Properties

Label 555.2.g.a.184.13
Level $555$
Weight $2$
Character 555.184
Analytic conductor $4.432$
Analytic rank $0$
Dimension $40$
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] = [555,2,Mod(184,555)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(555, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("555.184");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 555.g (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: \(4.43169731218\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 184.13
Character \(\chi\) \(=\) 555.184
Dual form 555.2.g.a.184.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.39280 q^{2} -1.00000i q^{3} -0.0601015 q^{4} +(2.20287 + 0.383884i) q^{5} +1.39280i q^{6} -0.344118i q^{7} +2.86931 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.39280 q^{2} -1.00000i q^{3} -0.0601015 q^{4} +(2.20287 + 0.383884i) q^{5} +1.39280i q^{6} -0.344118i q^{7} +2.86931 q^{8} -1.00000 q^{9} +(-3.06816 - 0.534675i) q^{10} -1.00065 q^{11} +0.0601015i q^{12} +4.37110 q^{13} +0.479288i q^{14} +(0.383884 - 2.20287i) q^{15} -3.87618 q^{16} -0.428787 q^{17} +1.39280 q^{18} +5.70197i q^{19} +(-0.132396 - 0.0230720i) q^{20} -0.344118 q^{21} +1.39371 q^{22} +2.35097 q^{23} -2.86931i q^{24} +(4.70527 + 1.69129i) q^{25} -6.08808 q^{26} +1.00000i q^{27} +0.0206820i q^{28} -7.62547i q^{29} +(-0.534675 + 3.06816i) q^{30} +4.55060i q^{31} -0.339869 q^{32} +1.00065i q^{33} +0.597215 q^{34} +(0.132101 - 0.758047i) q^{35} +0.0601015 q^{36} +(1.95109 - 5.76136i) q^{37} -7.94172i q^{38} -4.37110i q^{39} +(6.32072 + 1.10148i) q^{40} +2.50995 q^{41} +0.479288 q^{42} +8.58272 q^{43} +0.0601408 q^{44} +(-2.20287 - 0.383884i) q^{45} -3.27443 q^{46} -7.01935i q^{47} +3.87618i q^{48} +6.88158 q^{49} +(-6.55351 - 2.35564i) q^{50} +0.428787i q^{51} -0.262710 q^{52} -7.41870i q^{53} -1.39280i q^{54} +(-2.20431 - 0.384136i) q^{55} -0.987382i q^{56} +5.70197 q^{57} +10.6208i q^{58} -3.94753i q^{59} +(-0.0230720 + 0.132396i) q^{60} -2.18574i q^{61} -6.33808i q^{62} +0.344118i q^{63} +8.22574 q^{64} +(9.62897 + 1.67800i) q^{65} -1.39371i q^{66} +10.2635i q^{67} +0.0257707 q^{68} -2.35097i q^{69} +(-0.183991 + 1.05581i) q^{70} +1.92267 q^{71} -2.86931 q^{72} -9.22636i q^{73} +(-2.71748 + 8.02444i) q^{74} +(1.69129 - 4.70527i) q^{75} -0.342697i q^{76} +0.344343i q^{77} +6.08808i q^{78} +14.3679i q^{79} +(-8.53873 - 1.48801i) q^{80} +1.00000 q^{81} -3.49587 q^{82} +0.402746i q^{83} +0.0206820 q^{84} +(-0.944561 - 0.164604i) q^{85} -11.9540 q^{86} -7.62547 q^{87} -2.87119 q^{88} -7.34498i q^{89} +(3.06816 + 0.534675i) q^{90} -1.50417i q^{91} -0.141297 q^{92} +4.55060 q^{93} +9.77657i q^{94} +(-2.18890 + 12.5607i) q^{95} +0.339869i q^{96} -9.66376 q^{97} -9.58469 q^{98} +1.00065 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/555\mathbb{Z}\right)^\times\).

\(n\) \(76\) \(112\) \(371\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39280 −0.984860 −0.492430 0.870352i \(-0.663891\pi\)
−0.492430 + 0.870352i \(0.663891\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −0.0601015 −0.0300507
\(5\) 2.20287 + 0.383884i 0.985153 + 0.171678i
\(6\) 1.39280i 0.568609i
\(7\) 0.344118i 0.130064i −0.997883 0.0650322i \(-0.979285\pi\)
0.997883 0.0650322i \(-0.0207150\pi\)
\(8\) 2.86931 1.01446
\(9\) −1.00000 −0.333333
\(10\) −3.06816 0.534675i −0.970238 0.169079i
\(11\) −1.00065 −0.301709 −0.150854 0.988556i \(-0.548202\pi\)
−0.150854 + 0.988556i \(0.548202\pi\)
\(12\) 0.0601015i 0.0173498i
\(13\) 4.37110 1.21233 0.606163 0.795340i \(-0.292708\pi\)
0.606163 + 0.795340i \(0.292708\pi\)
\(14\) 0.479288i 0.128095i
\(15\) 0.383884 2.20287i 0.0991185 0.568778i
\(16\) −3.87618 −0.969046
\(17\) −0.428787 −0.103996 −0.0519980 0.998647i \(-0.516559\pi\)
−0.0519980 + 0.998647i \(0.516559\pi\)
\(18\) 1.39280 0.328287
\(19\) 5.70197i 1.30812i 0.756442 + 0.654061i \(0.226936\pi\)
−0.756442 + 0.654061i \(0.773064\pi\)
\(20\) −0.132396 0.0230720i −0.0296046 0.00515906i
\(21\) −0.344118 −0.0750927
\(22\) 1.39371 0.297141
\(23\) 2.35097 0.490211 0.245105 0.969496i \(-0.421177\pi\)
0.245105 + 0.969496i \(0.421177\pi\)
\(24\) 2.86931i 0.585696i
\(25\) 4.70527 + 1.69129i 0.941053 + 0.338259i
\(26\) −6.08808 −1.19397
\(27\) 1.00000i 0.192450i
\(28\) 0.0206820i 0.00390853i
\(29\) 7.62547i 1.41601i −0.706206 0.708007i \(-0.749595\pi\)
0.706206 0.708007i \(-0.250405\pi\)
\(30\) −0.534675 + 3.06816i −0.0976179 + 0.560167i
\(31\) 4.55060i 0.817311i 0.912689 + 0.408656i \(0.134002\pi\)
−0.912689 + 0.408656i \(0.865998\pi\)
\(32\) −0.339869 −0.0600809
\(33\) 1.00065i 0.174192i
\(34\) 0.597215 0.102422
\(35\) 0.132101 0.758047i 0.0223292 0.128133i
\(36\) 0.0601015 0.0100169
\(37\) 1.95109 5.76136i 0.320757 0.947162i
\(38\) 7.94172i 1.28832i
\(39\) 4.37110i 0.699937i
\(40\) 6.32072 + 1.10148i 0.999394 + 0.174160i
\(41\) 2.50995 0.391988 0.195994 0.980605i \(-0.437207\pi\)
0.195994 + 0.980605i \(0.437207\pi\)
\(42\) 0.479288 0.0739558
\(43\) 8.58272 1.30885 0.654426 0.756126i \(-0.272910\pi\)
0.654426 + 0.756126i \(0.272910\pi\)
\(44\) 0.0601408 0.00906657
\(45\) −2.20287 0.383884i −0.328384 0.0572261i
\(46\) −3.27443 −0.482789
\(47\) 7.01935i 1.02388i −0.859022 0.511939i \(-0.828928\pi\)
0.859022 0.511939i \(-0.171072\pi\)
\(48\) 3.87618i 0.559479i
\(49\) 6.88158 0.983083
\(50\) −6.55351 2.35564i −0.926806 0.333138i
\(51\) 0.428787i 0.0600421i
\(52\) −0.262710 −0.0364313
\(53\) 7.41870i 1.01904i −0.860460 0.509518i \(-0.829824\pi\)
0.860460 0.509518i \(-0.170176\pi\)
\(54\) 1.39280i 0.189536i
\(55\) −2.20431 0.384136i −0.297229 0.0517968i
\(56\) 0.987382i 0.131944i
\(57\) 5.70197 0.755245
\(58\) 10.6208i 1.39457i
\(59\) 3.94753i 0.513924i −0.966422 0.256962i \(-0.917278\pi\)
0.966422 0.256962i \(-0.0827215\pi\)
\(60\) −0.0230720 + 0.132396i −0.00297858 + 0.0170922i
\(61\) 2.18574i 0.279855i −0.990162 0.139927i \(-0.955313\pi\)
0.990162 0.139927i \(-0.0446869\pi\)
\(62\) 6.33808i 0.804937i
\(63\) 0.344118i 0.0433548i
\(64\) 8.22574 1.02822
