Properties

Label 1155.2.i.d.76.10
Level $1155$
Weight $2$
Character 1155.76
Analytic conductor $9.223$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(76,1155)]
 
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, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.i (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: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.10
Character \(\chi\) \(=\) 1155.76
Dual form 1155.2.i.d.76.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.859876i q^{2} -1.00000i q^{3} +1.26061 q^{4} -1.00000i q^{5} +0.859876 q^{6} +(-2.42783 + 1.05149i) q^{7} +2.80372i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+0.859876i q^{2} -1.00000i q^{3} +1.26061 q^{4} -1.00000i q^{5} +0.859876 q^{6} +(-2.42783 + 1.05149i) q^{7} +2.80372i q^{8} -1.00000 q^{9} +0.859876 q^{10} +(-3.22701 + 0.765761i) q^{11} -1.26061i q^{12} +3.49145 q^{13} +(-0.904149 - 2.08764i) q^{14} -1.00000 q^{15} +0.110370 q^{16} +5.22254 q^{17} -0.859876i q^{18} +4.83931 q^{19} -1.26061i q^{20} +(1.05149 + 2.42783i) q^{21} +(-0.658460 - 2.77483i) q^{22} +3.63160 q^{23} +2.80372 q^{24} -1.00000 q^{25} +3.00221i q^{26} +1.00000i q^{27} +(-3.06056 + 1.32552i) q^{28} +6.88482i q^{29} -0.859876i q^{30} +1.77159i q^{31} +5.70235i q^{32} +(0.765761 + 3.22701i) q^{33} +4.49074i q^{34} +(1.05149 + 2.42783i) q^{35} -1.26061 q^{36} +9.57378 q^{37} +4.16121i q^{38} -3.49145i q^{39} +2.80372 q^{40} -2.92000 q^{41} +(-2.08764 + 0.904149i) q^{42} -4.10056i q^{43} +(-4.06801 + 0.965328i) q^{44} +1.00000i q^{45} +3.12272i q^{46} -6.68244i q^{47} -0.110370i q^{48} +(4.78875 - 5.10567i) q^{49} -0.859876i q^{50} -5.22254i q^{51} +4.40136 q^{52} +7.05177 q^{53} -0.859876 q^{54} +(0.765761 + 3.22701i) q^{55} +(-2.94808 - 6.80697i) q^{56} -4.83931i q^{57} -5.92009 q^{58} -4.22390i q^{59} -1.26061 q^{60} +3.39295 q^{61} -1.52335 q^{62} +(2.42783 - 1.05149i) q^{63} -4.68258 q^{64} -3.49145i q^{65} +(-2.77483 + 0.658460i) q^{66} +10.7607 q^{67} +6.58360 q^{68} -3.63160i q^{69} +(-2.08764 + 0.904149i) q^{70} -12.6238 q^{71} -2.80372i q^{72} -7.34186 q^{73} +8.23226i q^{74} +1.00000i q^{75} +6.10050 q^{76} +(7.02946 - 5.25230i) q^{77} +3.00221 q^{78} +6.63289i q^{79} -0.110370i q^{80} +1.00000 q^{81} -2.51083i q^{82} -7.78700 q^{83} +(1.32552 + 3.06056i) q^{84} -5.22254i q^{85} +3.52598 q^{86} +6.88482 q^{87} +(-2.14698 - 9.04765i) q^{88} +13.2622i q^{89} -0.859876 q^{90} +(-8.47665 + 3.67121i) q^{91} +4.57804 q^{92} +1.77159 q^{93} +5.74607 q^{94} -4.83931i q^{95} +5.70235 q^{96} +12.8157i q^{97} +(4.39024 + 4.11773i) q^{98} +(3.22701 - 0.765761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.859876i 0.608024i 0.952668 + 0.304012i \(0.0983264\pi\)
−0.952668 + 0.304012i \(0.901674\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 1.26061 0.630306
\(5\) 1.00000i 0.447214i
\(6\) 0.859876 0.351043
\(7\) −2.42783 + 1.05149i −0.917635 + 0.397425i
\(8\) 2.80372i 0.991266i
\(9\) −1.00000 −0.333333
\(10\) 0.859876 0.271917
\(11\) −3.22701 + 0.765761i −0.972981 + 0.230886i
\(12\) 1.26061i 0.363908i
\(13\) 3.49145 0.968353 0.484177 0.874970i \(-0.339119\pi\)
0.484177 + 0.874970i \(0.339119\pi\)
\(14\) −0.904149 2.08764i −0.241644 0.557944i
\(15\) −1.00000 −0.258199
\(16\) 0.110370 0.0275924
\(17\) 5.22254 1.26665 0.633326 0.773886i \(-0.281689\pi\)
0.633326 + 0.773886i \(0.281689\pi\)
\(18\) 0.859876i 0.202675i
\(19\) 4.83931 1.11021 0.555107 0.831779i \(-0.312677\pi\)
0.555107 + 0.831779i \(0.312677\pi\)
\(20\) 1.26061i 0.281882i
\(21\) 1.05149 + 2.42783i 0.229453 + 0.529797i
\(22\) −0.658460 2.77483i −0.140384 0.591596i
\(23\) 3.63160 0.757240 0.378620 0.925552i \(-0.376399\pi\)
0.378620 + 0.925552i \(0.376399\pi\)
\(24\) 2.80372 0.572308
\(25\) −1.00000 −0.200000
\(26\) 3.00221i 0.588782i
\(27\) 1.00000i 0.192450i
\(28\) −3.06056 + 1.32552i −0.578391 + 0.250499i
\(29\) 6.88482i 1.27848i 0.769008 + 0.639239i \(0.220751\pi\)
−0.769008 + 0.639239i \(0.779249\pi\)
\(30\) 0.859876i 0.156991i
\(31\) 1.77159i 0.318186i 0.987264 + 0.159093i \(0.0508570\pi\)
−0.987264 + 0.159093i \(0.949143\pi\)
\(32\) 5.70235i 1.00804i
\(33\) 0.765761 + 3.22701i 0.133302 + 0.561751i
\(34\) 4.49074i 0.770155i
\(35\) 1.05149 + 2.42783i 0.177734 + 0.410379i
\(36\) −1.26061 −0.210102
\(37\) 9.57378 1.57392 0.786960 0.617004i \(-0.211654\pi\)
0.786960 + 0.617004i \(0.211654\pi\)
\(38\) 4.16121i 0.675038i
\(39\) 3.49145i 0.559079i
\(40\) 2.80372 0.443308
\(41\) −2.92000 −0.456027 −0.228013 0.973658i \(-0.573223\pi\)
−0.228013 + 0.973658i \(0.573223\pi\)
\(42\) −2.08764 + 0.904149i −0.322129 + 0.139513i
\(43\) 4.10056i 0.625330i −0.949864 0.312665i \(-0.898778\pi\)
0.949864 0.312665i \(-0.101222\pi\)
\(44\) −4.06801 + 0.965328i −0.613276 + 0.145529i
\(45\) 1.00000i 0.149071i
\(46\) 3.12272i 0.460420i
\(47\) 6.68244i 0.974734i −0.873197 0.487367i \(-0.837957\pi\)
0.873197 0.487367i \(-0.162043\pi\)
\(48\) 0.110370i 0.0159305i
\(49\) 4.78875 5.10567i 0.684107 0.729381i
\(50\) 0.859876i 0.121605i
\(51\) 5.22254i 0.731301i
\(52\) 4.40136 0.610359
\(53\) 7.05177 0.968635 0.484317 0.874892i \(-0.339068\pi\)
0.484317 + 0.874892i \(0.339068\pi\)
\(54\) −0.859876 −0.117014
\(55\) 0.765761 + 3.22701i 0.103255 + 0.435130i
\(56\) −2.94808 6.80697i −0.393954 0.909620i
\(57\) 4.83931i 0.640983i
\(58\) −5.92009 −0.777346
\(59\) 4.22390i 0.549905i −0.961458 0.274953i \(-0.911338\pi\)
0.961458 0.274953i \(-0.0886622\pi\)
\(60\) −1.26061 −0.162744
\(61\) 3.39295 0.434423 0.217211 0.976125i \(-0.430304\pi\)
0.217211 + 0.976125i \(0.430304\pi\)
\(62\) −1.52335 −0.193465
\(63\) 2.42783 1.05149i 0.305878 0.132475i
\(64\) −4.68258 −0.585322
\(65\) 3.49145i 0.433061i
\(66\) −2.77483 + 0.658460i −0.341558 + 0.0810508i
\(67\) 10.7607 1.31463 0.657316 0.753615i \(-0.271692\pi\)
0.657316 + 0.753615i \(0.271692\pi\)
\(68\) 6.58360 0.798378
