Properties

Label 819.2.fm.e.748.7
Level $819$
Weight $2$
Character 819.748
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(370,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.370");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 748.7
Character \(\chi\) \(=\) 819.748
Dual form 819.2.fm.e.496.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.11902 - 0.567791i) q^{2} +(2.43582 - 1.40632i) q^{4} +(3.00219 - 3.00219i) q^{5} +(-2.60148 - 0.481982i) q^{7} +(1.26060 - 1.26060i) q^{8} +O(q^{10})\) \(q+(2.11902 - 0.567791i) q^{2} +(2.43582 - 1.40632i) q^{4} +(3.00219 - 3.00219i) q^{5} +(-2.60148 - 0.481982i) q^{7} +(1.26060 - 1.26060i) q^{8} +(4.65710 - 8.06633i) q^{10} +(0.698323 + 2.60618i) q^{11} +(0.373866 - 3.58612i) q^{13} +(-5.78626 + 0.455764i) q^{14} +(-0.857159 + 1.48464i) q^{16} +(-0.599399 - 1.03819i) q^{17} +(1.89568 + 0.507945i) q^{19} +(3.09075 - 11.5349i) q^{20} +(2.95953 + 5.12605i) q^{22} +(4.65282 + 2.68631i) q^{23} -13.0263i q^{25} +(-1.24393 - 7.81134i) q^{26} +(-7.01456 + 2.48450i) q^{28} +(-1.47928 + 2.56220i) q^{29} +(-3.36721 + 3.36721i) q^{31} +(-1.89620 + 7.07671i) q^{32} +(-1.85961 - 1.85961i) q^{34} +(-9.25714 + 6.36314i) q^{35} +(-1.03769 - 3.87273i) q^{37} +4.30539 q^{38} -7.56914i q^{40} +(1.42770 + 5.32825i) q^{41} +(-9.78317 + 5.64832i) q^{43} +(5.36612 + 5.36612i) q^{44} +(11.3847 + 3.05052i) q^{46} +(2.97828 + 2.97828i) q^{47} +(6.53539 + 2.50773i) q^{49} +(-7.39621 - 27.6030i) q^{50} +(-4.13256 - 9.26092i) q^{52} +11.0603 q^{53} +(9.92075 + 5.72775i) q^{55} +(-3.88702 + 2.67184i) q^{56} +(-1.67985 + 6.26927i) q^{58} +(3.14721 - 11.7455i) q^{59} +(-4.55683 + 2.63089i) q^{61} +(-5.22332 + 9.04706i) q^{62} +12.6437i q^{64} +(-9.64379 - 11.8886i) q^{65} +(4.15530 - 1.11341i) q^{67} +(-2.92006 - 1.68590i) q^{68} +(-16.0032 + 18.7397i) q^{70} +(-0.800761 + 2.98848i) q^{71} +(4.78407 + 4.78407i) q^{73} +(-4.39780 - 7.61721i) q^{74} +(5.33186 - 1.42867i) q^{76} +(-0.560542 - 7.11650i) q^{77} -1.16895 q^{79} +(1.88383 + 7.03054i) q^{80} +(6.05066 + 10.4801i) q^{82} +(3.24002 - 3.24002i) q^{83} +(-4.91635 - 1.31733i) q^{85} +(-17.5237 + 17.5237i) q^{86} +(4.16566 + 2.40505i) q^{88} +(-4.80209 + 1.28672i) q^{89} +(-2.70105 + 9.14901i) q^{91} +15.1113 q^{92} +(8.00209 + 4.62001i) q^{94} +(7.21613 - 4.16623i) q^{95} +(-14.7483 - 3.95180i) q^{97} +(15.2725 + 1.60321i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.11902 0.567791i 1.49838 0.401489i 0.585820 0.810441i \(-0.300773\pi\)
0.912556 + 0.408953i \(0.134106\pi\)
\(3\) 0 0
\(4\) 2.43582 1.40632i 1.21791 0.703161i
\(5\) 3.00219 3.00219i 1.34262 1.34262i 0.449179 0.893442i \(-0.351717\pi\)
0.893442 0.449179i \(-0.148283\pi\)
\(6\) 0 0
\(7\) −2.60148 0.481982i −0.983267 0.182172i
\(8\) 1.26060 1.26060i 0.445690 0.445690i
\(9\) 0 0
\(10\) 4.65710 8.06633i 1.47270 2.55080i
\(11\) 0.698323 + 2.60618i 0.210552 + 0.785792i 0.987685 + 0.156455i \(0.0500068\pi\)
−0.777133 + 0.629337i \(0.783327\pi\)
\(12\) 0 0
\(13\) 0.373866 3.58612i 0.103692 0.994609i
\(14\) −5.78626 + 0.455764i −1.54644 + 0.121808i
\(15\) 0 0
\(16\) −0.857159 + 1.48464i −0.214290 + 0.371161i
\(17\) −0.599399 1.03819i −0.145376 0.251798i 0.784137 0.620587i \(-0.213106\pi\)
−0.929513 + 0.368789i \(0.879772\pi\)
\(18\) 0 0
\(19\) 1.89568 + 0.507945i 0.434898 + 0.116531i 0.469624 0.882866i \(-0.344389\pi\)
−0.0347266 + 0.999397i \(0.511056\pi\)
\(20\) 3.09075 11.5349i 0.691114 2.57927i
\(21\) 0 0
\(22\) 2.95953 + 5.12605i 0.630973 + 1.09288i
\(23\) 4.65282 + 2.68631i 0.970181 + 0.560134i 0.899291 0.437350i \(-0.144083\pi\)
0.0708893 + 0.997484i \(0.477416\pi\)
\(24\) 0 0
\(25\) 13.0263i 2.60526i
\(26\) −1.24393 7.81134i −0.243955 1.53193i
\(27\) 0 0
\(28\) −7.01456 + 2.48450i −1.32563 + 0.469526i
\(29\) −1.47928 + 2.56220i −0.274696 + 0.475788i −0.970058 0.242872i \(-0.921911\pi\)
0.695362 + 0.718659i \(0.255244\pi\)
\(30\) 0 0
\(31\) −3.36721 + 3.36721i −0.604768 + 0.604768i −0.941574 0.336806i \(-0.890653\pi\)
0.336806 + 0.941574i \(0.390653\pi\)
\(32\) −1.89620 + 7.07671i −0.335204 + 1.25100i
\(33\) 0 0
\(34\) −1.85961 1.85961i −0.318921 0.318921i
\(35\) −9.25714 + 6.36314i −1.56474 + 1.07557i
\(36\) 0 0
\(37\) −1.03769 3.87273i −0.170596 0.636673i −0.997260 0.0739770i \(-0.976431\pi\)
0.826664 0.562696i \(-0.190236\pi\)
\(38\) 4.30539 0.698426
\(39\) 0 0
\(40\) 7.56914i 1.19679i
\(41\) 1.42770 + 5.32825i 0.222969 + 0.832133i 0.983208 + 0.182489i \(0.0584154\pi\)
−0.760239 + 0.649644i \(0.774918\pi\)
\(42\) 0 0
\(43\) −9.78317 + 5.64832i −1.49192 + 0.861360i −0.999957 0.00925580i \(-0.997054\pi\)
−0.491963 + 0.870616i \(0.663720\pi\)
\(44\) 5.36612 + 5.36612i 0.808973 + 0.808973i
\(45\) 0 0
\(46\) 11.3847 + 3.05052i 1.67858 + 0.449775i