\(65\) 9.62897 + 1.67800i 1.19433 + 0.208130i
\(66\) 1.39371i 0.171554i
\(67\) 10.2635i 1.25389i 0.779064 + 0.626944i \(0.215695\pi\)
−0.779064 + 0.626944i \(0.784305\pi\)
\(68\) 0.0257707 0.00312516
\(69\) 2.35097i 0.283023i
\(70\) −0.183991 + 1.05581i −0.0219912 + 0.126193i
\(71\) 1.92267 0.228179 0.114090 0.993470i \(-0.463605\pi\)
0.114090 + 0.993470i \(0.463605\pi\)
\(72\) −2.86931 −0.338152
\(73\) 9.22636i 1.07986i −0.841709 0.539932i \(-0.818450\pi\)
0.841709 0.539932i \(-0.181550\pi\)
\(74\) −2.71748 + 8.02444i −0.315900 + 0.932822i
\(75\) 1.69129 4.70527i 0.195294 0.543317i
\(76\) 0.342697i 0.0393101i
\(77\) 0.344343i 0.0392415i
\(78\) 6.08808i 0.689340i
\(79\) 14.3679i 1.61652i 0.588828 + 0.808258i \(0.299589\pi\)
−0.588828 + 0.808258i \(0.700411\pi\)
\(80\) −8.53873 1.48801i −0.954659 0.166364i
\(81\) 1.00000 0.111111
\(82\) −3.49587 −0.386054
\(83\) 0.402746i 0.0442071i 0.999756 + 0.0221035i \(0.00703635\pi\)
−0.999756 + 0.0221035i \(0.992964\pi\)
\(84\) 0.0206820 0.00225659
\(85\) −0.944561 0.164604i −0.102452 0.0178539i
\(86\) −11.9540 −1.28904
\(87\) −7.62547 −0.817536
\(88\) −2.87119 −0.306070
\(89\) 7.34498i 0.778566i −0.921118 0.389283i \(-0.872723\pi\)
0.921118 0.389283i \(-0.127277\pi\)
\(90\) 3.06816 + 0.534675i 0.323413 + 0.0563597i
\(91\) 1.50417i 0.157680i
\(92\) −0.141297 −0.0147312
\(93\) 4.55060 0.471875
\(94\) 9.77657i 1.00838i
\(95\) −2.18890 + 12.5607i −0.224576 + 1.28870i
\(96\) 0.339869i 0.0346877i
\(97\) −9.66376 −0.981206 −0.490603 0.871383i \(-0.663224\pi\)
−0.490603 + 0.871383i \(0.663224\pi\)
\(98\) −9.58469 −0.968199
\(99\) 1.00065 0.100570
\(100\) −0.282793 0.101649i −0.0282793 0.0101649i
\(101\) −9.43463 −0.938781 −0.469391 0.882991i \(-0.655526\pi\)
−0.469391 + 0.882991i \(0.655526\pi\)
\(102\) 0.597215i 0.0591331i
\(103\) 3.60566 0.355276 0.177638 0.984096i \(-0.443154\pi\)
0.177638 + 0.984096i \(0.443154\pi\)
\(104\) 12.5421 1.22985
\(105\) −0.758047 0.132101i −0.0739778 0.0128918i
\(106\) 10.3328i 1.00361i
\(107\) 14.5128i 1.40300i 0.712669 + 0.701500i \(0.247486\pi\)
−0.712669 + 0.701500i \(0.752514\pi\)
\(108\) 0.0601015i 0.00578327i
\(109\) 5.44298i 0.521343i 0.965428 + 0.260671i \(0.0839439\pi\)
−0.965428 + 0.260671i \(0.916056\pi\)
\(110\) 3.07017 + 0.535025i 0.292729 + 0.0510126i
\(111\) −5.76136 1.95109i −0.546844 0.185189i
\(112\) 1.33386i 0.126038i
\(113\) 9.13297 0.859157 0.429579 0.903029i \(-0.358662\pi\)
0.429579 + 0.903029i \(0.358662\pi\)
\(114\) −7.94172 −0.743811
\(115\) 5.17887 + 0.902500i 0.482933 + 0.0841585i
\(116\) 0.458302i 0.0425522i
\(117\) −4.37110 −0.404109
\(118\) 5.49812i 0.506143i
\(119\) 0.147553i 0.0135262i
\(120\) 1.10148 6.32072i 0.100551 0.577001i
\(121\) −9.99869 −0.908972
\(122\) 3.04430i 0.275618i
\(123\) 2.50995i 0.226315i
\(124\) 0.273498i 0.0245608i
\(125\) 9.71582 + 5.53198i 0.869010 + 0.494795i
\(126\) 0.479288i 0.0426984i
\(127\) 21.0161i 1.86487i −0.361332 0.932437i \(-0.617678\pi\)
0.361332 0.932437i \(-0.382322\pi\)
\(128\) −10.7771 −0.952569
\(129\) 8.58272i 0.755666i
\(130\) −13.4113 2.33712i −1.17624 0.204979i
\(131\) 6.86428i 0.599735i 0.953981 + 0.299868i \(0.0969425\pi\)
−0.953981 + 0.299868i \(0.903057\pi\)
\(132\) 0.0601408i 0.00523459i
\(133\) 1.96215 0.170140
\(134\) 14.2951i 1.23490i
\(135\) −0.383884 + 2.20287i −0.0330395 + 0.189593i
\(136\) −1.23032 −0.105499
\(137\) 10.1126i 0.863976i 0.901879 + 0.431988i \(0.142188\pi\)
−0.901879 + 0.431988i \(0.857812\pi\)
\(138\) 3.27443i 0.278738i
\(139\) −3.55340 −0.301396 −0.150698 0.988580i \(-0.548152\pi\)
−0.150698 + 0.988580i \(0.548152\pi\)
\(140\) −0.00793949 + 0.0455597i −0.000671010 + 0.00385050i
\(141\) −7.01935 −0.591136
\(142\) −2.67790 −0.224724
\(143\) −4.37396 −0.365769
\(144\) 3.87618 0.323015
\(145\) 2.92730 16.7979i 0.243099 1.39499i
\(146\) 12.8505i 1.06351i
\(147\) 6.88158i 0.567583i
\(148\) −0.117263 + 0.346266i −0.00963897 + 0.0284629i
\(149\) −15.4708 −1.26742 −0.633710 0.773571i \(-0.718469\pi\)
−0.633710 + 0.773571i \(0.718469\pi\)
\(150\) −2.35564 + 6.55351i −0.192337 + 0.535091i
\(151\) −9.11731 −0.741956 −0.370978 0.928642i \(-0.620977\pi\)
−0.370978 + 0.928642i \(0.620977\pi\)
\(152\) 16.3608i 1.32703i
\(153\) 0.428787 0.0346653
\(154\) 0.479602i 0.0386474i
\(155\) −1.74690 + 10.0244i −0.140315 + 0.805177i
\(156\) 0.262710i 0.0210336i
\(157\) 13.2988i 1.06136i 0.847572 + 0.530680i \(0.178063\pi\)
−0.847572 + 0.530680i \(0.821937\pi\)
\(158\) 20.0117i 1.59204i
\(159\) −7.41870 −0.588341
\(160\) −0.748687 0.130470i −0.0591889 0.0103146i
\(161\) 0.809010i 0.0637589i
\(162\) −1.39280 −0.109429
\(163\) −19.7530 −1.54717 −0.773585 0.633692i \(-0.781539\pi\)
−0.773585 + 0.633692i \(0.781539\pi\)
\(164\) −0.150852 −0.0117795
\(165\) −0.384136 + 2.20431i −0.0299049 + 0.171605i
\(166\) 0.560945i 0.0435378i
\(167\) −7.51159 −0.581265 −0.290632 0.956835i \(-0.593866\pi\)
−0.290632 + 0.956835i \(0.593866\pi\)
\(168\) −0.987382 −0.0761782
\(169\) 6.10655 0.469735
\(170\) 1.31559 + 0.229261i 0.100901 + 0.0175835i
\(171\) 5.70197i 0.436041i
\(172\) −0.515834 −0.0393320
\(173\) 12.8334i 0.975706i 0.872926 + 0.487853i \(0.162220\pi\)
−0.872926 + 0.487853i \(0.837780\pi\)
\(174\) 10.6208 0.805158
\(175\) 0.582004 1.61917i 0.0439954 0.122397i
\(176\) 3.87872 0.292370
\(177\) −3.94753 −0.296714
\(178\) 10.2301i 0.766779i
\(179\) 7.40603i 0.553553i −0.960934 0.276777i \(-0.910734\pi\)
0.960934 0.276777i \(-0.0892662\pi\)
\(180\) 0.132396 + 0.0230720i 0.00986819 + 0.00171969i
\(181\) −14.6421 −1.08834 −0.544171 0.838974i \(-0.683156\pi\)
−0.544171 + 0.838974i \(0.683156\pi\)
\(182\) 2.09502i 0.155293i
\(183\) −2.18574 −0.161574
\(184\) 6.74567 0.497297
\(185\) 6.50968 11.9425i 0.478601 0.878032i
\(186\) −6.33808 −0.464731
\(187\) 0.429067 0.0313765
\(188\) 0.421873i 0.0307683i
\(189\) 0.344118 0.0250309
\(190\) 3.04870 17.4946i 0.221176 1.26919i
\(191\) 4.01324i 0.290388i −0.989403 0.145194i \(-0.953619\pi\)
0.989403 0.145194i \(-0.0463807\pi\)
\(192\) 8.22574i 0.593642i
