Properties

Label 1155.2.c.f.694.4
Level $1155$
Weight $2$
Character 1155.694
Analytic conductor $9.223$
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] = [1155,2,Mod(694,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.694");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + 22984 x^{4} + 3428 x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 694.4
Root \(-2.28323i\) of defining polynomial
Character \(\chi\) \(=\) 1155.694
Dual form 1155.2.c.f.694.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.28323i q^{2} -1.00000i q^{3} -3.21315 q^{4} +(-2.23363 - 0.104355i) q^{5} -2.28323 q^{6} -1.00000i q^{7} +2.76990i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-2.28323i q^{2} -1.00000i q^{3} -3.21315 q^{4} +(-2.23363 - 0.104355i) q^{5} -2.28323 q^{6} -1.00000i q^{7} +2.76990i q^{8} -1.00000 q^{9} +(-0.238267 + 5.09990i) q^{10} +1.00000 q^{11} +3.21315i q^{12} +4.08903i q^{13} -2.28323 q^{14} +(-0.104355 + 2.23363i) q^{15} -0.101977 q^{16} +0.333296i q^{17} +2.28323i q^{18} -4.72571 q^{19} +(7.17699 + 0.335308i) q^{20} -1.00000 q^{21} -2.28323i q^{22} +7.98665i q^{23} +2.76990 q^{24} +(4.97822 + 0.466182i) q^{25} +9.33621 q^{26} +1.00000i q^{27} +3.21315i q^{28} +0.373782 q^{29} +(5.09990 + 0.238267i) q^{30} -9.24196 q^{31} +5.77263i q^{32} -1.00000i q^{33} +0.760993 q^{34} +(-0.104355 + 2.23363i) q^{35} +3.21315 q^{36} +3.51370i q^{37} +10.7899i q^{38} +4.08903 q^{39} +(0.289053 - 6.18693i) q^{40} +7.35561 q^{41} +2.28323i q^{42} -2.50440i q^{43} -3.21315 q^{44} +(2.23363 + 0.104355i) q^{45} +18.2354 q^{46} -11.9625i q^{47} +0.101977i q^{48} -1.00000 q^{49} +(1.06440 - 11.3664i) q^{50} +0.333296 q^{51} -13.1387i q^{52} -12.8762i q^{53} +2.28323 q^{54} +(-2.23363 - 0.104355i) q^{55} +2.76990 q^{56} +4.72571i q^{57} -0.853432i q^{58} +2.46158 q^{59} +(0.335308 - 7.17699i) q^{60} -8.83037 q^{61} +21.1015i q^{62} +1.00000i q^{63} +12.9763 q^{64} +(0.426711 - 9.13339i) q^{65} -2.28323 q^{66} +11.1473i q^{67} -1.07093i q^{68} +7.98665 q^{69} +(5.09990 + 0.238267i) q^{70} +13.7980 q^{71} -2.76990i q^{72} +8.53510i q^{73} +8.02260 q^{74} +(0.466182 - 4.97822i) q^{75} +15.1844 q^{76} -1.00000i q^{77} -9.33621i q^{78} -6.95125 q^{79} +(0.227780 + 0.0106419i) q^{80} +1.00000 q^{81} -16.7946i q^{82} +9.02465i q^{83} +3.21315 q^{84} +(0.0347812 - 0.744461i) q^{85} -5.71812 q^{86} -0.373782i q^{87} +2.76990i q^{88} -17.9041 q^{89} +(0.238267 - 5.09990i) q^{90} +4.08903 q^{91} -25.6623i q^{92} +9.24196i q^{93} -27.3131 q^{94} +(10.5555 + 0.493152i) q^{95} +5.77263 q^{96} -7.95736i q^{97} +2.28323i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.28323i 1.61449i −0.590217 0.807244i \(-0.700958\pi\)
0.590217 0.807244i \(-0.299042\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −3.21315 −1.60657
\(5\) −2.23363 0.104355i −0.998910 0.0466690i
\(6\) −2.28323 −0.932125
\(7\) 1.00000i 0.377964i
\(8\) 2.76990i 0.979307i
\(9\) −1.00000 −0.333333
\(10\) −0.238267 + 5.09990i −0.0753466 + 1.61273i
\(11\) 1.00000 0.301511
\(12\) 3.21315i 0.927556i
\(13\) 4.08903i 1.13409i 0.823686 + 0.567047i \(0.191914\pi\)
−0.823686 + 0.567047i \(0.808086\pi\)
\(14\) −2.28323 −0.610219
\(15\) −0.104355 + 2.23363i −0.0269444 + 0.576721i
\(16\) −0.101977 −0.0254944
\(17\) 0.333296i 0.0808362i 0.999183 + 0.0404181i \(0.0128690\pi\)
−0.999183 + 0.0404181i \(0.987131\pi\)
\(18\) 2.28323i 0.538163i
\(19\) −4.72571 −1.08415 −0.542076 0.840330i \(-0.682361\pi\)
−0.542076 + 0.840330i \(0.682361\pi\)
\(20\) 7.17699 + 0.335308i 1.60482 + 0.0749772i
\(21\) −1.00000 −0.218218
\(22\) 2.28323i 0.486787i
\(23\) 7.98665i 1.66533i 0.553776 + 0.832666i \(0.313186\pi\)
−0.553776 + 0.832666i \(0.686814\pi\)
\(24\) 2.76990 0.565403
\(25\) 4.97822 + 0.466182i 0.995644 + 0.0932363i
\(26\) 9.33621 1.83098
\(27\) 1.00000i 0.192450i
\(28\) 3.21315i 0.607228i
\(29\) 0.373782 0.0694096 0.0347048 0.999398i \(-0.488951\pi\)
0.0347048 + 0.999398i \(0.488951\pi\)
\(30\) 5.09990 + 0.238267i 0.931110 + 0.0435014i
\(31\) −9.24196 −1.65990 −0.829952 0.557835i \(-0.811632\pi\)
−0.829952 + 0.557835i \(0.811632\pi\)
\(32\) 5.77263i 1.02047i
\(33\) 1.00000i 0.174078i
\(34\) 0.760993 0.130509
\(35\) −0.104355 + 2.23363i −0.0176392 + 0.377553i
\(36\) 3.21315 0.535525
\(37\) 3.51370i 0.577649i 0.957382 + 0.288825i \(0.0932645\pi\)
−0.957382 + 0.288825i \(0.906736\pi\)
\(38\) 10.7899i 1.75035i
\(39\) 4.08903 0.654769
\(40\) 0.289053 6.18693i 0.0457033 0.978240i
\(41\) 7.35561 1.14875 0.574377 0.818591i \(-0.305244\pi\)
0.574377 + 0.818591i \(0.305244\pi\)
\(42\) 2.28323i 0.352310i
\(43\) 2.50440i 0.381917i −0.981598 0.190959i \(-0.938840\pi\)
0.981598 0.190959i \(-0.0611596\pi\)
\(44\) −3.21315 −0.484400
\(45\) 2.23363 + 0.104355i 0.332970 + 0.0155563i
\(46\) 18.2354 2.68866
\(47\) 11.9625i 1.74490i −0.488699 0.872452i \(-0.662529\pi\)
0.488699 0.872452i \(-0.337471\pi\)
\(48\) 0.101977i 0.0147192i
\(49\) −1.00000 −0.142857
\(50\) 1.06440 11.3664i 0.150529 1.60746i
\(51\) 0.333296 0.0466708
\(52\) 13.1387i 1.82200i
\(53\) 12.8762i 1.76868i −0.466842 0.884341i \(-0.654608\pi\)
0.466842 0.884341i \(-0.345392\pi\)
\(54\) 2.28323 0.310708
\(55\) −2.23363 0.104355i −0.301183 0.0140712i
\(56\) 2.76990 0.370143
\(57\) 4.72571i 0.625935i
\(58\) 0.853432i 0.112061i
\(59\) 2.46158 0.320470 0.160235 0.987079i \(-0.448775\pi\)
0.160235 + 0.987079i \(0.448775\pi\)
\(60\) 0.335308 7.17699i 0.0432881 0.926545i
\(61\) −8.83037 −1.13061 −0.565306 0.824881i \(-0.691242\pi\)
−0.565306 + 0.824881i \(0.691242\pi\)
\(62\) 21.1015i 2.67990i
\(63\) 1.00000i 0.125988i
\(64\) 12.9763 1.62204
\(65\) 0.426711 9.13339i 0.0529270 1.13286i
\(66\) −2.28323 −0.281046
\(67\) 11.1473i 1.36186i 0.732350 + 0.680929i \(0.238424\pi\)
−0.732350 + 0.680929i \(0.761576\pi\)
\(68\) 1.07093i 0.129869i
\(69\) 7.98665 0.961480
