Properties

Label 1155.2.i.d.76.2
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 76.2
Character \(\chi\) \(=\) 1155.76
Dual form 1155.2.i.d.76.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.26491i q^{2} +1.00000i q^{3} +0.399993 q^{4} +1.00000i q^{5} -1.26491 q^{6} +(0.0556365 + 2.64517i) q^{7} +3.03578i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.26491i q^{2} +1.00000i q^{3} +0.399993 q^{4} +1.00000i q^{5} -1.26491 q^{6} +(0.0556365 + 2.64517i) q^{7} +3.03578i q^{8} -1.00000 q^{9} -1.26491 q^{10} +(-0.516444 + 3.27617i) q^{11} +0.399993i q^{12} +6.21341 q^{13} +(-3.34591 + 0.0703753i) q^{14} -1.00000 q^{15} -3.04002 q^{16} +1.62680 q^{17} -1.26491i q^{18} +4.38730 q^{19} +0.399993i q^{20} +(-2.64517 + 0.0556365i) q^{21} +(-4.14407 - 0.653257i) q^{22} -1.24003 q^{23} -3.03578 q^{24} -1.00000 q^{25} +7.85943i q^{26} -1.00000i q^{27} +(0.0222542 + 1.05805i) q^{28} -9.91159i q^{29} -1.26491i q^{30} -7.78246i q^{31} +2.22620i q^{32} +(-3.27617 - 0.516444i) q^{33} +2.05776i q^{34} +(-2.64517 + 0.0556365i) q^{35} -0.399993 q^{36} +1.61516 q^{37} +5.54956i q^{38} +6.21341i q^{39} -3.03578 q^{40} -4.95141 q^{41} +(-0.0703753 - 3.34591i) q^{42} +3.35295i q^{43} +(-0.206574 + 1.31044i) q^{44} -1.00000i q^{45} -1.56854i q^{46} -4.74958i q^{47} -3.04002i q^{48} +(-6.99381 + 0.294335i) q^{49} -1.26491i q^{50} +1.62680i q^{51} +2.48532 q^{52} -8.51450 q^{53} +1.26491 q^{54} +(-3.27617 - 0.516444i) q^{55} +(-8.03015 + 0.168900i) q^{56} +4.38730i q^{57} +12.5373 q^{58} +4.49064i q^{59} -0.399993 q^{60} -6.43034 q^{61} +9.84415 q^{62} +(-0.0556365 - 2.64517i) q^{63} -8.89600 q^{64} +6.21341i q^{65} +(0.653257 - 4.14407i) q^{66} +3.96452 q^{67} +0.650708 q^{68} -1.24003i q^{69} +(-0.0703753 - 3.34591i) q^{70} +11.2241 q^{71} -3.03578i q^{72} +8.16211 q^{73} +2.04303i q^{74} -1.00000i q^{75} +1.75489 q^{76} +(-8.69475 - 1.18381i) q^{77} -7.85943 q^{78} +13.4557i q^{79} -3.04002i q^{80} +1.00000 q^{81} -6.26310i q^{82} -2.78335 q^{83} +(-1.05805 + 0.0222542i) q^{84} +1.62680i q^{85} -4.24119 q^{86} +9.91159 q^{87} +(-9.94574 - 1.56781i) q^{88} +2.92087i q^{89} +1.26491 q^{90} +(0.345692 + 16.4355i) q^{91} -0.496005 q^{92} +7.78246 q^{93} +6.00780 q^{94} +4.38730i q^{95} -2.22620 q^{96} -15.7071i q^{97} +(-0.372309 - 8.84657i) q^{98} +(0.516444 - 3.27617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26491i 0.894429i 0.894427 + 0.447215i \(0.147584\pi\)
−0.894427 + 0.447215i \(0.852416\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 0.399993 0.199996
\(5\) 1.00000i 0.447214i
\(6\) −1.26491 −0.516399
\(7\) 0.0556365 + 2.64517i 0.0210286 + 0.999779i
\(8\) 3.03578i 1.07331i
\(9\) −1.00000 −0.333333
\(10\) −1.26491 −0.400001
\(11\) −0.516444 + 3.27617i −0.155714 + 0.987802i
\(12\) 0.399993i 0.115468i
\(13\) 6.21341 1.72329 0.861645 0.507511i \(-0.169434\pi\)
0.861645 + 0.507511i \(0.169434\pi\)
\(14\) −3.34591 + 0.0703753i −0.894231 + 0.0188086i
\(15\) −1.00000 −0.258199
\(16\) −3.04002 −0.760005
\(17\) 1.62680 0.394557 0.197278 0.980348i \(-0.436790\pi\)
0.197278 + 0.980348i \(0.436790\pi\)
\(18\) 1.26491i 0.298143i
\(19\) 4.38730 1.00652 0.503258 0.864136i \(-0.332134\pi\)
0.503258 + 0.864136i \(0.332134\pi\)
\(20\) 0.399993i 0.0894411i
\(21\) −2.64517 + 0.0556365i −0.577223 + 0.0121409i
\(22\) −4.14407 0.653257i −0.883519 0.139275i
\(23\) −1.24003 −0.258565 −0.129283 0.991608i \(-0.541267\pi\)
−0.129283 + 0.991608i \(0.541267\pi\)
\(24\) −3.03578 −0.619677
\(25\) −1.00000 −0.200000
\(26\) 7.85943i 1.54136i
\(27\) 1.00000i 0.192450i
\(28\) 0.0222542 + 1.05805i 0.00420564 + 0.199952i
\(29\) 9.91159i 1.84054i −0.391289 0.920268i \(-0.627971\pi\)
0.391289 0.920268i \(-0.372029\pi\)
\(30\) 1.26491i 0.230941i
\(31\) 7.78246i 1.39777i −0.715233 0.698886i \(-0.753680\pi\)
0.715233 0.698886i \(-0.246320\pi\)
\(32\) 2.22620i 0.393541i
\(33\) −3.27617 0.516444i −0.570308 0.0899014i
\(34\) 2.05776i 0.352903i
\(35\) −2.64517 + 0.0556365i −0.447115 + 0.00940428i
\(36\) −0.399993 −0.0666655
\(37\) 1.61516 0.265530 0.132765 0.991148i \(-0.457614\pi\)
0.132765 + 0.991148i \(0.457614\pi\)
\(38\) 5.54956i 0.900258i
\(39\) 6.21341i 0.994942i
\(40\) −3.03578 −0.480000
\(41\) −4.95141 −0.773280 −0.386640 0.922231i \(-0.626364\pi\)
−0.386640 + 0.922231i \(0.626364\pi\)
\(42\) −0.0703753 3.34591i −0.0108592 0.516285i
\(43\) 3.35295i 0.511320i 0.966767 + 0.255660i \(0.0822928\pi\)
−0.966767 + 0.255660i \(0.917707\pi\)
\(44\) −0.206574 + 1.31044i −0.0311422 + 0.197557i
\(45\) 1.00000i 0.149071i
\(46\) 1.56854i 0.231268i
\(47\) 4.74958i 0.692797i −0.938087 0.346398i \(-0.887405\pi\)
0.938087 0.346398i \(-0.112595\pi\)
\(48\) 3.04002i 0.438789i
\(49\) −6.99381 + 0.294335i −0.999116 + 0.0420479i
\(50\) 1.26491i 0.178886i
\(51\) 1.62680i 0.227797i
\(52\) 2.48532 0.344652
\(53\) −8.51450 −1.16956 −0.584778 0.811193i \(-0.698818\pi\)
−0.584778 + 0.811193i \(0.698818\pi\)
\(54\) 1.26491 0.172133
\(55\) −3.27617 0.516444i −0.441759 0.0696373i
\(56\) −8.03015 + 0.168900i −1.07307 + 0.0225703i
\(57\) 4.38730i 0.581113i
\(58\) 12.5373 1.64623
\(59\) 4.49064i 0.584632i 0.956322 + 0.292316i \(0.0944259\pi\)
−0.956322 + 0.292316i \(0.905574\pi\)
\(60\) −0.399993 −0.0516388
\(61\) −6.43034 −0.823320 −0.411660 0.911337i \(-0.635051\pi\)
−0.411660 + 0.911337i \(0.635051\pi\)
\(62\) 9.84415 1.25021
\(63\) −0.0556365 2.64517i −0.00700954 0.333260i
\(64\) −8.89600 −1.11200
\(65\) 6.21341i 0.770679i
\(66\) 0.653257 4.14407i 0.0804104 0.510100i
\(67\) 3.96452 0.484343 0.242172 0.970233i \(-0.422140\pi\)
0.242172 + 0.970233i \(0.422140\pi\)
\(68\) 0.650708 0.0789099
\(69\) 1.24003i 0.149283i
\(70\) −0.0703753 3.34591i −0.00841146 0.399912i
\(71\) 11.2241 1.33205 0.666025 0.745929i \(-0.267994\pi\)
0.666025 + 0.745929i \(0.267994\pi\)
\(72\) 3.03578i 0.357771i
\(73\) 8.16211 0.955303 0.477651 0.878549i \(-0.341488\pi\)