\(47\) 2.97828 + 2.97828i 0.434427 + 0.434427i 0.890131 0.455704i \(-0.150613\pi\)
−0.455704 + 0.890131i \(0.650613\pi\)
\(48\) 0 0
\(49\) 6.53539 + 2.50773i 0.933627 + 0.358248i
\(50\) −7.39621 27.6030i −1.04598 3.90366i
\(51\) 0 0
\(52\) −4.13256 9.26092i −0.573084 1.28426i
\(53\) 11.0603 1.51925 0.759627 0.650359i \(-0.225382\pi\)
0.759627 + 0.650359i \(0.225382\pi\)
\(54\) 0 0
\(55\) 9.92075 + 5.72775i 1.33771 + 0.772329i
\(56\) −3.88702 + 2.67184i −0.519424 + 0.357040i
\(57\) 0 0
\(58\) −1.67985 + 6.26927i −0.220575 + 0.823196i
\(59\) 3.14721 11.7455i 0.409731 1.52914i −0.385428 0.922738i \(-0.625946\pi\)
0.795160 0.606400i \(-0.207387\pi\)
\(60\) 0 0
\(61\) −4.55683 + 2.63089i −0.583442 + 0.336851i −0.762500 0.646988i \(-0.776028\pi\)
0.179058 + 0.983839i \(0.442695\pi\)
\(62\) −5.22332 + 9.04706i −0.663362 + 1.14898i
\(63\) 0 0
\(64\) 12.6437i 1.58046i
\(65\) −9.64379 11.8886i −1.19616 1.47460i
\(66\) 0 0
\(67\) 4.15530 1.11341i 0.507651 0.136025i 0.00410235 0.999992i \(-0.498694\pi\)
0.503549 + 0.863967i \(0.332028\pi\)
\(68\) −2.92006 1.68590i −0.354109 0.204445i
\(69\) 0 0
\(70\) −16.0032 + 18.7397i −1.91274 + 2.23983i
\(71\) −0.800761 + 2.98848i −0.0950329 + 0.354668i −0.997024 0.0770861i \(-0.975438\pi\)
0.901992 + 0.431754i \(0.142105\pi\)
\(72\) 0 0
\(73\) 4.78407 + 4.78407i 0.559933 + 0.559933i 0.929288 0.369355i \(-0.120421\pi\)
−0.369355 + 0.929288i \(0.620421\pi\)
\(74\) −4.39780 7.61721i −0.511234 0.885483i
\(75\) 0 0
\(76\) 5.33186 1.42867i 0.611607 0.163879i
\(77\) −0.560542 7.11650i −0.0638797 0.811000i
\(78\) 0 0
\(79\) −1.16895 −0.131517 −0.0657584 0.997836i \(-0.520947\pi\)
−0.0657584 + 0.997836i \(0.520947\pi\)
\(80\) 1.88383 + 7.03054i 0.210618 + 0.786038i
\(81\) 0 0
\(82\) 6.05066 + 10.4801i 0.668184 + 1.15733i
\(83\) 3.24002 3.24002i 0.355639 0.355639i −0.506564 0.862202i \(-0.669085\pi\)
0.862202 + 0.506564i \(0.169085\pi\)
\(84\) 0 0
\(85\) −4.91635 1.31733i −0.533253 0.142885i
\(86\) −17.5237 + 17.5237i −1.88963 + 1.88963i
\(87\) 0 0
\(88\) 4.16566 + 2.40505i 0.444061 + 0.256379i
\(89\) −4.80209 + 1.28672i −0.509020 + 0.136392i −0.504183 0.863597i \(-0.668206\pi\)
−0.00483713 + 0.999988i \(0.501540\pi\)
\(90\) 0 0
\(91\) −2.70105 + 9.14901i −0.283147 + 0.959077i
\(92\) 15.1113 1.57546
\(93\) 0 0
\(94\) 8.00209 + 4.62001i 0.825352 + 0.476517i
\(95\) 7.21613 4.16623i 0.740359 0.427447i
\(96\) 0 0
\(97\) −14.7483 3.95180i −1.49746 0.401244i −0.585214 0.810879i \(-0.698990\pi\)
−0.912250 + 0.409634i \(0.865656\pi\)
\(98\) 15.2725 + 1.60321i 1.54276 + 0.161949i
\(99\) 0 0
\(100\) −18.3192 31.7298i −1.83192 3.17298i
\(101\) 0.803086 1.39099i 0.0799101 0.138408i −0.823301 0.567605i \(-0.807870\pi\)
0.903211 + 0.429197i \(0.141203\pi\)
\(102\) 0 0
\(103\) −14.4997 −1.42870 −0.714351 0.699787i \(-0.753278\pi\)
−0.714351 + 0.699787i \(0.753278\pi\)
\(104\) −4.04937 4.99196i −0.397073 0.489502i
\(105\) 0 0
\(106\) 23.4371 6.27995i 2.27641 0.609963i
\(107\) −1.91021 + 3.30858i −0.184667 + 0.319852i −0.943464 0.331475i \(-0.892454\pi\)
0.758797 + 0.651327i \(0.225787\pi\)
\(108\) 0 0
\(109\) 9.59246 + 9.59246i 0.918791 + 0.918791i 0.996942 0.0781507i \(-0.0249015\pi\)
−0.0781507 + 0.996942i \(0.524902\pi\)
\(110\) 24.2745 + 6.50432i 2.31448 + 0.620163i
\(111\) 0 0
\(112\) 2.94545 3.44913i 0.278319 0.325912i
\(113\) 1.57880 + 2.73457i 0.148521 + 0.257247i 0.930681 0.365831i \(-0.119215\pi\)
−0.782160 + 0.623078i \(0.785882\pi\)
\(114\) 0 0
\(115\) 22.0335 5.90385i 2.05463 0.550537i
\(116\) 8.32140i 0.772623i
\(117\) 0 0
\(118\) 26.6760i 2.45573i
\(119\) 1.05893 + 2.98973i 0.0970724 + 0.274068i
\(120\) 0 0
\(121\) 3.22177 1.86009i 0.292888 0.169099i
\(122\) −8.16224 + 8.16224i −0.738974 + 0.738974i
\(123\) 0 0
\(124\) −3.46654 + 12.9373i −0.311304 + 1.16180i
\(125\) −24.0965 24.0965i −2.15526 2.15526i
\(126\) 0 0
\(127\) 5.77265 + 3.33284i 0.512240 + 0.295742i 0.733754 0.679415i \(-0.237767\pi\)
−0.221514 + 0.975157i \(0.571100\pi\)
\(128\) 3.38658 + 12.6389i 0.299335 + 1.11713i
\(129\) 0 0
\(130\) −27.1857 19.7166i −2.38434 1.72926i
\(131\) 9.80212i 0.856415i 0.903680 + 0.428207i \(0.140855\pi\)
−0.903680 + 0.428207i \(0.859145\pi\)
\(132\) 0 0
\(133\) −4.68674 2.23509i −0.406392 0.193807i
\(134\) 8.17300 4.71868i 0.706039 0.407632i
\(135\) 0 0
\(136\) −2.06435 0.553140i −0.177016 0.0474314i
\(137\) −6.48757 1.73834i −0.554271 0.148516i −0.0291978 0.999574i \(-0.509295\pi\)
−0.525073 + 0.851057i \(0.675962\pi\)
\(138\) 0 0
\(139\) −0.304839 + 0.175999i −0.0258561 + 0.0149280i −0.512872 0.858465i \(-0.671419\pi\)
0.487016 + 0.873393i \(0.338085\pi\)
\(140\) −13.6001 + 28.5180i −1.14942 + 2.41021i
\(141\) 0 0
\(142\) 6.78733i 0.569580i
\(143\) 9.60714 1.52991i 0.803389 0.127937i
\(144\) 0 0
\(145\) 3.25111 + 12.1333i 0.269990 + 1.00762i