\(69\) 3.63160i 0.437193i
\(70\) −2.08764 + 0.904149i −0.249520 + 0.108066i
\(71\) −12.6238 −1.49817 −0.749087 0.662472i \(-0.769507\pi\)
−0.749087 + 0.662472i \(0.769507\pi\)
\(72\) 2.80372i 0.330422i
\(73\) −7.34186 −0.859300 −0.429650 0.902996i \(-0.641363\pi\)
−0.429650 + 0.902996i \(0.641363\pi\)
\(74\) 8.23226i 0.956981i
\(75\) 1.00000i 0.115470i
\(76\) 6.10050 0.699776
\(77\) 7.02946 5.25230i 0.801082 0.598555i
\(78\) 3.00221 0.339934
\(79\) 6.63289i 0.746258i 0.927779 + 0.373129i \(0.121715\pi\)
−0.927779 + 0.373129i \(0.878285\pi\)
\(80\) 0.110370i 0.0123397i
\(81\) 1.00000 0.111111
\(82\) 2.51083i 0.277275i
\(83\) −7.78700 −0.854734 −0.427367 0.904078i \(-0.640559\pi\)
−0.427367 + 0.904078i \(0.640559\pi\)
\(84\) 1.32552 + 3.06056i 0.144626 + 0.333934i
\(85\) 5.22254i 0.566464i
\(86\) 3.52598 0.380216
\(87\) 6.88482 0.738130
\(88\) −2.14698 9.04765i −0.228869 0.964483i
\(89\) 13.2622i 1.40579i 0.711294 + 0.702894i \(0.248109\pi\)
−0.711294 + 0.702894i \(0.751891\pi\)
\(90\) −0.859876 −0.0906389
\(91\) −8.47665 + 3.67121i −0.888595 + 0.384847i
\(92\) 4.57804 0.477293
\(93\) 1.77159 0.183705
\(94\) 5.74607 0.592662
\(95\) 4.83931i 0.496503i
\(96\) 5.70235 0.581994
\(97\) 12.8157i 1.30124i 0.759403 + 0.650621i \(0.225491\pi\)
−0.759403 + 0.650621i \(0.774509\pi\)
\(98\) 4.39024 + 4.11773i 0.443482 + 0.415954i
\(99\) 3.22701 0.765761i 0.324327 0.0769619i
\(100\) −1.26061 −0.126061
\(101\) −3.67466 −0.365643 −0.182821 0.983146i \(-0.558523\pi\)
−0.182821 + 0.983146i \(0.558523\pi\)
\(102\) 4.49074 0.444649
\(103\) 17.3490i 1.70945i −0.519083 0.854724i \(-0.673726\pi\)
0.519083 0.854724i \(-0.326274\pi\)
\(104\) 9.78905i 0.959896i
\(105\) 2.42783 1.05149i 0.236932 0.102615i
\(106\) 6.06365i 0.588953i
\(107\) 1.09041i 0.105414i 0.998610 + 0.0527069i \(0.0167849\pi\)
−0.998610 + 0.0527069i \(0.983215\pi\)
\(108\) 1.26061i 0.121303i
\(109\) 8.17579i 0.783098i 0.920157 + 0.391549i \(0.128061\pi\)
−0.920157 + 0.391549i \(0.871939\pi\)
\(110\) −2.77483 + 0.658460i −0.264570 + 0.0627817i
\(111\) 9.57378i 0.908703i
\(112\) −0.267959 + 0.116052i −0.0253198 + 0.0109659i
\(113\) −7.87871 −0.741166 −0.370583 0.928799i \(-0.620842\pi\)
−0.370583 + 0.928799i \(0.620842\pi\)
\(114\) 4.16121 0.389733
\(115\) 3.63160i 0.338648i
\(116\) 8.67909i 0.805833i
\(117\) −3.49145 −0.322784
\(118\) 3.63203 0.334356
\(119\) −12.6794 + 5.49143i −1.16232 + 0.503398i
\(120\) 2.80372i 0.255944i
\(121\) 9.82722 4.94224i 0.893384 0.449295i
\(122\) 2.91752i 0.264140i
\(123\) 2.92000i 0.263287i
\(124\) 2.23329i 0.200555i
\(125\) 1.00000i 0.0894427i
\(126\) 0.904149 + 2.08764i 0.0805480 + 0.185981i
\(127\) 17.5475i 1.55709i −0.627592 0.778543i \(-0.715959\pi\)
0.627592 0.778543i \(-0.284041\pi\)
\(128\) 7.37827i 0.652153i
\(129\) −4.10056 −0.361034
\(130\) 3.00221 0.263311
\(131\) −14.6883 −1.28332 −0.641661 0.766988i \(-0.721755\pi\)
−0.641661 + 0.766988i \(0.721755\pi\)
\(132\) 0.965328 + 4.06801i 0.0840210 + 0.354075i
\(133\) −11.7491 + 5.08848i −1.01877 + 0.441227i
\(134\) 9.25290i 0.799329i
\(135\) 1.00000 0.0860663
\(136\) 14.6425i 1.25559i
\(137\) −6.08391 −0.519784 −0.259892 0.965638i \(-0.583687\pi\)
−0.259892 + 0.965638i \(0.583687\pi\)
\(138\) 3.12272 0.265824
\(139\) −5.11439 −0.433797 −0.216899 0.976194i \(-0.569594\pi\)
−0.216899 + 0.976194i \(0.569594\pi\)
\(140\) 1.32552 + 3.06056i 0.112027 + 0.258664i
\(141\) −6.68244 −0.562763
\(142\) 10.8549i 0.910926i
\(143\) −11.2669 + 2.67361i −0.942189 + 0.223579i
\(144\) −0.110370 −0.00919748
\(145\) 6.88482 0.571753
\(146\) 6.31309i 0.522475i
\(147\) −5.10567 4.78875i −0.421109 0.394970i
\(148\) 12.0688 0.992051
\(149\) 9.49040i 0.777484i 0.921347 + 0.388742i \(0.127090\pi\)
−0.921347 + 0.388742i \(0.872910\pi\)
\(150\) −0.859876 −0.0702086
\(151\) 6.00397i 0.488596i 0.969700 + 0.244298i \(0.0785575\pi\)
−0.969700 + 0.244298i \(0.921442\pi\)
\(152\) 13.5681i 1.10052i
\(153\) −5.22254 −0.422217
\(154\) 4.51633 + 6.04447i 0.363936 + 0.487077i
\(155\) 1.77159 0.142297
\(156\) 4.40136i 0.352391i
\(157\) 11.9244i 0.951671i 0.879534 + 0.475836i \(0.157854\pi\)
−0.879534 + 0.475836i \(0.842146\pi\)
\(158\) −5.70346 −0.453743
\(159\) 7.05177i 0.559241i
\(160\) 5.70235 0.450810
\(161\) −8.81691 + 3.81857i −0.694870 + 0.300946i
\(162\) 0.859876i 0.0675583i
\(163\) 10.3767 0.812768 0.406384 0.913702i \(-0.366790\pi\)
0.406384 + 0.913702i \(0.366790\pi\)
\(164\) −3.68098 −0.287436
\(165\) 3.22701 0.765761i 0.251223 0.0596144i
\(166\) 6.69586i 0.519699i
\(167\) 13.1741 1.01944 0.509721 0.860340i \(-0.329749\pi\)
0.509721 + 0.860340i \(0.329749\pi\)
\(168\) −6.80697 + 2.94808i −0.525169 + 0.227449i
\(169\) −0.809796 −0.0622920
\(170\) 4.49074 0.344424
\(171\) −4.83931 −0.370072
\(172\) 5.16922i 0.394149i
\(173\) 4.32866 0.329102 0.164551 0.986369i \(-0.447383\pi\)
0.164551 + 0.986369i \(0.447383\pi\)
\(174\) 5.92009i 0.448801i
\(175\) 2.42783 1.05149i 0.183527 0.0794849i
\(176\) −0.356165 + 0.0845169i −0.0268469 + 0.00637070i
\(177\) −4.22390 −0.317488
\(178\) −11.4038 −0.854754
\(179\) 18.8164 1.40640 0.703202 0.710990i \(-0.251753\pi\)
0.703202 + 0.710990i \(0.251753\pi\)
\(180\) 1.26061i 0.0939605i
\(181\) 15.4068i 1.14518i −0.819842 0.572590i \(-0.805939\pi\)
0.819842 0.572590i \(-0.194061\pi\)
\(182\) −3.15679 7.28887i −0.233997 0.540287i
\(183\) 3.39295i 0.250814i
\(184\) 10.1820i 0.750626i
\(185\) 9.57378i 0.703878i
\(186\) 1.52335i 0.111697i
\(187\) −16.8532 + 3.99921i −1.23243 + 0.292451i
\(188\) 8.42397i 0.614381i
\(189\) −1.05149 2.42783i −0.0764844 0.176599i
\(190\) 4.16121 0.301886
\(191\) −16.4135 −1.18764 −0.593821 0.804597i \(-0.702381\pi\)
−0.593821 + 0.804597i \(0.702381\pi\)
\(192\) 4.68258i 0.337936i
\(193\) 11.8298i 0.851527i 0.904834 + 0.425764i \(0.139995\pi\)
−0.904834 + 0.425764i \(0.860005\pi\)
\(194\) −11.0200 −0.791187
\(195\) −3.49145 −0.250028