0.477651 + 0.878549i \(0.341488\pi\)
\(74\) 2.04303i 0.237498i
\(75\) 1.00000i 0.115470i
\(76\) 1.75489 0.201300
\(77\) −8.69475 1.18381i −0.990858 0.134907i
\(78\) −7.85943 −0.889905
\(79\) 13.4557i 1.51389i 0.653481 + 0.756943i \(0.273308\pi\)
−0.653481 + 0.756943i \(0.726692\pi\)
\(80\) 3.04002i 0.339885i
\(81\) 1.00000 0.111111
\(82\) 6.26310i 0.691644i
\(83\) −2.78335 −0.305512 −0.152756 0.988264i \(-0.548815\pi\)
−0.152756 + 0.988264i \(0.548815\pi\)
\(84\) −1.05805 + 0.0222542i −0.115442 + 0.00242813i
\(85\) 1.62680i 0.176451i
\(86\) −4.24119 −0.457340
\(87\) 9.91159 1.06263
\(88\) −9.94574 1.56781i −1.06022 0.167129i
\(89\) 2.92087i 0.309612i 0.987945 + 0.154806i \(0.0494752\pi\)
−0.987945 + 0.154806i \(0.950525\pi\)
\(90\) 1.26491 0.133334
\(91\) 0.345692 + 16.4355i 0.0362384 + 1.72291i
\(92\) −0.496005 −0.0517121
\(93\) 7.78246 0.807004
\(94\) 6.00780 0.619658
\(95\) 4.38730i 0.450128i
\(96\) −2.22620 −0.227211
\(97\) 15.7071i 1.59482i −0.603439 0.797409i \(-0.706203\pi\)
0.603439 0.797409i \(-0.293797\pi\)
\(98\) −0.372309 8.84657i −0.0376089 0.893638i
\(99\) 0.516444 3.27617i 0.0519046 0.329267i
\(100\) −0.399993 −0.0399993
\(101\) −12.6777 −1.26148 −0.630740 0.775994i \(-0.717248\pi\)
−0.630740 + 0.775994i \(0.717248\pi\)
\(102\) −2.05776 −0.203749
\(103\) 15.6509i 1.54213i −0.636756 0.771065i \(-0.719724\pi\)
0.636756 0.771065i \(-0.280276\pi\)
\(104\) 18.8626i 1.84963i
\(105\) −0.0556365 2.64517i −0.00542956 0.258142i
\(106\) 10.7701i 1.04609i
\(107\) 3.10573i 0.300242i 0.988668 + 0.150121i \(0.0479663\pi\)
−0.988668 + 0.150121i \(0.952034\pi\)
\(108\) 0.399993i 0.0384893i
\(109\) 3.01992i 0.289256i −0.989486 0.144628i \(-0.953801\pi\)
0.989486 0.144628i \(-0.0461985\pi\)
\(110\) 0.653257 4.14407i 0.0622856 0.395122i
\(111\) 1.61516i 0.153304i
\(112\) −0.169136 8.04136i −0.0159818 0.759837i
\(113\) 14.5147 1.36543 0.682713 0.730686i \(-0.260800\pi\)
0.682713 + 0.730686i \(0.260800\pi\)
\(114\) −5.54956 −0.519764
\(115\) 1.24003i 0.115634i
\(116\) 3.96456i 0.368100i
\(117\) −6.21341 −0.574430
\(118\) −5.68027 −0.522912
\(119\) 0.0905093 + 4.30315i 0.00829698 + 0.394469i
\(120\) 3.03578i 0.277128i
\(121\) −10.4666 3.38392i −0.951506 0.307629i
\(122\) 8.13382i 0.736402i
\(123\) 4.95141i 0.446453i
\(124\) 3.11293i 0.279549i
\(125\) 1.00000i 0.0894427i
\(126\) 3.34591 0.0703753i 0.298077 0.00626953i
\(127\) 19.3903i 1.72061i −0.509780 0.860305i \(-0.670273\pi\)
0.509780 0.860305i \(-0.329727\pi\)
\(128\) 6.80026i 0.601064i
\(129\) −3.35295 −0.295211
\(130\) −7.85943 −0.689318
\(131\) −3.50671 −0.306383 −0.153192 0.988197i \(-0.548955\pi\)
−0.153192 + 0.988197i \(0.548955\pi\)
\(132\) −1.31044 0.206574i −0.114059 0.0179799i
\(133\) 0.244094 + 11.6051i 0.0211656 + 1.00629i
\(134\) 5.01478i 0.433211i
\(135\) 1.00000 0.0860663
\(136\) 4.93861i 0.423482i
\(137\) 4.53186 0.387183 0.193591 0.981082i \(-0.437986\pi\)
0.193591 + 0.981082i \(0.437986\pi\)
\(138\) 1.56854 0.133523
\(139\) 13.8980 1.17882 0.589408 0.807836i \(-0.299361\pi\)
0.589408 + 0.807836i \(0.299361\pi\)
\(140\) −1.05805 + 0.0222542i −0.0894213 + 0.00188082i
\(141\) 4.74958 0.399986
\(142\) 14.1975i 1.19142i
\(143\) −3.20888 + 20.3562i −0.268340 + 1.70227i
\(144\) 3.04002 0.253335
\(145\) 9.91159 0.823113
\(146\) 10.3244i 0.854451i
\(147\) −0.294335 6.99381i −0.0242764 0.576840i
\(148\) 0.646050 0.0531050
\(149\) 4.75210i 0.389307i −0.980872 0.194653i \(-0.937642\pi\)
0.980872 0.194653i \(-0.0623582\pi\)
\(150\) 1.26491 0.103280
\(151\) 3.90311i 0.317630i 0.987308 + 0.158815i \(0.0507674\pi\)
−0.987308 + 0.158815i \(0.949233\pi\)
\(152\) 13.3189i 1.08031i
\(153\) −1.62680 −0.131519
\(154\) 1.49741 10.9981i 0.120665 0.886253i
\(155\) 7.78246 0.625103
\(156\) 2.48532i 0.198985i
\(157\) 11.3424i 0.905223i −0.891708 0.452612i \(-0.850492\pi\)
0.891708 0.452612i \(-0.149508\pi\)
\(158\) −17.0203 −1.35406
\(159\) 8.51450i 0.675244i
\(160\) −2.22620 −0.175997
\(161\) −0.0689912 3.28010i −0.00543727 0.258508i
\(162\) 1.26491i 0.0993810i
\(163\) 4.05059 0.317267 0.158633 0.987338i \(-0.449291\pi\)
0.158633 + 0.987338i \(0.449291\pi\)
\(164\) −1.98053 −0.154653
\(165\) 0.516444 3.27617i 0.0402051 0.255049i
\(166\) 3.52070i 0.273259i
\(167\) 18.2979 1.41593 0.707967 0.706246i \(-0.249613\pi\)
0.707967 + 0.706246i \(0.249613\pi\)
\(168\) −0.168900 8.03015i −0.0130309 0.619540i
\(169\) 25.6065 1.96973
\(170\) −2.05776 −0.157823
\(171\) −4.38730 −0.335505
\(172\) 1.34116i 0.102262i
\(173\) −5.19325 −0.394835 −0.197418 0.980319i \(-0.563256\pi\)
−0.197418 + 0.980319i \(0.563256\pi\)
\(174\) 12.5373i 0.950451i
\(175\) −0.0556365 2.64517i −0.00420572 0.199956i
\(176\) 1.57000 9.95962i 0.118343 0.750735i
\(177\) −4.49064 −0.337537
\(178\) −3.69465 −0.276926
\(179\) −15.8800 −1.18692 −0.593462 0.804862i \(-0.702239\pi\)
−0.593462 + 0.804862i \(0.702239\pi\)
\(180\) 0.399993i 0.0298137i
\(181\) 14.5061i 1.07823i −0.842232 0.539115i \(-0.818759\pi\)
0.842232 0.539115i \(-0.181241\pi\)
\(182\) −20.7895 + 0.437271i −1.54102 + 0.0324127i
\(183\) 6.43034i 0.475344i
\(184\) 3.76448i 0.277521i
\(185\) 1.61516i 0.118749i
\(186\) 9.84415i 0.721808i
\(187\) −0.840151 + 5.32967i −0.0614379 + 0.389744i
\(188\) 1.89980i 0.138557i
\(189\) 2.64517 0.0556365i 0.192408 0.00404696i
\(190\) −5.54956 −0.402607
\(191\) 15.8476 1.14669 0.573345 0.819314i \(-0.305645\pi\)
0.573345 + 0.819314i \(0.305645\pi\)
\(192\) 8.89600i 0.642013i
\(193\) 8.94943i 0.644194i 0.946707 + 0.322097i \(0.104388\pi\)
−0.946707 + 0.322097i \(0.895612\pi\)
\(194\) 19.8682 1.42645
\(195\) −6.21341 −0.444952
\(196\) −2.79747 + 0.117732i −0.199819 + 0.00840943i
\(197\) 1.43075i 0.101936i −0.998700 0.0509682i \(-0.983769\pi\)
0.998700 0.0509682i \(-0.0162307\pi\)
\(198\) 4.14407 + 0.653257i 0.294506 + 0.0464250i