\(146\) 12.8539 + 7.42121i 1.06380 + 0.614184i
\(147\) 0 0
\(148\) −7.97395 7.97395i −0.655455 0.655455i
\(149\) −3.05452 + 11.3996i −0.250236 + 0.933892i 0.720443 + 0.693514i \(0.243938\pi\)
−0.970679 + 0.240379i \(0.922728\pi\)
\(150\) 0 0
\(151\) −12.2745 + 12.2745i −0.998884 + 0.998884i −0.999999 0.00111530i \(-0.999645\pi\)
0.00111530 + 0.999999i \(0.499645\pi\)
\(152\) 3.03001 1.74938i 0.245766 0.141893i
\(153\) 0 0
\(154\) −5.22848 14.7618i −0.421323 1.18954i
\(155\) 20.2180i 1.62395i
\(156\) 0 0
\(157\) 4.41109i 0.352043i −0.984386 0.176022i \(-0.943677\pi\)
0.984386 0.176022i \(-0.0563228\pi\)
\(158\) −2.47702 + 0.663716i −0.197061 + 0.0528024i
\(159\) 0 0
\(160\) 15.5529 + 26.9384i 1.22956 + 2.12967i
\(161\) −10.8095 9.23095i −0.851905 0.727501i
\(162\) 0 0
\(163\) −0.610931 0.163698i −0.0478518 0.0128219i 0.234814 0.972040i \(-0.424552\pi\)
−0.282666 + 0.959219i \(0.591219\pi\)
\(164\) 10.9709 + 10.9709i 0.856680 + 0.856680i
\(165\) 0 0
\(166\) 5.02603 8.70534i 0.390096 0.675665i
\(167\) 16.3769 4.38817i 1.26728 0.339567i 0.438292 0.898833i \(-0.355584\pi\)
0.828988 + 0.559266i \(0.188917\pi\)
\(168\) 0 0
\(169\) −12.7204 2.68145i −0.978496 0.206266i
\(170\) −11.1658 −0.856380
\(171\) 0 0
\(172\) −15.8867 + 27.5166i −1.21135 + 2.09812i
\(173\) −4.60670 7.97903i −0.350241 0.606634i 0.636051 0.771647i \(-0.280567\pi\)
−0.986291 + 0.165013i \(0.947234\pi\)
\(174\) 0 0
\(175\) −6.27845 + 33.8877i −0.474606 + 2.56167i
\(176\) −4.46782 1.19715i −0.336774 0.0902384i
\(177\) 0 0
\(178\) −9.44515 + 5.45316i −0.707944 + 0.408732i
\(179\) −2.35631 1.36042i −0.176119 0.101682i 0.409349 0.912378i \(-0.365756\pi\)
−0.585468 + 0.810696i \(0.699089\pi\)
\(180\) 0 0
\(181\) −15.4525 −1.14858 −0.574288 0.818653i \(-0.694721\pi\)
−0.574288 + 0.818653i \(0.694721\pi\)
\(182\) −0.528864 + 20.9206i −0.0392020 + 1.55074i
\(183\) 0 0
\(184\) 9.25172 2.47899i 0.682046 0.182754i
\(185\) −14.7420 8.51132i −1.08386 0.625765i
\(186\) 0 0
\(187\) 2.28713 2.28713i 0.167252 0.167252i
\(188\) 11.4430 + 3.06614i 0.834566 + 0.223621i
\(189\) 0 0
\(190\) 12.9256 12.9256i 0.937721 0.937721i
\(191\) −1.63770 2.83658i −0.118500 0.205248i 0.800673 0.599101i \(-0.204475\pi\)
−0.919173 + 0.393853i \(0.871142\pi\)
\(192\) 0 0
\(193\) −5.44447 20.3190i −0.391901 1.46260i −0.826995 0.562210i \(-0.809951\pi\)
0.435093 0.900385i \(-0.356715\pi\)
\(194\) −33.4958 −2.40486
\(195\) 0 0
\(196\) 19.4457 3.08247i 1.38898 0.220176i
\(197\) −20.1959 + 5.41149i −1.43890 + 0.385553i −0.892149 0.451741i \(-0.850803\pi\)
−0.546753 + 0.837294i \(0.684136\pi\)
\(198\) 0 0
\(199\) −12.4685 21.5960i −0.883867 1.53090i −0.847007 0.531582i \(-0.821598\pi\)
−0.0368601 0.999320i \(-0.511736\pi\)
\(200\) −16.4210 16.4210i −1.16114 1.16114i
\(201\) 0 0
\(202\) 0.911969 3.40352i 0.0641659 0.239471i
\(203\) 5.08326 5.95251i 0.356775 0.417784i
\(204\) 0 0
\(205\) 20.2827 + 11.7102i 1.41660 + 0.817876i
\(206\) −30.7253 + 8.23282i −2.14073 + 0.573608i
\(207\) 0 0
\(208\) 5.00364 + 3.62893i 0.346940 + 0.251621i
\(209\) 5.29518i 0.366275i
\(210\) 0 0
\(211\) 5.46157 9.45972i 0.375990 0.651234i −0.614485 0.788929i \(-0.710636\pi\)
0.990475 + 0.137695i \(0.0439694\pi\)
\(212\) 26.9410 15.5544i 1.85032 1.06828i
\(213\) 0 0
\(214\) −2.16919 + 8.09554i −0.148283 + 0.553400i
\(215\) −12.4136 + 46.3283i −0.846602 + 3.15956i
\(216\) 0 0
\(217\) 10.3827 7.13678i 0.704820 0.484476i
\(218\) 25.7731 + 14.8801i 1.74558 + 1.00781i
\(219\) 0 0
\(220\) 32.2202 2.17229
\(221\) −3.94716 + 1.76137i −0.265515 + 0.118483i
\(222\) 0 0
\(223\) −3.99267 14.9009i −0.267369 0.997835i −0.960784 0.277297i \(-0.910561\pi\)
0.693415 0.720538i \(-0.256105\pi\)
\(224\) 8.34376 17.4960i 0.557491 1.16900i
\(225\) 0 0
\(226\) 4.89819 + 4.89819i 0.325823 + 0.325823i
\(227\) 18.6556 + 4.99875i 1.23822 + 0.331779i 0.817773 0.575541i \(-0.195208\pi\)
0.420442 + 0.907319i \(0.361875\pi\)
\(228\) 0 0
\(229\) 12.6136 + 12.6136i 0.833528 + 0.833528i 0.987998 0.154470i \(-0.0493669\pi\)
−0.154470 + 0.987998i \(0.549367\pi\)
\(230\) 43.3373 25.0208i 2.85758 1.64982i
\(231\) 0 0
\(232\) 1.36512 + 5.09470i 0.0896245 + 0.334483i
\(233\) 24.9418i 1.63399i −0.576643 0.816996i \(-0.695638\pi\)
0.576643 0.816996i \(-0.304362\pi\)
\(234\) 0 0
\(235\) 17.8827 1.16654
\(236\) −8.85197 33.0360i −0.576214 2.15046i
\(237\) 0 0
\(238\) 3.94145 + 5.73405i 0.255486 + 0.371683i
\(239\) 4.67931 + 4.67931i 0.302680 + 0.302680i 0.842061 0.539382i \(-0.181342\pi\)
−0.539382 + 0.842061i \(0.681342\pi\)
\(240\) 0 0
\(241\) −0.169033 + 0.630839i −0.0108884 + 0.0406359i −0.971156 0.238444i \(-0.923363\pi\)
0.960268 + 0.279080i \(0.0900294\pi\)
\(242\) 5.77086 5.77086i 0.370965 0.370965i
\(243\) 0 0