\(196\) 6.03676 6.43627i 0.431197 0.459734i
\(197\) 19.9535i 1.42163i −0.703380 0.710814i \(-0.748327\pi\)
0.703380 0.710814i \(-0.251673\pi\)
\(198\) 0.658460 + 2.77483i 0.0467947 + 0.197199i
\(199\) 8.38493i 0.594392i −0.954816 0.297196i \(-0.903949\pi\)
0.954816 0.297196i \(-0.0960515\pi\)
\(200\) 2.80372i 0.198253i
\(201\) 10.7607i 0.759003i
\(202\) 3.15976i 0.222320i
\(203\) −7.23930 16.7152i −0.508099 1.17318i
\(204\) 6.58360i 0.460944i
\(205\) 2.92000i 0.203941i
\(206\) 14.9180 1.03939
\(207\) −3.63160 −0.252413
\(208\) 0.385350 0.0267192
\(209\) −15.6165 + 3.70576i −1.08022 + 0.256333i
\(210\) 0.904149 + 2.08764i 0.0623922 + 0.144061i
\(211\) 9.12184i 0.627973i −0.949427 0.313987i \(-0.898335\pi\)
0.949427 0.313987i \(-0.101665\pi\)
\(212\) 8.88955 0.610537
\(213\) 12.6238i 0.864971i
\(214\) −0.937617 −0.0640942
\(215\) −4.10056 −0.279656
\(216\) −2.80372 −0.190769
\(217\) −1.86280 4.30112i −0.126455 0.291979i
\(218\) −7.03017 −0.476143
\(219\) 7.34186i 0.496117i
\(220\) 0.965328 + 4.06801i 0.0650824 + 0.274265i
\(221\) 18.2342 1.22657
\(222\) 8.23226 0.552513
\(223\) 12.2066i 0.817415i 0.912665 + 0.408707i \(0.134020\pi\)
−0.912665 + 0.408707i \(0.865980\pi\)
\(224\) −5.99595 13.8444i −0.400621 0.925015i
\(225\) 1.00000 0.0666667
\(226\) 6.77471i 0.450647i
\(227\) −20.4996 −1.36061 −0.680304 0.732931i \(-0.738152\pi\)
−0.680304 + 0.732931i \(0.738152\pi\)
\(228\) 6.10050i 0.404016i
\(229\) 12.1756i 0.804583i −0.915512 0.402292i \(-0.868214\pi\)
0.915512 0.402292i \(-0.131786\pi\)
\(230\) 3.12272 0.205906
\(231\) −5.25230 7.02946i −0.345576 0.462505i
\(232\) −19.3031 −1.26731
\(233\) 11.7860i 0.772128i 0.922472 + 0.386064i \(0.126166\pi\)
−0.922472 + 0.386064i \(0.873834\pi\)
\(234\) 3.00221i 0.196261i
\(235\) −6.68244 −0.435914
\(236\) 5.32471i 0.346609i
\(237\) 6.63289 0.430852
\(238\) −4.72195 10.9028i −0.306078 0.706721i
\(239\) 1.17430i 0.0759591i −0.999279 0.0379795i \(-0.987908\pi\)
0.999279 0.0379795i \(-0.0120922\pi\)
\(240\) −0.110370 −0.00712434
\(241\) 26.6462 1.71644 0.858218 0.513286i \(-0.171572\pi\)
0.858218 + 0.513286i \(0.171572\pi\)
\(242\) 4.24972 + 8.45019i 0.273182 + 0.543199i
\(243\) 1.00000i 0.0641500i
\(244\) 4.27720 0.273819
\(245\) −5.10567 4.78875i −0.326189 0.305942i
\(246\) −2.51083 −0.160085
\(247\) 16.8962 1.07508
\(248\) −4.96704 −0.315407
\(249\) 7.78700i 0.493481i
\(250\) −0.859876 −0.0543834
\(251\) 4.59032i 0.289738i 0.989451 + 0.144869i \(0.0462761\pi\)
−0.989451 + 0.144869i \(0.953724\pi\)
\(252\) 3.06056 1.32552i 0.192797 0.0834998i
\(253\) −11.7192 + 2.78093i −0.736780 + 0.174836i
\(254\) 15.0886 0.946746
\(255\) −5.22254 −0.327048
\(256\) −15.7096 −0.981847
\(257\) 0.226898i 0.0141535i 0.999975 + 0.00707677i \(0.00225262\pi\)
−0.999975 + 0.00707677i \(0.997747\pi\)
\(258\) 3.52598i 0.219518i
\(259\) −23.2435 + 10.0667i −1.44428 + 0.625514i
\(260\) 4.40136i 0.272961i
\(261\) 6.88482i 0.426160i
\(262\) 12.6301i 0.780291i
\(263\) 19.6401i 1.21106i 0.795823 + 0.605530i \(0.207039\pi\)
−0.795823 + 0.605530i \(0.792961\pi\)
\(264\) −9.04765 + 2.14698i −0.556844 + 0.132138i
\(265\) 7.05177i 0.433187i
\(266\) −4.37546 10.1027i −0.268277 0.619438i
\(267\) 13.2622 0.811632
\(268\) 13.5651 0.828621
\(269\) 27.9427i 1.70370i −0.523786 0.851850i \(-0.675481\pi\)
0.523786 0.851850i \(-0.324519\pi\)
\(270\) 0.859876i 0.0523304i
\(271\) −26.5685 −1.61392 −0.806962 0.590603i \(-0.798890\pi\)
−0.806962 + 0.590603i \(0.798890\pi\)
\(272\) 0.576410 0.0349500
\(273\) 3.67121 + 8.47665i 0.222192 + 0.513030i
\(274\) 5.23141i 0.316041i
\(275\) 3.22701 0.765761i 0.194596 0.0461771i
\(276\) 4.57804i 0.275565i
\(277\) 2.38638i 0.143383i −0.997427 0.0716917i \(-0.977160\pi\)
0.997427 0.0716917i \(-0.0228398\pi\)
\(278\) 4.39775i 0.263759i
\(279\) 1.77159i 0.106062i
\(280\) −6.80697 + 2.94808i −0.406795 + 0.176181i
\(281\) 30.2645i 1.80543i −0.430241 0.902714i \(-0.641571\pi\)
0.430241 0.902714i \(-0.358429\pi\)
\(282\) 5.74607i 0.342173i
\(283\) −14.1871 −0.843334 −0.421667 0.906751i \(-0.638555\pi\)
−0.421667 + 0.906751i \(0.638555\pi\)
\(284\) −15.9138 −0.944308
\(285\) −4.83931 −0.286656
\(286\) −2.29898 9.68818i −0.135941 0.572874i
\(287\) 7.08926 3.07034i 0.418466 0.181236i
\(288\) 5.70235i 0.336014i
\(289\) 10.2749 0.604405
\(290\) 5.92009i 0.347640i
\(291\) 12.8157 0.751272
\(292\) −9.25524 −0.541622
\(293\) −18.0515 −1.05458 −0.527289 0.849686i \(-0.676792\pi\)
−0.527289 + 0.849686i \(0.676792\pi\)
\(294\) 4.11773 4.39024i 0.240151 0.256044i
\(295\) −4.22390 −0.245925
\(296\) 26.8422i 1.56017i
\(297\) −0.765761 3.22701i −0.0444340 0.187250i
\(298\) −8.16057 −0.472729
\(299\) 12.6795 0.733276
\(300\) 1.26061i 0.0727815i
\(301\) 4.31169 + 9.95548i 0.248521 + 0.573824i
\(302\) −5.16267 −0.297078
\(303\) 3.67466i 0.211104i
\(304\) 0.534114 0.0306336
\(305\) 3.39295i 0.194280i
\(306\) 4.49074i 0.256718i
\(307\) 6.64367 0.379174 0.189587 0.981864i \(-0.439285\pi\)
0.189587 + 0.981864i \(0.439285\pi\)
\(308\) 8.86143 6.62112i 0.504927 0.377273i
\(309\) −17.3490 −0.986950
\(310\) 1.52335i 0.0865202i
\(311\) 27.7125i 1.57143i 0.618589 + 0.785715i \(0.287705\pi\)
−0.618589 + 0.785715i \(0.712295\pi\)
\(312\) 9.78905 0.554196
\(313\) 14.0995i 0.796952i 0.917179 + 0.398476i \(0.130461\pi\)
−0.917179 + 0.398476i \(0.869539\pi\)
\(314\) −10.2535 −0.578639
\(315\) −1.05149 2.42783i −0.0592446 0.136793i
\(316\) 8.36150i 0.470371i
\(317\) 21.3049 1.19660 0.598301 0.801272i \(-0.295843\pi\)
0.598301 + 0.801272i \(0.295843\pi\)
\(318\) 6.06365 0.340032
\(319\) −5.27213 22.2174i −0.295182 1.24394i
\(320\) 4.68258i 0.261764i
\(321\) 1.09041 0.0608607
\(322\) −3.28350 7.58145i −0.182982 0.422498i
\(323\) 25.2735 1.40625
\(324\) 1.26061 0.0700340
\(325\) −3.49145 −0.193671
\(326\) 8.92270i 0.494183i
\(327\) 8.17579 0.452122
\(328\) 8.18686i 0.452044i