\(199\) 1.09103i 0.0773410i −0.999252 0.0386705i \(-0.987688\pi\)
0.999252 0.0386705i \(-0.0123123\pi\)
\(200\) 3.03578i 0.214662i
\(201\) 3.96452i 0.279636i
\(202\) 16.0362i 1.12830i
\(203\) 26.2178 0.551446i 1.84013 0.0387039i
\(204\) 0.650708i 0.0455586i
\(205\) 4.95141i 0.345821i
\(206\) 19.7971 1.37933
\(207\) 1.24003 0.0861884
\(208\) −18.8889 −1.30971
\(209\) −2.26580 + 14.3735i −0.156728 + 0.994239i
\(210\) 3.34591 0.0703753i 0.230890 0.00485636i
\(211\) 7.95189i 0.547430i 0.961811 + 0.273715i \(0.0882526\pi\)
−0.961811 + 0.273715i \(0.911747\pi\)
\(212\) −3.40574 −0.233907
\(213\) 11.2241i 0.769060i
\(214\) −3.92848 −0.268545
\(215\) −3.35295 −0.228669
\(216\) 3.03578 0.206559
\(217\) 20.5859 0.432989i 1.39746 0.0293932i
\(218\) 3.81994 0.258719
\(219\) 8.16211i 0.551544i
\(220\) −1.31044 0.206574i −0.0883501 0.0139272i
\(221\) 10.1080 0.679936
\(222\) −2.04303 −0.137119
\(223\) 22.6413i 1.51618i 0.652152 + 0.758088i \(0.273866\pi\)
−0.652152 + 0.758088i \(0.726134\pi\)
\(224\) −5.88868 + 0.123858i −0.393454 + 0.00827562i
\(225\) 1.00000 0.0666667
\(226\) 18.3598i 1.22128i
\(227\) −14.6344 −0.971317 −0.485658 0.874149i \(-0.661420\pi\)
−0.485658 + 0.874149i \(0.661420\pi\)
\(228\) 1.75489i 0.116220i
\(229\) 25.4139i 1.67940i 0.543053 + 0.839698i \(0.317268\pi\)
−0.543053 + 0.839698i \(0.682732\pi\)
\(230\) 1.56854 0.103426
\(231\) 1.18381 8.69475i 0.0778887 0.572072i
\(232\) 30.0894 1.97547
\(233\) 26.6512i 1.74598i 0.487741 + 0.872988i \(0.337821\pi\)
−0.487741 + 0.872988i \(0.662179\pi\)
\(234\) 7.85943i 0.513787i
\(235\) 4.74958 0.309828
\(236\) 1.79622i 0.116924i
\(237\) −13.4557 −0.874043
\(238\) −5.44312 + 0.114487i −0.352825 + 0.00742106i
\(239\) 5.40933i 0.349901i −0.984577 0.174950i \(-0.944024\pi\)
0.984577 0.174950i \(-0.0559765\pi\)
\(240\) 3.04002 0.196232
\(241\) 7.63142 0.491583 0.245791 0.969323i \(-0.420952\pi\)
0.245791 + 0.969323i \(0.420952\pi\)
\(242\) 4.28036 13.2393i 0.275152 0.851055i
\(243\) 1.00000i 0.0641500i
\(244\) −2.57209 −0.164661
\(245\) −0.294335 6.99381i −0.0188044 0.446818i
\(246\) 6.26310 0.399321
\(247\) 27.2601 1.73452
\(248\) 23.6259 1.50024
\(249\) 2.78335i 0.176387i
\(250\) 1.26491 0.0800002
\(251\) 6.92390i 0.437033i −0.975833 0.218516i \(-0.929878\pi\)
0.975833 0.218516i \(-0.0701217\pi\)
\(252\) −0.0222542 1.05805i −0.00140188 0.0666507i
\(253\) 0.640409 4.06256i 0.0402621 0.255411i
\(254\) 24.5270 1.53896
\(255\) −1.62680 −0.101874
\(256\) −9.19025 −0.574390
\(257\) 9.73821i 0.607453i −0.952759 0.303727i \(-0.901769\pi\)
0.952759 0.303727i \(-0.0982309\pi\)
\(258\) 4.24119i 0.264045i
\(259\) 0.0898615 + 4.27235i 0.00558372 + 0.265471i
\(260\) 2.48532i 0.154133i
\(261\) 9.91159i 0.613512i
\(262\) 4.43569i 0.274038i
\(263\) 28.3755i 1.74971i 0.484386 + 0.874854i \(0.339043\pi\)
−0.484386 + 0.874854i \(0.660957\pi\)
\(264\) 1.56781 9.94574i 0.0964922 0.612118i
\(265\) 8.51450i 0.523041i
\(266\) −14.6795 + 0.308758i −0.900059 + 0.0189312i
\(267\) −2.92087 −0.178754
\(268\) 1.58578 0.0968669
\(269\) 2.07759i 0.126673i −0.997992 0.0633364i \(-0.979826\pi\)
0.997992 0.0633364i \(-0.0201741\pi\)
\(270\) 1.26491i 0.0769802i
\(271\) −15.0097 −0.911773 −0.455886 0.890038i \(-0.650678\pi\)
−0.455886 + 0.890038i \(0.650678\pi\)
\(272\) −4.94550 −0.299865
\(273\) −16.4355 + 0.345692i −0.994722 + 0.0209222i
\(274\) 5.73241i 0.346308i
\(275\) 0.516444 3.27617i 0.0311427 0.197560i
\(276\) 0.496005i 0.0298560i
\(277\) 8.87985i 0.533539i 0.963760 + 0.266769i \(0.0859562\pi\)
−0.963760 + 0.266769i \(0.914044\pi\)
\(278\) 17.5798i 1.05437i
\(279\) 7.78246i 0.465924i
\(280\) −0.168900 8.03015i −0.0100937 0.479893i
\(281\) 26.5925i 1.58638i −0.608976 0.793189i \(-0.708419\pi\)
0.608976 0.793189i \(-0.291581\pi\)
\(282\) 6.00780i 0.357760i
\(283\) 17.3320 1.03028 0.515141 0.857105i \(-0.327739\pi\)
0.515141 + 0.857105i \(0.327739\pi\)
\(284\) 4.48954 0.266405
\(285\) −4.38730 −0.259881
\(286\) −25.7488 4.05896i −1.52256 0.240011i
\(287\) −0.275479 13.0973i −0.0162610 0.773109i
\(288\) 2.22620i 0.131180i
\(289\) −14.3535 −0.844325
\(290\) 12.5373i 0.736216i
\(291\) 15.7071 0.920769
\(292\) 3.26478 0.191057
\(293\) 25.9648 1.51688 0.758440 0.651743i \(-0.225962\pi\)
0.758440 + 0.651743i \(0.225962\pi\)
\(294\) 8.84657 0.372309i 0.515942 0.0217135i
\(295\) −4.49064 −0.261455
\(296\) 4.90326i 0.284996i
\(297\) 3.27617 + 0.516444i 0.190103 + 0.0299671i
\(298\) 6.01099 0.348207
\(299\) −7.70485 −0.445583
\(300\) 0.399993i 0.0230936i
\(301\) −8.86911 + 0.186546i −0.511207 + 0.0107524i
\(302\) −4.93709 −0.284098
\(303\) 12.6777i 0.728316i
\(304\) −13.3375 −0.764958
\(305\) 6.43034i 0.368200i
\(306\) 2.05776i 0.117634i
\(307\) −20.9514 −1.19576 −0.597879 0.801586i \(-0.703990\pi\)
−0.597879 + 0.801586i \(0.703990\pi\)
\(308\) −3.47783 0.473514i −0.198168 0.0269809i
\(309\) 15.6509 0.890349
\(310\) 9.84415i 0.559110i
\(311\) 15.3862i 0.872471i 0.899832 + 0.436236i \(0.143689\pi\)
−0.899832 + 0.436236i \(0.856311\pi\)
\(312\) −18.8626 −1.06788
\(313\) 1.85796i 0.105018i 0.998620 + 0.0525092i \(0.0167219\pi\)
−0.998620 + 0.0525092i \(0.983278\pi\)
\(314\) 14.3472 0.809658
\(315\) 2.64517 0.0556365i 0.149038 0.00313476i
\(316\) 5.38219i 0.302772i
\(317\) −7.48284 −0.420278 −0.210139 0.977671i \(-0.567392\pi\)
−0.210139 + 0.977671i \(0.567392\pi\)
\(318\) 10.7701 0.603958
\(319\) 32.4720 + 5.11878i 1.81809 + 0.286597i
\(320\) 8.89600i 0.497301i
\(321\) −3.10573 −0.173345
\(322\) 4.14904 0.0872679i 0.231217 0.00486325i
\(323\) 7.13726 0.397128
\(324\) 0.399993 0.0222218
\(325\) −6.21341 −0.344658
\(326\) 5.12365i 0.283773i
\(327\) 3.01992 0.167002
\(328\) 15.0314i 0.829970i
\(329\) 12.5634 0.264250i 0.692644 0.0145686i
\(330\) 4.14407 + 0.653257i 0.228124 + 0.0359606i
\(331\) −5.79400 −0.318467 −0.159233 0.987241i \(-0.550902\pi\)
−0.159233 + 0.987241i \(0.550902\pi\)