\(244\) −7.39975 + 12.8167i −0.473721 + 0.820508i
\(245\) 27.1492 12.0918i 1.73450 0.772516i
\(246\) 0 0
\(247\) 2.53028 6.60821i 0.160998 0.420470i
\(248\) 8.48941i 0.539078i
\(249\) 0 0
\(250\) −64.7428 37.3793i −4.09470 2.36407i
\(251\) −9.89477 17.1382i −0.624552 1.08176i −0.988627 0.150386i \(-0.951948\pi\)
0.364075 0.931370i \(-0.381385\pi\)
\(252\) 0 0
\(253\) −3.75182 + 14.0020i −0.235875 + 0.880298i
\(254\) 14.1247 + 3.78471i 0.886265 + 0.237474i
\(255\) 0 0
\(256\) 1.70879 + 2.95971i 0.106799 + 0.184982i
\(257\) 7.97194 13.8078i 0.497276 0.861307i −0.502719 0.864450i \(-0.667667\pi\)
0.999995 + 0.00314245i \(0.00100027\pi\)
\(258\) 0 0
\(259\) 0.832955 + 10.5750i 0.0517573 + 0.657097i
\(260\) −40.2098 15.3963i −2.49371 0.954838i
\(261\) 0 0
\(262\) 5.56555 + 20.7709i 0.343841 + 1.28323i
\(263\) 0.217727 0.377114i 0.0134256 0.0232538i −0.859235 0.511582i \(-0.829060\pi\)
0.872660 + 0.488328i \(0.162393\pi\)
\(264\) 0 0
\(265\) 33.2052 33.2052i 2.03978 2.03978i
\(266\) −11.2004 2.07512i −0.686739 0.127234i
\(267\) 0 0
\(268\) 8.55576 8.55576i 0.522626 0.522626i
\(269\) −14.2630 + 8.23477i −0.869633 + 0.502083i −0.867226 0.497914i \(-0.834099\pi\)
−0.00240680 + 0.999997i \(0.500766\pi\)
\(270\) 0 0
\(271\) −22.4966 + 6.02794i −1.36657 + 0.366171i −0.866224 0.499655i \(-0.833460\pi\)
−0.500345 + 0.865826i \(0.666793\pi\)
\(272\) 2.05512 0.124610
\(273\) 0 0
\(274\) −14.7343 −0.890133
\(275\) 33.9489 9.09658i 2.04719 0.548544i
\(276\) 0 0
\(277\) 7.08167 4.08860i 0.425496 0.245660i −0.271930 0.962317i \(-0.587662\pi\)
0.697426 + 0.716657i \(0.254329\pi\)
\(278\) −0.546031 + 0.546031i −0.0327488 + 0.0327488i
\(279\) 0 0
\(280\) −3.64819 + 19.6909i −0.218021 + 1.17676i
\(281\) −3.14177 + 3.14177i −0.187422 + 0.187422i −0.794581 0.607159i \(-0.792309\pi\)
0.607159 + 0.794581i \(0.292309\pi\)
\(282\) 0 0
\(283\) 6.35147 11.0011i 0.377555 0.653945i −0.613151 0.789966i \(-0.710098\pi\)
0.990706 + 0.136021i \(0.0434314\pi\)
\(284\) 2.25226 + 8.40554i 0.133647 + 0.498777i
\(285\) 0 0
\(286\) 19.4891 8.69675i 1.15241 0.514250i
\(287\) −1.14601 14.5495i −0.0676469 0.858827i
\(288\) 0 0
\(289\) 7.78144 13.4779i 0.457732 0.792815i
\(290\) 13.7783 + 23.8648i 0.809092 + 1.40139i
\(291\) 0 0
\(292\) 18.3811 + 4.92520i 1.07567 + 0.288226i
\(293\) 1.47718 5.51290i 0.0862977 0.322067i −0.909259 0.416231i \(-0.863351\pi\)
0.995557 + 0.0941633i \(0.0300176\pi\)
\(294\) 0 0
\(295\) −25.8138 44.7109i −1.50294 2.60317i
\(296\) −6.19009 3.57385i −0.359792 0.207726i
\(297\) 0 0
\(298\) 25.8904i 1.49979i
\(299\) 11.3729 15.6812i 0.657714 0.906870i
\(300\) 0 0
\(301\) 28.1731 9.97867i 1.62387 0.575161i
\(302\) −19.0406 + 32.9793i −1.09566 + 1.89774i
\(303\) 0 0
\(304\) −2.37901 + 2.37901i −0.136446 + 0.136446i
\(305\) −5.78205 + 21.5789i −0.331079 + 1.23560i
\(306\) 0 0
\(307\) 10.2283 + 10.2283i 0.583760 + 0.583760i 0.935934 0.352174i \(-0.114558\pi\)
−0.352174 + 0.935934i \(0.614558\pi\)
\(308\) −11.3735 16.5462i −0.648064 0.942808i
\(309\) 0 0
\(310\) 11.4796 + 42.8424i 0.651997 + 2.43328i
\(311\) −14.6147 −0.828724 −0.414362 0.910112i \(-0.635995\pi\)
−0.414362 + 0.910112i \(0.635995\pi\)
\(312\) 0 0
\(313\) 17.9984i 1.01733i 0.860965 + 0.508665i \(0.169861\pi\)
−0.860965 + 0.508665i \(0.830139\pi\)
\(314\) −2.50457 9.34720i −0.141341 0.527493i
\(315\) 0 0
\(316\) −2.84734 + 1.64392i −0.160176 + 0.0924775i
\(317\) 12.0835 + 12.0835i 0.678674 + 0.678674i 0.959700 0.281026i \(-0.0906747\pi\)
−0.281026 + 0.959700i \(0.590675\pi\)
\(318\) 0 0
\(319\) −7.71056 2.06604i −0.431708 0.115676i
\(320\) 37.9588 + 37.9588i 2.12196 + 2.12196i
\(321\) 0 0
\(322\) −28.1468 13.4231i −1.56856 0.748040i
\(323\) −0.608923 2.27253i −0.0338814 0.126447i
\(324\) 0 0
\(325\) −46.7138 4.87009i −2.59122 0.270144i
\(326\) −1.38752 −0.0768478
\(327\) 0 0
\(328\) 8.51656 + 4.91704i 0.470248 + 0.271498i
\(329\) −6.31246 9.18341i −0.348017 0.506298i
\(330\) 0 0
\(331\) 2.57122 9.59594i 0.141327 0.527441i −0.858564 0.512706i \(-0.828643\pi\)
0.999891 0.0147345i \(-0.00469030\pi\)
\(332\) 3.33560 12.4486i 0.183065 0.683208i
\(333\) 0 0
\(334\) 32.2114 18.5973i 1.76253 1.01760i
\(335\) 9.13234 15.8177i 0.498953 0.864212i
\(336\) 0 0
\(337\) 6.44780i 0.351234i 0.984459 + 0.175617i \(0.0561920\pi\)
−0.984459 + 0.175617i \(0.943808\pi\)
\(338\) −28.4774 + 1.54049i −1.54897 + 0.0837915i
\(339\) 0 0
\(340\) −13.8280 + 3.70519i −0.749926 + 0.200942i
\(341\) −11.1269 6.42414i −0.602558 0.347887i
\(342\) 0 0
\(343\) −15.7930 9.67375i −0.852741 0.522334i
\(344\) −5.21241 + 19.4530i −0.281034 + 1.04883i
\(345\) 0 0
\(346\) −14.2921 14.2921i −0.768349 0.768349i
\(347\) −6.00501 10.4010i −0.322366 0.558354i 0.658610 0.752484i \(-0.271145\pi\)
−0.980976 + 0.194131i \(0.937811\pi\)
\(348\) 0 0