\(70\) 5.09990 + 0.238267i 0.609554 + 0.0284783i
\(71\) 13.7980 1.63752 0.818761 0.574134i \(-0.194661\pi\)
0.818761 + 0.574134i \(0.194661\pi\)
\(72\) 2.76990i 0.326436i
\(73\) 8.53510i 0.998958i 0.866326 + 0.499479i \(0.166475\pi\)
−0.866326 + 0.499479i \(0.833525\pi\)
\(74\) 8.02260 0.932608
\(75\) 0.466182 4.97822i 0.0538300 0.574835i
\(76\) 15.1844 1.74177
\(77\) 1.00000i 0.113961i
\(78\) 9.33621i 1.05712i
\(79\) −6.95125 −0.782077 −0.391039 0.920374i \(-0.627884\pi\)
−0.391039 + 0.920374i \(0.627884\pi\)
\(80\) 0.227780 + 0.0106419i 0.0254666 + 0.00118980i
\(81\) 1.00000 0.111111
\(82\) 16.7946i 1.85465i
\(83\) 9.02465i 0.990584i 0.868727 + 0.495292i \(0.164939\pi\)
−0.868727 + 0.495292i \(0.835061\pi\)
\(84\) 3.21315 0.350583
\(85\) 0.0347812 0.744461i 0.00377255 0.0807482i
\(86\) −5.71812 −0.616601
\(87\) 0.373782i 0.0400737i
\(88\) 2.76990i 0.295272i
\(89\) −17.9041 −1.89783 −0.948915 0.315531i \(-0.897817\pi\)
−0.948915 + 0.315531i \(0.897817\pi\)
\(90\) 0.238267 5.09990i 0.0251155 0.537577i
\(91\) 4.08903 0.428647
\(92\) 25.6623i 2.67548i
\(93\) 9.24196i 0.958346i
\(94\) −27.3131 −2.81713
\(95\) 10.5555 + 0.493152i 1.08297 + 0.0505963i
\(96\) 5.77263 0.589167
\(97\) 7.95736i 0.807948i −0.914771 0.403974i \(-0.867629\pi\)
0.914771 0.403974i \(-0.132371\pi\)
\(98\) 2.28323i 0.230641i
\(99\) −1.00000 −0.100504
\(100\) −15.9958 1.49791i −1.59958 0.149791i
\(101\) 7.33584 0.729943 0.364972 0.931019i \(-0.381079\pi\)
0.364972 + 0.931019i \(0.381079\pi\)
\(102\) 0.760993i 0.0753495i
\(103\) 16.6422i 1.63980i 0.572505 + 0.819901i \(0.305972\pi\)
−0.572505 + 0.819901i \(0.694028\pi\)
\(104\) −11.3262 −1.11063
\(105\) 2.23363 + 0.104355i 0.217980 + 0.0101840i
\(106\) −29.3993 −2.85552
\(107\) 17.7684i 1.71774i 0.512196 + 0.858869i \(0.328832\pi\)
−0.512196 + 0.858869i \(0.671168\pi\)
\(108\) 3.21315i 0.309185i
\(109\) −14.9455 −1.43152 −0.715760 0.698347i \(-0.753919\pi\)
−0.715760 + 0.698347i \(0.753919\pi\)
\(110\) −0.238267 + 5.09990i −0.0227179 + 0.486256i
\(111\) 3.51370 0.333506
\(112\) 0.101977i 0.00963596i
\(113\) 4.90620i 0.461537i 0.973009 + 0.230768i \(0.0741240\pi\)
−0.973009 + 0.230768i \(0.925876\pi\)
\(114\) 10.7899 1.01057
\(115\) 0.833447 17.8392i 0.0777194 1.66352i
\(116\) −1.20102 −0.111512
\(117\) 4.08903i 0.378031i
\(118\) 5.62036i 0.517396i
\(119\) 0.333296 0.0305532
\(120\) −6.18693 0.289053i −0.564787 0.0263868i
\(121\) 1.00000 0.0909091
\(122\) 20.1618i 1.82536i
\(123\) 7.35561i 0.663233i
\(124\) 29.6958 2.66676
\(125\) −11.0709 1.56078i −0.990208 0.139600i
\(126\) 2.28323 0.203406
\(127\) 6.50360i 0.577101i −0.957465 0.288551i \(-0.906827\pi\)
0.957465 0.288551i \(-0.0931734\pi\)
\(128\) 18.0826i 1.59830i
\(129\) −2.50440 −0.220500
\(130\) −20.8537 0.974281i −1.82899 0.0854501i
\(131\) −8.42573 −0.736159 −0.368080 0.929794i \(-0.619985\pi\)
−0.368080 + 0.929794i \(0.619985\pi\)
\(132\) 3.21315i 0.279669i
\(133\) 4.72571i 0.409771i
\(134\) 25.4518 2.19870
\(135\) 0.104355 2.23363i 0.00898145 0.192240i
\(136\) −0.923197 −0.0791635
\(137\) 13.5898i 1.16106i 0.814240 + 0.580529i \(0.197154\pi\)
−0.814240 + 0.580529i \(0.802846\pi\)
\(138\) 18.2354i 1.55230i
\(139\) −11.0612 −0.938196 −0.469098 0.883146i \(-0.655421\pi\)
−0.469098 + 0.883146i \(0.655421\pi\)
\(140\) 0.335308 7.17699i 0.0283387 0.606566i
\(141\) −11.9625 −1.00742
\(142\) 31.5041i 2.64376i
\(143\) 4.08903i 0.341942i
\(144\) 0.101977 0.00849812
\(145\) −0.834892 0.0390061i −0.0693340 0.00323928i
\(146\) 19.4876 1.61281
\(147\) 1.00000i 0.0824786i
\(148\) 11.2900i 0.928036i
\(149\) −18.5727 −1.52153 −0.760766 0.649026i \(-0.775177\pi\)
−0.760766 + 0.649026i \(0.775177\pi\)
\(150\) −11.3664 1.06440i −0.928065 0.0869079i
\(151\) −3.07826 −0.250505 −0.125253 0.992125i \(-0.539974\pi\)
−0.125253 + 0.992125i \(0.539974\pi\)
\(152\) 13.0897i 1.06172i
\(153\) 0.333296i 0.0269454i
\(154\) −2.28323 −0.183988
\(155\) 20.6431 + 0.964445i 1.65810 + 0.0774661i
\(156\) −13.1387 −1.05194
\(157\) 4.25537i 0.339616i 0.985477 + 0.169808i \(0.0543147\pi\)
−0.985477 + 0.169808i \(0.945685\pi\)
\(158\) 15.8713i 1.26265i
\(159\) −12.8762 −1.02115
\(160\) 0.602404 12.8939i 0.0476242 1.01936i
\(161\) 7.98665 0.629436
\(162\) 2.28323i 0.179388i
\(163\) 13.7375i 1.07601i 0.842943 + 0.538003i \(0.180821\pi\)
−0.842943 + 0.538003i \(0.819179\pi\)
\(164\) −23.6347 −1.84556
\(165\) −0.104355 + 2.23363i −0.00812403 + 0.173888i
\(166\) 20.6054 1.59929
\(167\) 10.1244i 0.783447i 0.920083 + 0.391724i \(0.128121\pi\)
−0.920083 + 0.391724i \(0.871879\pi\)
\(168\) 2.76990i 0.213702i
\(169\) −3.72018 −0.286168
\(170\) −1.69978 0.0794135i −0.130367 0.00609073i
\(171\) 4.72571 0.361384
\(172\) 8.04700i 0.613578i
\(173\) 24.2008i 1.83995i −0.391977 0.919975i \(-0.628209\pi\)
0.391977 0.919975i \(-0.371791\pi\)
\(174\) −0.853432 −0.0646985
\(175\) 0.466182 4.97822i 0.0352400 0.376318i
\(176\) −0.101977 −0.00768684
\(177\) 2.46158i 0.185024i
\(178\) 40.8792i 3.06403i
\(179\) 3.90862 0.292144 0.146072 0.989274i \(-0.453337\pi\)
0.146072 + 0.989274i \(0.453337\pi\)
\(180\) −7.17699 0.335308i −0.534941 0.0249924i
\(181\) −7.76620 −0.577257 −0.288628 0.957441i \(-0.593199\pi\)
−0.288628 + 0.957441i \(0.593199\pi\)
\(182\) 9.33621i 0.692046i
\(183\) 8.83037i 0.652759i
\(184\) −22.1222 −1.63087
\(185\) 0.366673 7.84832i 0.0269583 0.577020i
\(186\) 21.1015 1.54724
\(187\) 0.333296i 0.0243730i
\(188\) 38.4372i 2.80332i
\(189\) 1.00000 0.0727393
\(190\) 1.12598 24.1006i 0.0816871 1.74844i
\(191\) −6.99980 −0.506488 −0.253244 0.967402i \(-0.581498\pi\)
−0.253244 + 0.967402i \(0.581498\pi\)
\(192\) 12.9763i 0.936484i
\(193\) 8.84126i 0.636408i −0.948022 0.318204i \(-0.896920\pi\)
0.948022 0.318204i \(-0.103080\pi\)
\(194\) −18.1685 −1.30442
\(195\) −9.13339 0.426711i −0.654056 0.0305574i
\(196\) 3.21315 0.229511