\(193\) 24.0591 1.73181 0.865906 0.500207i \(-0.166743\pi\)
0.865906 + 0.500207i \(0.166743\pi\)
\(194\) 13.4597 0.966351
\(195\) 1.67800 9.62897i 0.120164 0.689545i
\(196\) −0.413593 −0.0295424
\(197\) 4.81990i 0.343403i 0.985149 + 0.171702i \(0.0549265\pi\)
−0.985149 + 0.171702i \(0.945073\pi\)
\(198\) −1.39371 −0.0990469
\(199\) 27.1785i 1.92663i 0.268372 + 0.963315i \(0.413514\pi\)
−0.268372 + 0.963315i \(0.586486\pi\)
\(200\) 13.5009 + 4.85285i 0.954657 + 0.343149i
\(201\) 10.2635 0.723933
\(202\) 13.1406 0.924568
\(203\) −2.62406 −0.184173
\(204\) 0.0257707i 0.00180431i
\(205\) 5.52909 + 0.963531i 0.386169 + 0.0672959i
\(206\) −5.02197 −0.349897
\(207\) −2.35097 −0.163404
\(208\) −16.9432 −1.17480
\(209\) 5.70571i 0.394672i
\(210\) 1.05581 + 0.183991i 0.0728577 + 0.0126966i
\(211\) 9.18627 0.632409 0.316204 0.948691i \(-0.397591\pi\)
0.316204 + 0.948691i \(0.397591\pi\)
\(212\) 0.445875i 0.0306228i
\(213\) 1.92267i 0.131739i
\(214\) 20.2134i 1.38176i
\(215\) 18.9066 + 3.29477i 1.28942 + 0.224702i
\(216\) 2.86931i 0.195232i
\(217\) 1.56594 0.106303
\(218\) 7.58100i 0.513450i
\(219\) −9.22636 −0.623459
\(220\) 0.132482 + 0.0230871i 0.00893196 + 0.00155653i
\(221\) −1.87427 −0.126077
\(222\) 8.02444 + 2.71748i 0.538565 + 0.182385i
\(223\) 5.05112i 0.338248i −0.985595 0.169124i \(-0.945906\pi\)
0.985595 0.169124i \(-0.0540939\pi\)
\(224\) 0.116955i 0.00781438i
\(225\) −4.70527 1.69129i −0.313684 0.112753i
\(226\) −12.7204 −0.846150
\(227\) 13.1231 0.871011 0.435506 0.900186i \(-0.356570\pi\)
0.435506 + 0.900186i \(0.356570\pi\)
\(228\) −0.342697 −0.0226957
\(229\) 10.8507 0.717032 0.358516 0.933524i \(-0.383283\pi\)
0.358516 + 0.933524i \(0.383283\pi\)
\(230\) −7.21315 1.25700i −0.475621 0.0828844i
\(231\) 0.344343 0.0226561
\(232\) 21.8799i 1.43648i
\(233\) 17.1449i 1.12320i −0.827410 0.561598i \(-0.810187\pi\)
0.827410 0.561598i \(-0.189813\pi\)
\(234\) 6.08808 0.397991
\(235\) 2.69462 15.4627i 0.175778 1.00868i
\(236\) 0.237252i 0.0154438i
\(237\) 14.3679 0.933296
\(238\) 0.205512i 0.0133214i
\(239\) 1.53255i 0.0991323i −0.998771 0.0495662i \(-0.984216\pi\)
0.998771 0.0495662i \(-0.0157839\pi\)
\(240\) −1.48801 + 8.53873i −0.0960504 + 0.551173i
\(241\) 3.84894i 0.247932i −0.992286 0.123966i \(-0.960439\pi\)
0.992286 0.123966i \(-0.0395614\pi\)
\(242\) 13.9262 0.895210
\(243\) 1.00000i 0.0641500i
\(244\) 0.131366i 0.00840984i
\(245\) 15.1592 + 2.64173i 0.968488 + 0.168774i
\(246\) 3.49587i 0.222888i
\(247\) 24.9239i 1.58587i
\(248\) 13.0571i 0.829126i
\(249\) 0.402746 0.0255230
\(250\) −13.5322 7.70495i −0.855853 0.487304i
\(251\) 5.32686i 0.336229i 0.985767 + 0.168114i \(0.0537678\pi\)
−0.985767 + 0.168114i \(0.946232\pi\)
\(252\) 0.0206820i 0.00130284i
\(253\) −2.35251 −0.147901
\(254\) 29.2712i 1.83664i
\(255\) −0.164604 + 0.944561i −0.0103079 + 0.0591507i
\(256\) −1.44112 −0.0900700
\(257\) −5.23877 −0.326786 −0.163393 0.986561i \(-0.552244\pi\)
−0.163393 + 0.986561i \(0.552244\pi\)
\(258\) 11.9540i 0.744226i
\(259\) −1.98259 0.671404i −0.123192 0.0417190i
\(260\) −0.578715 0.100850i −0.0358904 0.00625446i
\(261\) 7.62547i 0.472004i
\(262\) 9.56059i 0.590655i
\(263\) 7.96305i 0.491022i 0.969394 + 0.245511i \(0.0789558\pi\)
−0.969394 + 0.245511i \(0.921044\pi\)
\(264\) 2.87119i 0.176710i
\(265\) 2.84792 16.3424i 0.174946 1.00391i
\(266\) −2.73289 −0.167564
\(267\) −7.34498 −0.449506
\(268\) 0.616853i 0.0376803i
\(269\) −9.37825 −0.571802 −0.285901 0.958259i \(-0.592293\pi\)
−0.285901 + 0.958259i \(0.592293\pi\)
\(270\) 0.534675 3.06816i 0.0325393 0.186722i
\(271\) 26.6529 1.61905 0.809524 0.587087i \(-0.199725\pi\)
0.809524 + 0.587087i \(0.199725\pi\)
\(272\) 1.66206 0.100777
\(273\) −1.50417 −0.0910368
\(274\) 14.0848i 0.850895i
\(275\) −4.70834 1.69240i −0.283924 0.102056i
\(276\) 0.141297i 0.00850506i
\(277\) 9.95700 0.598258 0.299129 0.954213i \(-0.403304\pi\)
0.299129 + 0.954213i \(0.403304\pi\)
\(278\) 4.94919 0.296833
\(279\) 4.55060i 0.272437i
\(280\) 0.379041 2.17507i 0.0226520 0.129986i
\(281\) 18.2638i 1.08953i 0.838589 + 0.544764i \(0.183381\pi\)
−0.838589 + 0.544764i \(0.816619\pi\)
\(282\) 9.77657 0.582186
\(283\) −18.6227 −1.10700 −0.553501 0.832848i \(-0.686709\pi\)
−0.553501 + 0.832848i \(0.686709\pi\)
\(284\) −0.115555 −0.00685695
\(285\) 12.5607 + 2.18890i 0.744032 + 0.129659i
\(286\) 6.09207 0.360232
\(287\) 0.863719i 0.0509837i
\(288\) 0.339869 0.0200270
\(289\) −16.8161 −0.989185
\(290\) −4.07715 + 23.3962i −0.239418 + 1.37387i
\(291\) 9.66376i 0.566500i
\(292\) 0.554518i 0.0324507i
\(293\) 29.8367i 1.74308i −0.490327 0.871538i \(-0.663123\pi\)
0.490327 0.871538i \(-0.336877\pi\)
\(294\) 9.58469i 0.558990i
\(295\) 1.51539 8.69588i 0.0882296 0.506294i
\(296\) 5.59828 16.5312i 0.325393 0.960854i
\(297\) 1.00065i 0.0580639i
\(298\) 21.5478 1.24823
\(299\) 10.2763 0.594295
\(300\) −0.101649 + 0.282793i −0.00586872 + 0.0163271i
\(301\) 2.95347i 0.170235i
\(302\) 12.6986 0.730723
\(303\) 9.43463i 0.542006i
\(304\) 22.1019i 1.26763i
\(305\) 0.839070 4.81489i 0.0480450 0.275700i
\(306\) −0.597215 −0.0341405
\(307\) 19.6530i 1.12166i −0.827932 0.560828i \(-0.810483\pi\)
0.827932 0.560828i \(-0.189517\pi\)
\(308\) 0.0206955i 0.00117924i
\(309\) 3.60566i 0.205119i
\(310\) 2.43309 13.9620i 0.138190 0.792986i
\(311\) 23.0782i 1.30864i −0.756217 0.654321i \(-0.772954\pi\)
0.756217 0.654321i \(-0.227046\pi\)
\(312\) 12.5421i 0.710055i
\(313\) −12.0135 −0.679043 −0.339522 0.940598i \(-0.610265\pi\)
−0.339522 + 0.940598i \(0.610265\pi\)
\(314\) 18.5226i 1.04529i
\(315\) −0.132101 + 0.758047i −0.00744307 + 0.0427111i
\(316\) 0.863533i 0.0485775i
\(317\) 9.84245i 0.552807i −0.961042 0.276404i \(-0.910857\pi\)
0.961042 0.276404i \(-0.0891427\pi\)
\(318\) 10.3328 0.579433
\(319\) 7.63045i 0.427223i
\(320\) 18.1202 + 3.15773i 1.01295 + 0.176523i
\(321\) 14.5128 0.810023
\(322\) 1.12679i 0.0627936i
\(323\) 2.44493i 0.136040i
\(324\) −0.0601015 −0.00333897
\(325\) 20.5672 + 7.39282i 1.14086 + 0.410080i