\(329\) 7.02650 + 16.2238i 0.387383 + 0.894450i
\(330\) 0.658460 + 2.77483i 0.0362470 + 0.152749i
\(331\) 12.2216 0.671762 0.335881 0.941904i \(-0.390966\pi\)
0.335881 + 0.941904i \(0.390966\pi\)
\(332\) −9.81639 −0.538744
\(333\) −9.57378 −0.524640
\(334\) 11.3281i 0.619846i
\(335\) 10.7607i 0.587922i
\(336\) 0.116052 + 0.267959i 0.00633118 + 0.0146184i
\(337\) 25.4345i 1.38550i −0.721176 0.692752i \(-0.756398\pi\)
0.721176 0.692752i \(-0.243602\pi\)
\(338\) 0.696324i 0.0378751i
\(339\) 7.87871i 0.427913i
\(340\) 6.58360i 0.357046i
\(341\) −1.35661 5.71693i −0.0734647 0.309589i
\(342\) 4.16121i 0.225013i
\(343\) −6.25774 + 17.4310i −0.337886 + 0.941187i
\(344\) 11.4968 0.619868
\(345\) −3.63160 −0.195519
\(346\) 3.72211i 0.200102i
\(347\) 22.7915i 1.22351i −0.791046 0.611756i \(-0.790463\pi\)
0.791046 0.611756i \(-0.209537\pi\)
\(348\) 8.67909 0.465248
\(349\) −30.6580 −1.64108 −0.820542 0.571586i \(-0.806329\pi\)
−0.820542 + 0.571586i \(0.806329\pi\)
\(350\) 0.904149 + 2.08764i 0.0483288 + 0.111589i
\(351\) 3.49145i 0.186360i
\(352\) −4.36664 18.4016i −0.232743 0.980806i
\(353\) 19.4293i 1.03412i −0.855950 0.517058i \(-0.827027\pi\)
0.855950 0.517058i \(-0.172973\pi\)
\(354\) 3.63203i 0.193040i
\(355\) 12.6238i 0.670004i
\(356\) 16.7185i 0.886077i
\(357\) 5.49143 + 12.6794i 0.290637 + 0.671068i
\(358\) 16.1798i 0.855128i
\(359\) 10.1311i 0.534701i −0.963599 0.267350i \(-0.913852\pi\)
0.963599 0.267350i \(-0.0861481\pi\)
\(360\) −2.80372 −0.147769
\(361\) 4.41897 0.232577
\(362\) 13.2480 0.696297
\(363\) −4.94224 9.82722i −0.259400 0.515795i
\(364\) −10.6858 + 4.62798i −0.560087 + 0.242572i
\(365\) 7.34186i 0.384291i
\(366\) 2.91752 0.152501
\(367\) 22.2494i 1.16141i −0.814115 0.580704i \(-0.802777\pi\)
0.814115 0.580704i \(-0.197223\pi\)
\(368\) 0.400818 0.0208941
\(369\) 2.92000 0.152009
\(370\) 8.23226 0.427975
\(371\) −17.1205 + 7.41484i −0.888853 + 0.384959i
\(372\) 2.23329 0.115790
\(373\) 5.98171i 0.309721i −0.987936 0.154861i \(-0.950507\pi\)
0.987936 0.154861i \(-0.0494928\pi\)
\(374\) −3.43883 14.4917i −0.177818 0.749346i
\(375\) 1.00000 0.0516398
\(376\) 18.7357 0.966220
\(377\) 24.0380i 1.23802i
\(378\) 2.08764 0.904149i 0.107376 0.0465044i
\(379\) −21.7826 −1.11890 −0.559448 0.828865i \(-0.688987\pi\)
−0.559448 + 0.828865i \(0.688987\pi\)
\(380\) 6.10050i 0.312949i
\(381\) −17.5475 −0.898984
\(382\) 14.1136i 0.722116i
\(383\) 1.71341i 0.0875510i −0.999041 0.0437755i \(-0.986061\pi\)
0.999041 0.0437755i \(-0.0139386\pi\)
\(384\) 7.37827 0.376521
\(385\) −5.25230 7.02946i −0.267682 0.358255i
\(386\) −10.1722 −0.517749
\(387\) 4.10056i 0.208443i
\(388\) 16.1557i 0.820181i
\(389\) −9.67848 −0.490719 −0.245359 0.969432i \(-0.578906\pi\)
−0.245359 + 0.969432i \(0.578906\pi\)
\(390\) 3.00221i 0.152023i
\(391\) 18.9661 0.959159
\(392\) 14.3149 + 13.4263i 0.723011 + 0.678132i
\(393\) 14.6883i 0.740927i
\(394\) 17.1576 0.864385
\(395\) 6.63289 0.333737
\(396\) 4.06801 0.965328i 0.204425 0.0485096i
\(397\) 29.8418i 1.49772i −0.662729 0.748860i \(-0.730602\pi\)
0.662729 0.748860i \(-0.269398\pi\)
\(398\) 7.21000 0.361405
\(399\) 5.08848 + 11.7491i 0.254742 + 0.588188i
\(400\) −0.110370 −0.00551849
\(401\) 18.9321 0.945425 0.472712 0.881217i \(-0.343275\pi\)
0.472712 + 0.881217i \(0.343275\pi\)
\(402\) 9.25290 0.461493
\(403\) 6.18540i 0.308117i
\(404\) −4.63233 −0.230467
\(405\) 1.00000i 0.0496904i
\(406\) 14.3730 6.22490i 0.713320 0.308937i
\(407\) −30.8947 + 7.33122i −1.53139 + 0.363395i
\(408\) 14.6425 0.724914
\(409\) 22.3336 1.10432 0.552162 0.833737i \(-0.313803\pi\)
0.552162 + 0.833737i \(0.313803\pi\)
\(410\) −2.51083 −0.124001
\(411\) 6.08391i 0.300097i
\(412\) 21.8704i 1.07748i
\(413\) 4.44138 + 10.2549i 0.218546 + 0.504612i
\(414\) 3.12272i 0.153473i
\(415\) 7.78700i 0.382249i
\(416\) 19.9095i 0.976142i
\(417\) 5.11439i 0.250453i
\(418\) −3.18649 13.4283i −0.155856 0.656799i
\(419\) 1.95078i 0.0953018i 0.998864 + 0.0476509i \(0.0151735\pi\)
−0.998864 + 0.0476509i \(0.984827\pi\)
\(420\) 3.06056 1.32552i 0.149340 0.0646786i
\(421\) −33.4148 −1.62854 −0.814270 0.580487i \(-0.802862\pi\)
−0.814270 + 0.580487i \(0.802862\pi\)
\(422\) 7.84365 0.381823
\(423\) 6.68244i 0.324911i
\(424\) 19.7712i 0.960175i
\(425\) −5.22254 −0.253330
\(426\) −10.8549 −0.525923
\(427\) −8.23752 + 3.56764i −0.398641 + 0.172650i
\(428\) 1.37458i 0.0664430i
\(429\) 2.67361 + 11.2669i 0.129083 + 0.543973i
\(430\) 3.52598i 0.170038i
\(431\) 25.9291i 1.24896i −0.781041 0.624480i \(-0.785311\pi\)
0.781041 0.624480i \(-0.214689\pi\)
\(432\) 0.110370i 0.00531017i
\(433\) 11.7810i 0.566159i −0.959096 0.283080i \(-0.908644\pi\)
0.959096 0.283080i \(-0.0913561\pi\)
\(434\) 3.69843 1.60178i 0.177530 0.0768878i
\(435\) 6.88482i 0.330102i
\(436\) 10.3065i 0.493592i
\(437\) 17.5744 0.840699
\(438\) −6.31309 −0.301651
\(439\) −0.0940499 −0.00448876 −0.00224438 0.999997i \(-0.500714\pi\)
−0.00224438 + 0.999997i \(0.500714\pi\)
\(440\) −9.04765 + 2.14698i −0.431330 + 0.102353i
\(441\) −4.78875 + 5.10567i −0.228036 + 0.243127i
\(442\) 15.6792i 0.745782i
\(443\) 23.1055 1.09778 0.548889 0.835896i \(-0.315051\pi\)
0.548889 + 0.835896i \(0.315051\pi\)
\(444\) 12.0688i 0.572761i
\(445\) 13.2622 0.628688
\(446\) −10.4962 −0.497008
\(447\) 9.49040 0.448880
\(448\) 11.3685 4.92367i 0.537112 0.232621i
\(449\) −30.1507 −1.42290 −0.711451 0.702736i \(-0.751961\pi\)
−0.711451 + 0.702736i \(0.751961\pi\)
\(450\) 0.859876i 0.0405350i
\(451\) 9.42286 2.23602i 0.443705 0.105290i
\(452\) −9.93200 −0.467162
\(453\) 6.00397 0.282091
\(454\) 17.6271i 0.827282i
\(455\) 3.67121 + 8.47665i 0.172109 + 0.397392i
\(456\) 13.5681 0.635385
\(457\) 26.3725i 1.23365i −0.787099 0.616826i \(-0.788418\pi\)
0.787099 0.616826i \(-0.211582\pi\)
\(458\) 10.4695 0.489206
\(459\) 5.22254i 0.243767i
\(460\) 4.57804i 0.213452i