\(349\) 24.5954 6.59031i 1.31656 0.352771i 0.468872 0.883266i \(-0.344661\pi\)
0.847688 + 0.530495i \(0.177994\pi\)
\(350\) 5.93692 + 75.3736i 0.317342 + 4.02889i
\(351\) 0 0
\(352\) −19.7673 −1.05360
\(353\) −2.43053 9.07084i −0.129364 0.482792i 0.870594 0.492003i \(-0.163735\pi\)
−0.999958 + 0.00921021i \(0.997068\pi\)
\(354\) 0 0
\(355\) 6.56796 + 11.3760i 0.348591 + 0.603777i
\(356\) −9.88750 + 9.88750i −0.524036 + 0.524036i
\(357\) 0 0
\(358\) −5.76551 1.54486i −0.304716 0.0816485i
\(359\) 16.2790 16.2790i 0.859171 0.859171i −0.132070 0.991240i \(-0.542162\pi\)
0.991240 + 0.132070i \(0.0421622\pi\)
\(360\) 0 0
\(361\) −13.1189 7.57420i −0.690469 0.398642i
\(362\) −32.7442 + 8.77379i −1.72100 + 0.461140i
\(363\) 0 0
\(364\) 6.28718 + 26.0839i 0.329538 + 1.36717i
\(365\) 28.7254 1.50356
\(366\) 0 0
\(367\) 19.6200 + 11.3276i 1.02416 + 0.591297i 0.915305 0.402761i \(-0.131949\pi\)
0.108851 + 0.994058i \(0.465283\pi\)
\(368\) −7.97642 + 4.60519i −0.415799 + 0.240062i
\(369\) 0 0
\(370\) −36.0714 9.66529i −1.87526 0.502475i
\(371\) −28.7732 5.33088i −1.49383 0.276766i
\(372\) 0 0
\(373\) 11.0535 + 19.1453i 0.572330 + 0.991305i 0.996326 + 0.0856409i \(0.0272938\pi\)
−0.423996 + 0.905664i \(0.639373\pi\)
\(374\) 3.54787 6.14510i 0.183456 0.317755i
\(375\) 0 0
\(376\) 7.50885 0.387240
\(377\) 8.63527 + 6.26280i 0.444739 + 0.322551i
\(378\) 0 0
\(379\) −1.03041 + 0.276097i −0.0529284 + 0.0141821i −0.285186 0.958472i \(-0.592055\pi\)
0.232258 + 0.972654i \(0.425389\pi\)
\(380\) 11.7181 20.2964i 0.601128 1.04118i
\(381\) 0 0
\(382\) −5.08092 5.08092i −0.259962 0.259962i
\(383\) −12.0580 3.23092i −0.616133 0.165092i −0.0627635 0.998028i \(-0.519991\pi\)
−0.553369 + 0.832936i \(0.686658\pi\)
\(384\) 0 0
\(385\) −23.0479 19.6822i −1.17463 1.00310i
\(386\) −23.0739 39.9652i −1.17443 2.03417i
\(387\) 0 0
\(388\) −41.4818 + 11.1150i −2.10592 + 0.564279i
\(389\) 19.0137i 0.964031i −0.876163 0.482015i \(-0.839905\pi\)
0.876163 0.482015i \(-0.160095\pi\)
\(390\) 0 0
\(391\) 6.44068i 0.325719i
\(392\) 11.3998 5.07727i 0.575775 0.256441i
\(393\) 0 0
\(394\) −39.7231 + 22.9341i −2.00122 + 1.15541i
\(395\) −3.50940 + 3.50940i −0.176577 + 0.176577i
\(396\) 0 0
\(397\) −0.702815 + 2.62294i −0.0352733 + 0.131642i −0.981317 0.192397i \(-0.938374\pi\)
0.946044 + 0.324038i \(0.105041\pi\)
\(398\) −38.6830 38.6830i −1.93900 1.93900i
\(399\) 0 0
\(400\) 19.3394 + 11.1656i 0.966970 + 0.558281i
\(401\) −0.821135 3.06452i −0.0410055 0.153035i 0.942388 0.334523i \(-0.108575\pi\)
−0.983393 + 0.181488i \(0.941909\pi\)
\(402\) 0 0
\(403\) 10.8163 + 13.3341i 0.538799 + 0.664218i
\(404\) 4.51759i 0.224759i
\(405\) 0 0
\(406\) 7.39177 15.4997i 0.366847 0.769239i
\(407\) 9.36838 5.40884i 0.464373 0.268106i
\(408\) 0 0
\(409\) −2.97815 0.797992i −0.147260 0.0394582i 0.184436 0.982845i \(-0.440954\pi\)
−0.331696 + 0.943386i \(0.607621\pi\)
\(410\) 49.6284 + 13.2979i 2.45097 + 0.656735i
\(411\) 0 0
\(412\) −35.3188 + 20.3913i −1.74003 + 1.00461i
\(413\) −13.8485 + 29.0389i −0.681442 + 1.42891i
\(414\) 0 0
\(415\) 19.4543i 0.954976i
\(416\) 24.6690 + 9.44572i 1.20950 + 0.463115i
\(417\) 0 0
\(418\) 3.00655 + 11.2206i 0.147055 + 0.548818i
\(419\) 29.0623 + 16.7791i 1.41979 + 0.819715i 0.996280 0.0861779i \(-0.0274653\pi\)
0.423508 + 0.905893i \(0.360799\pi\)
\(420\) 0 0
\(421\) 18.2634 + 18.2634i 0.890104 + 0.890104i 0.994532 0.104429i \(-0.0333014\pi\)
−0.104429 + 0.994532i \(0.533301\pi\)
\(422\) 6.20205 23.1464i 0.301911 1.12675i
\(423\) 0 0
\(424\) 13.9427 13.9427i 0.677116 0.677116i
\(425\) −13.5238 + 7.80795i −0.655999 + 0.378741i
\(426\) 0 0
\(427\) 13.1225 4.64789i 0.635044 0.224927i
\(428\) 10.7455i 0.519402i
\(429\) 0 0
\(430\) 105.219i 5.07411i
\(431\) 16.9380 4.53851i 0.815873 0.218612i 0.173331 0.984864i \(-0.444547\pi\)
0.642541 + 0.766251i \(0.277880\pi\)
\(432\) 0 0
\(433\) −17.6656 30.5978i −0.848957 1.47044i −0.882140 0.470987i \(-0.843898\pi\)
0.0331835 0.999449i \(-0.489435\pi\)
\(434\) 17.9489 21.0182i 0.861574 1.00890i
\(435\) 0 0
\(436\) 36.8556 + 9.87543i 1.76506 + 0.472947i
\(437\) 7.45575 + 7.45575i 0.356657 + 0.356657i
\(438\) 0 0
\(439\) −9.35887 + 16.2100i −0.446674 + 0.773663i −0.998167 0.0605168i \(-0.980725\pi\)
0.551493 + 0.834180i \(0.314058\pi\)
\(440\) 19.7265 5.28570i 0.940425 0.251986i
\(441\) 0 0
\(442\) −7.36404 + 5.97354i −0.350272 + 0.284133i
\(443\) −30.4948 −1.44885 −0.724426 0.689353i \(-0.757895\pi\)
−0.724426 + 0.689353i \(0.757895\pi\)
\(444\) 0 0
\(445\) −10.5538 + 18.2798i −0.500299 + 0.866544i
\(446\) −16.9211 29.3083i −0.801239 1.38779i
\(447\) 0 0
\(448\) 6.09404 32.8924i 0.287917 1.55402i
\(449\) 19.0888 + 5.11484i 0.900859 + 0.241384i 0.679385 0.733782i \(-0.262247\pi\)
0.221474 + 0.975166i \(0.428913\pi\)