\(326\) 27.5120 1.52375
\(327\) 5.44298 0.300997
\(328\) 7.20184 0.397655
\(329\) −2.41548 −0.133170
\(330\) 0.535025 3.07017i 0.0294521 0.169007i
\(331\) 12.5516i 0.689896i 0.938622 + 0.344948i \(0.112104\pi\)
−0.938622 + 0.344948i \(0.887896\pi\)
\(332\) 0.0242056i 0.00132846i
\(333\) −1.95109 + 5.76136i −0.106919 + 0.315721i
\(334\) 10.4622 0.572464
\(335\) −3.94000 + 22.6092i −0.215265 + 1.23527i
\(336\) 1.33386 0.0727683
\(337\) 24.4199i 1.33024i 0.746738 + 0.665118i \(0.231619\pi\)
−0.746738 + 0.665118i \(0.768381\pi\)
\(338\) −8.50522 −0.462623
\(339\) 9.13297i 0.496035i
\(340\) 0.0567695 + 0.00989297i 0.00307876 + 0.000536522i
\(341\) 4.55357i 0.246590i
\(342\) 7.94172i 0.429439i
\(343\) 4.77690i 0.257928i
\(344\) 24.6265 1.32777
\(345\) 0.902500 5.17887i 0.0485889 0.278821i
\(346\) 17.8744i 0.960934i
\(347\) −4.91405 −0.263800 −0.131900 0.991263i \(-0.542108\pi\)
−0.131900 + 0.991263i \(0.542108\pi\)
\(348\) 0.458302 0.0245676
\(349\) −7.69210 −0.411749 −0.205874 0.978578i \(-0.566004\pi\)
−0.205874 + 0.978578i \(0.566004\pi\)
\(350\) −0.810617 + 2.25518i −0.0433293 + 0.120544i
\(351\) 4.37110i 0.233312i
\(352\) 0.340091 0.0181269
\(353\) −5.78846 −0.308089 −0.154044 0.988064i \(-0.549230\pi\)
−0.154044 + 0.988064i \(0.549230\pi\)
\(354\) 5.49812 0.292222
\(355\) 4.23539 + 0.738083i 0.224791 + 0.0391734i
\(356\) 0.441444i 0.0233965i
\(357\) 0.147553 0.00780934
\(358\) 10.3151i 0.545172i
\(359\) −23.3366 −1.23166 −0.615830 0.787879i \(-0.711179\pi\)
−0.615830 + 0.787879i \(0.711179\pi\)
\(360\) −6.32072 1.10148i −0.333131 0.0580533i
\(361\) −13.5125 −0.711185
\(362\) 20.3936 1.07186
\(363\) 9.99869i 0.524795i
\(364\) 0.0904031i 0.00473841i
\(365\) 3.54185 20.3245i 0.185389 1.06383i
\(366\) 3.04430 0.159128
\(367\) 0.996653i 0.0520249i −0.999662 0.0260124i \(-0.991719\pi\)
0.999662 0.0260124i \(-0.00828095\pi\)
\(368\) −9.11279 −0.475037
\(369\) −2.50995 −0.130663
\(370\) −9.06670 + 16.6336i −0.471355 + 0.864739i
\(371\) −2.55291 −0.132540
\(372\) −0.273498 −0.0141802
\(373\) 25.4727i 1.31893i 0.751737 + 0.659463i \(0.229216\pi\)
−0.751737 + 0.659463i \(0.770784\pi\)
\(374\) −0.597606 −0.0309015
\(375\) 5.53198 9.71582i 0.285670 0.501723i
\(376\) 20.1407i 1.03868i
\(377\) 33.3317i 1.71667i
\(378\) −0.479288 −0.0246519
\(379\) −13.7468 −0.706124 −0.353062 0.935600i \(-0.614859\pi\)
−0.353062 + 0.935600i \(0.614859\pi\)
\(380\) 0.131556 0.754917i 0.00674868 0.0387264i
\(381\) −21.0161 −1.07669
\(382\) 5.58966i 0.285992i
\(383\) −31.5653 −1.61291 −0.806456 0.591294i \(-0.798617\pi\)
−0.806456 + 0.591294i \(0.798617\pi\)
\(384\) 10.7771i 0.549966i
\(385\) −0.132188 + 0.758543i −0.00673692 + 0.0386589i
\(386\) −33.5096 −1.70559
\(387\) −8.58272 −0.436284
\(388\) 0.580806 0.0294860
\(389\) 32.3554i 1.64049i 0.572016 + 0.820243i \(0.306162\pi\)
−0.572016 + 0.820243i \(0.693838\pi\)
\(390\) −2.33712 + 13.4113i −0.118345 + 0.679105i
\(391\) −1.00806 −0.0509799
\(392\) 19.7454 0.997295
\(393\) 6.86428 0.346257
\(394\) 6.71316i 0.338204i
\(395\) −5.51562 + 31.6506i −0.277521 + 1.59252i
\(396\) −0.0601408 −0.00302219
\(397\) 19.2972i 0.968501i −0.874929 0.484250i \(-0.839092\pi\)
0.874929 0.484250i \(-0.160908\pi\)
\(398\) 37.8542i 1.89746i
\(399\) 1.96215i 0.0982304i
\(400\) −18.2385 6.55577i −0.911924 0.327788i
\(401\) 27.7461i 1.38558i 0.721141 + 0.692788i \(0.243618\pi\)
−0.721141 + 0.692788i \(0.756382\pi\)
\(402\) −14.2951 −0.712972
\(403\) 19.8911i 0.990848i
\(404\) 0.567036 0.0282111
\(405\) 2.20287 + 0.383884i 0.109461 + 0.0190754i
\(406\) 3.65479 0.181384
\(407\) −1.95236 + 5.76513i −0.0967750 + 0.285767i
\(408\) 1.23032i 0.0609101i
\(409\) 30.8229i 1.52409i 0.647522 + 0.762047i \(0.275806\pi\)
−0.647522 + 0.762047i \(0.724194\pi\)
\(410\) −7.70093 1.34201i −0.380322 0.0662771i
\(411\) 10.1126 0.498817
\(412\) −0.216706 −0.0106763
\(413\) −1.35841 −0.0668432
\(414\) 3.27443 0.160930
\(415\) −0.154608 + 0.887196i −0.00758940 + 0.0435508i
\(416\) −1.48560 −0.0728377
\(417\) 3.55340i 0.174011i
\(418\) 7.94692i 0.388697i
\(419\) −29.0149 −1.41747 −0.708735 0.705475i \(-0.750734\pi\)
−0.708735 + 0.705475i \(0.750734\pi\)
\(420\) 0.0455597 + 0.00793949i 0.00222309 + 0.000387408i
\(421\) 24.1020i 1.17466i −0.809348 0.587329i \(-0.800180\pi\)
0.809348 0.587329i \(-0.199820\pi\)
\(422\) −12.7947 −0.622834
\(423\) 7.01935i 0.341292i
\(424\) 21.2866i 1.03377i
\(425\) −2.01755 0.725204i −0.0978658 0.0351776i
\(426\) 2.67790i 0.129745i
\(427\) −0.752151 −0.0363991
\(428\) 0.872238i 0.0421612i
\(429\) 4.37396i 0.211177i
\(430\) −26.3332 4.58897i −1.26990 0.221300i
\(431\) 19.5238i 0.940427i −0.882553 0.470214i \(-0.844177\pi\)
0.882553 0.470214i \(-0.155823\pi\)
\(432\) 3.87618i 0.186493i
\(433\) 28.2340i 1.35684i 0.734675 + 0.678419i \(0.237335\pi\)
−0.734675 + 0.678419i \(0.762665\pi\)
\(434\) −2.18105 −0.104694
\(435\) −16.7979 2.92730i −0.805398 0.140353i
\(436\) 0.327131i 0.0156667i
\(437\) 13.4052i 0.641256i
\(438\) 12.8505 0.614020
\(439\) 0.0399408i 0.00190627i 1.00000 0.000953135i \(0.000303392\pi\)
−1.00000 0.000953135i \(0.999697\pi\)
\(440\) −6.32486 1.10221i −0.301526 0.0525456i
\(441\) −6.88158 −0.327694
\(442\) 2.61049 0.124168
\(443\) 32.6233i 1.54998i −0.631973 0.774990i \(-0.717755\pi\)
0.631973 0.774990i \(-0.282245\pi\)
\(444\) 0.346266 + 0.117263i 0.0164331 + 0.00556506i
\(445\) 2.81962 16.1800i 0.133663 0.767007i
\(446\) 7.03522i 0.333127i
\(447\) 15.4708i 0.731745i
\(448\) 2.83062i 0.133734i
\(449\) 7.95302i 0.375326i −0.982233 0.187663i \(-0.939909\pi\)
0.982233 0.187663i \(-0.0600913\pi\)
\(450\) 6.55351 + 2.35564i 0.308935 + 0.111046i
\(451\) −2.51159 −0.118266
\(452\) −0.548905 −0.0258183
\(453\) 9.11731i 0.428368i
\(454\) −18.2779 −0.857824
\(455\) 0.577429 3.31350i 0.0270703 0.155339i
\(456\) 16.3608 0.766163
\(457\) 11.4750 0.536776 0.268388 0.963311i \(-0.413509\pi\)
0.268388 + 0.963311i \(0.413509\pi\)
\(458\) −15.1128 −0.706176
\(459\) 0.428787i 0.0200140i
\(460\) −0.311258 0.0542416i −0.0145125 0.00252903i