\(461\) 15.0909 0.702853 0.351426 0.936216i \(-0.385697\pi\)
0.351426 + 0.936216i \(0.385697\pi\)
\(462\) 6.04447 4.51633i 0.281214 0.210119i
\(463\) −2.97704 −0.138355 −0.0691775 0.997604i \(-0.522037\pi\)
−0.0691775 + 0.997604i \(0.522037\pi\)
\(464\) 0.759876i 0.0352764i
\(465\) 1.77159i 0.0821554i
\(466\) −10.1345 −0.469473
\(467\) 11.3706i 0.526168i 0.964773 + 0.263084i \(0.0847396\pi\)
−0.964773 + 0.263084i \(0.915260\pi\)
\(468\) −4.40136 −0.203453
\(469\) −26.1253 + 11.3148i −1.20635 + 0.522467i
\(470\) 5.74607i 0.265046i
\(471\) 11.9244 0.549448
\(472\) 11.8427 0.545102
\(473\) 3.14005 + 13.2326i 0.144380 + 0.608434i
\(474\) 5.70346i 0.261969i
\(475\) −4.83931 −0.222043
\(476\) −15.9839 + 6.92256i −0.732620 + 0.317295i
\(477\) −7.05177 −0.322878
\(478\) 1.00975 0.0461850
\(479\) −7.17697 −0.327924 −0.163962 0.986467i \(-0.552427\pi\)
−0.163962 + 0.986467i \(0.552427\pi\)
\(480\) 5.70235i 0.260276i
\(481\) 33.4263 1.52411
\(482\) 22.9125i 1.04363i
\(483\) 3.81857 + 8.81691i 0.173751 + 0.401183i
\(484\) 12.3883 6.23025i 0.563105 0.283193i
\(485\) 12.8157 0.581933
\(486\) 0.859876 0.0390048
\(487\) 15.0191 0.680580 0.340290 0.940321i \(-0.389475\pi\)
0.340290 + 0.940321i \(0.389475\pi\)
\(488\) 9.51289i 0.430628i
\(489\) 10.3767i 0.469252i
\(490\) 4.11773 4.39024i 0.186020 0.198331i
\(491\) 1.66709i 0.0752348i −0.999292 0.0376174i \(-0.988023\pi\)
0.999292 0.0376174i \(-0.0119768\pi\)
\(492\) 3.68098i 0.165952i
\(493\) 35.9562i 1.61939i
\(494\) 14.5287i 0.653675i
\(495\) −0.765761 3.22701i −0.0344184 0.145043i
\(496\) 0.195530i 0.00877954i
\(497\) 30.6486 13.2738i 1.37478 0.595411i
\(498\) −6.69586 −0.300048
\(499\) −18.4748 −0.827047 −0.413523 0.910494i \(-0.635702\pi\)
−0.413523 + 0.910494i \(0.635702\pi\)
\(500\) 1.26061i 0.0563763i
\(501\) 13.1741i 0.588575i
\(502\) −3.94711 −0.176168
\(503\) 5.88295 0.262308 0.131154 0.991362i \(-0.458132\pi\)
0.131154 + 0.991362i \(0.458132\pi\)
\(504\) 2.94808 + 6.80697i 0.131318 + 0.303207i
\(505\) 3.67466i 0.163520i
\(506\) −2.39126 10.0771i −0.106304 0.447980i
\(507\) 0.809796i 0.0359643i
\(508\) 22.1206i 0.981441i
\(509\) 27.2518i 1.20791i 0.797017 + 0.603957i \(0.206410\pi\)
−0.797017 + 0.603957i \(0.793590\pi\)
\(510\) 4.49074i 0.198853i
\(511\) 17.8248 7.71987i 0.788524 0.341507i
\(512\) 1.24826i 0.0551658i
\(513\) 4.83931i 0.213661i
\(514\) −0.195105 −0.00860569
\(515\) −17.3490 −0.764488
\(516\) −5.16922 −0.227562
\(517\) 5.11715 + 21.5643i 0.225052 + 0.948397i
\(518\) −8.65612 19.9866i −0.380328 0.878159i
\(519\) 4.32866i 0.190007i
\(520\) 9.78905 0.429278
\(521\) 24.1726i 1.05902i −0.848303 0.529510i \(-0.822376\pi\)
0.848303 0.529510i \(-0.177624\pi\)
\(522\) 5.92009 0.259115
\(523\) −19.6895 −0.860963 −0.430482 0.902599i \(-0.641656\pi\)
−0.430482 + 0.902599i \(0.641656\pi\)
\(524\) −18.5163 −0.808886
\(525\) −1.05149 2.42783i −0.0458906 0.105959i
\(526\) −16.8880 −0.736354
\(527\) 9.25218i 0.403031i
\(528\) 0.0845169 + 0.356165i 0.00367812 + 0.0155001i
\(529\) −9.81152 −0.426588
\(530\) 6.06365 0.263388
\(531\) 4.22390i 0.183302i
\(532\) −14.8110 + 6.41460i −0.642138 + 0.278108i
\(533\) −10.1950 −0.441595
\(534\) 11.4038i 0.493492i
\(535\) 1.09041 0.0471425
\(536\) 30.1701i 1.30315i
\(537\) 18.8164i 0.811988i
\(538\) 24.0273 1.03589
\(539\) −11.5436 + 20.1431i −0.497220 + 0.867625i
\(540\) 1.26061 0.0542481
\(541\) 42.3962i 1.82276i 0.411570 + 0.911378i \(0.364981\pi\)
−0.411570 + 0.911378i \(0.635019\pi\)
\(542\) 22.8457i 0.981305i
\(543\) −15.4068 −0.661170
\(544\) 29.7807i 1.27684i
\(545\) 8.17579 0.350212
\(546\) −7.28887 + 3.15679i −0.311935 + 0.135098i
\(547\) 32.4310i 1.38665i 0.720625 + 0.693325i \(0.243855\pi\)
−0.720625 + 0.693325i \(0.756145\pi\)
\(548\) −7.66945 −0.327623
\(549\) −3.39295 −0.144808
\(550\) 0.658460 + 2.77483i 0.0280768 + 0.118319i
\(551\) 33.3178i 1.41939i
\(552\) 10.1820 0.433374
\(553\) −6.97439 16.1035i −0.296581 0.684793i
\(554\) 2.05199 0.0871806
\(555\) −9.57378 −0.406384
\(556\) −6.44727 −0.273425
\(557\) 42.7904i 1.81309i −0.422110 0.906545i \(-0.638710\pi\)
0.422110 0.906545i \(-0.361290\pi\)
\(558\) 1.52335 0.0644884
\(559\) 14.3169i 0.605540i
\(560\) 0.116052 + 0.267959i 0.00490411 + 0.0113234i
\(561\) 3.99921 + 16.8532i 0.168847 + 0.711542i
\(562\) 26.0237 1.09774
\(563\) 6.74548 0.284288 0.142144 0.989846i \(-0.454600\pi\)
0.142144 + 0.989846i \(0.454600\pi\)
\(564\) −8.42397 −0.354713
\(565\) 7.87871i 0.331460i
\(566\) 12.1991i 0.512767i
\(567\) −2.42783 + 1.05149i −0.101959 + 0.0441583i
\(568\) 35.3937i 1.48509i
\(569\) 32.5796i 1.36581i −0.730507 0.682905i \(-0.760716\pi\)
0.730507 0.682905i \(-0.239284\pi\)
\(570\) 4.16121i 0.174294i
\(571\) 1.96737i 0.0823318i −0.999152 0.0411659i \(-0.986893\pi\)
0.999152 0.0411659i \(-0.0131072\pi\)
\(572\) −14.2033 + 3.37039i −0.593868 + 0.140923i
\(573\) 16.4135i 0.685686i
\(574\) 2.64011 + 6.09589i 0.110196 + 0.254437i
\(575\) −3.63160 −0.151448
\(576\) 4.68258 0.195107
\(577\) 24.9783i 1.03986i 0.854209 + 0.519930i \(0.174042\pi\)
−0.854209 + 0.519930i \(0.825958\pi\)
\(578\) 8.83513i 0.367493i
\(579\) 11.8298 0.491630
\(580\) 8.67909 0.360380
\(581\) 18.9055 8.18793i 0.784334 0.339692i
\(582\) 11.0200i 0.456792i
\(583\) −22.7561 + 5.39997i −0.942463 + 0.223644i
\(584\) 20.5846i 0.851795i
\(585\) 3.49145i 0.144354i
\(586\) 15.5220i 0.641210i
\(587\) 18.5839i 0.767039i 0.923533 + 0.383520i \(0.125288\pi\)
−0.923533 + 0.383520i \(0.874712\pi\)
\(588\) −6.43627 6.03676i −0.265427 0.248952i
\(589\) 8.57327i 0.353255i
\(590\) 3.63203i 0.149528i
\(591\) −19.9535 −0.820778
\(592\) 1.05666 0.0434283
\(593\) 38.4539 1.57911 0.789556 0.613678i \(-0.210311\pi\)
0.789556 + 0.613678i \(0.210311\pi\)
\(594\) 2.77483 0.658460i 0.113853 0.0270169i
\(595\) 5.49143 + 12.6794i 0.225127 + 0.519807i
\(596\) 11.9637i 0.490053i
\(597\) −8.38493 −0.343172