\(332\) −1.11332 −0.0611013
\(333\) −1.61516 −0.0885100
\(334\) 23.1453i 1.26645i
\(335\) 3.96452i 0.216605i
\(336\) 8.04136 0.169136i 0.438692 0.00922712i
\(337\) 29.3608i 1.59938i −0.600412 0.799691i \(-0.704997\pi\)
0.600412 0.799691i \(-0.295003\pi\)
\(338\) 32.3900i 1.76178i
\(339\) 14.5147i 0.788329i
\(340\) 0.650708i 0.0352896i
\(341\) 25.4967 + 4.01921i 1.38072 + 0.217652i
\(342\) 5.54956i 0.300086i
\(343\) −1.16768 18.4834i −0.0630486 0.998010i
\(344\) −10.1788 −0.548806
\(345\) 1.24003 0.0667612
\(346\) 6.56901i 0.353152i
\(347\) 14.1803i 0.761241i 0.924731 + 0.380620i \(0.124289\pi\)
−0.924731 + 0.380620i \(0.875711\pi\)
\(348\) 3.96456 0.212523
\(349\) −26.3065 −1.40815 −0.704076 0.710124i \(-0.748639\pi\)
−0.704076 + 0.710124i \(0.748639\pi\)
\(350\) 3.34591 0.0703753i 0.178846 0.00376172i
\(351\) 6.21341i 0.331647i
\(352\) −7.29342 1.14971i −0.388741 0.0612797i
\(353\) 6.86576i 0.365428i 0.983166 + 0.182714i \(0.0584882\pi\)
−0.983166 + 0.182714i \(0.941512\pi\)
\(354\) 5.68027i 0.301903i
\(355\) 11.2241i 0.595711i
\(356\) 1.16833i 0.0619212i
\(357\) −4.30315 + 0.0905093i −0.227747 + 0.00479026i
\(358\) 20.0868i 1.06162i
\(359\) 7.03693i 0.371395i 0.982607 + 0.185697i \(0.0594544\pi\)
−0.982607 + 0.185697i \(0.940546\pi\)
\(360\) 3.03578 0.160000
\(361\) 0.248432 0.0130753
\(362\) 18.3490 0.964401
\(363\) 3.38392 10.4666i 0.177610 0.549353i
\(364\) 0.138274 + 6.57408i 0.00724755 + 0.344576i
\(365\) 8.16211i 0.427224i
\(366\) 8.13382 0.425162
\(367\) 19.8324i 1.03524i −0.855610 0.517621i \(-0.826818\pi\)
0.855610 0.517621i \(-0.173182\pi\)
\(368\) 3.76973 0.196511
\(369\) 4.95141 0.257760
\(370\) −2.04303 −0.106212
\(371\) −0.473717 22.5223i −0.0245941 1.16930i
\(372\) 3.11293 0.161398
\(373\) 26.5572i 1.37508i 0.726146 + 0.687540i \(0.241309\pi\)
−0.726146 + 0.687540i \(0.758691\pi\)
\(374\) −6.74157 1.06272i −0.348598 0.0549518i
\(375\) 1.00000 0.0516398
\(376\) 14.4187 0.743587
\(377\) 61.5848i 3.17178i
\(378\) 0.0703753 + 3.34591i 0.00361972 + 0.172095i
\(379\) 27.7011 1.42291 0.711454 0.702732i \(-0.248037\pi\)
0.711454 + 0.702732i \(0.248037\pi\)
\(380\) 1.75489i 0.0900239i
\(381\) 19.3903 0.993395
\(382\) 20.0458i 1.02563i
\(383\) 8.53084i 0.435906i −0.975959 0.217953i \(-0.930062\pi\)
0.975959 0.217953i \(-0.0699379\pi\)
\(384\) 6.80026 0.347024
\(385\) 1.18381 8.69475i 0.0603323 0.443125i
\(386\) −11.3203 −0.576186
\(387\) 3.35295i 0.170440i
\(388\) 6.28274i 0.318958i
\(389\) 20.8906 1.05920 0.529598 0.848249i \(-0.322343\pi\)
0.529598 + 0.848249i \(0.322343\pi\)
\(390\) 7.85943i 0.397978i
\(391\) −2.01729 −0.102019
\(392\) −0.893539 21.2317i −0.0451305 1.07236i
\(393\) 3.50671i 0.176890i
\(394\) 1.80977 0.0911749
\(395\) −13.4557 −0.677031
\(396\) 0.206574 1.31044i 0.0103807 0.0658523i
\(397\) 22.2712i 1.11776i 0.829249 + 0.558879i \(0.188768\pi\)
−0.829249 + 0.558879i \(0.811232\pi\)
\(398\) 1.38006 0.0691761
\(399\) −11.6051 + 0.244094i −0.580984 + 0.0122200i
\(400\) 3.04002 0.152001
\(401\) 12.3669 0.617574 0.308787 0.951131i \(-0.400077\pi\)
0.308787 + 0.951131i \(0.400077\pi\)
\(402\) −5.01478 −0.250114
\(403\) 48.3557i 2.40877i
\(404\) −5.07099 −0.252291
\(405\) 1.00000i 0.0496904i
\(406\) 0.697531 + 33.1633i 0.0346179 + 1.64586i
\(407\) −0.834137 + 5.29152i −0.0413467 + 0.262291i
\(408\) −4.93861 −0.244498
\(409\) −32.5287 −1.60844 −0.804221 0.594331i \(-0.797417\pi\)
−0.804221 + 0.594331i \(0.797417\pi\)
\(410\) 6.26310 0.309313
\(411\) 4.53186i 0.223540i
\(412\) 6.26025i 0.308420i
\(413\) −11.8785 + 0.249843i −0.584502 + 0.0122940i
\(414\) 1.56854i 0.0770894i
\(415\) 2.78335i 0.136629i
\(416\) 13.8323i 0.678186i
\(417\) 13.8980i 0.680589i
\(418\) −18.1813 2.86604i −0.889277 0.140182i
\(419\) 9.85219i 0.481311i 0.970611 + 0.240656i \(0.0773624\pi\)
−0.970611 + 0.240656i \(0.922638\pi\)
\(420\) −0.0222542 1.05805i −0.00108589 0.0516274i
\(421\) −8.55665 −0.417026 −0.208513 0.978020i \(-0.566862\pi\)
−0.208513 + 0.978020i \(0.566862\pi\)
\(422\) −10.0585 −0.489638
\(423\) 4.74958i 0.230932i
\(424\) 25.8482i 1.25530i
\(425\) −1.62680 −0.0789113
\(426\) −14.1975 −0.687869
\(427\) −0.357761 17.0093i −0.0173133 0.823138i
\(428\) 1.24227i 0.0600473i
\(429\) −20.3562 3.20888i −0.982806 0.154926i
\(430\) 4.24119i 0.204529i
\(431\) 10.5938i 0.510284i −0.966904 0.255142i \(-0.917878\pi\)
0.966904 0.255142i \(-0.0821222\pi\)
\(432\) 3.04002i 0.146263i
\(433\) 40.6553i 1.95377i 0.213771 + 0.976884i \(0.431425\pi\)
−0.213771 + 0.976884i \(0.568575\pi\)
\(434\) 0.547694 + 26.0394i 0.0262901 + 1.24993i
\(435\) 9.91159i 0.475224i
\(436\) 1.20795i 0.0578501i
\(437\) −5.44041 −0.260250
\(438\) −10.3244 −0.493317
\(439\) 0.794637 0.0379260 0.0189630 0.999820i \(-0.493964\pi\)
0.0189630 + 0.999820i \(0.493964\pi\)
\(440\) 1.56781 9.94574i 0.0747425 0.474145i
\(441\) 6.99381 0.294335i 0.333039 0.0140160i
\(442\) 12.7857i 0.608154i
\(443\) −23.4248 −1.11295 −0.556473 0.830866i \(-0.687846\pi\)
−0.556473 + 0.830866i \(0.687846\pi\)
\(444\) 0.646050i 0.0306602i
\(445\) −2.92087 −0.138463
\(446\) −28.6394 −1.35611
\(447\) 4.75210 0.224766
\(448\) −0.494942 23.5314i −0.0233838 1.11175i
\(449\) −31.4075 −1.48221 −0.741106 0.671388i \(-0.765698\pi\)
−0.741106 + 0.671388i \(0.765698\pi\)
\(450\) 1.26491i 0.0596286i
\(451\) 2.55712 16.2216i 0.120410 0.763847i
\(452\) 5.80577 0.273080
\(453\) −3.90311 −0.183384
\(454\) 18.5112i 0.868774i
\(455\) −16.4355 + 0.345692i −0.770508 + 0.0162063i
\(456\) −13.3189 −0.623715
\(457\) 35.9351i 1.68097i 0.541831 + 0.840487i \(0.317731\pi\)
−0.541831 + 0.840487i \(0.682269\pi\)
\(458\) −32.1464 −1.50210
\(459\) 1.62680i 0.0759325i
\(460\) 0.496005i 0.0231264i
\(461\) 26.6282 1.24020 0.620100 0.784523i \(-0.287092\pi\)
0.620100 + 0.784523i \(0.287092\pi\)
\(462\) 10.9981 + 1.49741i 0.511678 + 0.0696659i