\(461\) 1.19985i 0.0558824i 0.999610 + 0.0279412i \(0.00889512\pi\)
−0.999610 + 0.0279412i \(0.991105\pi\)
\(462\) −0.479602 −0.0223131
\(463\) −10.2734 −0.477448 −0.238724 0.971088i \(-0.576729\pi\)
−0.238724 + 0.971088i \(0.576729\pi\)
\(464\) 29.5577i 1.37218i
\(465\) 10.0244 + 1.74690i 0.464869 + 0.0810107i
\(466\) 23.8794i 1.10619i
\(467\) −37.1879 −1.72085 −0.860426 0.509575i \(-0.829803\pi\)
−0.860426 + 0.509575i \(0.829803\pi\)
\(468\) 0.262710 0.0121438
\(469\) 3.53186 0.163086
\(470\) −3.75307 + 21.5365i −0.173116 + 0.993405i
\(471\) 13.2988 0.612777
\(472\) 11.3267i 0.521353i
\(473\) −8.58834 −0.394892
\(474\) −20.0117 −0.919166
\(475\) −9.64371 + 26.8293i −0.442484 + 1.23101i
\(476\) 0.00886816i 0.000406471i
\(477\) 7.41870i 0.339679i
\(478\) 2.13454i 0.0976315i
\(479\) 9.73753i 0.444919i 0.974942 + 0.222460i \(0.0714086\pi\)
−0.974942 + 0.222460i \(0.928591\pi\)
\(480\) −0.130470 + 0.748687i −0.00595513 + 0.0341727i
\(481\) 8.52840 25.1835i 0.388862 1.14827i
\(482\) 5.36082i 0.244178i
\(483\) −0.809010 −0.0368112
\(484\) 0.600936 0.0273153
\(485\) −21.2880 3.70977i −0.966638 0.168452i
\(486\) 1.39280i 0.0631788i
\(487\) −35.6585 −1.61584 −0.807920 0.589293i \(-0.799407\pi\)
−0.807920 + 0.589293i \(0.799407\pi\)
\(488\) 6.27156i 0.283900i
\(489\) 19.7530i 0.893259i
\(490\) −21.1138 3.67941i −0.953825 0.166219i
\(491\) 26.4591 1.19408 0.597041 0.802211i \(-0.296343\pi\)
0.597041 + 0.802211i \(0.296343\pi\)
\(492\) 0.150852i 0.00680092i
\(493\) 3.26970i 0.147260i
\(494\) 34.7141i 1.56186i
\(495\) 2.20431 + 0.384136i 0.0990764 + 0.0172656i
\(496\) 17.6390i 0.792013i
\(497\) 0.661625i 0.0296779i
\(498\) −0.560945 −0.0251366
\(499\) 15.1576i 0.678545i −0.940688 0.339273i \(-0.889819\pi\)
0.940688 0.339273i \(-0.110181\pi\)
\(500\) −0.583935 0.332480i −0.0261144 0.0148690i
\(501\) 7.51159i 0.335593i
\(502\) 7.41927i 0.331138i
\(503\) 9.89357 0.441132 0.220566 0.975372i \(-0.429210\pi\)
0.220566 + 0.975372i \(0.429210\pi\)
\(504\) 0.987382i 0.0439815i
\(505\) −20.7833 3.62181i −0.924843 0.161168i
\(506\) 3.27658 0.145662
\(507\) 6.10655i 0.271201i
\(508\) 1.26310i 0.0560409i
\(509\) 36.1879 1.60400 0.802000 0.597324i \(-0.203769\pi\)
0.802000 + 0.597324i \(0.203769\pi\)
\(510\) 0.229261 1.31559i 0.0101519 0.0582551i
\(511\) −3.17495 −0.140452
\(512\) 23.5614 1.04128
\(513\) −5.70197 −0.251748
\(514\) 7.29657 0.321838
\(515\) 7.94280 + 1.38416i 0.350002 + 0.0609932i
\(516\) 0.515834i 0.0227083i
\(517\) 7.02394i 0.308913i
\(518\) 2.76135 + 0.935133i 0.121327 + 0.0410874i
\(519\) 12.8334 0.563324
\(520\) 27.6285 + 4.81470i 1.21159 + 0.211139i
\(521\) 32.0406 1.40373 0.701863 0.712312i \(-0.252352\pi\)
0.701863 + 0.712312i \(0.252352\pi\)
\(522\) 10.6208i 0.464858i
\(523\) −3.11083 −0.136027 −0.0680136 0.997684i \(-0.521666\pi\)
−0.0680136 + 0.997684i \(0.521666\pi\)
\(524\) 0.412554i 0.0180225i
\(525\) −1.61917 0.582004i −0.0706662 0.0254008i
\(526\) 11.0909i 0.483588i
\(527\) 1.95123i 0.0849971i
\(528\) 3.87872i 0.168800i
\(529\) −17.4730 −0.759694
\(530\) −3.96659 + 22.7618i −0.172298 + 0.988708i
\(531\) 3.94753i 0.171308i
\(532\) −0.117928 −0.00511284
\(533\) 10.9713 0.475218
\(534\) 10.2301 0.442700
\(535\) −5.57122 + 31.9697i −0.240865 + 1.38217i
\(536\) 29.4493i 1.27201i
\(537\) −7.40603 −0.319594
\(538\) 13.0620 0.563145
\(539\) −6.88609 −0.296605
\(540\) 0.0230720 0.132396i 0.000992862 0.00569740i
\(541\) 40.0599i 1.72231i −0.508341 0.861156i \(-0.669741\pi\)
0.508341 0.861156i \(-0.330259\pi\)
\(542\) −37.1222 −1.59453
\(543\) 14.6421i 0.628355i
\(544\) 0.145731 0.00624818
\(545\) −2.08947 + 11.9902i −0.0895033 + 0.513603i
\(546\) 2.09502 0.0896585
\(547\) −29.0324 −1.24134 −0.620669 0.784073i \(-0.713139\pi\)
−0.620669 + 0.784073i \(0.713139\pi\)
\(548\) 0.607781i 0.0259631i
\(549\) 2.18574i 0.0932849i
\(550\) 6.55779 + 2.35718i 0.279625 + 0.100510i
\(551\) 43.4802 1.85232
\(552\) 6.74567i 0.287115i
\(553\) 4.94425 0.210251
\(554\) −13.8681 −0.589201
\(555\) −11.9425 6.50968i −0.506932 0.276321i
\(556\) 0.213565 0.00905717
\(557\) −0.496954 −0.0210566 −0.0105283 0.999945i \(-0.503351\pi\)
−0.0105283 + 0.999945i \(0.503351\pi\)
\(558\) 6.33808i 0.268312i
\(559\) 37.5160 1.58676
\(560\) −0.512050 + 2.93833i −0.0216380 + 0.124167i
\(561\) 0.429067i 0.0181152i
\(562\) 25.4379i 1.07303i
\(563\) −24.9566 −1.05179 −0.525897 0.850548i \(-0.676270\pi\)
−0.525897 + 0.850548i \(0.676270\pi\)
\(564\) 0.421873 0.0177641
\(565\) 20.1187 + 3.50600i 0.846402 + 0.147499i
\(566\) 25.9377 1.09024
\(567\) 0.344118i 0.0144516i
\(568\) 5.51675 0.231478
\(569\) 24.1825i 1.01379i 0.862009 + 0.506893i \(0.169206\pi\)
−0.862009 + 0.506893i \(0.830794\pi\)
\(570\) −17.4946 3.04870i −0.732767 0.127696i
\(571\) 36.7544 1.53812 0.769062 0.639175i \(-0.220724\pi\)
0.769062 + 0.639175i \(0.220724\pi\)
\(572\) 0.262882 0.0109916
\(573\) −4.01324 −0.167656
\(574\) 1.20299i 0.0502118i
\(575\) 11.0619 + 3.97618i 0.461314 + 0.165818i
\(576\) −8.22574 −0.342739
\(577\) −28.8512 −1.20109 −0.600545 0.799591i \(-0.705050\pi\)
−0.600545 + 0.799591i \(0.705050\pi\)
\(578\) 23.4216 0.974209
\(579\) 24.0591i 0.999862i
\(580\) −0.175935 + 1.00958i −0.00730530 + 0.0419205i
\(581\) 0.138592 0.00574977
\(582\) 13.4597i 0.557923i
\(583\) 7.42355i 0.307452i
\(584\) 26.4733i 1.09547i
\(585\) −9.62897 1.67800i −0.398109 0.0693767i
\(586\) 41.5566i 1.71669i
\(587\) −11.1675 −0.460933 −0.230466 0.973080i \(-0.574025\pi\)
−0.230466 + 0.973080i \(0.574025\pi\)
\(588\) 0.413593i 0.0170563i
\(589\) −25.9474 −1.06914
\(590\) −2.11064 + 12.1116i −0.0868938 + 0.498629i
\(591\) 4.81990 0.198264
\(592\) −7.56277 + 22.3321i −0.310828 + 0.917843i
\(593\) 3.72900i 0.153132i −0.997065 0.0765658i \(-0.975604\pi\)
0.997065 0.0765658i \(-0.0243955\pi\)
\(594\) 1.39371i 0.0571848i
\(595\) −0.0566433 + 0.325040i −0.00232215 + 0.0133253i
\(596\) 0.929820 0.0380869
\(597\) 27.1785 1.11234
\(598\) −14.3129 −0.585298
\(599\) −20.9040 −0.854113 −0.427056 0.904225i \(-0.640449\pi\)