\(598\) 10.9028i 0.445850i
\(599\) 33.7186 1.37771 0.688853 0.724901i \(-0.258115\pi\)
0.688853 + 0.724901i \(0.258115\pi\)
\(600\) −2.80372 −0.114462
\(601\) 12.8064 0.522385 0.261193 0.965287i \(-0.415884\pi\)
0.261193 + 0.965287i \(0.415884\pi\)
\(602\) −8.56048 + 3.70752i −0.348899 + 0.151107i
\(603\) −10.7607 −0.438211
\(604\) 7.56868i 0.307965i
\(605\) −4.94224 9.82722i −0.200931 0.399533i
\(606\) −3.15976 −0.128356
\(607\) −38.5457 −1.56452 −0.782261 0.622951i \(-0.785934\pi\)
−0.782261 + 0.622951i \(0.785934\pi\)
\(608\) 27.5955i 1.11914i
\(609\) −16.7152 + 7.23930i −0.677334 + 0.293351i
\(610\) 2.91752 0.118127
\(611\) 23.3314i 0.943887i
\(612\) −6.58360 −0.266126
\(613\) 31.0256i 1.25311i 0.779376 + 0.626556i \(0.215536\pi\)
−0.779376 + 0.626556i \(0.784464\pi\)
\(614\) 5.71274i 0.230547i
\(615\) 2.92000 0.117746
\(616\) 14.7260 + 19.7087i 0.593328 + 0.794085i
\(617\) −7.29895 −0.293845 −0.146922 0.989148i \(-0.546937\pi\)
−0.146922 + 0.989148i \(0.546937\pi\)
\(618\) 14.9180i 0.600090i
\(619\) 6.40581i 0.257471i −0.991679 0.128736i \(-0.958908\pi\)
0.991679 0.128736i \(-0.0410919\pi\)
\(620\) 2.23329 0.0896909
\(621\) 3.63160i 0.145731i
\(622\) −23.8293 −0.955468
\(623\) −13.9450 32.1984i −0.558695 1.29000i
\(624\) 0.385350i 0.0154264i
\(625\) 1.00000 0.0400000
\(626\) −12.1238 −0.484566
\(627\) 3.70576 + 15.6165i 0.147994 + 0.623664i
\(628\) 15.0321i 0.599845i
\(629\) 49.9994 1.99361
\(630\) 2.08764 0.904149i 0.0831734 0.0360221i
\(631\) 10.0326 0.399392 0.199696 0.979858i \(-0.436005\pi\)
0.199696 + 0.979858i \(0.436005\pi\)
\(632\) −18.5968 −0.739740
\(633\) −9.12184 −0.362561
\(634\) 18.3196i 0.727563i
\(635\) −17.5475 −0.696350
\(636\) 8.88955i 0.352493i
\(637\) 16.7197 17.8262i 0.662457 0.706299i
\(638\) 19.1042 4.53338i 0.756343 0.179478i
\(639\) 12.6238 0.499391
\(640\) 7.37827 0.291652
\(641\) 10.1330 0.400229 0.200115 0.979773i \(-0.435869\pi\)
0.200115 + 0.979773i \(0.435869\pi\)
\(642\) 0.937617i 0.0370048i
\(643\) 20.7462i 0.818151i 0.912501 + 0.409075i \(0.134149\pi\)
−0.912501 + 0.409075i \(0.865851\pi\)
\(644\) −11.1147 + 4.81374i −0.437981 + 0.189688i
\(645\) 4.10056i 0.161459i
\(646\) 21.7321i 0.855037i
\(647\) 24.6487i 0.969042i −0.874780 0.484521i \(-0.838994\pi\)
0.874780 0.484521i \(-0.161006\pi\)
\(648\) 2.80372i 0.110141i
\(649\) 3.23450 + 13.6306i 0.126965 + 0.535047i
\(650\) 3.00221i 0.117756i
\(651\) −4.30112 + 1.86280i −0.168574 + 0.0730089i
\(652\) 13.0810 0.512293
\(653\) 25.2179 0.986851 0.493425 0.869788i \(-0.335745\pi\)
0.493425 + 0.869788i \(0.335745\pi\)
\(654\) 7.03017i 0.274901i
\(655\) 14.6883i 0.573919i
\(656\) −0.322279 −0.0125829
\(657\) 7.34186 0.286433
\(658\) −13.9505 + 6.04192i −0.543847 + 0.235538i
\(659\) 27.1494i 1.05759i 0.848749 + 0.528796i \(0.177356\pi\)
−0.848749 + 0.528796i \(0.822644\pi\)
\(660\) 4.06801 0.965328i 0.158347 0.0375753i
\(661\) 34.6718i 1.34858i 0.738469 + 0.674288i \(0.235549\pi\)
−0.738469 + 0.674288i \(0.764451\pi\)
\(662\) 10.5091i 0.408448i
\(663\) 18.2342i 0.708158i
\(664\) 21.8326i 0.847269i
\(665\) 5.08848 + 11.7491i 0.197323 + 0.455609i
\(666\) 8.23226i 0.318994i
\(667\) 25.0029i 0.968115i
\(668\) 16.6074 0.642561
\(669\) 12.2066 0.471935
\(670\) 9.25290 0.357471
\(671\) −10.9491 + 2.59819i −0.422685 + 0.100302i
\(672\) −13.8444 + 5.99595i −0.534058 + 0.231299i
\(673\) 50.2414i 1.93667i 0.249663 + 0.968333i \(0.419680\pi\)
−0.249663 + 0.968333i \(0.580320\pi\)
\(674\) 21.8705 0.842420
\(675\) 1.00000i 0.0384900i
\(676\) −1.02084 −0.0392630
\(677\) 38.9406 1.49661 0.748304 0.663356i \(-0.230868\pi\)
0.748304 + 0.663356i \(0.230868\pi\)
\(678\) −6.77471 −0.260181
\(679\) −13.4756 31.1145i −0.517146 1.19406i
\(680\) 14.6425 0.561516
\(681\) 20.4996i 0.785547i
\(682\) 4.91586 1.16652i 0.188238 0.0446683i
\(683\) −23.1688 −0.886531 −0.443265 0.896390i \(-0.646180\pi\)
−0.443265 + 0.896390i \(0.646180\pi\)
\(684\) −6.10050 −0.233259
\(685\) 6.08391i 0.232454i
\(686\) −14.9885 5.38089i −0.572265 0.205443i
\(687\) −12.1756 −0.464526
\(688\) 0.452578i 0.0172544i
\(689\) 24.6209 0.937980
\(690\) 3.12272i 0.118880i
\(691\) 3.18446i 0.121142i −0.998164 0.0605712i \(-0.980708\pi\)
0.998164 0.0605712i \(-0.0192922\pi\)
\(692\) 5.45676 0.207435
\(693\) −7.02946 + 5.25230i −0.267027 + 0.199518i
\(694\) 19.5979 0.743926
\(695\) 5.11439i 0.194000i
\(696\) 19.3031i 0.731683i
\(697\) −15.2498 −0.577627
\(698\) 26.3621i 0.997820i
\(699\) 11.7860 0.445789
\(700\) 3.06056 1.32552i 0.115678 0.0500999i
\(701\) 36.3597i 1.37329i −0.726994 0.686644i \(-0.759083\pi\)
0.726994 0.686644i \(-0.240917\pi\)
\(702\) −3.00221 −0.113311
\(703\) 46.3305 1.74739
\(704\) 15.1107 3.58573i 0.569507 0.135142i
\(705\) 6.68244i 0.251675i
\(706\) 16.7068 0.628768
\(707\) 8.92147 3.86386i 0.335526 0.145315i
\(708\) −5.32471 −0.200115
\(709\) −9.34795 −0.351070 −0.175535 0.984473i \(-0.556165\pi\)
−0.175535 + 0.984473i \(0.556165\pi\)
\(710\) −10.8549 −0.407378
\(711\) 6.63289i 0.248753i
\(712\) −37.1835 −1.39351
\(713\) 6.43369i 0.240944i
\(714\) −10.9028 + 4.72195i −0.408025 + 0.176715i
\(715\) 2.67361 + 11.2669i 0.0999875 + 0.421360i
\(716\) 23.7202 0.886466
\(717\) −1.17430 −0.0438550
\(718\) 8.71152 0.325111
\(719\) 5.43495i 0.202689i −0.994851 0.101345i \(-0.967686\pi\)
0.994851 0.101345i \(-0.0323145\pi\)
\(720\) 0.110370i 0.00411324i
\(721\) 18.2423 + 42.1205i 0.679377 + 1.56865i
\(722\) 3.79977i 0.141413i
\(723\) 26.6462i 0.990985i
\(724\) 19.4220i 0.721814i
\(725\) 6.88482i 0.255696i
\(726\) 8.45019 4.24972i 0.313616 0.157722i
\(727\) 38.4305i 1.42531i −0.701515 0.712655i \(-0.747493\pi\)
0.701515 0.712655i \(-0.252507\pi\)
\(728\) −10.2931 23.7662i −0.381486 0.880834i
\(729\) −1.00000 −0.0370370
\(730\) −6.31309 −0.233658
\(731\) 21.4153i 0.792074i
\(732\) 4.27720i 0.158090i
\(733\) 2.10130 0.0776131 0.0388066 0.999247i \(-0.487644\pi\)