\(463\) −11.6033 −0.539253 −0.269627 0.962965i \(-0.586900\pi\)
−0.269627 + 0.962965i \(0.586900\pi\)
\(464\) 30.1314i 1.39882i
\(465\) 7.78246i 0.360903i
\(466\) −33.7115 −1.56165
\(467\) 24.2952i 1.12425i 0.827054 + 0.562123i \(0.190015\pi\)
−0.827054 + 0.562123i \(0.809985\pi\)
\(468\) −2.48532 −0.114884
\(469\) 0.220572 + 10.4868i 0.0101851 + 0.484236i
\(470\) 6.00780i 0.277119i
\(471\) 11.3424 0.522631
\(472\) −13.6326 −0.627492
\(473\) −10.9848 1.73161i −0.505083 0.0796196i
\(474\) 17.0203i 0.781769i
\(475\) −4.38730 −0.201303
\(476\) 0.0362031 + 1.72123i 0.00165937 + 0.0788924i
\(477\) 8.51450 0.389852
\(478\) 6.84234 0.312961
\(479\) −10.1317 −0.462929 −0.231465 0.972843i \(-0.574352\pi\)
−0.231465 + 0.972843i \(0.574352\pi\)
\(480\) 2.22620i 0.101612i
\(481\) 10.0356 0.457585
\(482\) 9.65309i 0.439686i
\(483\) 3.28010 0.0689912i 0.149250 0.00313921i
\(484\) −4.18655 1.35354i −0.190298 0.0615246i
\(485\) 15.7071 0.713225
\(486\) −1.26491 −0.0573777
\(487\) 1.18274 0.0535952 0.0267976 0.999641i \(-0.491469\pi\)
0.0267976 + 0.999641i \(0.491469\pi\)
\(488\) 19.5211i 0.883679i
\(489\) 4.05059i 0.183174i
\(490\) 8.84657 0.372309i 0.399647 0.0168192i
\(491\) 36.8069i 1.66107i −0.556964 0.830536i \(-0.688034\pi\)
0.556964 0.830536i \(-0.311966\pi\)
\(492\) 1.98053i 0.0892890i
\(493\) 16.1242i 0.726196i
\(494\) 34.4817i 1.55141i
\(495\) 3.27617 + 0.516444i 0.147253 + 0.0232124i
\(496\) 23.6588i 1.06231i
\(497\) 0.624467 + 29.6895i 0.0280112 + 1.33176i
\(498\) 3.52070 0.157766
\(499\) 3.70034 0.165650 0.0828250 0.996564i \(-0.473606\pi\)
0.0828250 + 0.996564i \(0.473606\pi\)
\(500\) 0.399993i 0.0178882i
\(501\) 18.2979i 0.817490i
\(502\) 8.75814 0.390895
\(503\) −14.2284 −0.634412 −0.317206 0.948357i \(-0.602745\pi\)
−0.317206 + 0.948357i \(0.602745\pi\)
\(504\) 8.03015 0.168900i 0.357691 0.00752342i
\(505\) 12.6777i 0.564151i
\(506\) 5.13879 + 0.810062i 0.228447 + 0.0360116i
\(507\) 25.6065i 1.13722i
\(508\) 7.75597i 0.344116i
\(509\) 30.1161i 1.33487i −0.744666 0.667437i \(-0.767391\pi\)
0.744666 0.667437i \(-0.232609\pi\)
\(510\) 2.05776i 0.0911192i
\(511\) 0.454111 + 21.5901i 0.0200887 + 0.955091i
\(512\) 25.2254i 1.11482i
\(513\) 4.38730i 0.193704i
\(514\) 12.3180 0.543324
\(515\) 15.6509 0.689662
\(516\) −1.34116 −0.0590411
\(517\) 15.5604 + 2.45289i 0.684346 + 0.107878i
\(518\) −5.40416 + 0.113667i −0.237445 + 0.00499425i
\(519\) 5.19325i 0.227958i
\(520\) −18.8626 −0.827179
\(521\) 40.1175i 1.75758i −0.477210 0.878790i \(-0.658352\pi\)
0.477210 0.878790i \(-0.341648\pi\)
\(522\) −12.5373 −0.548743
\(523\) 34.5565 1.51105 0.755526 0.655119i \(-0.227381\pi\)
0.755526 + 0.655119i \(0.227381\pi\)
\(524\) −1.40266 −0.0612755
\(525\) 2.64517 0.0556365i 0.115445 0.00242817i
\(526\) −35.8926 −1.56499
\(527\) 12.6605i 0.551500i
\(528\) 9.95962 + 1.57000i 0.433437 + 0.0683255i
\(529\) −21.4623 −0.933144
\(530\) 10.7701 0.467824
\(531\) 4.49064i 0.194877i
\(532\) 0.0976358 + 4.64197i 0.00423305 + 0.201255i
\(533\) −30.7651 −1.33259
\(534\) 3.69465i 0.159883i
\(535\) −3.10573 −0.134272
\(536\) 12.0354i 0.519851i
\(537\) 15.8800i 0.685271i
\(538\) 2.62797 0.113300
\(539\) 2.64762 23.0649i 0.114041 0.993476i
\(540\) 0.399993 0.0172129
\(541\) 12.9976i 0.558809i 0.960174 + 0.279404i \(0.0901370\pi\)
−0.960174 + 0.279404i \(0.909863\pi\)
\(542\) 18.9859i 0.815516i
\(543\) 14.5061 0.622516
\(544\) 3.62159i 0.155274i
\(545\) 3.01992 0.129359
\(546\) −0.437271 20.7895i −0.0187135 0.889709i
\(547\) 17.7677i 0.759690i −0.925050 0.379845i \(-0.875977\pi\)
0.925050 0.379845i \(-0.124023\pi\)
\(548\) 1.81271 0.0774351
\(549\) 6.43034 0.274440
\(550\) 4.14407 + 0.653257i 0.176704 + 0.0278550i
\(551\) 43.4851i 1.85253i
\(552\) 3.76448 0.160227
\(553\) −35.5926 + 0.748629i −1.51355 + 0.0318349i
\(554\) −11.2323 −0.477213
\(555\) −1.61516 −0.0685595
\(556\) 5.55911 0.235759
\(557\) 40.3959i 1.71163i −0.517283 0.855814i \(-0.673057\pi\)
0.517283 0.855814i \(-0.326943\pi\)
\(558\) −9.84415 −0.416736
\(559\) 20.8333i 0.881153i
\(560\) 8.04136 0.169136i 0.339809 0.00714730i
\(561\) −5.32967 0.840151i −0.225019 0.0354712i
\(562\) 33.6373 1.41890
\(563\) 26.5897 1.12062 0.560311 0.828282i \(-0.310682\pi\)
0.560311 + 0.828282i \(0.310682\pi\)
\(564\) 1.89980 0.0799958
\(565\) 14.5147i 0.610637i
\(566\) 21.9235i 0.921515i
\(567\) 0.0556365 + 2.64517i 0.00233651 + 0.111087i
\(568\) 34.0738i 1.42971i
\(569\) 18.6104i 0.780188i −0.920775 0.390094i \(-0.872442\pi\)
0.920775 0.390094i \(-0.127558\pi\)
\(570\) 5.54956i 0.232446i
\(571\) 24.0931i 1.00826i 0.863627 + 0.504132i \(0.168187\pi\)
−0.863627 + 0.504132i \(0.831813\pi\)
\(572\) −1.28353 + 8.14233i −0.0536670 + 0.340448i
\(573\) 15.8476i 0.662042i
\(574\) 16.5669 0.348457i 0.691491 0.0145443i
\(575\) 1.24003 0.0517130
\(576\) 8.89600 0.370667
\(577\) 2.60480i 0.108439i −0.998529 0.0542195i \(-0.982733\pi\)
0.998529 0.0542195i \(-0.0172671\pi\)
\(578\) 18.1560i 0.755189i
\(579\) −8.94943 −0.371926
\(580\) 3.96456 0.164620
\(581\) −0.154856 7.36242i −0.00642449 0.305445i
\(582\) 19.8682i 0.823563i
\(583\) 4.39726 27.8949i 0.182116 1.15529i
\(584\) 24.7784i 1.02534i
\(585\) 6.21341i 0.256893i
\(586\) 32.8432i 1.35674i
\(587\) 10.3722i 0.428107i 0.976822 + 0.214054i \(0.0686667\pi\)
−0.976822 + 0.214054i \(0.931333\pi\)
\(588\) −0.117732 2.79747i −0.00485519 0.115366i
\(589\) 34.1440i 1.40688i
\(590\) 5.68027i 0.233853i
\(591\) 1.43075 0.0588530
\(592\) −4.91010 −0.201804
\(593\) −2.87360 −0.118005 −0.0590024 0.998258i \(-0.518792\pi\)
−0.0590024 + 0.998258i \(0.518792\pi\)
\(594\) −0.653257 + 4.14407i −0.0268035 + 0.170033i
\(595\) −4.30315 + 0.0905093i −0.176412 + 0.00371052i
\(596\) 1.90080i 0.0778600i
\(597\) 1.09103 0.0446529
\(598\) 9.74597i 0.398542i
\(599\) 6.32064 0.258254 0.129127 0.991628i \(-0.458782\pi\)
0.129127 + 0.991628i \(0.458782\pi\)
