(981\) 470.387 0.479498
\(982\) 490.578 490.578i 0.499570 0.499570i
\(983\) −351.121 351.121i −0.357194 0.357194i 0.505584 0.862778i \(-0.331277\pi\)
−0.862778 + 0.505584i \(0.831277\pi\)
\(984\) 42.6508i 0.0433443i
\(985\) −713.430 + 1113.32i −0.724295 + 1.13027i
\(986\) −1050.40 −1.06531
\(987\) 141.417 141.417i 0.143280 0.143280i
\(988\) −161.525 161.525i −0.163487 0.163487i
\(989\) 180.430i 0.182436i
\(990\) −188.150 120.569i −0.190051 0.121787i
\(991\) −1558.95 −1.57311 −0.786555 0.617520i \(-0.788137\pi\)
−0.786555 + 0.617520i \(0.788137\pi\)
\(992\) 108.094 108.094i 0.108966 0.108966i
\(993\) −74.8908 74.8908i −0.0754187 0.0754187i
\(994\) 453.071i 0.455806i
\(995\) 391.268 + 1787.36i 0.393234 + 1.79634i
\(996\) −231.965 −0.232897
\(997\) −947.149 + 947.149i −0.949999 + 0.949999i −0.998808 0.0488095i \(-0.984457\pi\)
0.0488095 + 0.998808i \(0.484457\pi\)
\(998\) 668.332 + 668.332i 0.669672 + 0.669672i
\(999\) 421.245i 0.421667i
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.a.93.6 yes 20
5.2 odd 4 inner 230.3.f.a.47.6 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.3.f.a.47.6 20 5.2 odd 4 inner
230.3.f.a.93.6 yes 20 1.1 even 1 trivial