\(197\) 7.51103i 0.535139i −0.963539 0.267569i \(-0.913780\pi\)
0.963539 0.267569i \(-0.0862204\pi\)
\(198\) 2.28323i 0.162262i
\(199\) −21.5564 −1.52810 −0.764048 0.645160i \(-0.776791\pi\)
−0.764048 + 0.645160i \(0.776791\pi\)
\(200\) −1.29128 + 13.7892i −0.0913069 + 0.975041i
\(201\) 11.1473 0.786269
\(202\) 16.7494i 1.17849i
\(203\) 0.373782i 0.0262344i
\(204\) −1.07093 −0.0749801
\(205\) −16.4297 0.767595i −1.14750 0.0536112i
\(206\) 37.9980 2.64744
\(207\) 7.98665i 0.555111i
\(208\) 0.416989i 0.0289130i
\(209\) −4.72571 −0.326884
\(210\) 0.238267 5.09990i 0.0164420 0.351926i
\(211\) 4.98337 0.343069 0.171535 0.985178i \(-0.445127\pi\)
0.171535 + 0.985178i \(0.445127\pi\)
\(212\) 41.3731i 2.84152i
\(213\) 13.7980i 0.945424i
\(214\) 40.5694 2.77327
\(215\) −0.261347 + 5.59390i −0.0178237 + 0.381501i
\(216\) −2.76990 −0.188468
\(217\) 9.24196i 0.627385i
\(218\) 34.1240i 2.31117i
\(219\) 8.53510 0.576749
\(220\) 7.17699 + 0.335308i 0.483872 + 0.0226065i
\(221\) −1.36286 −0.0916759
\(222\) 8.02260i 0.538442i
\(223\) 1.31258i 0.0878967i 0.999034 + 0.0439484i \(0.0139937\pi\)
−0.999034 + 0.0439484i \(0.986006\pi\)
\(224\) 5.77263 0.385700
\(225\) −4.97822 0.466182i −0.331881 0.0310788i
\(226\) 11.2020 0.745146
\(227\) 24.4941i 1.62573i 0.582451 + 0.812866i \(0.302094\pi\)
−0.582451 + 0.812866i \(0.697906\pi\)
\(228\) 15.1844i 1.00561i
\(229\) 17.6904 1.16901 0.584506 0.811390i \(-0.301288\pi\)
0.584506 + 0.811390i \(0.301288\pi\)
\(230\) −40.7311 1.90295i −2.68573 0.125477i
\(231\) −1.00000 −0.0657952
\(232\) 1.03534i 0.0679733i
\(233\) 15.2475i 0.998898i −0.866343 0.499449i \(-0.833536\pi\)
0.866343 0.499449i \(-0.166464\pi\)
\(234\) −9.33621 −0.610327
\(235\) −1.24834 + 26.7197i −0.0814330 + 1.74300i
\(236\) −7.90942 −0.514859
\(237\) 6.95125i 0.451532i
\(238\) 0.760993i 0.0493278i
\(239\) 6.67755 0.431935 0.215967 0.976401i \(-0.430710\pi\)
0.215967 + 0.976401i \(0.430710\pi\)
\(240\) 0.0106419 0.227780i 0.000686930 0.0147031i
\(241\) 4.97410 0.320410 0.160205 0.987084i \(-0.448785\pi\)
0.160205 + 0.987084i \(0.448785\pi\)
\(242\) 2.28323i 0.146772i
\(243\) 1.00000i 0.0641500i
\(244\) 28.3733 1.81641
\(245\) 2.23363 + 0.104355i 0.142701 + 0.00666700i
\(246\) −16.7946 −1.07078
\(247\) 19.3236i 1.22953i
\(248\) 25.5993i 1.62556i
\(249\) 9.02465 0.571914
\(250\) −3.56362 + 25.2773i −0.225383 + 1.59868i
\(251\) −10.7702 −0.679810 −0.339905 0.940460i \(-0.610395\pi\)
−0.339905 + 0.940460i \(0.610395\pi\)
\(252\) 3.21315i 0.202409i
\(253\) 7.98665i 0.502116i
\(254\) −14.8492 −0.931724
\(255\) −0.744461 0.0347812i −0.0466200 0.00217808i
\(256\) −15.3343 −0.958391
\(257\) 3.36008i 0.209596i 0.994494 + 0.104798i \(0.0334196\pi\)
−0.994494 + 0.104798i \(0.966580\pi\)
\(258\) 5.71812i 0.355995i
\(259\) 3.51370 0.218331
\(260\) −1.37109 + 29.3469i −0.0850312 + 1.82002i
\(261\) −0.373782 −0.0231365
\(262\) 19.2379i 1.18852i
\(263\) 16.8761i 1.04063i −0.853975 0.520313i \(-0.825815\pi\)
0.853975 0.520313i \(-0.174185\pi\)
\(264\) 2.76990 0.170475
\(265\) −1.34370 + 28.7607i −0.0825426 + 1.76675i
\(266\) 10.7899 0.661570
\(267\) 17.9041i 1.09571i
\(268\) 35.8179i 2.18792i
\(269\) −13.5808 −0.828039 −0.414019 0.910268i \(-0.635875\pi\)
−0.414019 + 0.910268i \(0.635875\pi\)
\(270\) −5.09990 0.238267i −0.310370 0.0145005i
\(271\) 5.53292 0.336101 0.168050 0.985778i \(-0.446253\pi\)
0.168050 + 0.985778i \(0.446253\pi\)
\(272\) 0.0339887i 0.00206087i
\(273\) 4.08903i 0.247479i
\(274\) 31.0287 1.87451
\(275\) 4.97822 + 0.466182i 0.300198 + 0.0281118i
\(276\) −25.6623 −1.54469
\(277\) 6.03226i 0.362444i −0.983442 0.181222i \(-0.941995\pi\)
0.983442 0.181222i \(-0.0580052\pi\)
\(278\) 25.2552i 1.51471i
\(279\) 9.24196 0.553301
\(280\) −6.18693 0.289053i −0.369740 0.0172742i
\(281\) 9.15740 0.546285 0.273142 0.961974i \(-0.411937\pi\)
0.273142 + 0.961974i \(0.411937\pi\)
\(282\) 27.3131i 1.62647i
\(283\) 6.85266i 0.407348i −0.979039 0.203674i \(-0.934712\pi\)
0.979039 0.203674i \(-0.0652883\pi\)
\(284\) −44.3351 −2.63080
\(285\) 0.493152 10.5555i 0.0292118 0.625253i
\(286\) 9.33621 0.552062
\(287\) 7.35561i 0.434188i
\(288\) 5.77263i 0.340156i
\(289\) 16.8889 0.993466
\(290\) −0.0890599 + 1.90625i −0.00522978 + 0.111939i
\(291\) −7.95736 −0.466469
\(292\) 27.4245i 1.60490i
\(293\) 8.34763i 0.487674i 0.969816 + 0.243837i \(0.0784061\pi\)
−0.969816 + 0.243837i \(0.921594\pi\)
\(294\) 2.28323 0.133161
\(295\) −5.49826 0.256878i −0.320121 0.0149560i
\(296\) −9.73260 −0.565696
\(297\) 1.00000i 0.0580259i
\(298\) 42.4057i 2.45650i
\(299\) −32.6577 −1.88864
\(300\) −1.49791 + 15.9958i −0.0864819 + 0.923515i
\(301\) −2.50440 −0.144351
\(302\) 7.02838i 0.404438i
\(303\) 7.33584i 0.421433i
\(304\) 0.481916 0.0276398
\(305\) 19.7238 + 0.921493i 1.12938 + 0.0527646i
\(306\) −0.760993 −0.0435031
\(307\) 4.85539i 0.277112i 0.990355 + 0.138556i \(0.0442461\pi\)
−0.990355 + 0.138556i \(0.955754\pi\)
\(308\) 3.21315i 0.183086i
\(309\) 16.6422 0.946741
\(310\) 2.20205 47.1330i 0.125068 2.67698i
\(311\) −31.3660 −1.77861 −0.889303 0.457319i \(-0.848810\pi\)
−0.889303 + 0.457319i \(0.848810\pi\)
\(312\) 11.3262i 0.641220i
\(313\) 10.7766i 0.609129i 0.952492 + 0.304564i \(0.0985109\pi\)
−0.952492 + 0.304564i \(0.901489\pi\)
\(314\) 9.71600 0.548306
\(315\) 0.104355 2.23363i 0.00587974 0.125851i
\(316\) 22.3354 1.25646
\(317\) 8.66340i 0.486585i 0.969953 + 0.243293i \(0.0782275\pi\)
−0.969953 + 0.243293i \(0.921772\pi\)
\(318\) 29.3993i 1.64863i
\(319\) 0.373782 0.0209278
\(320\) −28.9843 1.35414i −1.62027 0.0756989i
\(321\) 17.7684 0.991736
\(322\) 18.2354i 1.01622i
\(323\) 1.57506i 0.0876388i
\(324\) −3.21315 −0.178508
\(325\) −1.90623 + 20.3561i −0.105739 + 1.12915i
\(326\) 31.3660 1.73720
\(327\) 14.9455i 0.826488i
\(328\) 20.3743i 1.12498i
\(329\) −11.9625 −0.659512