\(600\) 3.03578 0.123935
\(601\) 17.0259 0.694502 0.347251 0.937772i \(-0.387115\pi\)
0.347251 + 0.937772i \(0.387115\pi\)
\(602\) −0.235965 11.2187i −0.00961722 0.457239i
\(603\) −3.96452 −0.161448
\(604\) 1.56121i 0.0635249i
\(605\) 3.38392 10.4666i 0.137576 0.425527i
\(606\) 16.0362 0.651427
\(607\) −17.1498 −0.696089 −0.348044 0.937478i \(-0.613154\pi\)
−0.348044 + 0.937478i \(0.613154\pi\)
\(608\) 9.76703i 0.396106i
\(609\) 0.551446 + 26.2178i 0.0223457 + 1.06240i
\(610\) 8.13382 0.329329
\(611\) 29.5111i 1.19389i
\(612\) −0.650708 −0.0263033
\(613\) 16.9312i 0.683844i 0.939728 + 0.341922i \(0.111078\pi\)
−0.939728 + 0.341922i \(0.888922\pi\)
\(614\) 26.5017i 1.06952i
\(615\) 4.95141 0.199660
\(616\) 3.59378 26.3954i 0.144797 1.06350i
\(617\) −40.9282 −1.64771 −0.823854 0.566803i \(-0.808180\pi\)
−0.823854 + 0.566803i \(0.808180\pi\)
\(618\) 19.7971i 0.796354i
\(619\) 4.37850i 0.175987i −0.996121 0.0879934i \(-0.971955\pi\)
0.996121 0.0879934i \(-0.0280455\pi\)
\(620\) 3.11293 0.125018
\(621\) 1.24003i 0.0497609i
\(622\) −19.4622 −0.780364
\(623\) −7.72619 + 0.162507i −0.309543 + 0.00651070i
\(624\) 18.8889i 0.756161i
\(625\) 1.00000 0.0400000
\(626\) −2.35017 −0.0939315
\(627\) −14.3735 2.26580i −0.574024 0.0904872i
\(628\) 4.53688i 0.181041i
\(629\) 2.62753 0.104767
\(630\) 0.0703753 + 3.34591i 0.00280382 + 0.133304i
\(631\) −25.8773 −1.03016 −0.515079 0.857143i \(-0.672237\pi\)
−0.515079 + 0.857143i \(0.672237\pi\)
\(632\) −40.8487 −1.62487
\(633\) −7.95189 −0.316059
\(634\) 9.46515i 0.375909i
\(635\) 19.3903 0.769480
\(636\) 3.40574i 0.135046i
\(637\) −43.4554 + 1.82883i −1.72177 + 0.0724608i
\(638\) −6.47482 + 41.0743i −0.256340 + 1.62615i
\(639\) −11.2241 −0.444017
\(640\) 6.80026 0.268804
\(641\) −29.0849 −1.14879 −0.574393 0.818580i \(-0.694762\pi\)
−0.574393 + 0.818580i \(0.694762\pi\)
\(642\) 3.92848i 0.155045i
\(643\) 17.5627i 0.692606i 0.938123 + 0.346303i \(0.112563\pi\)
−0.938123 + 0.346303i \(0.887437\pi\)
\(644\) −0.0275960 1.31202i −0.00108743 0.0517007i
\(645\) 3.35295i 0.132022i
\(646\) 9.02802i 0.355203i
\(647\) 34.6069i 1.36054i 0.732962 + 0.680270i \(0.238137\pi\)
−0.732962 + 0.680270i \(0.761863\pi\)
\(648\) 3.03578i 0.119257i
\(649\) −14.7121 2.31916i −0.577500 0.0910352i
\(650\) 7.85943i 0.308272i
\(651\) 0.432989 + 20.5859i 0.0169702 + 0.806825i
\(652\) 1.62021 0.0634522
\(653\) 6.83133 0.267331 0.133665 0.991027i \(-0.457325\pi\)
0.133665 + 0.991027i \(0.457325\pi\)
\(654\) 3.81994i 0.149371i
\(655\) 3.50671i 0.137019i
\(656\) 15.0524 0.587697
\(657\) −8.16211 −0.318434
\(658\) 0.334253 + 15.8916i 0.0130305 + 0.619521i
\(659\) 13.2657i 0.516759i −0.966044 0.258379i \(-0.916812\pi\)
0.966044 0.258379i \(-0.0831884\pi\)
\(660\) 0.206574 1.31044i 0.00804088 0.0510090i
\(661\) 26.8096i 1.04277i −0.853321 0.521385i \(-0.825415\pi\)
0.853321 0.521385i \(-0.174585\pi\)
\(662\) 7.32891i 0.284846i
\(663\) 10.1080i 0.392561i
\(664\) 8.44964i 0.327910i
\(665\) −11.6051 + 0.244094i −0.450028 + 0.00946556i
\(666\) 2.04303i 0.0791659i
\(667\) 12.2907i 0.475898i
\(668\) 7.31902 0.283182
\(669\) −22.6413 −0.875365
\(670\) −5.01478 −0.193738
\(671\) 3.32091 21.0669i 0.128202 0.813277i
\(672\) −0.123858 5.88868i −0.00477793 0.227161i
\(673\) 4.86973i 0.187714i −0.995586 0.0938572i \(-0.970080\pi\)
0.995586 0.0938572i \(-0.0299197\pi\)
\(674\) 37.1388 1.43053
\(675\) 1.00000i 0.0384900i
\(676\) 10.2424 0.393939
\(677\) −28.7691 −1.10569 −0.552844 0.833285i \(-0.686457\pi\)
−0.552844 + 0.833285i \(0.686457\pi\)
\(678\) −18.3598 −0.705105
\(679\) 41.5480 0.873890i 1.59447 0.0335368i
\(680\) −4.93861 −0.189387
\(681\) 14.6344i 0.560790i
\(682\) −5.08395 + 32.2511i −0.194675 + 1.23496i
\(683\) 42.3628 1.62097 0.810484 0.585761i \(-0.199204\pi\)
0.810484 + 0.585761i \(0.199204\pi\)
\(684\) −1.75489 −0.0670999
\(685\) 4.53186i 0.173153i
\(686\) 23.3799 1.47701i 0.892650 0.0563925i
\(687\) −25.4139 −0.969600
\(688\) 10.1930i 0.388606i
\(689\) −52.9041 −2.01549
\(690\) 1.56854i 0.0597132i
\(691\) 5.30501i 0.201812i −0.994896 0.100906i \(-0.967826\pi\)
0.994896 0.100906i \(-0.0321742\pi\)
\(692\) −2.07726 −0.0789656
\(693\) 8.69475 + 1.18381i 0.330286 + 0.0449691i
\(694\) −17.9369 −0.680876
\(695\) 13.8980i 0.527182i
\(696\) 30.0894i 1.14054i
\(697\) −8.05494 −0.305103
\(698\) 33.2754i 1.25949i
\(699\) −26.6512 −1.00804
\(700\) −0.0222542 1.05805i −0.000841129 0.0399904i
\(701\) 20.2558i 0.765053i 0.923945 + 0.382526i \(0.124946\pi\)
−0.923945 + 0.382526i \(0.875054\pi\)
\(702\) 7.85943 0.296635
\(703\) 7.08618 0.267260
\(704\) 4.59428 29.1448i 0.173154 1.09844i
\(705\) 4.74958i 0.178879i
\(706\) −8.68460 −0.326849
\(707\) −0.705343 33.5347i −0.0265272 1.26120i
\(708\) −1.79622 −0.0675062
\(709\) −11.0545 −0.415160 −0.207580 0.978218i \(-0.566559\pi\)
−0.207580 + 0.978218i \(0.566559\pi\)
\(710\) −14.1975 −0.532821
\(711\) 13.4557i 0.504629i
\(712\) −8.86713 −0.332310
\(713\) 9.65053i 0.361415i
\(714\) −0.114487 5.44312i −0.00428455 0.203704i
\(715\) −20.3562 3.20888i −0.761278 0.120005i
\(716\) −6.35187 −0.237380
\(717\) 5.40933 0.202015
\(718\) −8.90111 −0.332186
\(719\) 51.4013i 1.91694i −0.285188 0.958472i \(-0.592056\pi\)
0.285188 0.958472i \(-0.407944\pi\)
\(720\) 3.04002i 0.113295i
\(721\) 41.3993 0.870761i 1.54179 0.0324289i
\(722\) 0.314245i 0.0116950i
\(723\) 7.63142i 0.283815i
\(724\) 5.80234i 0.215642i
\(725\) 9.91159i 0.368107i
\(726\) 13.2393 + 4.28036i 0.491357 + 0.158859i
\(727\) 20.4356i 0.757915i 0.925414 + 0.378958i \(0.123717\pi\)
−0.925414 + 0.378958i \(0.876283\pi\)
\(728\) −49.8947 + 1.04945i −1.84922 + 0.0388951i
\(729\) −1.00000 −0.0370370
\(730\) −10.3244 −0.382122
\(731\) 5.45458i 0.201745i
\(732\) 2.57209i 0.0950671i
\(733\) −26.7268 −0.987178 −0.493589 0.869695i \(-0.664315\pi\)
−0.493589 + 0.869695i \(0.664315\pi\)