−0.427056 + 0.904225i \(0.640449\pi\)
\(600\) 4.85285 13.5009i 0.198117 0.551171i
\(601\) 25.2037 1.02808 0.514041 0.857766i \(-0.328148\pi\)
0.514041 + 0.857766i \(0.328148\pi\)
\(602\) 4.11360i 0.167658i
\(603\) 10.2635i 0.417963i
\(604\) 0.547964 0.0222963
\(605\) −22.0258 3.83834i −0.895476 0.156051i
\(606\) 13.1406i 0.533800i
\(607\) 0.485148 0.0196916 0.00984578 0.999952i \(-0.496866\pi\)
0.00984578 + 0.999952i \(0.496866\pi\)
\(608\) 1.93792i 0.0785932i
\(609\) 2.62406i 0.106332i
\(610\) −1.16866 + 6.70619i −0.0473176 + 0.271526i
\(611\) 30.6823i 1.24127i
\(612\) −0.0257707 −0.00104172
\(613\) 39.1708i 1.58210i −0.611755 0.791048i \(-0.709536\pi\)
0.611755 0.791048i \(-0.290464\pi\)
\(614\) 27.3727i 1.10467i
\(615\) 0.963531 5.52909i 0.0388533 0.222955i
\(616\) 0.988028i 0.0398088i
\(617\) 27.8220i 1.12007i 0.828468 + 0.560036i \(0.189213\pi\)
−0.828468 + 0.560036i \(0.810787\pi\)
\(618\) 5.02197i 0.202013i
\(619\) −0.946919 −0.0380599 −0.0190299 0.999819i \(-0.506058\pi\)
−0.0190299 + 0.999819i \(0.506058\pi\)
\(620\) 0.104991 0.602480i 0.00421656 0.0241962i
\(621\) 2.35097i 0.0943411i
\(622\) 32.1433i 1.28883i
\(623\) −2.52754 −0.101264
\(624\) 16.9432i 0.678271i
\(625\) 19.2790 + 15.9160i 0.771162 + 0.636639i
\(626\) 16.7324 0.668762
\(627\) −5.70571 −0.227864
\(628\) 0.799278i 0.0318947i
\(629\) −0.836599 + 2.47039i −0.0333574 + 0.0985010i
\(630\) 0.183991 1.05581i 0.00733038 0.0420644i
\(631\) 2.30783i 0.0918734i −0.998944 0.0459367i \(-0.985373\pi\)
0.998944 0.0459367i \(-0.0146273\pi\)
\(632\) 41.2261i 1.63988i
\(633\) 9.18627i 0.365121i
\(634\) 13.7086i 0.544438i
\(635\) 8.06774 46.2957i 0.320159 1.83719i
\(636\) 0.445875 0.0176801
\(637\) 30.0801 1.19182
\(638\) 10.6277i 0.420755i
\(639\) −1.92267 −0.0760597
\(640\) −23.7405 4.13716i −0.938427 0.163535i
\(641\) −48.9069 −1.93171 −0.965853 0.259091i \(-0.916577\pi\)
−0.965853 + 0.259091i \(0.916577\pi\)
\(642\) −20.2134 −0.797759
\(643\) 24.4145 0.962814 0.481407 0.876497i \(-0.340126\pi\)
0.481407 + 0.876497i \(0.340126\pi\)
\(644\) 0.0486227i 0.00191600i
\(645\) 3.29477 18.9066i 0.129731 0.744447i
\(646\) 3.40530i 0.133980i
\(647\) −21.3926 −0.841028 −0.420514 0.907286i \(-0.638150\pi\)
−0.420514 + 0.907286i \(0.638150\pi\)
\(648\) 2.86931 0.112717
\(649\) 3.95011i 0.155055i
\(650\) −28.6461 10.2967i −1.12359 0.403871i
\(651\) 1.56594i 0.0613741i
\(652\) 1.18718 0.0464936
\(653\) 28.7548 1.12526 0.562631 0.826708i \(-0.309789\pi\)
0.562631 + 0.826708i \(0.309789\pi\)
\(654\) −7.58100 −0.296440
\(655\) −2.63509 + 15.1211i −0.102962 + 0.590831i
\(656\) −9.72903 −0.379855
\(657\) 9.22636i 0.359954i
\(658\) 3.36429 0.131154
\(659\) 36.1968 1.41003 0.705014 0.709193i \(-0.250941\pi\)
0.705014 + 0.709193i \(0.250941\pi\)
\(660\) 0.0230871 0.132482i 0.000898665 0.00515687i
\(661\) 26.4419i 1.02847i 0.857649 + 0.514235i \(0.171924\pi\)
−0.857649 + 0.514235i \(0.828076\pi\)
\(662\) 17.4819i 0.679451i
\(663\) 1.87427i 0.0727906i
\(664\) 1.15560i 0.0448461i
\(665\) 4.32236 + 0.753239i 0.167614 + 0.0292094i
\(666\) 2.71748 8.02444i 0.105300 0.310941i
\(667\) 17.9272i 0.694145i
\(668\) 0.451458 0.0174674
\(669\) −5.05112 −0.195288
\(670\) 5.48765 31.4901i 0.212006 1.21657i
\(671\) 2.18717i 0.0844346i
\(672\) 0.116955 0.00451164
\(673\) 12.6452i 0.487438i −0.969846 0.243719i \(-0.921633\pi\)
0.969846 0.243719i \(-0.0783674\pi\)
\(674\) 34.0121i 1.31010i
\(675\) −1.69129 + 4.70527i −0.0650979 + 0.181106i
\(676\) −0.367013 −0.0141159
\(677\) 24.2473i 0.931900i −0.884811 0.465950i \(-0.845713\pi\)
0.884811 0.465950i \(-0.154287\pi\)
\(678\) 12.7204i 0.488525i
\(679\) 3.32547i 0.127620i
\(680\) −2.71024 0.472302i −0.103933 0.0181119i
\(681\) 13.1231i 0.502878i
\(682\) 6.34223i 0.242857i
\(683\) 13.8062 0.528279 0.264140 0.964484i \(-0.414912\pi\)
0.264140 + 0.964484i \(0.414912\pi\)
\(684\) 0.342697i 0.0131034i
\(685\) −3.88206 + 22.2767i −0.148326 + 0.851149i
\(686\) 6.65328i 0.254023i
\(687\) 10.8507i 0.413979i
\(688\) −33.2682 −1.26834
\(689\) 32.4279i 1.23540i
\(690\) −1.25700 + 7.21315i −0.0478533 + 0.274600i
\(691\) 19.4603 0.740303 0.370151 0.928971i \(-0.379306\pi\)
0.370151 + 0.928971i \(0.379306\pi\)
\(692\) 0.771307i 0.0293207i
\(693\) 0.344343i 0.0130805i
\(694\) 6.84431 0.259806
\(695\) −7.82768 1.36410i −0.296921 0.0517431i
\(696\) −21.8799 −0.829354
\(697\) −1.07623 −0.0407652
\(698\) 10.7136 0.405515
\(699\) −17.1449 −0.648478
\(700\) −0.0349793 + 0.0973143i −0.00132209 + 0.00367813i
\(701\) 33.8058i 1.27683i 0.769694 + 0.638413i \(0.220409\pi\)
−0.769694 + 0.638413i \(0.779591\pi\)
\(702\) 6.08808i 0.229780i
\(703\) 32.8511 + 11.1250i 1.23900 + 0.419589i
\(704\) −8.23112 −0.310222
\(705\) −15.4627 2.69462i −0.582359 0.101485i
\(706\) 8.06218 0.303424
\(707\) 3.24663i 0.122102i
\(708\) 0.237252 0.00891648
\(709\) 17.1515i 0.644137i −0.946716 0.322069i \(-0.895622\pi\)
0.946716 0.322069i \(-0.104378\pi\)
\(710\) −5.89906 1.02800i −0.221388 0.0385803i
\(711\) 14.3679i 0.538839i
\(712\) 21.0751i 0.789821i
\(713\) 10.6983i 0.400655i
\(714\) −0.205512 −0.00769110
\(715\) −9.63527 1.67910i −0.360339 0.0627946i
\(716\) 0.445114i 0.0166347i
\(717\) −1.53255 −0.0572341
\(718\) 32.5033 1.21301
\(719\) −20.0146 −0.746419 −0.373209 0.927747i \(-0.621743\pi\)
−0.373209 + 0.927747i \(0.621743\pi\)
\(720\) 8.53873 + 1.48801i 0.318220 + 0.0554547i
\(721\) 1.24077i 0.0462088i
\(722\) 18.8203 0.700418
\(723\) −3.84894 −0.143144
\(724\) 0.880015 0.0327055
\(725\) 12.8969 35.8798i 0.478979 1.33254i
\(726\) 13.9262i 0.516850i
\(727\) 20.5563 0.762390 0.381195 0.924495i \(-0.375513\pi\)
0.381195 + 0.924495i \(0.375513\pi\)
\(728\) 4.31595i 0.159960i
\(729\) −1.00000 −0.0370370
\(730\) −4.93310 + 28.3079i −0.182582 + 1.04772i
\(731\) −3.68015 −0.136115
\(732\) 0.131366 0.00485543
\(733\) 4.14889i 0.153243i −0.997060 0.0766213i \(-0.975587\pi\)
0.997060 0.0766213i \(-0.0244132\pi\)
\(734\) 1.38814i 0.0512372i
\(735\) 2.64173 15.1592i 0.0974417 0.559157i