\(330\) 5.09990 + 0.238267i 0.280740 + 0.0131162i
\(331\) 2.72257 0.149646 0.0748230 0.997197i \(-0.476161\pi\)
0.0748230 + 0.997197i \(0.476161\pi\)
\(332\) 28.9975i 1.59145i
\(333\) 3.51370i 0.192550i
\(334\) 23.1163 1.26487
\(335\) 1.16328 24.8989i 0.0635565 1.36037i
\(336\) 0.101977 0.00556333
\(337\) 10.2202i 0.556727i −0.960476 0.278364i \(-0.910208\pi\)
0.960476 0.278364i \(-0.0897920\pi\)
\(338\) 8.49404i 0.462015i
\(339\) 4.90620 0.266468
\(340\) −0.111757 + 2.39206i −0.00606088 + 0.129728i
\(341\) −9.24196 −0.500480
\(342\) 10.7899i 0.583450i
\(343\) 1.00000i 0.0539949i
\(344\) 6.93692 0.374014
\(345\) −17.8392 0.833447i −0.960432 0.0448713i
\(346\) −55.2559 −2.97058
\(347\) 5.99829i 0.322005i 0.986954 + 0.161002i \(0.0514727\pi\)
−0.986954 + 0.161002i \(0.948527\pi\)
\(348\) 1.20102i 0.0643813i
\(349\) −11.4244 −0.611533 −0.305767 0.952106i \(-0.598913\pi\)
−0.305767 + 0.952106i \(0.598913\pi\)
\(350\) −11.3664 1.06440i −0.607561 0.0568946i
\(351\) −4.08903 −0.218256
\(352\) 5.77263i 0.307682i
\(353\) 3.54554i 0.188710i 0.995539 + 0.0943551i \(0.0300789\pi\)
−0.995539 + 0.0943551i \(0.969921\pi\)
\(354\) −5.62036 −0.298719
\(355\) −30.8197 1.43989i −1.63574 0.0764216i
\(356\) 57.5285 3.04900
\(357\) 0.333296i 0.0176399i
\(358\) 8.92429i 0.471664i
\(359\) 26.3556 1.39099 0.695497 0.718529i \(-0.255184\pi\)
0.695497 + 0.718529i \(0.255184\pi\)
\(360\) −0.289053 + 6.18693i −0.0152344 + 0.326080i
\(361\) 3.33232 0.175385
\(362\) 17.7320i 0.931975i
\(363\) 1.00000i 0.0524864i
\(364\) −13.1387 −0.688653
\(365\) 0.890681 19.0643i 0.0466204 0.997869i
\(366\) 20.1618 1.05387
\(367\) 18.6763i 0.974897i −0.873152 0.487449i \(-0.837928\pi\)
0.873152 0.487449i \(-0.162072\pi\)
\(368\) 0.814458i 0.0424566i
\(369\) −7.35561 −0.382918
\(370\) −17.9195 0.837199i −0.931592 0.0435239i
\(371\) −12.8762 −0.668499
\(372\) 29.6958i 1.53965i
\(373\) 23.4194i 1.21261i −0.795231 0.606307i \(-0.792650\pi\)
0.795231 0.606307i \(-0.207350\pi\)
\(374\) 0.760993 0.0393500
\(375\) −1.56078 + 11.0709i −0.0805984 + 0.571697i
\(376\) 33.1348 1.70880
\(377\) 1.52841i 0.0787170i
\(378\) 2.28323i 0.117437i
\(379\) −29.5437 −1.51756 −0.758779 0.651349i \(-0.774204\pi\)
−0.758779 + 0.651349i \(0.774204\pi\)
\(380\) −33.9164 1.58457i −1.73987 0.0812867i
\(381\) −6.50360 −0.333190
\(382\) 15.9822i 0.817719i
\(383\) 6.00131i 0.306652i −0.988176 0.153326i \(-0.951001\pi\)
0.988176 0.153326i \(-0.0489985\pi\)
\(384\) −18.0826 −0.922776
\(385\) −0.104355 + 2.23363i −0.00531843 + 0.113836i
\(386\) −20.1866 −1.02747
\(387\) 2.50440i 0.127306i
\(388\) 25.5682i 1.29803i
\(389\) 22.6232 1.14704 0.573520 0.819192i \(-0.305577\pi\)
0.573520 + 0.819192i \(0.305577\pi\)
\(390\) −0.974281 + 20.8537i −0.0493346 + 1.05597i
\(391\) −2.66192 −0.134619
\(392\) 2.76990i 0.139901i
\(393\) 8.42573i 0.425022i
\(394\) −17.1494 −0.863975
\(395\) 15.5265 + 0.725398i 0.781225 + 0.0364988i
\(396\) 3.21315 0.161467
\(397\) 12.0631i 0.605428i 0.953081 + 0.302714i \(0.0978927\pi\)
−0.953081 + 0.302714i \(0.902107\pi\)
\(398\) 49.2183i 2.46709i
\(399\) 4.72571 0.236581
\(400\) −0.507666 0.0475400i −0.0253833 0.00237700i
\(401\) 1.19718 0.0597842 0.0298921 0.999553i \(-0.490484\pi\)
0.0298921 + 0.999553i \(0.490484\pi\)
\(402\) 25.4518i 1.26942i
\(403\) 37.7907i 1.88249i
\(404\) −23.5711 −1.17271
\(405\) −2.23363 0.104355i −0.110990 0.00518545i
\(406\) −0.853432 −0.0423551
\(407\) 3.51370i 0.174168i
\(408\) 0.923197i 0.0457050i
\(409\) 9.52123 0.470795 0.235397 0.971899i \(-0.424361\pi\)
0.235397 + 0.971899i \(0.424361\pi\)
\(410\) −1.75260 + 37.5129i −0.0865547 + 1.85263i
\(411\) 13.5898 0.670337
\(412\) 53.4738i 2.63446i
\(413\) 2.46158i 0.121126i
\(414\) −18.2354 −0.896220
\(415\) 0.941768 20.1577i 0.0462296 0.989505i
\(416\) −23.6045 −1.15730
\(417\) 11.0612i 0.541668i
\(418\) 10.7899i 0.527751i
\(419\) −22.1761 −1.08338 −0.541688 0.840580i \(-0.682215\pi\)
−0.541688 + 0.840580i \(0.682215\pi\)
\(420\) −7.17699 0.335308i −0.350201 0.0163614i
\(421\) 10.7062 0.521789 0.260895 0.965367i \(-0.415983\pi\)
0.260895 + 0.965367i \(0.415983\pi\)
\(422\) 11.3782i 0.553881i
\(423\) 11.9625i 0.581635i
\(424\) 35.6657 1.73208
\(425\) −0.155377 + 1.65922i −0.00753687 + 0.0804841i
\(426\) −31.5041 −1.52638
\(427\) 8.83037i 0.427331i
\(428\) 57.0925i 2.75967i
\(429\) 4.08903 0.197420
\(430\) 12.7722 + 0.596715i 0.615929 + 0.0287761i
\(431\) −23.5902 −1.13630 −0.568151 0.822924i \(-0.692341\pi\)
−0.568151 + 0.822924i \(0.692341\pi\)
\(432\) 0.101977i 0.00490639i
\(433\) 30.0656i 1.44486i 0.691445 + 0.722429i \(0.256975\pi\)
−0.691445 + 0.722429i \(0.743025\pi\)
\(434\) 21.1015 1.01291
\(435\) −0.0390061 + 0.834892i −0.00187020 + 0.0400300i
\(436\) 48.0221 2.29984
\(437\) 37.7426i 1.80547i
\(438\) 19.4876i 0.931154i
\(439\) −15.7721 −0.752764 −0.376382 0.926465i \(-0.622832\pi\)
−0.376382 + 0.926465i \(0.622832\pi\)
\(440\) 0.289053 6.18693i 0.0137801 0.294950i
\(441\) 1.00000 0.0476190
\(442\) 3.11172i 0.148010i
\(443\) 30.7895i 1.46285i −0.681919 0.731427i \(-0.738855\pi\)
0.681919 0.731427i \(-0.261145\pi\)
\(444\) −11.2900 −0.535802
\(445\) 39.9912 + 1.86838i 1.89576 + 0.0885699i
\(446\) 2.99692 0.141908
\(447\) 18.5727i 0.878457i
\(448\) 12.9763i 0.613073i
\(449\) 18.8430 0.889257 0.444628 0.895715i \(-0.353336\pi\)
0.444628 + 0.895715i \(0.353336\pi\)
\(450\) −1.06440 + 11.3664i −0.0501763 + 0.535819i
\(451\) 7.35561 0.346362
\(452\) 15.7644i 0.741493i
\(453\) 3.07826i 0.144629i
\(454\) 55.9258 2.62473
\(455\) −9.13339 0.426711i −0.428180 0.0200045i
\(456\) −13.0897 −0.612983
\(457\) 6.78391i 0.317338i −0.987332 0.158669i \(-0.949280\pi\)
0.987332 0.158669i \(-0.0507203\pi\)
\(458\) 40.3912i 1.88736i
\(459\) −0.333296 −0.0155569
\(460\) −2.67799 + 57.3201i −0.124862 + 2.67256i