0.0388066 + 0.999247i \(0.487644\pi\)
\(734\) 19.1317 0.706164
\(735\) −4.78875 + 5.10567i −0.176636 + 0.188325i
\(736\) 20.7086i 0.763330i
\(737\) −34.7250 + 8.24015i −1.27911 + 0.303530i
\(738\) 2.51083i 0.0924251i
\(739\) 32.3860i 1.19134i −0.803230 0.595669i \(-0.796887\pi\)
0.803230 0.595669i \(-0.203113\pi\)
\(740\) 12.0688i 0.443659i
\(741\) 16.8962i 0.620698i
\(742\) −6.37585 14.7215i −0.234065 0.540444i
\(743\) 18.1188i 0.664715i −0.943153 0.332358i \(-0.892156\pi\)
0.943153 0.332358i \(-0.107844\pi\)
\(744\) 4.96704i 0.182101i
\(745\) 9.49040 0.347701
\(746\) 5.14353 0.188318
\(747\) 7.78700 0.284911
\(748\) −21.2453 + 5.04146i −0.776807 + 0.184334i
\(749\) −1.14655 2.64733i −0.0418941 0.0967314i
\(750\) 0.859876i 0.0313982i
\(751\) −6.77040 −0.247055 −0.123528 0.992341i \(-0.539421\pi\)
−0.123528 + 0.992341i \(0.539421\pi\)
\(752\) 0.737539i 0.0268953i
\(753\) 4.59032 0.167281
\(754\) −20.6697 −0.752746
\(755\) 6.00397 0.218507
\(756\) −1.32552 3.06056i −0.0482086 0.111311i
\(757\) −47.4205 −1.72353 −0.861763 0.507310i \(-0.830640\pi\)
−0.861763 + 0.507310i \(0.830640\pi\)
\(758\) 18.7303i 0.680316i
\(759\) 2.78093 + 11.7192i 0.100941 + 0.425380i
\(760\) 13.5681 0.492167
\(761\) 13.1779 0.477700 0.238850 0.971056i \(-0.423230\pi\)
0.238850 + 0.971056i \(0.423230\pi\)
\(762\) 15.0886i 0.546604i
\(763\) −8.59673 19.8495i −0.311223 0.718598i
\(764\) −20.6911 −0.748579
\(765\) 5.22254i 0.188821i
\(766\) 1.47332 0.0532331
\(767\) 14.7475i 0.532503i
\(768\) 15.7096i 0.566870i
\(769\) −13.7275 −0.495026 −0.247513 0.968885i \(-0.579613\pi\)
−0.247513 + 0.968885i \(0.579613\pi\)
\(770\) 6.04447 4.51633i 0.217827 0.162757i
\(771\) 0.226898 0.00817155
\(772\) 14.9128i 0.536723i
\(773\) 31.2038i 1.12232i −0.827707 0.561161i \(-0.810355\pi\)
0.827707 0.561161i \(-0.189645\pi\)
\(774\) −3.52598 −0.126739
\(775\) 1.77159i 0.0636373i
\(776\) −35.9318 −1.28988
\(777\) 10.0667 + 23.2435i 0.361141 + 0.833857i
\(778\) 8.32230i 0.298369i
\(779\) −14.1308 −0.506288
\(780\) −4.40136 −0.157594
\(781\) 40.7373 9.66684i 1.45769 0.345907i
\(782\) 16.3085i 0.583192i
\(783\) −6.88482 −0.246043
\(784\) 0.528533 0.563512i 0.0188762 0.0201254i
\(785\) 11.9244 0.425600
\(786\) −12.6301 −0.450502
\(787\) −11.7020 −0.417130 −0.208565 0.978008i \(-0.566879\pi\)
−0.208565 + 0.978008i \(0.566879\pi\)
\(788\) 25.1537i 0.896062i
\(789\) 19.6401 0.699206
\(790\) 5.70346i 0.202920i
\(791\) 19.1282 8.28436i 0.680120 0.294558i
\(792\) 2.14698 + 9.04765i 0.0762897 + 0.321494i
\(793\) 11.8463 0.420675
\(794\) 25.6603 0.910650
\(795\) −7.05177 −0.250100
\(796\) 10.5702i 0.374649i
\(797\) 25.7788i 0.913133i 0.889689 + 0.456566i \(0.150921\pi\)
−0.889689 + 0.456566i \(0.849079\pi\)
\(798\) −10.1027 + 4.37546i −0.357633 + 0.154890i
\(799\) 34.8993i 1.23465i
\(800\) 5.70235i 0.201609i
\(801\) 13.2622i 0.468596i
\(802\) 16.2793i 0.574841i
\(803\) 23.6923 5.62211i 0.836082 0.198400i
\(804\) 13.5651i 0.478405i
\(805\) 3.81857 + 8.81691i 0.134587 + 0.310755i
\(806\) −5.31868 −0.187343
\(807\) −27.9427 −0.983631
\(808\) 10.3027i 0.362449i
\(809\) 32.3910i 1.13881i −0.822058 0.569404i \(-0.807174\pi\)
0.822058 0.569404i \(-0.192826\pi\)
\(810\) 0.859876 0.0302130
\(811\) −12.9674 −0.455345 −0.227673 0.973738i \(-0.573112\pi\)
−0.227673 + 0.973738i \(0.573112\pi\)
\(812\) −9.12595 21.0714i −0.320258 0.739461i
\(813\) 26.5685i 0.931800i
\(814\) −6.30395 26.5656i −0.220953 0.931125i
\(815\) 10.3767i 0.363481i
\(816\) 0.576410i 0.0201784i
\(817\) 19.8439i 0.694250i
\(818\) 19.2041i 0.671456i
\(819\) 8.47665 3.67121i 0.296198 0.128282i
\(820\) 3.68098i 0.128546i
\(821\) 13.9004i 0.485126i −0.970136 0.242563i \(-0.922012\pi\)
0.970136 0.242563i \(-0.0779880\pi\)
\(822\) −5.23141 −0.182466
\(823\) 39.8119 1.38775 0.693877 0.720094i \(-0.255901\pi\)
0.693877 + 0.720094i \(0.255901\pi\)
\(824\) 48.6418 1.69452
\(825\) −0.765761 3.22701i −0.0266604 0.112350i
\(826\) −8.81797 + 3.81904i −0.306817 + 0.132881i
\(827\) 49.2671i 1.71318i 0.515994 + 0.856592i \(0.327423\pi\)
−0.515994 + 0.856592i \(0.672577\pi\)
\(828\) −4.57804 −0.159098
\(829\) 33.0804i 1.14893i −0.818530 0.574464i \(-0.805210\pi\)
0.818530 0.574464i \(-0.194790\pi\)
\(830\) −6.69586 −0.232417
\(831\) −2.38638 −0.0827825
\(832\) −16.3490 −0.566799
\(833\) 25.0094 26.6645i 0.866525 0.923872i
\(834\) −4.39775 −0.152281
\(835\) 13.1741i 0.455909i
\(836\) −19.6864 + 4.67153i −0.680868 + 0.161568i
\(837\) −1.77159 −0.0612350
\(838\) −1.67743 −0.0579458
\(839\) 8.90021i 0.307270i 0.988128 + 0.153635i \(0.0490979\pi\)
−0.988128 + 0.153635i \(0.950902\pi\)
\(840\) 2.94808 + 6.80697i 0.101718 + 0.234863i
\(841\) −18.4007 −0.634509
\(842\) 28.7326i 0.990192i
\(843\) −30.2645 −1.04236
\(844\) 11.4991i 0.395816i
\(845\) 0.809796i 0.0278578i
\(846\) −5.74607 −0.197554
\(847\) −18.6622 + 22.3321i −0.641239 + 0.767341i
\(848\) 0.778302 0.0267270
\(849\) 14.1871i 0.486899i
\(850\) 4.49074i 0.154031i
\(851\) 34.7681 1.19183
\(852\) 15.9138i 0.545197i
\(853\) −4.37084 −0.149655 −0.0748274 0.997196i \(-0.523841\pi\)
−0.0748274 + 0.997196i \(0.523841\pi\)
\(854\) −3.06773 7.08325i −0.104976 0.242384i
\(855\) 4.83931i 0.165501i
\(856\) −3.05721 −0.104493
\(857\) 37.3470 1.27575 0.637874 0.770141i \(-0.279814\pi\)
0.637874 + 0.770141i \(0.279814\pi\)
\(858\) −9.68818 + 2.29898i −0.330749 + 0.0784858i
\(859\) 4.84550i 0.165326i 0.996578 + 0.0826631i \(0.0263425\pi\)
−0.996578 + 0.0826631i \(0.973657\pi\)
\(860\) −5.16922 −0.176269
\(861\) −3.07034 7.08926i −0.104637 0.241601i
\(862\) 22.2958 0.759398
\(863\) −21.9148 −0.745989 −0.372994 0.927834i \(-0.621669\pi\)
−0.372994 + 0.927834i \(0.621669\pi\)
\(864\) −5.70235 −0.193998
\(865\) 4.32866i 0.147179i
\(866\) 10.1302 0.344239
\(867\) 10.2749i 0.348953i
\(868\) −2.34827 5.42205i −0.0797055 0.184036i
\(869\) −5.07921 21.4044i −0.172300 0.726095i