\(736\) −0.799021 −0.0294523
\(737\) 10.2702i 0.378309i
\(738\) 3.49587 0.128685
\(739\) −47.3841 −1.74305 −0.871527 0.490348i \(-0.836870\pi\)
−0.871527 + 0.490348i \(0.836870\pi\)
\(740\) −0.391242 + 0.717764i −0.0143823 + 0.0263855i
\(741\) 24.9239 0.915603
\(742\) 3.55569 0.130534
\(743\) 7.43386i 0.272722i 0.990659 + 0.136361i \(0.0435407\pi\)
−0.990659 + 0.136361i \(0.956459\pi\)
\(744\) 13.0571 0.478696
\(745\) −34.0802 5.93901i −1.24860 0.217588i
\(746\) 35.4784i 1.29896i
\(747\) 0.402746i 0.0147357i
\(748\) −0.0257876 −0.000942887
\(749\) 4.99410 0.182480
\(750\) −7.70495 + 13.5322i −0.281345 + 0.494127i
\(751\) 2.00815 0.0732786 0.0366393 0.999329i \(-0.488335\pi\)
0.0366393 + 0.999329i \(0.488335\pi\)
\(752\) 27.2083i 0.992184i
\(753\) 5.32686 0.194122
\(754\) 46.4245i 1.69068i
\(755\) −20.0842 3.49999i −0.730940 0.127378i
\(756\) −0.0206820 −0.000752197
\(757\) 24.4281 0.887853 0.443926 0.896063i \(-0.353585\pi\)
0.443926 + 0.896063i \(0.353585\pi\)
\(758\) 19.1465 0.695433
\(759\) 2.35251i 0.0853906i
\(760\) −6.28064 + 36.0406i −0.227823 + 1.30733i
\(761\) 33.4813 1.21370 0.606848 0.794818i \(-0.292434\pi\)
0.606848 + 0.794818i \(0.292434\pi\)
\(762\) 29.2712 1.06038
\(763\) 1.87303 0.0678081
\(764\) 0.241202i 0.00872638i
\(765\) 0.944561 + 0.164604i 0.0341507 + 0.00595129i
\(766\) 43.9642 1.58849
\(767\) 17.2550i 0.623044i
\(768\) 1.44112i 0.0520019i
\(769\) 39.7615i 1.43384i −0.697158 0.716918i \(-0.745552\pi\)
0.697158 0.716918i \(-0.254448\pi\)
\(770\) 0.184112 1.05650i 0.00663492 0.0380736i
\(771\) 5.23877i 0.188670i
\(772\) −1.44599 −0.0520422
\(773\) 17.4578i 0.627912i 0.949437 + 0.313956i \(0.101655\pi\)
−0.949437 + 0.313956i \(0.898345\pi\)
\(774\) 11.9540 0.429679
\(775\) −7.69640 + 21.4118i −0.276463 + 0.769133i
\(776\) −27.7284 −0.995390
\(777\) −0.671404 + 1.98259i −0.0240865 + 0.0711249i
\(778\) 45.0647i 1.61565i
\(779\) 14.3117i 0.512769i
\(780\) −0.100850 + 0.578715i −0.00361102 + 0.0207213i
\(781\) −1.92393 −0.0688436
\(782\) 1.40403 0.0502081
\(783\) 7.62547 0.272512
\(784\) −26.6743 −0.952653
\(785\) −5.10520 + 29.2955i −0.182212 + 1.04560i
\(786\) −9.56059 −0.341015
\(787\) 2.56830i 0.0915499i −0.998952 0.0457749i \(-0.985424\pi\)
0.998952 0.0457749i \(-0.0145757\pi\)
\(788\) 0.289683i 0.0103195i
\(789\) 7.96305 0.283492
\(790\) 7.68216 44.0831i 0.273319 1.56841i
\(791\) 3.14282i 0.111746i
\(792\) 2.87119 0.102023
\(793\) 9.55408i 0.339275i
\(794\) 26.8772i 0.953838i
\(795\) −16.3424 2.84792i −0.579606 0.101005i
\(796\) 1.63347i 0.0578967i
\(797\) 12.9875 0.460040 0.230020 0.973186i \(-0.426121\pi\)
0.230020 + 0.973186i \(0.426121\pi\)
\(798\) 2.73289i 0.0967432i
\(799\) 3.00980i 0.106479i
\(800\) −1.59917 0.574818i −0.0565393 0.0203229i
\(801\) 7.34498i 0.259522i
\(802\) 38.6449i 1.36460i
\(803\) 9.23239i 0.325804i
\(804\) −0.616853 −0.0217547
\(805\) 0.310566 1.78214i 0.0109460 0.0628123i
\(806\) 27.7044i 0.975847i
\(807\) 9.37825i 0.330130i
\(808\) −27.0709 −0.952352
\(809\) 32.4055i 1.13932i 0.821882 + 0.569658i \(0.192924\pi\)
−0.821882 + 0.569658i \(0.807076\pi\)
\(810\) −3.06816 0.534675i −0.107804 0.0187866i
\(811\) −9.17716 −0.322254 −0.161127 0.986934i \(-0.551513\pi\)
−0.161127 + 0.986934i \(0.551513\pi\)
\(812\) 0.157710 0.00553453
\(813\) 26.6529i 0.934757i
\(814\) 2.71926 8.02969i 0.0953099 0.281440i
\(815\) −43.5132 7.58285i −1.52420 0.265616i
\(816\) 1.66206i 0.0581836i
\(817\) 48.9384i 1.71214i
\(818\) 42.9302i 1.50102i
\(819\) 1.50417i 0.0525601i
\(820\) −0.332307 0.0579096i −0.0116047 0.00202229i
\(821\) 21.9824 0.767190 0.383595 0.923501i \(-0.374686\pi\)
0.383595 + 0.923501i \(0.374686\pi\)
\(822\) −14.0848 −0.491265
\(823\) 1.23098i 0.0429092i 0.999770 + 0.0214546i \(0.00682974\pi\)
−0.999770 + 0.0214546i \(0.993170\pi\)
\(824\) 10.3458 0.360412
\(825\) −1.69240 + 4.70834i −0.0589218 + 0.163924i
\(826\) 1.89200 0.0658312
\(827\) 41.6469 1.44820 0.724102 0.689693i \(-0.242254\pi\)
0.724102 + 0.689693i \(0.242254\pi\)
\(828\) 0.141297 0.00491040
\(829\) 24.0119i 0.833969i −0.908914 0.416985i \(-0.863087\pi\)
0.908914 0.416985i \(-0.136913\pi\)
\(830\) 0.215338 1.23569i 0.00747450 0.0428914i
\(831\) 9.95700i 0.345405i
\(832\) 35.9556 1.24653
\(833\) −2.95073 −0.102237
\(834\) 4.94919i 0.171376i
\(835\) −16.5471 2.88358i −0.572635 0.0997905i
\(836\) 0.342921i 0.0118602i
\(837\) −4.55060 −0.157292
\(838\) 40.4120 1.39601
\(839\) −47.1610 −1.62818 −0.814090 0.580739i \(-0.802764\pi\)
−0.814090 + 0.580739i \(0.802764\pi\)
\(840\) −2.17507 0.379041i −0.0750472 0.0130781i
\(841\) −29.1477 −1.00509
\(842\) 33.5693i 1.15687i
\(843\) 18.2638 0.629039
\(844\) −0.552108 −0.0190043
\(845\) 13.4519 + 2.34421i 0.462761 + 0.0806432i
\(846\) 9.77657i 0.336125i
\(847\) 3.44073i 0.118225i
\(848\) 28.7562i 0.987493i
\(849\) 18.6227i 0.639128i
\(850\) 2.81005 + 1.01007i 0.0963841 + 0.0346450i
\(851\) 4.58694 13.5448i 0.157238 0.464309i
\(852\) 0.115555i 0.00395886i
\(853\) 1.13310 0.0387967 0.0193983 0.999812i \(-0.493825\pi\)
0.0193983 + 0.999812i \(0.493825\pi\)
\(854\) 1.04760 0.0358480
\(855\) 2.18890 12.5607i 0.0748588 0.429567i
\(856\) 41.6416i 1.42328i
\(857\) 34.5092 1.17881 0.589406 0.807837i \(-0.299362\pi\)
0.589406 + 0.807837i \(0.299362\pi\)
\(858\) 6.09207i 0.207980i
\(859\) 3.75019i 0.127955i 0.997951 + 0.0639774i \(0.0203785\pi\)
−0.997951 + 0.0639774i \(0.979621\pi\)
\(860\) −1.13632 0.198021i −0.0387480 0.00675245i
\(861\) −0.863719 −0.0294355
\(862\) 27.1928i 0.926189i
\(863\) 9.79362i 0.333379i 0.986009 + 0.166689i \(0.0533077\pi\)
−0.986009 + 0.166689i \(0.946692\pi\)
\(864\) 0.339869i 0.0115626i
\(865\) −4.92655 + 28.2703i −0.167508 + 0.961220i
\(866\) 39.3244i 1.33630i
\(867\) 16.8161i 0.571106i
\(868\) −0.0941154 −0.00319449
\(869\) 14.3773i 0.487717i
\(870\) 23.3962 + 4.07715i 0.793204 + 0.138228i
\(871\) 44.8629i 1.52012i
\(872\) 15.6176i 0.528879i
\(873\) 9.66376 0.327069
\(874\) 18.6707i 0.631547i
\(875\) 1.90365 3.34339i 0.0643552 0.113027i
\(876\) 0.554518 0.0187354