\(734\) 25.0863 0.925951
\(735\) 6.99381 0.294335i 0.257971 0.0108567i
\(736\) 2.76057i 0.101756i
\(737\) −2.04745 + 12.9884i −0.0754189 + 0.478435i
\(738\) 6.26310i 0.230548i
\(739\) 34.5733i 1.27180i 0.771772 + 0.635899i \(0.219371\pi\)
−0.771772 + 0.635899i \(0.780629\pi\)
\(740\) 0.646050i 0.0237493i
\(741\) 27.2601i 1.00143i
\(742\) 28.4887 0.599211i 1.04585 0.0219977i
\(743\) 22.7283i 0.833821i 0.908948 + 0.416911i \(0.136887\pi\)
−0.908948 + 0.416911i \(0.863113\pi\)
\(744\) 23.6259i 0.866167i
\(745\) 4.75210 0.174103
\(746\) −33.5926 −1.22991
\(747\) 2.78335 0.101837
\(748\) −0.336054 + 2.13183i −0.0122874 + 0.0779474i
\(749\) −8.21517 + 0.172792i −0.300176 + 0.00631367i
\(750\) 1.26491i 0.0461881i
\(751\) 15.5678 0.568076 0.284038 0.958813i \(-0.408326\pi\)
0.284038 + 0.958813i \(0.408326\pi\)
\(752\) 14.4388i 0.526529i
\(753\) 6.92390 0.252321
\(754\) 77.8994 2.83693
\(755\) −3.90311 −0.142049
\(756\) 1.05805 0.0222542i 0.0384808 0.000809377i
\(757\) 2.20307 0.0800718 0.0400359 0.999198i \(-0.487253\pi\)
0.0400359 + 0.999198i \(0.487253\pi\)
\(758\) 35.0395i 1.27269i
\(759\) 4.06256 + 0.640409i 0.147462 + 0.0232454i
\(760\) −13.3189 −0.483128
\(761\) 31.3430 1.13618 0.568092 0.822965i \(-0.307682\pi\)
0.568092 + 0.822965i \(0.307682\pi\)
\(762\) 24.5270i 0.888521i
\(763\) 7.98819 0.168018i 0.289192 0.00608265i
\(764\) 6.33891 0.229334
\(765\) 1.62680i 0.0588170i
\(766\) 10.7908 0.389887
\(767\) 27.9022i 1.00749i
\(768\) 9.19025i 0.331625i
\(769\) −17.8883 −0.645069 −0.322535 0.946558i \(-0.604535\pi\)
−0.322535 + 0.946558i \(0.604535\pi\)
\(770\) 10.9981 + 1.49741i 0.396344 + 0.0539630i
\(771\) 9.73821 0.350713
\(772\) 3.57971i 0.128837i
\(773\) 37.4966i 1.34866i −0.738430 0.674330i \(-0.764433\pi\)
0.738430 0.674330i \(-0.235567\pi\)
\(774\) 4.24119 0.152447
\(775\) 7.78246i 0.279554i
\(776\) 47.6835 1.71174
\(777\) −4.27235 + 0.0898615i −0.153270 + 0.00322376i
\(778\) 26.4248i 0.947376i
\(779\) −21.7233 −0.778319
\(780\) −2.48532 −0.0889887
\(781\) −5.79660 + 36.7719i −0.207419 + 1.31580i
\(782\) 2.55169i 0.0912484i
\(783\) −9.91159 −0.354211
\(784\) 21.2613 0.894786i 0.759333 0.0319566i
\(785\) 11.3424 0.404828
\(786\) 4.43569 0.158216
\(787\) 1.23343 0.0439671 0.0219835 0.999758i \(-0.493002\pi\)
0.0219835 + 0.999758i \(0.493002\pi\)
\(788\) 0.572288i 0.0203869i
\(789\) −28.3755 −1.01019
\(790\) 17.0203i 0.605556i
\(791\) 0.807546 + 38.3937i 0.0287130 + 1.36512i
\(792\) 9.94574 + 1.56781i 0.353407 + 0.0557098i
\(793\) −39.9543 −1.41882
\(794\) −28.1711 −0.999755
\(795\) 8.51450 0.301978
\(796\) 0.436404i 0.0154679i
\(797\) 27.5155i 0.974651i −0.873220 0.487325i \(-0.837973\pi\)
0.873220 0.487325i \(-0.162027\pi\)
\(798\) −0.308758 14.6795i −0.0109299 0.519649i
\(799\) 7.72660i 0.273348i
\(800\) 2.22620i 0.0787082i
\(801\) 2.92087i 0.103204i
\(802\) 15.6431i 0.552376i
\(803\) −4.21527 + 26.7405i −0.148754 + 0.943650i
\(804\) 1.58578i 0.0559261i
\(805\) 3.28010 0.0689912i 0.115608 0.00243162i
\(806\) 61.1657 2.15447
\(807\) 2.07759 0.0731345
\(808\) 38.4868i 1.35396i
\(809\) 39.7878i 1.39886i 0.714699 + 0.699432i \(0.246564\pi\)
−0.714699 + 0.699432i \(0.753436\pi\)
\(810\) −1.26491 −0.0444445
\(811\) 23.6701 0.831170 0.415585 0.909554i \(-0.363577\pi\)
0.415585 + 0.909554i \(0.363577\pi\)
\(812\) 10.4869 0.220574i 0.368019 0.00774064i
\(813\) 15.0097i 0.526412i
\(814\) −6.69332 1.05511i −0.234601 0.0369817i
\(815\) 4.05059i 0.141886i
\(816\) 4.94550i 0.173127i
\(817\) 14.7104i 0.514652i
\(818\) 41.1460i 1.43864i
\(819\) −0.345692 16.4355i −0.0120795 0.574303i
\(820\) 1.98053i 0.0691630i
\(821\) 36.8760i 1.28698i 0.765454 + 0.643490i \(0.222514\pi\)
−0.765454 + 0.643490i \(0.777486\pi\)
\(822\) −5.73241 −0.199941
\(823\) 40.0752 1.39693 0.698467 0.715642i \(-0.253866\pi\)
0.698467 + 0.715642i \(0.253866\pi\)
\(824\) 47.5128 1.65519
\(825\) 3.27617 + 0.516444i 0.114062 + 0.0179803i
\(826\) −0.316030 15.0253i −0.0109961 0.522796i
\(827\) 2.31803i 0.0806058i −0.999188 0.0403029i \(-0.987168\pi\)
0.999188 0.0403029i \(-0.0128323\pi\)
\(828\) 0.496005 0.0172374
\(829\) 47.9666i 1.66595i 0.553311 + 0.832975i \(0.313364\pi\)
−0.553311 + 0.832975i \(0.686636\pi\)
\(830\) 3.52070 0.122205
\(831\) −8.87985 −0.308039
\(832\) −55.2745 −1.91630
\(833\) −11.3775 + 0.478824i −0.394208 + 0.0165903i
\(834\) −17.5798 −0.608739
\(835\) 18.2979i 0.633225i
\(836\) −0.906302 + 5.74931i −0.0313451 + 0.198844i
\(837\) −7.78246 −0.269001
\(838\) −12.4622 −0.430499
\(839\) 6.13941i 0.211956i −0.994368 0.105978i \(-0.966203\pi\)
0.994368 0.105978i \(-0.0337973\pi\)
\(840\) 8.03015 0.168900i 0.277067 0.00582761i
\(841\) −69.2396 −2.38757
\(842\) 10.8234i 0.373000i
\(843\) 26.5925 0.915896
\(844\) 3.18070i 0.109484i
\(845\) 25.6065i 0.880890i
\(846\) −6.00780 −0.206553
\(847\) 8.36870 27.8741i 0.287552 0.957765i
\(848\) 25.8842 0.888869
\(849\) 17.3320i 0.594834i
\(850\) 2.05776i 0.0705806i
\(851\) −2.00285 −0.0686568
\(852\) 4.48954i 0.153809i
\(853\) 9.43350 0.322997 0.161498 0.986873i \(-0.448367\pi\)
0.161498 + 0.986873i \(0.448367\pi\)
\(854\) 21.5153 0.452537i 0.736239 0.0154855i
\(855\) 4.38730i 0.150043i
\(856\) −9.42832 −0.322253
\(857\) −48.1302 −1.64410 −0.822049 0.569417i \(-0.807169\pi\)
−0.822049 + 0.569417i \(0.807169\pi\)
\(858\) 4.05896 25.7488i 0.138570 0.879051i
\(859\) 46.8091i 1.59711i −0.601924 0.798553i \(-0.705599\pi\)
0.601924 0.798553i \(-0.294401\pi\)
\(860\) −1.34116 −0.0457330
\(861\) 13.0973 0.275479i 0.446355 0.00938829i
\(862\) 13.4002 0.456413
\(863\) −30.9748 −1.05440 −0.527198 0.849743i \(-0.676757\pi\)
−0.527198 + 0.849743i \(0.676757\pi\)
\(864\) 2.22620 0.0757370
\(865\) 5.19325i 0.176576i
\(866\) −51.4254 −1.74751
\(867\) 14.3535i 0.487471i
\(868\) 8.23421 0.173192i 0.279487 0.00587853i
\(869\) −44.0832 6.94912i −1.49542 0.235733i
\(870\) −12.5373 −0.425054