\(450\) 0 0
\(451\) −12.8894 + 7.44168i −0.606937 + 0.350415i
\(452\) 7.69138 + 4.44062i 0.361772 + 0.208869i
\(453\) 0 0
\(454\) 42.3699 1.98852
\(455\) 19.3580 + 35.5761i 0.907517 + 1.66784i
\(456\) 0 0
\(457\) 7.87442 2.10994i 0.368350 0.0986990i −0.0698958 0.997554i \(-0.522267\pi\)
0.438246 + 0.898855i \(0.355600\pi\)
\(458\) 33.8903 + 19.5666i 1.58359 + 0.914286i
\(459\) 0 0
\(460\) 45.3669 45.3669i 2.11524 2.11524i
\(461\) −32.2015 8.62836i −1.49977 0.401863i −0.586748 0.809769i \(-0.699592\pi\)
−0.913024 + 0.407907i \(0.866259\pi\)
\(462\) 0 0
\(463\) 1.66118 1.66118i 0.0772018 0.0772018i −0.667452 0.744653i \(-0.732615\pi\)
0.744653 + 0.667452i \(0.232615\pi\)
\(464\) −2.53596 4.39242i −0.117729 0.203913i
\(465\) 0 0
\(466\) −14.1617 52.8523i −0.656029 2.44833i
\(467\) 12.2930 0.568854 0.284427 0.958698i \(-0.408197\pi\)
0.284427 + 0.958698i \(0.408197\pi\)
\(468\) 0 0
\(469\) −11.3466 + 0.893731i −0.523936 + 0.0412687i
\(470\) 37.8939 10.1537i 1.74792 0.468353i
\(471\) 0 0
\(472\) −10.8391 18.7738i −0.498908 0.864135i
\(473\) −21.5523 21.5523i −0.990978 0.990978i
\(474\) 0 0
\(475\) 6.61664 24.6937i 0.303592 1.13302i
\(476\) 6.78390 + 5.79324i 0.310939 + 0.265533i
\(477\) 0 0
\(478\) 12.5724 + 7.25871i 0.575050 + 0.332005i
\(479\) −22.8035 + 6.11018i −1.04192 + 0.279181i −0.738908 0.673806i \(-0.764658\pi\)
−0.303010 + 0.952987i \(0.597992\pi\)
\(480\) 0 0
\(481\) −14.2760 + 2.27341i −0.650930 + 0.103659i
\(482\) 1.43274i 0.0652594i
\(483\) 0 0
\(484\) 5.23177 9.06169i 0.237808 0.411895i
\(485\) −56.1413 + 32.4132i −2.54925 + 1.47181i
\(486\) 0 0
\(487\) −2.73616 + 10.2115i −0.123987 + 0.462726i −0.999802 0.0199217i \(-0.993658\pi\)
0.875814 + 0.482648i \(0.160325\pi\)
\(488\) −2.42785 + 9.06085i −0.109903 + 0.410165i
\(489\) 0 0
\(490\) 50.6641 41.0378i 2.28877 1.85390i
\(491\) −9.46863 5.46672i −0.427313 0.246710i 0.270888 0.962611i \(-0.412683\pi\)
−0.698201 + 0.715901i \(0.746016\pi\)
\(492\) 0 0
\(493\) 3.54672 0.159736
\(494\) 1.60964 15.4396i 0.0724210 0.694661i
\(495\) 0 0
\(496\) −2.11287 7.88533i −0.0948705 0.354062i
\(497\) 3.52356 7.38852i 0.158053 0.331420i
\(498\) 0 0
\(499\) −21.1483 21.1483i −0.946727 0.946727i 0.0519238 0.998651i \(-0.483465\pi\)
−0.998651 + 0.0519238i \(0.983465\pi\)
\(500\) −92.5823 24.8073i −4.14041 1.10942i
\(501\) 0 0
\(502\) −30.6982 30.6982i −1.37013 1.37013i
\(503\) 6.00891 3.46924i 0.267924 0.154686i −0.360020 0.932945i \(-0.617230\pi\)
0.627944 + 0.778259i \(0.283897\pi\)
\(504\) 0 0
\(505\) −1.76499 6.58703i −0.0785409 0.293119i
\(506\) 31.8008i 1.41372i
\(507\) 0 0
\(508\) 18.7482 0.831817
\(509\) 2.48325 + 9.26762i 0.110068 + 0.410780i 0.998871 0.0475103i \(-0.0151287\pi\)
−0.888803 + 0.458290i \(0.848462\pi\)
\(510\) 0 0
\(511\) −10.1398 14.7515i −0.448560 0.652568i
\(512\) −13.2032 13.2032i −0.583504 0.583504i
\(513\) 0 0
\(514\) 9.05279 33.7855i 0.399301 1.49021i
\(515\) −43.5310 + 43.5310i −1.91821 + 1.91821i
\(516\) 0 0
\(517\) −5.68213 + 9.84174i −0.249900 + 0.432839i
\(518\) 7.76942 + 21.9357i 0.341369 + 0.963798i
\(519\) 0 0
\(520\) −27.1438 2.82984i −1.19033 0.124097i
\(521\) 17.8193i 0.780676i −0.920672 0.390338i \(-0.872358\pi\)
0.920672 0.390338i \(-0.127642\pi\)
\(522\) 0 0
\(523\) 6.40070 + 3.69545i 0.279883 + 0.161591i 0.633370 0.773849i \(-0.281671\pi\)
−0.353487 + 0.935439i \(0.615004\pi\)
\(524\) 13.7849 + 23.8762i 0.602198 + 1.04304i
\(525\) 0 0
\(526\) 0.247246 0.922736i 0.0107805 0.0402332i
\(527\) 5.51410 + 1.47750i 0.240198 + 0.0643608i
\(528\) 0 0
\(529\) 2.93251 + 5.07925i 0.127500 + 0.220837i
\(530\) 51.5090 89.2163i 2.23741 3.87531i
\(531\) 0 0
\(532\) −14.5593 + 1.14679i −0.631227 + 0.0497196i
\(533\) 19.6415 3.12785i 0.850767 0.135482i
\(534\) 0 0
\(535\) 4.19817 + 15.6678i 0.181503 + 0.677377i
\(536\) 3.83461 6.64175i 0.165630 0.286880i
\(537\) 0 0
\(538\) −25.5481 + 25.5481i −1.10146 + 1.10146i
\(539\) −1.97179 + 18.7836i −0.0849308 + 0.809067i
\(540\) 0 0
\(541\) −17.3442 + 17.3442i −0.745687 + 0.745687i −0.973666 0.227979i \(-0.926788\pi\)
0.227979 + 0.973666i \(0.426788\pi\)
\(542\) −44.2481 + 25.5467i −1.90062 + 1.09732i
\(543\) 0 0
\(544\) 8.48354 2.27316i 0.363729 0.0974608i
\(545\) 57.5968 2.46718
\(546\) 0 0
\(547\) 26.8037 1.14604 0.573022 0.819540i \(-0.305771\pi\)
0.573022 + 0.819540i \(0.305771\pi\)
\(548\) −18.2472 + 4.88933i −0.779483 + 0.208862i
\(549\) 0 0
\(550\) 66.7735 38.5517i 2.84723 1.64385i
\(551\) −4.10570 + 4.10570i −0.174909 + 0.174909i
\(552\) 0 0
\(553\) 3.04099 + 0.563411i 0.129316 + 0.0239587i
\(554\) 12.6847 12.6847i 0.538923 0.538923i
\(555\) 0 0
\(556\) −0.495023 + 0.857405i −0.0209936 + 0.0363621i
\(557\) 3.42508 + 12.7826i 0.145125 + 0.541615i 0.999750 + 0.0223686i \(0.00712072\pi\)