\(877\) 13.4128i 0.452919i −0.974021 0.226459i \(-0.927285\pi\)
0.974021 0.226459i \(-0.0727150\pi\)
\(878\) 0.0556296i 0.00187741i
\(879\) −29.8367 −1.00637
\(880\) 8.54432 + 1.48898i 0.288029 + 0.0501935i
\(881\) 10.4429 0.351832 0.175916 0.984405i \(-0.443711\pi\)
0.175916 + 0.984405i \(0.443711\pi\)
\(882\) 9.58469 0.322733
\(883\) 32.1571 1.08217 0.541086 0.840967i \(-0.318013\pi\)
0.541086 + 0.840967i \(0.318013\pi\)
\(884\) 0.112646 0.00378871
\(885\) −8.69588 1.51539i −0.292309 0.0509394i
\(886\) 45.4378i 1.52651i
\(887\) 44.3996i 1.49079i −0.666621 0.745397i \(-0.732260\pi\)
0.666621 0.745397i \(-0.267740\pi\)
\(888\) −16.5312 5.59828i −0.554749 0.187866i
\(889\) −7.23200 −0.242554
\(890\) −3.92718 + 22.5356i −0.131639 + 0.755395i
\(891\) −1.00065 −0.0335232
\(892\) 0.303580i 0.0101646i
\(893\) 40.0242 1.33936
\(894\) 21.5478i 0.720667i
\(895\) 2.84306 16.3145i 0.0950330 0.545334i
\(896\) 3.70859i 0.123895i
\(897\) 10.2763i 0.343116i
\(898\) 11.0770i 0.369644i
\(899\) 34.7004 1.15732
\(900\) 0.282793 + 0.101649i 0.00942645 + 0.00338831i
\(901\) 3.18104i 0.105976i
\(902\) 3.49815 0.116476
\(903\) −2.95347 −0.0982852
\(904\) 26.2054 0.871577
\(905\) −32.2547 5.62089i −1.07218 0.186845i
\(906\) 12.6986i 0.421883i
\(907\) 3.69899 0.122823 0.0614115 0.998113i \(-0.480440\pi\)
0.0614115 + 0.998113i \(0.480440\pi\)
\(908\) −0.788718 −0.0261745
\(909\) 9.43463 0.312927
\(910\) −0.804245 + 4.61505i −0.0266605 + 0.152987i
\(911\) 42.9518i 1.42306i −0.702658 0.711528i \(-0.748003\pi\)
0.702658 0.711528i \(-0.251997\pi\)
\(912\) −22.1019 −0.731867
\(913\) 0.403009i 0.0133377i
\(914\) −15.9824 −0.528649
\(915\) −4.81489 0.839070i −0.159175 0.0277388i
\(916\) −0.652141 −0.0215473
\(917\) 2.36212 0.0780042
\(918\) 0.597215i 0.0197110i
\(919\) 17.4354i 0.575142i 0.957759 + 0.287571i \(0.0928477\pi\)
−0.957759 + 0.287571i \(0.907152\pi\)
\(920\) 14.8598 + 2.58956i 0.489914 + 0.0853751i
\(921\) −19.6530 −0.647588
\(922\) 1.67115i 0.0550363i
\(923\) 8.40419 0.276627
\(924\) −0.0206955 −0.000680833
\(925\) 18.9245 23.8089i 0.622235 0.782831i
\(926\) 14.3089 0.470219
\(927\) −3.60566 −0.118425
\(928\) 2.59166i 0.0850754i
\(929\) −47.5276 −1.55933 −0.779666 0.626196i \(-0.784611\pi\)
−0.779666 + 0.626196i \(0.784611\pi\)
\(930\) −13.9620 2.43309i −0.457831 0.0797842i
\(931\) 39.2386i 1.28599i
\(932\) 1.03043i 0.0337529i
\(933\) −23.0782 −0.755545
\(934\) 51.7955 1.69480
\(935\) 0.945179 + 0.164712i 0.0309106 + 0.00538666i
\(936\) −12.5421 −0.409950
\(937\) 40.3594i 1.31848i −0.751931 0.659241i \(-0.770878\pi\)
0.751931 0.659241i \(-0.229122\pi\)
\(938\) −4.91918 −0.160617
\(939\) 12.0135i 0.392046i
\(940\) −0.161951 + 0.929332i −0.00528224 + 0.0303115i
\(941\) −47.6850 −1.55449 −0.777244 0.629199i \(-0.783383\pi\)
−0.777244 + 0.629199i \(0.783383\pi\)
\(942\) −18.5226 −0.603499
\(943\) 5.90081 0.192157
\(944\) 15.3013i 0.498016i
\(945\) 0.758047 + 0.132101i 0.0246593 + 0.00429726i
\(946\) 11.9619 0.388913
\(947\) −33.1655 −1.07773 −0.538866 0.842391i \(-0.681147\pi\)
−0.538866 + 0.842391i \(0.681147\pi\)
\(948\) −0.863533 −0.0280462
\(949\) 40.3294i 1.30915i
\(950\) 13.4318 37.3679i 0.435785 1.21238i
\(951\) −9.84245 −0.319163
\(952\) 0.423376i 0.0137217i
\(953\) 35.1011i 1.13704i 0.822671 + 0.568518i \(0.192483\pi\)
−0.822671 + 0.568518i \(0.807517\pi\)
\(954\) 10.3328i 0.334536i
\(955\) 1.54062 8.84065i 0.0498533 0.286077i
\(956\) 0.0921085i 0.00297900i
\(957\) 7.63045 0.246658
\(958\) 13.5625i 0.438183i
\(959\) 3.47992 0.112372
\(960\) 3.15773 18.1202i 0.101915 0.584828i
\(961\) 10.2921 0.332002
\(962\) −11.8784 + 35.0756i −0.382974 + 1.13088i
\(963\) 14.5128i 0.467667i
\(964\) 0.231327i 0.00745054i
\(965\) 52.9991 + 9.23591i 1.70610 + 0.297315i
\(966\) 1.12679 0.0362539
\(967\) −23.1104 −0.743180 −0.371590 0.928397i \(-0.621187\pi\)
−0.371590 + 0.928397i \(0.621187\pi\)
\(968\) −28.6894 −0.922112
\(969\) −2.44493 −0.0785425
\(970\) 29.6500 + 5.16697i 0.952003 + 0.165901i
\(971\) −31.6046 −1.01424 −0.507120 0.861875i \(-0.669290\pi\)
−0.507120 + 0.861875i \(0.669290\pi\)
\(972\) 0.0601015i 0.00192776i
\(973\) 1.22279i 0.0392008i
\(974\) 49.6652 1.59138
\(975\) 7.39282 20.5672i 0.236760 0.658678i
\(976\) 8.47232i 0.271192i
\(977\) −19.9276 −0.637539 −0.318770 0.947832i \(-0.603270\pi\)
−0.318770 + 0.947832i \(0.603270\pi\)
\(978\) 27.5120i 0.879735i
\(979\) 7.34979i 0.234900i
\(980\) −0.911092 0.158772i −0.0291038 0.00507179i
\(981\) 5.44298i 0.173781i
\(982\) −36.8523 −1.17600
\(983\) 21.5507i 0.687361i −0.939087 0.343680i \(-0.888326\pi\)
0.939087 0.343680i \(-0.111674\pi\)
\(984\) 7.20184i 0.229586i
\(985\) −1.85028 + 10.6176i −0.0589549 + 0.338305i
\(986\) 4.55404i 0.145030i
\(987\) 2.41548i 0.0768857i
\(988\) 1.49796i 0.0476566i
\(989\) 20.1777 0.641613
\(990\) −3.07017 0.535025i −0.0975764 0.0170042i
\(991\) 12.5861i 0.399810i 0.979815 + 0.199905i \(0.0640633\pi\)
−0.979815 + 0.199905i \(0.935937\pi\)
\(992\) 1.54661i 0.0491048i
\(993\) 12.5516 0.398312
\(994\) 0.921513i 0.0292286i
\(995\) −10.4334 + 59.8706i −0.330761 + 1.89803i
\(996\) −0.0242056 −0.000766984
\(997\) 57.5782 1.82352 0.911760 0.410723i \(-0.134724\pi\)
0.911760 + 0.410723i \(0.134724\pi\)
\(998\) 21.1115i 0.668272i
\(999\) 5.76136 + 1.95109i 0.182281 + 0.0617296i
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 555.2.g.a.184.13 40
3.2 odd 2 1665.2.g.e.739.28 40
5.4 even 2 inner 555.2.g.a.184.28 yes 40
15.14 odd 2 1665.2.g.e.739.13 40
37.36 even 2 inner 555.2.g.a.184.27 yes 40
111.110 odd 2 1665.2.g.e.739.14 40
185.184 even 2 inner 555.2.g.a.184.14 yes 40
555.554 odd 2 1665.2.g.e.739.27 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
555.2.g.a.184.13 40 1.1 even 1 trivial
555.2.g.a.184.14 yes 40 185.184 even 2 inner
555.2.g.a.184.27 yes 40 37.36 even 2 inner
555.2.g.a.184.28 yes 40 5.4 even 2 inner
1665.2.g.e.739.13 40 15.14 odd 2
1665.2.g.e.739.14 40 111.110 odd 2
1665.2.g.e.739.27 40 555.554 odd 2
1665.2.g.e.739.28 40 3.2 odd 2