\(461\) 3.24599 0.151181 0.0755905 0.997139i \(-0.475916\pi\)
0.0755905 + 0.997139i \(0.475916\pi\)
\(462\) 2.28323i 0.106226i
\(463\) 2.48973i 0.115708i 0.998325 + 0.0578538i \(0.0184257\pi\)
−0.998325 + 0.0578538i \(0.981574\pi\)
\(464\) −0.0381174 −0.00176955
\(465\) 0.964445 20.6431i 0.0447251 0.957302i
\(466\) −34.8136 −1.61271
\(467\) 11.1908i 0.517847i 0.965898 + 0.258923i \(0.0833677\pi\)
−0.965898 + 0.258923i \(0.916632\pi\)
\(468\) 13.1387i 0.607335i
\(469\) 11.1473 0.514734
\(470\) 61.0073 + 2.85026i 2.81406 + 0.131473i
\(471\) 4.25537 0.196077
\(472\) 6.81832i 0.313839i
\(473\) 2.50440i 0.115152i
\(474\) 15.8713 0.728994
\(475\) −23.5256 2.20304i −1.07943 0.101082i
\(476\) −1.07093 −0.0490860
\(477\) 12.8762i 0.589560i
\(478\) 15.2464i 0.697354i
\(479\) 24.2516 1.10808 0.554042 0.832489i \(-0.313085\pi\)
0.554042 + 0.832489i \(0.313085\pi\)
\(480\) −12.8939 0.602404i −0.588525 0.0274958i
\(481\) −14.3676 −0.655108
\(482\) 11.3570i 0.517298i
\(483\) 7.98665i 0.363405i
\(484\) −3.21315 −0.146052
\(485\) −0.830391 + 17.7738i −0.0377061 + 0.807067i
\(486\) −2.28323 −0.103569
\(487\) 17.1527i 0.777264i 0.921393 + 0.388632i \(0.127052\pi\)
−0.921393 + 0.388632i \(0.872948\pi\)
\(488\) 24.4592i 1.10722i
\(489\) 13.7375 0.621232
\(490\) 0.238267 5.09990i 0.0107638 0.230390i
\(491\) −31.9038 −1.43980 −0.719899 0.694079i \(-0.755812\pi\)
−0.719899 + 0.694079i \(0.755812\pi\)
\(492\) 23.6347i 1.06553i
\(493\) 0.124580i 0.00561081i
\(494\) −44.1202 −1.98506
\(495\) 2.23363 + 0.104355i 0.100394 + 0.00469041i
\(496\) 0.942471 0.0423182
\(497\) 13.7980i 0.618925i
\(498\) 20.6054i 0.923348i
\(499\) 21.3522 0.955858 0.477929 0.878399i \(-0.341388\pi\)
0.477929 + 0.878399i \(0.341388\pi\)
\(500\) 35.5723 + 5.01502i 1.59084 + 0.224278i
\(501\) 10.1244 0.452323
\(502\) 24.5909i 1.09755i
\(503\) 28.7233i 1.28071i −0.768079 0.640355i \(-0.778787\pi\)
0.768079 0.640355i \(-0.221213\pi\)
\(504\) −2.76990 −0.123381
\(505\) −16.3856 0.765532i −0.729148 0.0340657i
\(506\) 18.2354 0.810661
\(507\) 3.72018i 0.165219i
\(508\) 20.8970i 0.927156i
\(509\) −27.9961 −1.24091 −0.620453 0.784244i \(-0.713051\pi\)
−0.620453 + 0.784244i \(0.713051\pi\)
\(510\) −0.0794135 + 1.69978i −0.00351649 + 0.0752674i
\(511\) 8.53510 0.377571
\(512\) 1.15361i 0.0509830i
\(513\) 4.72571i 0.208645i
\(514\) 7.67183 0.338390
\(515\) 1.73670 37.1725i 0.0765280 1.63802i
\(516\) 8.04700 0.354249
\(517\) 11.9625i 0.526108i
\(518\) 8.02260i 0.352493i
\(519\) −24.2008 −1.06230
\(520\) 25.2986 + 1.18195i 1.10942 + 0.0518318i
\(521\) 31.1067 1.36281 0.681405 0.731907i \(-0.261369\pi\)
0.681405 + 0.731907i \(0.261369\pi\)
\(522\) 0.853432i 0.0373537i
\(523\) 2.20540i 0.0964354i −0.998837 0.0482177i \(-0.984646\pi\)
0.998837 0.0482177i \(-0.0153541\pi\)
\(524\) 27.0731 1.18269
\(525\) −4.97822 0.466182i −0.217267 0.0203458i
\(526\) −38.5321 −1.68008
\(527\) 3.08031i 0.134180i
\(528\) 0.101977i 0.00443800i
\(529\) −40.7866 −1.77333
\(530\) 65.6673 + 3.06797i 2.85240 + 0.133264i
\(531\) −2.46158 −0.106823
\(532\) 15.1844i 0.658327i
\(533\) 30.0773i 1.30279i
\(534\) 40.8792 1.76902
\(535\) 1.85422 39.6881i 0.0801651 1.71587i
\(536\) −30.8768 −1.33368
\(537\) 3.90862i 0.168670i
\(538\) 31.0082i 1.33686i
\(539\) −1.00000 −0.0430730
\(540\) −0.335308 + 7.17699i −0.0144294 + 0.308848i
\(541\) −7.33898 −0.315527 −0.157764 0.987477i \(-0.550428\pi\)
−0.157764 + 0.987477i \(0.550428\pi\)
\(542\) 12.6329i 0.542631i
\(543\) 7.76620i 0.333279i
\(544\) −1.92400 −0.0824907
\(545\) 33.3827 + 1.55964i 1.42996 + 0.0668076i
\(546\) −9.33621 −0.399553
\(547\) 19.4589i 0.832001i 0.909364 + 0.416001i \(0.136569\pi\)
−0.909364 + 0.416001i \(0.863431\pi\)
\(548\) 43.6661i 1.86532i
\(549\) 8.83037 0.376871
\(550\) 1.06440 11.3664i 0.0453862 0.484666i
\(551\) −1.76639 −0.0752506
\(552\) 22.1222i 0.941583i
\(553\) 6.95125i 0.295597i
\(554\) −13.7731 −0.585161
\(555\) −7.84832 0.366673i −0.333143 0.0155644i
\(556\) 35.5412 1.50728
\(557\) 4.79104i 0.203003i 0.994835 + 0.101501i \(0.0323646\pi\)
−0.994835 + 0.101501i \(0.967635\pi\)
\(558\) 21.1015i 0.893299i
\(559\) 10.2406 0.433130
\(560\) 0.0106419 0.227780i 0.000449701 0.00962547i
\(561\) 0.333296 0.0140718
\(562\) 20.9085i 0.881970i
\(563\) 33.4653i 1.41040i −0.709010 0.705198i \(-0.750858\pi\)
0.709010 0.705198i \(-0.249142\pi\)
\(564\) 38.4372 1.61850
\(565\) 0.511987 10.9586i 0.0215395 0.461034i
\(566\) −15.6462 −0.657659
\(567\) 1.00000i 0.0419961i
\(568\) 38.2191i 1.60364i
\(569\) −9.03326 −0.378694 −0.189347 0.981910i \(-0.560637\pi\)
−0.189347 + 0.981910i \(0.560637\pi\)
\(570\) −24.1006 1.12598i −1.00946 0.0471621i
\(571\) 34.8782 1.45961 0.729803 0.683658i \(-0.239612\pi\)
0.729803 + 0.683658i \(0.239612\pi\)
\(572\) 13.1387i 0.549355i
\(573\) 6.99980i 0.292421i
\(574\) −16.7946 −0.700992
\(575\) −3.72323 + 39.7593i −0.155269 + 1.65808i
\(576\) −12.9763 −0.540679
\(577\) 11.0507i 0.460049i −0.973185 0.230024i \(-0.926119\pi\)
0.973185 0.230024i \(-0.0738806\pi\)
\(578\) 38.5613i 1.60394i
\(579\) −8.84126 −0.367430
\(580\) 2.68263 + 0.125332i 0.111390 + 0.00520414i
\(581\) 9.02465 0.374406
\(582\) 18.1685i 0.753109i
\(583\) 12.8762i 0.533278i
\(584\) −23.6413 −0.978286
\(585\) −0.426711 + 9.13339i −0.0176423 + 0.377619i
\(586\) 19.0596 0.787344
\(587\) 12.0202i 0.496127i 0.968744 + 0.248064i \(0.0797942\pi\)
−0.968744 + 0.248064i \(0.920206\pi\)
\(588\) 3.21315i 0.132508i
\(589\) 43.6748 1.79959
\(590\) −0.586513 + 12.5538i −0.0241464 + 0.516832i
\(591\) −7.51103 −0.308962
\(592\) 0.358319i 0.0147268i
\(593\) 33.1150i 1.35987i −0.733272 0.679936i \(-0.762008\pi\)
0.733272 0.679936i \(-0.237992\pi\)
\(594\) 2.28323 0.0936821
\(595\) −0.744461 0.0347812i −0.0305199 0.00142589i
\(596\) 59.6768 2.44445
\(597\) 21.5564i 0.882246i
\(598\) 74.5650i 3.04919i