−0.854624 + 0.519247i \(0.826213\pi\)
\(558\) 0 0
\(559\) 16.5979 + 37.1953i 0.702017 + 1.57319i
\(560\) −1.51214 19.1978i −0.0638997 0.811254i
\(561\) 0 0
\(562\) −4.87361 + 8.44134i −0.205581 + 0.356077i
\(563\) 8.52959 + 14.7737i 0.359479 + 0.622636i 0.987874 0.155258i \(-0.0496210\pi\)
−0.628395 + 0.777895i \(0.716288\pi\)
\(564\) 0 0
\(565\) 12.9496 + 3.46983i 0.544793 + 0.145977i
\(566\) 7.21260 26.9178i 0.303168 1.13144i
\(567\) 0 0
\(568\) 2.75784 + 4.77673i 0.115717 + 0.200427i
\(569\) 26.6276 + 15.3735i 1.11629 + 0.644489i 0.940450 0.339931i \(-0.110404\pi\)
0.175837 + 0.984419i \(0.443737\pi\)
\(570\) 0 0
\(571\) 4.14822i 0.173598i −0.996226 0.0867988i \(-0.972336\pi\)
0.996226 0.0867988i \(-0.0276637\pi\)
\(572\) 21.2497 17.2373i 0.888496 0.720728i
\(573\) 0 0
\(574\) −10.6895 30.1799i −0.446170 1.25969i
\(575\) 34.9927 60.6091i 1.45930 2.52757i
\(576\) 0 0
\(577\) 8.22860 8.22860i 0.342561 0.342561i −0.514768 0.857329i \(-0.672122\pi\)
0.857329 + 0.514768i \(0.172122\pi\)
\(578\) 8.83646 32.9781i 0.367548 1.37171i
\(579\) 0 0
\(580\) 24.9824 + 24.9824i 1.03734 + 1.03734i
\(581\) −9.99049 + 6.86722i −0.414475 + 0.284900i
\(582\) 0 0
\(583\) 7.72369 + 28.8252i 0.319883 + 1.19382i
\(584\) 12.0616 0.499113
\(585\) 0 0
\(586\) 12.5207i 0.517225i
\(587\) −2.86420 10.6893i −0.118218 0.441196i 0.881289 0.472577i \(-0.156676\pi\)
−0.999508 + 0.0313808i \(0.990010\pi\)
\(588\) 0 0
\(589\) −8.09348 + 4.67278i −0.333486 + 0.192538i
\(590\) −80.0865 80.0865i −3.29711 3.29711i
\(591\) 0 0
\(592\) 6.63909 + 1.77894i 0.272865 + 0.0731139i
\(593\) 9.97769 + 9.97769i 0.409734 + 0.409734i 0.881646 0.471911i \(-0.156436\pi\)
−0.471911 + 0.881646i \(0.656436\pi\)
\(594\) 0 0
\(595\) 12.1549 + 5.79661i 0.498301 + 0.237638i
\(596\) 8.59127 + 32.0631i 0.351912 + 1.31335i
\(597\) 0 0
\(598\) 15.1959 39.6864i 0.621406 1.62290i
\(599\) −34.7079 −1.41813 −0.709063 0.705145i \(-0.750882\pi\)
−0.709063 + 0.705145i \(0.750882\pi\)
\(600\) 0 0
\(601\) −11.2636 6.50302i −0.459450 0.265264i 0.252363 0.967633i \(-0.418792\pi\)
−0.711813 + 0.702369i \(0.752126\pi\)
\(602\) 54.0337 37.1414i 2.20225 1.51377i
\(603\) 0 0
\(604\) −12.6366 + 47.1604i −0.514175 + 1.91893i
\(605\) 4.08802 15.2567i 0.166202 0.620273i
\(606\) 0 0
\(607\) 18.9672 10.9507i 0.769856 0.444477i −0.0629670 0.998016i \(-0.520056\pi\)
0.832823 + 0.553539i \(0.186723\pi\)
\(608\) −7.18915 + 12.4520i −0.291559 + 0.504994i
\(609\) 0 0
\(610\) 49.0092i 1.98432i
\(611\) 11.7939 9.56698i 0.477132 0.387039i
\(612\) 0 0
\(613\) −10.3087 + 2.76221i −0.416365 + 0.111565i −0.460919 0.887442i \(-0.652480\pi\)
0.0445537 + 0.999007i \(0.485813\pi\)
\(614\) 27.4815 + 15.8665i 1.10906 + 0.640319i
\(615\) 0 0
\(616\) −9.67769 8.26445i −0.389925 0.332984i
\(617\) −5.78797 + 21.6010i −0.233015 + 0.869624i 0.746019 + 0.665925i \(0.231963\pi\)
−0.979034 + 0.203699i \(0.934704\pi\)
\(618\) 0 0
\(619\) 5.50453 + 5.50453i 0.221246 + 0.221246i 0.809023 0.587777i \(-0.199997\pi\)
−0.587777 + 0.809023i \(0.699997\pi\)
\(620\) 28.4330 + 49.2474i 1.14190 + 1.97782i
\(621\) 0 0
\(622\) −30.9689 + 8.29810i −1.24174 + 0.332723i
\(623\) 13.1127 1.03284i 0.525349 0.0413800i
\(624\) 0 0
\(625\) −79.5531 −3.18213
\(626\) 10.2193 + 38.1390i 0.408446 + 1.52434i
\(627\) 0 0
\(628\) −6.20341 10.7446i −0.247543 0.428757i
\(629\) −3.39863 + 3.39863i −0.135512 + 0.135512i
\(630\) 0 0
\(631\) −20.7278 5.55399i −0.825160 0.221101i −0.178559 0.983929i \(-0.557143\pi\)
−0.646601 + 0.762828i \(0.723810\pi\)
\(632\) −1.47358 + 1.47358i −0.0586157 + 0.0586157i
\(633\) 0 0
\(634\) 32.4660 + 18.7442i 1.28939 + 0.744429i
\(635\) 27.3364 7.32477i 1.08481 0.290675i
\(636\) 0 0
\(637\) 11.4364 22.4991i 0.453126 0.891447i
\(638\) −17.5119 −0.693304
\(639\) 0 0
\(640\) 48.1116 + 27.7772i 1.90178 + 1.09799i
\(641\) 40.6530 23.4710i 1.60570 0.927050i 0.615379 0.788231i \(-0.289003\pi\)
0.990318 0.138818i \(-0.0443304\pi\)
\(642\) 0 0
\(643\) −22.4152 6.00613i −0.883968 0.236859i −0.211850 0.977302i \(-0.567949\pi\)
−0.672118 + 0.740444i \(0.734615\pi\)
\(644\) −39.3116 7.28336i −1.54910 0.287005i
\(645\) 0 0
\(646\) −2.58064 4.46981i −0.101534 0.175862i
\(647\) −6.98028 + 12.0902i −0.274423 + 0.475315i −0.969989 0.243147i \(-0.921820\pi\)
0.695566 + 0.718462i \(0.255154\pi\)
\(648\) 0 0
\(649\) 32.8087 1.28786
\(650\) −101.753 + 16.2038i −3.99108 + 0.635567i
\(651\) 0 0
\(652\) −1.71833 + 0.460426i −0.0672951 + 0.0180317i
\(653\) 13.4921 23.3689i 0.527985 0.914497i −0.471483 0.881875i \(-0.656281\pi\)
0.999468 0.0326216i \(-0.0103856\pi\)
\(654\) 0 0
\(655\) 29.4278 + 29.4278i 1.14984 + 1.14984i
\(656\) −9.13431 2.44753i −0.356635 0.0955601i
\(657\) 0 0
\(658\) −18.5905 15.8757i −0.724733 0.618900i