\(870\) 5.92009 0.200710
\(871\) 37.5705 1.27303
\(872\) −22.9226 −0.776259
\(873\) 12.8157i 0.433747i
\(874\) 15.1118i 0.511166i
\(875\) −1.05149 2.42783i −0.0355467 0.0820758i
\(876\) 9.25524i 0.312706i
\(877\) 54.4055i 1.83714i 0.395253 + 0.918572i \(0.370657\pi\)
−0.395253 + 0.918572i \(0.629343\pi\)
\(878\) 0.0808713i 0.00272927i
\(879\) 18.0515i 0.608861i
\(880\) 0.0845169 + 0.356165i 0.00284906 + 0.0120063i
\(881\) 47.6792i 1.60635i 0.595742 + 0.803176i \(0.296858\pi\)
−0.595742 + 0.803176i \(0.703142\pi\)
\(882\) −4.39024 4.11773i −0.147827 0.138651i
\(883\) 49.0965 1.65223 0.826114 0.563503i \(-0.190547\pi\)
0.826114 + 0.563503i \(0.190547\pi\)
\(884\) 22.9863 0.773112
\(885\) 4.22390i 0.141985i
\(886\) 19.8679i 0.667475i
\(887\) −31.7068 −1.06461 −0.532304 0.846553i \(-0.678674\pi\)
−0.532304 + 0.846553i \(0.678674\pi\)
\(888\) 26.8422 0.900766
\(889\) 18.4509 + 42.6023i 0.618824 + 1.42884i
\(890\) 11.4038i 0.382257i
\(891\) −3.22701 + 0.765761i −0.108109 + 0.0256540i
\(892\) 15.3878i 0.515222i
\(893\) 32.3384i 1.08216i
\(894\) 8.16057i 0.272930i
\(895\) 18.8164i 0.628963i
\(896\) −7.75815 17.9132i −0.259182 0.598438i
\(897\) 12.6795i 0.423357i
\(898\) 25.9259i 0.865159i
\(899\) −12.1971 −0.406795
\(900\) 1.26061 0.0420204
\(901\) 36.8281 1.22692
\(902\) 1.92270 + 8.10250i 0.0640189 + 0.269784i
\(903\) 9.95548 4.31169i 0.331298 0.143484i
\(904\) 22.0897i 0.734693i
\(905\) −15.4068 −0.512140
\(906\) 5.16267i 0.171518i
\(907\) 3.45523 0.114729 0.0573645 0.998353i \(-0.481730\pi\)
0.0573645 + 0.998353i \(0.481730\pi\)
\(908\) −25.8421 −0.857599
\(909\) 3.67466 0.121881
\(910\) −7.28887 + 3.15679i −0.241624 + 0.104646i
\(911\) 5.82319 0.192931 0.0964654 0.995336i \(-0.469246\pi\)
0.0964654 + 0.995336i \(0.469246\pi\)
\(912\) 0.534114i 0.0176863i
\(913\) 25.1287 5.96298i 0.831640 0.197346i
\(914\) 22.6771 0.750091
\(915\) −3.39295 −0.112167
\(916\) 15.3487i 0.507134i
\(917\) 35.6607 15.4446i 1.17762 0.510024i
\(918\) −4.49074 −0.148216
\(919\) 44.3255i 1.46216i 0.682291 + 0.731081i \(0.260984\pi\)
−0.682291 + 0.731081i \(0.739016\pi\)
\(920\) 10.1820 0.335690
\(921\) 6.64367i 0.218916i
\(922\) 12.9763i 0.427352i
\(923\) −44.0755 −1.45076
\(924\) −6.62112 8.86143i −0.217819 0.291520i
\(925\) −9.57378 −0.314784
\(926\) 2.55989i 0.0841232i
\(927\) 17.3490i 0.569816i
\(928\) −39.2597 −1.28876
\(929\) 33.0971i 1.08588i 0.839771 + 0.542940i \(0.182689\pi\)
−0.839771 + 0.542940i \(0.817311\pi\)
\(930\) 1.52335 0.0499525
\(931\) 23.1743 24.7079i 0.759506 0.809770i
\(932\) 14.8576i 0.486677i
\(933\) 27.7125 0.907265
\(934\) −9.77730 −0.319923
\(935\) 3.99921 + 16.8532i 0.130788 + 0.551158i
\(936\) 9.78905i 0.319965i
\(937\) −8.45222 −0.276122 −0.138061 0.990424i \(-0.544087\pi\)
−0.138061 + 0.990424i \(0.544087\pi\)
\(938\) −9.72930 22.4645i −0.317673 0.733492i
\(939\) 14.0995 0.460120
\(940\) −8.42397 −0.274759
\(941\) −41.7728 −1.36175 −0.680876 0.732398i \(-0.738401\pi\)
−0.680876 + 0.732398i \(0.738401\pi\)
\(942\) 10.2535i 0.334078i
\(943\) −10.6042 −0.345322
\(944\) 0.466191i 0.0151732i
\(945\) −2.42783 + 1.05149i −0.0789774 + 0.0342049i
\(946\) −11.3784 + 2.70005i −0.369943 + 0.0877863i
\(947\) −25.8994 −0.841617 −0.420808 0.907150i \(-0.638253\pi\)
−0.420808 + 0.907150i \(0.638253\pi\)
\(948\) 8.36150 0.271569
\(949\) −25.6337 −0.832106
\(950\) 4.16121i 0.135008i
\(951\) 21.3049i 0.690858i
\(952\) −15.3964 35.5497i −0.499002 1.15217i
\(953\) 13.7313i 0.444801i −0.974955 0.222401i \(-0.928611\pi\)
0.974955 0.222401i \(-0.0713893\pi\)
\(954\) 6.06365i 0.196318i
\(955\) 16.4135i 0.531130i
\(956\) 1.48034i 0.0478775i
\(957\) −22.2174 + 5.27213i −0.718187 + 0.170424i
\(958\) 6.17131i 0.199386i
\(959\) 14.7707 6.39715i 0.476971 0.206575i
\(960\) 4.68258 0.151130
\(961\) 27.8615 0.898757
\(962\) 28.7425i 0.926696i
\(963\) 1.09041i 0.0351379i
\(964\) 33.5906 1.08188
\(965\) 11.8298 0.380815
\(966\) −7.58145 + 3.28350i −0.243929 + 0.105645i
\(967\) 59.2046i 1.90389i −0.306268 0.951945i \(-0.599080\pi\)
0.306268 0.951945i \(-0.400920\pi\)
\(968\) 13.8567 + 27.5528i 0.445370 + 0.885581i
\(969\) 25.2735i 0.811902i
\(970\) 11.0200i 0.353830i
\(971\) 21.6584i 0.695052i −0.937670 0.347526i \(-0.887022\pi\)
0.937670 0.347526i \(-0.112978\pi\)
\(972\) 1.26061i 0.0404342i
\(973\) 12.4169 5.37772i 0.398067 0.172402i
\(974\) 12.9146i 0.413809i
\(975\) 3.49145i 0.111816i
\(976\) 0.374479 0.0119868
\(977\) 42.3558 1.35508 0.677541 0.735485i \(-0.263046\pi\)
0.677541 + 0.735485i \(0.263046\pi\)
\(978\) 8.92270 0.285316
\(979\) −10.1557 42.7972i −0.324576 1.36781i
\(980\) −6.43627 6.03676i −0.205599 0.192837i
\(981\) 8.17579i 0.261033i
\(982\) 1.43349 0.0457446
\(983\) 35.6348i 1.13657i 0.822831 + 0.568287i \(0.192394\pi\)
−0.822831 + 0.568287i \(0.807606\pi\)
\(984\) −8.18686 −0.260988
\(985\) −19.9535 −0.635772
\(986\) −30.9179 −0.984627
\(987\) 16.2238 7.02650i 0.516411 0.223656i
\(988\) 21.2996 0.677630
\(989\) 14.8916i 0.473525i
\(990\) 2.77483 0.658460i 0.0881899 0.0209272i
\(991\) 19.3208 0.613746 0.306873 0.951751i \(-0.400717\pi\)
0.306873 + 0.951751i \(0.400717\pi\)
\(992\) −10.1022 −0.320746
\(993\) 12.2216i 0.387842i
\(994\) 11.4138 + 26.3540i 0.362024 + 0.835897i
\(995\) −8.38493 −0.265820
\(996\) 9.81639i 0.311044i
\(997\) −39.8048 −1.26063 −0.630316 0.776339i \(-0.717075\pi\)
−0.630316 + 0.776339i \(0.717075\pi\)
\(998\) 15.8861i 0.502865i
\(999\) 9.57378i 0.302901i
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.i.d.76.10 yes 32
7.6 odd 2 inner 1155.2.i.d.76.24 yes 32
11.10 odd 2 inner 1155.2.i.d.76.23 yes 32
77.76 even 2 inner 1155.2.i.d.76.9 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.i.d.76.9 32 77.76 even 2 inner
1155.2.i.d.76.10 yes 32 1.1 even 1 trivial
1155.2.i.d.76.23 yes 32 11.10 odd 2 inner
1155.2.i.d.76.24 yes 32 7.6 odd 2 inner