\(599\) −24.4768 −1.00009 −0.500047 0.865999i \(-0.666684\pi\)
−0.500047 + 0.865999i \(0.666684\pi\)
\(600\) 13.7892 + 1.29128i 0.562940 + 0.0527161i
\(601\) 4.80295 0.195917 0.0979583 0.995191i \(-0.468769\pi\)
0.0979583 + 0.995191i \(0.468769\pi\)
\(602\) 5.71812i 0.233053i
\(603\) 11.1473i 0.453953i
\(604\) 9.89091 0.402455
\(605\) −2.23363 0.104355i −0.0908100 0.00424264i
\(606\) −16.7494 −0.680399
\(607\) 14.0235i 0.569196i 0.958647 + 0.284598i \(0.0918601\pi\)
−0.958647 + 0.284598i \(0.908140\pi\)
\(608\) 27.2798i 1.10634i
\(609\) −0.373782 −0.0151464
\(610\) 2.10398 45.0340i 0.0851878 1.82337i
\(611\) 48.9149 1.97888
\(612\) 1.07093i 0.0432898i
\(613\) 36.7612i 1.48477i −0.669974 0.742385i \(-0.733695\pi\)
0.669974 0.742385i \(-0.266305\pi\)
\(614\) 11.0860 0.447394
\(615\) −0.767595 + 16.4297i −0.0309524 + 0.662510i
\(616\) 2.76990 0.111602
\(617\) 13.0689i 0.526135i −0.964777 0.263068i \(-0.915266\pi\)
0.964777 0.263068i \(-0.0847343\pi\)
\(618\) 37.9980i 1.52850i
\(619\) −7.47221 −0.300334 −0.150167 0.988661i \(-0.547981\pi\)
−0.150167 + 0.988661i \(0.547981\pi\)
\(620\) −66.3294 3.09890i −2.66385 0.124455i
\(621\) −7.98665 −0.320493
\(622\) 71.6160i 2.87154i
\(623\) 17.9041i 0.717312i
\(624\) −0.416989 −0.0166929
\(625\) 24.5653 + 4.64151i 0.982614 + 0.185660i
\(626\) 24.6055 0.983432
\(627\) 4.72571i 0.188727i
\(628\) 13.6731i 0.545618i
\(629\) −1.17110 −0.0466950
\(630\) −5.09990 0.238267i −0.203185 0.00949278i
\(631\) −35.9123 −1.42965 −0.714824 0.699305i \(-0.753493\pi\)
−0.714824 + 0.699305i \(0.753493\pi\)
\(632\) 19.2543i 0.765893i
\(633\) 4.98337i 0.198071i
\(634\) 19.7806 0.785586
\(635\) −0.678684 + 14.5267i −0.0269327 + 0.576473i
\(636\) 41.3731 1.64055
\(637\) 4.08903i 0.162013i
\(638\) 0.853432i 0.0337877i
\(639\) −13.7980 −0.545841
\(640\) −1.88702 + 40.3900i −0.0745909 + 1.59655i
\(641\) −5.22403 −0.206337 −0.103168 0.994664i \(-0.532898\pi\)
−0.103168 + 0.994664i \(0.532898\pi\)
\(642\) 40.5694i 1.60115i
\(643\) 4.17844i 0.164782i 0.996600 + 0.0823908i \(0.0262556\pi\)
−0.996600 + 0.0823908i \(0.973744\pi\)
\(644\) −25.6623 −1.01124
\(645\) 5.59390 + 0.261347i 0.220260 + 0.0102905i
\(646\) −3.59623 −0.141492
\(647\) 10.7576i 0.422923i 0.977386 + 0.211462i \(0.0678224\pi\)
−0.977386 + 0.211462i \(0.932178\pi\)
\(648\) 2.76990i 0.108812i
\(649\) 2.46158 0.0966255
\(650\) 46.4777 + 4.35237i 1.82301 + 0.170714i
\(651\) 9.24196 0.362221
\(652\) 44.1407i 1.72868i
\(653\) 0.714816i 0.0279729i 0.999902 + 0.0139864i \(0.00445217\pi\)
−0.999902 + 0.0139864i \(0.995548\pi\)
\(654\) 34.1240 1.33436
\(655\) 18.8200 + 0.879268i 0.735357 + 0.0343558i
\(656\) −0.750107 −0.0292867
\(657\) 8.53510i 0.332986i
\(658\) 27.3131i 1.06477i
\(659\) −40.6003 −1.58156 −0.790782 0.612098i \(-0.790326\pi\)
−0.790782 + 0.612098i \(0.790326\pi\)
\(660\) 0.335308 7.17699i 0.0130519 0.279364i
\(661\) 5.98602 0.232829 0.116415 0.993201i \(-0.462860\pi\)
0.116415 + 0.993201i \(0.462860\pi\)
\(662\) 6.21626i 0.241602i
\(663\) 1.36286i 0.0529291i
\(664\) −24.9973 −0.970085
\(665\) 0.493152 10.5555i 0.0191236 0.409324i
\(666\) −8.02260 −0.310869
\(667\) 2.98527i 0.115590i
\(668\) 32.5311i 1.25867i
\(669\) 1.31258 0.0507472
\(670\) −56.8500 2.65603i −2.19631 0.102611i
\(671\) −8.83037 −0.340892
\(672\) 5.77263i 0.222684i
\(673\) 25.8542i 0.996608i −0.867002 0.498304i \(-0.833956\pi\)
0.867002 0.498304i \(-0.166044\pi\)
\(674\) −23.3350 −0.898830
\(675\) −0.466182 + 4.97822i −0.0179433 + 0.191612i
\(676\) 11.9535 0.459750
\(677\) 32.9500i 1.26637i −0.774000 0.633186i \(-0.781747\pi\)
0.774000 0.633186i \(-0.218253\pi\)
\(678\) 11.2020i 0.430210i
\(679\) −7.95736 −0.305376
\(680\) 2.06208 + 0.0963403i 0.0790772 + 0.00369448i
\(681\) 24.4941 0.938617
\(682\) 21.1015i 0.808019i
\(683\) 19.2301i 0.735818i −0.929862 0.367909i \(-0.880074\pi\)
0.929862 0.367909i \(-0.119926\pi\)
\(684\) −15.1844 −0.580590
\(685\) 1.41817 30.3547i 0.0541854 1.15979i
\(686\) 2.28323 0.0871742
\(687\) 17.6904i 0.674929i
\(688\) 0.255392i 0.00973673i
\(689\) 52.6512 2.00585
\(690\) −1.90295 + 40.7311i −0.0724442 + 1.55061i
\(691\) 31.5635 1.20073 0.600366 0.799725i \(-0.295021\pi\)
0.600366 + 0.799725i \(0.295021\pi\)
\(692\) 77.7606i 2.95602i
\(693\) 1.00000i 0.0379869i
\(694\) 13.6955 0.519873
\(695\) 24.7066 + 1.15429i 0.937174 + 0.0437847i
\(696\) 1.03534 0.0392444
\(697\) 2.45160i 0.0928609i
\(698\) 26.0845i 0.987314i
\(699\) −15.2475 −0.576714
\(700\) −1.49791 + 15.9958i −0.0566157 + 0.604583i
\(701\) −29.5304 −1.11535 −0.557675 0.830060i \(-0.688306\pi\)
−0.557675 + 0.830060i \(0.688306\pi\)
\(702\) 9.33621i 0.352372i
\(703\) 16.6047i 0.626260i
\(704\) 12.9763 0.489063
\(705\) 26.7197 + 1.24834i 1.00632 + 0.0470153i
\(706\) 8.09530 0.304671
\(707\) 7.33584i 0.275893i
\(708\) 7.90942i 0.297254i
\(709\) −11.1002 −0.416877 −0.208438 0.978035i \(-0.566838\pi\)
−0.208438 + 0.978035i \(0.566838\pi\)
\(710\) −3.28761 + 70.3685i −0.123382 + 2.64088i
\(711\) 6.95125 0.260692
\(712\) 49.5925i 1.85856i
\(713\) 73.8123i 2.76429i
\(714\) −0.760993 −0.0284794
\(715\) 0.426711 9.13339i 0.0159581 0.341569i
\(716\) −12.5590 −0.469351
\(717\) 6.67755i 0.249378i
\(718\) 60.1759i 2.24574i
\(719\) 32.6862 1.21899 0.609495 0.792790i \(-0.291372\pi\)
0.609495 + 0.792790i \(0.291372\pi\)
\(720\) −0.227780 0.0106419i −0.00848886 0.000396599i
\(721\) 16.6422 0.619787
\(722\) 7.60846i 0.283157i
\(723\) 4.97410i 0.184989i
\(724\) 24.9539 0.927406
\(725\) 1.86077 + 0.174250i 0.0691073 + 0.00647150i
\(726\) −2.28323 −0.0847387
\(727\) 39.4688i 1.46382i 0.681404 + 0.731908i \(0.261370\pi\)
−0.681404 + 0.731908i \(0.738630\pi\)
\(728\) 11.3262i 0.419777i
\(729\) −1.00000 −0.0370370
\(730\) −43.5281 2.03363i −1.61105 0.0752681i
\(731\) 0.834706 0.0308727
\(732\) 28.3733i 1.04871i
\(733\) 26.7103i 0.986569i −0.869868 0.493284i \(-0.835796\pi\)