\(871\) 24.6332 0.834664
\(872\) 9.16782 0.310462
\(873\) 15.7071i 0.531606i
\(874\) 6.88165i 0.232775i
\(875\) 2.64517 0.0556365i 0.0894229 0.00188086i
\(876\) 3.26478i 0.110307i
\(877\) 34.3921i 1.16134i −0.814140 0.580669i \(-0.802791\pi\)
0.814140 0.580669i \(-0.197209\pi\)
\(878\) 1.00515i 0.0339221i
\(879\) 25.9648i 0.875771i
\(880\) 9.95962 + 1.57000i 0.335739 + 0.0529247i
\(881\) 40.8658i 1.37680i −0.725330 0.688401i \(-0.758313\pi\)
0.725330 0.688401i \(-0.241687\pi\)
\(882\) 0.372309 + 8.84657i 0.0125363 + 0.297879i
\(883\) 0.236721 0.00796629 0.00398314 0.999992i \(-0.498732\pi\)
0.00398314 + 0.999992i \(0.498732\pi\)
\(884\) 4.04311 0.135985
\(885\) 4.49064i 0.150951i
\(886\) 29.6304i 0.995451i
\(887\) 13.3787 0.449211 0.224606 0.974450i \(-0.427891\pi\)
0.224606 + 0.974450i \(0.427891\pi\)
\(888\) −4.90326 −0.164543
\(889\) 51.2905 1.07881i 1.72023 0.0361820i
\(890\) 3.69465i 0.123845i
\(891\) −0.516444 + 3.27617i −0.0173015 + 0.109756i
\(892\) 9.05637i 0.303230i
\(893\) 20.8378i 0.697311i
\(894\) 6.01099i 0.201038i
\(895\) 15.8800i 0.530808i
\(896\) 17.9878 0.378343i 0.600931 0.0126395i
\(897\) 7.70485i 0.257257i
\(898\) 39.7278i 1.32573i
\(899\) −77.1366 −2.57265
\(900\) 0.399993 0.0133331
\(901\) −13.8514 −0.461456
\(902\) 20.5190 + 3.23454i 0.683207 + 0.107698i
\(903\) −0.186546 8.86911i −0.00620787 0.295146i
\(904\) 44.0634i 1.46553i
\(905\) 14.5061 0.482199
\(906\) 4.93709i 0.164024i
\(907\) 42.2499 1.40288 0.701442 0.712726i \(-0.252540\pi\)
0.701442 + 0.712726i \(0.252540\pi\)
\(908\) −5.85364 −0.194260
\(909\) 12.6777 0.420493
\(910\) −0.437271 20.7895i −0.0144954 0.689165i
\(911\) 45.9937 1.52384 0.761919 0.647672i \(-0.224257\pi\)
0.761919 + 0.647672i \(0.224257\pi\)
\(912\) 13.3375i 0.441648i
\(913\) 1.43744 9.11872i 0.0475724 0.301786i
\(914\) −45.4549 −1.50351
\(915\) 6.43034 0.212580
\(916\) 10.1654i 0.335873i
\(917\) −0.195101 9.27584i −0.00644281 0.306315i
\(918\) 2.05776 0.0679162
\(919\) 13.7556i 0.453755i 0.973923 + 0.226878i \(0.0728518\pi\)
−0.973923 + 0.226878i \(0.927148\pi\)
\(920\) 3.76448 0.124111
\(921\) 20.9514i 0.690371i
\(922\) 33.6824i 1.10927i
\(923\) 69.7397 2.29551
\(924\) 0.473514 3.47783i 0.0155775 0.114412i
\(925\) −1.61516 −0.0531060
\(926\) 14.6772i 0.482324i
\(927\) 15.6509i 0.514043i
\(928\) 22.0652 0.724326
\(929\) 40.1490i 1.31725i −0.752473 0.658624i \(-0.771139\pi\)
0.752473 0.658624i \(-0.228861\pi\)
\(930\) −9.84415 −0.322802
\(931\) −30.6840 + 1.29134i −1.00563 + 0.0423219i
\(932\) 10.6603i 0.349189i
\(933\) −15.3862 −0.503722
\(934\) −30.7313 −1.00556
\(935\) −5.32967 0.840151i −0.174299 0.0274759i
\(936\) 18.8626i 0.616543i
\(937\) 49.9501 1.63180 0.815899 0.578195i \(-0.196243\pi\)
0.815899 + 0.578195i \(0.196243\pi\)
\(938\) −13.2649 + 0.279004i −0.433115 + 0.00910982i
\(939\) −1.85796 −0.0606324
\(940\) 1.89980 0.0619645
\(941\) −4.24177 −0.138278 −0.0691388 0.997607i \(-0.522025\pi\)
−0.0691388 + 0.997607i \(0.522025\pi\)
\(942\) 14.3472i 0.467456i
\(943\) 6.13992 0.199943
\(944\) 13.6516i 0.444323i
\(945\) 0.0556365 + 2.64517i 0.00180985 + 0.0860473i
\(946\) 2.19034 13.8949i 0.0712141 0.451761i
\(947\) −11.5681 −0.375912 −0.187956 0.982177i \(-0.560186\pi\)
−0.187956 + 0.982177i \(0.560186\pi\)
\(948\) −5.38219 −0.174805
\(949\) 50.7146 1.64626
\(950\) 5.54956i 0.180052i
\(951\) 7.48284i 0.242648i
\(952\) −13.0634 + 0.274767i −0.423389 + 0.00890524i
\(953\) 24.5357i 0.794790i −0.917648 0.397395i \(-0.869914\pi\)
0.917648 0.397395i \(-0.130086\pi\)
\(954\) 10.7701i 0.348695i
\(955\) 15.8476i 0.512815i
\(956\) 2.16369i 0.0699789i
\(957\) −5.11878 + 32.4720i −0.165467 + 1.04967i
\(958\) 12.8157i 0.414057i
\(959\) 0.252137 + 11.9875i 0.00814191 + 0.387097i
\(960\) 8.89600 0.287117
\(961\) −29.5667 −0.953766
\(962\) 12.6942i 0.409278i
\(963\) 3.10573i 0.100081i
\(964\) 3.05251 0.0983148
\(965\) −8.94943 −0.288092
\(966\) 0.0872679 + 4.14904i 0.00280780 + 0.133493i
\(967\) 13.9191i 0.447609i 0.974634 + 0.223805i \(0.0718478\pi\)
−0.974634 + 0.223805i \(0.928152\pi\)
\(968\) 10.2728 31.7743i 0.330182 1.02126i
\(969\) 7.13726i 0.229282i
\(970\) 19.8682i 0.637929i
\(971\) 40.5634i 1.30174i 0.759189 + 0.650870i \(0.225596\pi\)
−0.759189 + 0.650870i \(0.774404\pi\)
\(972\) 0.399993i 0.0128298i
\(973\) 0.773237 + 36.7626i 0.0247888 + 1.17855i
\(974\) 1.49607i 0.0479371i
\(975\) 6.21341i 0.198988i
\(976\) 19.5484 0.625728
\(977\) 26.2257 0.839036 0.419518 0.907747i \(-0.362199\pi\)
0.419518 + 0.907747i \(0.362199\pi\)
\(978\) −5.12365 −0.163836
\(979\) −9.56927 1.50847i −0.305835 0.0482108i
\(980\) −0.117732 2.79747i −0.00376081 0.0893620i
\(981\) 3.01992i 0.0964186i
\(982\) 46.5576 1.48571
\(983\) 41.6641i 1.32888i −0.747343 0.664439i \(-0.768671\pi\)
0.747343 0.664439i \(-0.231329\pi\)
\(984\) 15.0314 0.479184
\(985\) 1.43075 0.0455873
\(986\) 20.3957 0.649531
\(987\) 0.264250 + 12.5634i 0.00841116 + 0.399898i
\(988\) 10.9039 0.346898
\(989\) 4.15778i 0.132210i
\(990\) −0.653257 + 4.14407i −0.0207619 + 0.131707i
\(991\) 13.5033 0.428946 0.214473 0.976730i \(-0.431197\pi\)
0.214473 + 0.976730i \(0.431197\pi\)
\(992\) 17.3254 0.550081
\(993\) 5.79400i 0.183867i
\(994\) −37.5546 + 0.789897i −1.19116 + 0.0250540i
\(995\) 1.09103 0.0345880
\(996\) 1.11332i 0.0352769i
\(997\) 41.4277 1.31203 0.656014 0.754749i \(-0.272241\pi\)
0.656014 + 0.754749i \(0.272241\pi\)
\(998\) 4.68061i 0.148162i
\(999\) 1.61516i 0.0511013i
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.76.2 yes 32
7.6 odd 2 inner 1155.2.i.d.76.32 yes 32
11.10 odd 2 inner 1155.2.i.d.76.31 yes 32
77.76 even 2 inner 1155.2.i.d.76.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.i.d.76.1 32 77.76 even 2 inner
1155.2.i.d.76.2 yes 32 1.1 even 1 trivial
1155.2.i.d.76.31 yes 32 11.10 odd 2 inner
1155.2.i.d.76.32 yes 32 7.6 odd 2 inner