0.869868 0.493284i \(-0.164204\pi\)
\(734\) −42.6424 −1.57396
\(735\) 0.104355 2.23363i 0.00384919 0.0823887i
\(736\) −46.1040 −1.69942
\(737\) 11.1473i 0.410616i
\(738\) 16.7946i 0.618216i
\(739\) 3.88131 0.142776 0.0713882 0.997449i \(-0.477257\pi\)
0.0713882 + 0.997449i \(0.477257\pi\)
\(740\) −1.17817 + 25.2178i −0.0433105 + 0.927025i
\(741\) −19.3236 −0.709869
\(742\) 29.3993i 1.07928i
\(743\) 10.7320i 0.393717i 0.980432 + 0.196859i \(0.0630740\pi\)
−0.980432 + 0.196859i \(0.936926\pi\)
\(744\) −25.5993 −0.938515
\(745\) 41.4845 + 1.93815i 1.51988 + 0.0710084i
\(746\) −53.4720 −1.95775
\(747\) 9.02465i 0.330195i
\(748\) 1.07093i 0.0391571i
\(749\) 17.7684 0.649244
\(750\) 25.2773 + 3.56362i 0.922998 + 0.130125i
\(751\) 9.05305 0.330351 0.165175 0.986264i \(-0.447181\pi\)
0.165175 + 0.986264i \(0.447181\pi\)
\(752\) 1.21990i 0.0444852i
\(753\) 10.7702i 0.392488i
\(754\) 3.48971 0.127088
\(755\) 6.87570 + 0.321232i 0.250232 + 0.0116908i
\(756\) −3.21315 −0.116861
\(757\) 50.2974i 1.82809i 0.405612 + 0.914045i \(0.367058\pi\)
−0.405612 + 0.914045i \(0.632942\pi\)
\(758\) 67.4551i 2.45008i
\(759\) 7.98665 0.289897
\(760\) −1.36598 + 29.2376i −0.0495493 + 1.06056i
\(761\) 46.5455 1.68727 0.843637 0.536914i \(-0.180410\pi\)
0.843637 + 0.536914i \(0.180410\pi\)
\(762\) 14.8492i 0.537931i
\(763\) 14.9455i 0.541063i
\(764\) 22.4914 0.813710
\(765\) −0.0347812 + 0.744461i −0.00125752 + 0.0269161i
\(766\) −13.7024 −0.495087
\(767\) 10.0655i 0.363443i
\(768\) 15.3343i 0.553328i
\(769\) −10.6989 −0.385813 −0.192907 0.981217i \(-0.561791\pi\)
−0.192907 + 0.981217i \(0.561791\pi\)
\(770\) 5.09990 + 0.238267i 0.183788 + 0.00858654i
\(771\) 3.36008 0.121010
\(772\) 28.4083i 1.02244i
\(773\) 13.3630i 0.480634i 0.970694 + 0.240317i \(0.0772514\pi\)
−0.970694 + 0.240317i \(0.922749\pi\)
\(774\) 5.71812 0.205534
\(775\) −46.0085 4.30843i −1.65267 0.154763i
\(776\) 22.0411 0.791228
\(777\) 3.51370i 0.126053i
\(778\) 51.6539i 1.85188i
\(779\) −34.7605 −1.24542
\(780\) 29.3469 + 1.37109i 1.05079 + 0.0490928i
\(781\) 13.7980 0.493732
\(782\) 6.07778i 0.217341i
\(783\) 0.373782i 0.0133579i
\(784\) 0.101977 0.00364205
\(785\) 0.444070 9.50493i 0.0158495 0.339246i
\(786\) 19.2379 0.686193
\(787\) 15.3830i 0.548345i 0.961681 + 0.274172i \(0.0884039\pi\)
−0.961681 + 0.274172i \(0.911596\pi\)
\(788\) 24.1340i 0.859740i
\(789\) −16.8761 −0.600806
\(790\) 1.65625 35.4507i 0.0589268 1.26128i
\(791\) 4.90620 0.174444
\(792\) 2.76990i 0.0984240i
\(793\) 36.1076i 1.28222i
\(794\) 27.5428 0.977457
\(795\) 28.7607 + 1.34370i 1.02004 + 0.0476560i
\(796\) 69.2640 2.45500
\(797\) 9.55195i 0.338348i 0.985586 + 0.169174i \(0.0541099\pi\)
−0.985586 + 0.169174i \(0.945890\pi\)
\(798\) 10.7899i 0.381958i
\(799\) 3.98704 0.141052
\(800\) −2.69110 + 28.7374i −0.0951446 + 1.01602i
\(801\) 17.9041 0.632610
\(802\) 2.73344i 0.0965210i
\(803\) 8.53510i 0.301197i
\(804\) −35.8179 −1.26320
\(805\) −17.8392 0.833447i −0.628750 0.0293752i
\(806\) −86.2848 −3.03925
\(807\) 13.5808i 0.478068i
\(808\) 20.3195i 0.714838i
\(809\) 45.5218 1.60046 0.800230 0.599693i \(-0.204711\pi\)
0.800230 + 0.599693i \(0.204711\pi\)
\(810\) −0.238267 + 5.09990i −0.00837184 + 0.179192i
\(811\) 3.34608 0.117497 0.0587484 0.998273i \(-0.481289\pi\)
0.0587484 + 0.998273i \(0.481289\pi\)
\(812\) 1.20102i 0.0421475i
\(813\) 5.53292i 0.194048i
\(814\) 8.02260 0.281192
\(815\) 1.43358 30.6846i 0.0502161 1.07483i
\(816\) −0.0339887 −0.00118984
\(817\) 11.8351i 0.414056i
\(818\) 21.7392i 0.760093i
\(819\) −4.08903 −0.142882
\(820\) 52.7911 + 2.46640i 1.84355 + 0.0861303i
\(821\) 29.5150 1.03008 0.515040 0.857166i \(-0.327777\pi\)
0.515040 + 0.857166i \(0.327777\pi\)
\(822\) 31.0287i 1.08225i
\(823\) 3.27997i 0.114333i −0.998365 0.0571664i \(-0.981793\pi\)
0.998365 0.0571664i \(-0.0182065\pi\)
\(824\) −46.0971 −1.60587
\(825\) 0.466182 4.97822i 0.0162304 0.173319i
\(826\) −5.62036 −0.195557
\(827\) 40.6064i 1.41202i −0.708200 0.706012i \(-0.750493\pi\)
0.708200 0.706012i \(-0.249507\pi\)
\(828\) 25.6623i 0.891826i
\(829\) −47.2963 −1.64267 −0.821335 0.570446i \(-0.806770\pi\)
−0.821335 + 0.570446i \(0.806770\pi\)
\(830\) −46.0248 2.15027i −1.59754 0.0746371i
\(831\) −6.03226 −0.209257
\(832\) 53.0605i 1.83954i
\(833\) 0.333296i 0.0115480i
\(834\) 25.2552 0.874516
\(835\) 1.05653 22.6141i 0.0365627 0.782593i
\(836\) 15.1844 0.525163
\(837\) 9.24196i 0.319449i
\(838\) 50.6333i 1.74910i
\(839\) 6.46419 0.223169 0.111584 0.993755i \(-0.464408\pi\)
0.111584 + 0.993755i \(0.464408\pi\)
\(840\) −0.289053 + 6.18693i −0.00997327 + 0.213469i
\(841\) −28.8603 −0.995182
\(842\) 24.4448i 0.842423i
\(843\) 9.15740i 0.315398i
\(844\) −16.0123 −0.551166
\(845\) 8.30952 + 0.388220i 0.285856 + 0.0133552i
\(846\) 27.3131 0.939043
\(847\) 1.00000i 0.0343604i
\(848\) 1.31308i 0.0450914i
\(849\) −6.85266 −0.235183
\(850\) 3.78839 + 0.354761i 0.129941 + 0.0121682i
\(851\) −28.0627 −0.961978
\(852\) 44.3351i 1.51889i
\(853\) 26.2091i 0.897384i 0.893687 + 0.448692i \(0.148110\pi\)
−0.893687 + 0.448692i \(0.851890\pi\)
\(854\) 20.1618 0.689922
\(855\) −10.5555 0.493152i −0.360990 0.0168654i
\(856\) −49.2167 −1.68219
\(857\) 5.66404i 0.193480i −0.995310 0.0967400i \(-0.969158\pi\)
0.995310 0.0967400i \(-0.0308415\pi\)
\(858\) 9.33621i 0.318733i
\(859\) −30.3158 −1.03436 −0.517181 0.855876i \(-0.673019\pi\)
−0.517181 + 0.855876i \(0.673019\pi\)
\(860\) 0.839745 17.9740i 0.0286351 0.612909i
\(861\) −7.35561 −0.250679
\(862\) 53.8620i 1.83455i
\(863\) 22.5684i 0.768238i 0.923284 + 0.384119i \(0.125495\pi\)
−0.923284 + 0.384119i \(0.874505\pi\)
\(864\) −5.77263 −0.196389
\(865\) −2.52547 + 54.0556i −0.0858686 + 1.83794i
\(866\) 68.6467 2.33271
\(867\) 16.8889i 0.573578i
\(868\) 29.6958i 1.00794i
\(869\) −6.95125 −0.235805
\(870\) 1.90625 + 0.0890599i 0.0646280 + 0.00301941i
\(871\) −45.5816 −1.54447
\(872\) 41.3975i 1.40190i
\(873\) 7.95736i 0.269316i
\(874\) −86.1751 −2.91491
\(875\) −1.56078 + 11.0709i −0.0527640 + 0.374263i
\(876\) −27.4245 −0.926589
\(877\) 23.0829i 0.779453i 0.920931 + 0.389727i \(0.127430\pi\)
−0.920931 + 0.389727i \(0.872570\pi\)
\(878\) 36.0115i 1.21533i
\(879\) 8.34763 0.281559
\(880\) 0.227780 + 0.0106419i 0.00767847 + 0.000358737i
\(881\) −16.2468 −0.547368 −0.273684 0.961820i \(-0.588242\pi\)
−0.273684 + 0.961820i \(0.588242\pi\)
\(882\) 2.28323i 0.0768804i
\(883\) 40.6837i 1.36912i −0.728958 0.684558i \(-0.759995\pi\)
0.728958 0.684558i \(-0.240005\pi\)
\(884\) 4.37907 0.147284
\(885\) −0.256878 + 5.49826i −0.00863487 + 0.184822i
\(886\) −70.2996 −2.36176
\(887\) 6.41283i 0.215322i −0.994188 0.107661i \(-0.965664\pi\)
0.994188 0.107661i \(-0.0343361\pi\)
\(888\) 9.73260i 0.326605i
\(889\) −6.50360 −0.218124
\(890\) 4.26595 91.3091i 0.142995 3.06069i
\(891\) 1.00000 0.0335013
\(892\) 4.21751i 0.141213i
\(893\) 56.5311i 1.89174i
\(894\) 42.4057 1.41826
\(895\) −8.73043 0.407885i −0.291826 0.0136341i
\(896\) −18.0826 −0.604099
\(897\) 32.6577i 1.09041i
\(898\) 43.0230i 1.43569i
\(899\) −3.45448 −0.115213
\(900\) 15.9958 + 1.49791i 0.533192 + 0.0499303i
\(901\) 4.29159 0.142974
\(902\) 16.7946i 0.559198i
\(903\) 2.50440i 0.0833411i
\(904\) −13.5897 −0.451986
\(905\) 17.3468 + 0.810442i 0.576628 + 0.0269400i
\(906\) 7.02838 0.233502
\(907\) 31.8085i 1.05619i 0.849187 + 0.528093i \(0.177093\pi\)
−0.849187 + 0.528093i \(0.822907\pi\)
\(908\) 78.7032i 2.61186i
\(909\) −7.33584 −0.243314
\(910\) −0.974281 + 20.8537i −0.0322971 + 0.691292i
\(911\) −5.87685 −0.194709 −0.0973544 0.995250i \(-0.531038\pi\)
−0.0973544 + 0.995250i \(0.531038\pi\)
\(912\) 0.481916i 0.0159578i
\(913\) 9.02465i 0.298672i
\(914\) −15.4893 −0.512339
\(915\) 0.921493 19.7238i 0.0304636 0.652048i
\(916\) −56.8417 −1.87810
\(917\) 8.42573i 0.278242i
\(918\) 0.760993i 0.0251165i
\(919\) −43.6491 −1.43985 −0.719925 0.694052i \(-0.755824\pi\)
−0.719925 + 0.694052i \(0.755824\pi\)
\(920\) 49.4128 + 2.30856i 1.62909 + 0.0761111i
\(921\) 4.85539 0.159991
\(922\) 7.41135i 0.244080i
\(923\) 56.4205i 1.85710i
\(924\) 3.21315 0.105705
\(925\) −1.63802 + 17.4920i −0.0538579 + 0.575133i
\(926\) 5.68463 0.186808
\(927\) 16.6422i 0.546601i
\(928\) 2.15771i 0.0708302i
\(929\) −53.2435 −1.74686 −0.873432 0.486946i \(-0.838111\pi\)
−0.873432 + 0.486946i \(0.838111\pi\)
\(930\) −47.1330 2.20205i −1.54555 0.0722081i
\(931\) 4.72571 0.154879
\(932\) 48.9925i 1.60480i
\(933\) 31.3660i 1.02688i
\(934\) 25.5511 0.836058
\(935\) 0.0347812 0.744461i 0.00113747 0.0243465i
\(936\) 11.3262 0.370208
\(937\) 1.30555i 0.0426505i 0.999773 + 0.0213253i \(0.00678855\pi\)
−0.999773 + 0.0213253i \(0.993211\pi\)
\(938\) 25.4518i 0.831032i
\(939\) 10.7766 0.351681
\(940\) 4.01111 85.8544i 0.130828 2.80026i
\(941\) −12.3370 −0.402176 −0.201088 0.979573i \(-0.564448\pi\)
−0.201088 + 0.979573i \(0.564448\pi\)
\(942\) 9.71600i 0.316564i
\(943\) 58.7467i 1.91306i
\(944\) −0.251026 −0.00817019
\(945\) −2.23363 0.104355i −0.0726600 0.00339467i
\(946\) −5.71812 −0.185912
\(947\) 55.9077i 1.81676i 0.418149 + 0.908379i \(0.362679\pi\)
−0.418149 + 0.908379i \(0.637321\pi\)
\(948\) 22.3354i 0.725420i
\(949\) −34.9003 −1.13291
\(950\) −5.03005 + 53.7144i −0.163196 + 1.74273i
\(951\) 8.66340 0.280930
\(952\) 0.923197i 0.0299210i
\(953\) 45.8913i 1.48656i −0.668978 0.743282i \(-0.733268\pi\)
0.668978 0.743282i \(-0.266732\pi\)
\(954\) 29.3993 0.951839
\(955\) 15.6350 + 0.730465i 0.505936 + 0.0236373i
\(956\) −21.4559 −0.693935
\(957\) 0.373782i 0.0120827i
\(958\) 55.3721i 1.78899i
\(959\) 13.5898 0.438839
\(960\) −1.35414 + 28.9843i −0.0437048 + 0.935464i
\(961\) 54.4137 1.75528
\(962\) 32.8047i 1.05766i
\(963\) 17.7684i 0.572579i
\(964\) −15.9825 −0.514762
\(965\) −0.922630 + 19.7481i −0.0297005 + 0.635714i
\(966\) −18.2354 −0.586714
\(967\) 21.9288i 0.705182i −0.935778 0.352591i \(-0.885301\pi\)
0.935778 0.352591i \(-0.114699\pi\)
\(968\) 2.76990i 0.0890279i
\(969\) −1.57506 −0.0505983
\(970\) 40.5817 + 1.89598i 1.30300 + 0.0608761i
\(971\) −45.1675 −1.44949 −0.724746 0.689016i \(-0.758043\pi\)
−0.724746 + 0.689016i \(0.758043\pi\)
\(972\) 3.21315i 0.103062i
\(973\) 11.0612i 0.354605i
\(974\) 39.1637 1.25488
\(975\) 20.3561 + 1.90623i 0.651917 + 0.0610483i
\(976\) 0.900498 0.0288242
\(977\) 9.57855i 0.306445i 0.988192 + 0.153223i \(0.0489651\pi\)
−0.988192 + 0.153223i \(0.951035\pi\)
\(978\) 31.3660i 1.00297i
\(979\) −17.9041 −0.572217
\(980\) −7.17699 0.335308i −0.229260 0.0107110i
\(981\) 14.9455 0.477173
\(982\) 72.8438i 2.32454i
\(983\) 29.0482i 0.926493i −0.886229 0.463247i \(-0.846684\pi\)
0.886229 0.463247i \(-0.153316\pi\)
\(984\) 20.3743 0.649509
\(985\) −0.783814 + 16.7769i −0.0249744 + 0.534555i
\(986\) 0.284446 0.00905859
\(987\) 11.9625i 0.380769i
\(988\) 62.0895i 1.97533i
\(989\) 20.0017 0.636018
\(990\) 0.238267 5.09990i 0.00757262 0.162085i
\(991\) 4.77270 0.151610 0.0758049 0.997123i \(-0.475847\pi\)
0.0758049 + 0.997123i \(0.475847\pi\)
\(992\) 53.3504i 1.69388i
\(993\) 2.72257i 0.0863981i
\(994\) −31.5041 −0.999248
\(995\) 48.1491 + 2.24952i 1.52643 + 0.0713147i
\(996\) −28.9975 −0.918822
\(997\) 15.4478i 0.489236i −0.969620 0.244618i \(-0.921337\pi\)
0.969620 0.244618i \(-0.0786625\pi\)
\(998\) 48.7521i 1.54322i
\(999\) −3.51370 −0.111169
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 1155.2.c.f.694.4 20
5.2 odd 4 5775.2.a.cn.1.9 10
5.3 odd 4 5775.2.a.co.1.2 10
5.4 even 2 inner 1155.2.c.f.694.17 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.c.f.694.4 20 1.1 even 1 trivial
1155.2.c.f.694.17 yes 20 5.4 even 2 inner
5775.2.a.cn.1.9 10 5.2 odd 4
5775.2.a.co.1.2 10 5.3 odd 4