\(659\) −2.76889 4.79586i −0.107861 0.186820i 0.807043 0.590493i \(-0.201067\pi\)
−0.914903 + 0.403673i \(0.867733\pi\)
\(660\) 0 0
\(661\) −36.8331 + 9.86941i −1.43264 + 0.383875i −0.889951 0.456057i \(-0.849261\pi\)
−0.542692 + 0.839932i \(0.682595\pi\)
\(662\) 21.7939i 0.847046i
\(663\) 0 0
\(664\) 8.16876i 0.317009i
\(665\) −20.7807 + 7.36032i −0.805839 + 0.285421i
\(666\) 0 0
\(667\) −13.7657 + 7.94763i −0.533010 + 0.307733i
\(668\) 33.7200 33.7200i 1.30466 1.30466i
\(669\) 0 0
\(670\) 10.3705 38.7033i 0.400648 1.49524i
\(671\) −10.0387 10.0387i −0.387540 0.387540i
\(672\) 0 0
\(673\) 5.72219 + 3.30371i 0.220574 + 0.127349i 0.606216 0.795300i \(-0.292687\pi\)
−0.385642 + 0.922649i \(0.626020\pi\)
\(674\) 3.66100 + 13.6630i 0.141016 + 0.526281i
\(675\) 0 0
\(676\) −34.7557 + 11.3575i −1.33676 + 0.436827i
\(677\) 21.3320i 0.819855i 0.912118 + 0.409928i \(0.134446\pi\)
−0.912118 + 0.409928i \(0.865554\pi\)
\(678\) 0 0
\(679\) 36.4627 + 17.3889i 1.39931 + 0.667326i
\(680\) −7.85819 + 4.53693i −0.301348 + 0.173983i
\(681\) 0 0
\(682\) −27.2258 7.29513i −1.04253 0.279345i
\(683\) 1.32430 + 0.354846i 0.0506730 + 0.0135778i 0.284067 0.958805i \(-0.408316\pi\)
−0.233393 + 0.972382i \(0.574983\pi\)
\(684\) 0 0
\(685\) −24.6958 + 14.2581i −0.943576 + 0.544774i
\(686\) −38.9584 11.5318i −1.48744 0.440286i
\(687\) 0 0
\(688\) 19.3660i 0.738323i
\(689\) 4.13508 39.6636i 0.157534 1.51106i
\(690\) 0 0
\(691\) −8.87327 33.1155i −0.337555 1.25977i −0.901072 0.433669i \(-0.857219\pi\)
0.563517 0.826104i \(-0.309448\pi\)
\(692\) −22.4422 12.9570i −0.853124 0.492551i
\(693\) 0 0
\(694\) −18.6303 18.6303i −0.707197 0.707197i
\(695\) −0.386803 + 1.44357i −0.0146723 + 0.0547577i
\(696\) 0 0
\(697\) 4.67597 4.67597i 0.177115 0.177115i
\(698\) 48.3762 27.9300i 1.83107 1.05717i
\(699\) 0 0
\(700\) 32.3638 + 91.3738i 1.22324 + 3.45361i
\(701\) 42.5906i 1.60862i 0.594208 + 0.804312i \(0.297466\pi\)
−0.594208 + 0.804312i \(0.702534\pi\)
\(702\) 0 0
\(703\) 7.86853i 0.296767i
\(704\) −32.9518 + 8.82940i −1.24192 + 0.332771i
\(705\) 0 0
\(706\) −10.3007 17.8413i −0.387671 0.671466i
\(707\) −2.75964 + 3.23155i −0.103787 + 0.121535i
\(708\) 0 0
\(709\) 37.3239 + 10.0009i 1.40173 + 0.375592i 0.878965 0.476886i \(-0.158234\pi\)
0.522764 + 0.852478i \(0.324901\pi\)
\(710\) 20.3769 + 20.3769i 0.764730 + 0.764730i
\(711\) 0 0
\(712\) −4.43148 + 7.67556i −0.166077 + 0.287654i
\(713\) −24.7124 + 6.62166i −0.925486 + 0.247983i
\(714\) 0 0
\(715\) 24.2494 33.4355i 0.906876 1.25042i
\(716\) −7.65273 −0.285996
\(717\) 0 0
\(718\) 25.2525 43.7385i 0.942413 1.63231i
\(719\) 25.0297 + 43.3527i 0.933450 + 1.61678i 0.777375 + 0.629038i \(0.216551\pi\)
0.156076 + 0.987745i \(0.450116\pi\)
\(720\) 0 0
\(721\) 37.7208 + 6.98862i 1.40480 + 0.260270i
\(722\) −32.0998 8.60112i −1.19463 0.320101i
\(723\) 0 0
\(724\) −37.6396 + 21.7312i −1.39886 + 0.807634i
\(725\) 33.3759 + 19.2696i 1.23955 + 0.715655i
\(726\) 0 0
\(727\) −5.22923 −0.193941 −0.0969707 0.995287i \(-0.530915\pi\)
−0.0969707 + 0.995287i \(0.530915\pi\)
\(728\) 8.12831 + 14.9382i 0.301255 + 0.553647i
\(729\) 0 0
\(730\) 60.8698 16.3100i 2.25289 0.603661i
\(731\) 11.7280 + 6.77119i 0.433777 + 0.250442i
\(732\) 0 0
\(733\) 10.0406 10.0406i 0.370858 0.370858i −0.496932 0.867790i \(-0.665540\pi\)
0.867790 + 0.496932i \(0.165540\pi\)
\(734\) 48.0070 + 12.8634i 1.77197 + 0.474798i
\(735\) 0 0
\(736\) −27.8329 + 27.8329i −1.02593 + 1.02593i
\(737\) 5.80349 + 10.0519i 0.213774 + 0.370268i
\(738\) 0 0
\(739\) −1.48318 5.53532i −0.0545598 0.203620i 0.933265 0.359187i \(-0.116946\pi\)
−0.987825 + 0.155567i \(0.950279\pi\)
\(740\) −47.8786 −1.76005
\(741\) 0 0
\(742\) −63.9979 + 5.04090i −2.34944 + 0.185057i
\(743\) −0.617584 + 0.165481i −0.0226569 + 0.00607091i −0.270130 0.962824i \(-0.587067\pi\)
0.247473 + 0.968895i \(0.420400\pi\)
\(744\) 0 0
\(745\) 25.0536 + 43.3941i 0.917892 + 1.58984i
\(746\) 34.2932 + 34.2932i 1.25556 + 1.25556i
\(747\) 0 0
\(748\) 2.35460 8.78749i 0.0860928 0.321303i
\(749\) 6.56404 7.68650i 0.239845 0.280859i
\(750\) 0 0
\(751\) −22.0888 12.7530i −0.806031 0.465362i 0.0395448 0.999218i \(-0.487409\pi\)
−0.845576 + 0.533856i \(0.820743\pi\)
\(752\) −6.97454 + 1.86882i −0.254335 + 0.0681490i
\(753\) 0 0
\(754\) 21.8543 + 8.36799i 0.795887 + 0.304744i
\(755\) 73.7008i 2.68225i
\(756\) 0 0
\(757\) 8.06785 13.9739i 0.293231 0.507891i −0.681341 0.731966i \(-0.738603\pi\)
0.974572 + 0.224075i \(0.0719362\pi\)
\(758\) −2.02669 + 1.17011i −0.0736127 + 0.0425003i
\(759\) 0 0
\(760\) 3.84470 14.3486i 0.139462 0.520479i
\(761\) −6.42639 + 23.9836i −0.232957 + 0.869406i 0.746103 + 0.665831i \(0.231923\pi\)
−0.979059 + 0.203575i \(0.934744\pi\)
\(762\) 0 0
\(763\) −20.3312 29.5780i −0.736038 1.07079i
\(764\) −7.97831 4.60628i −0.288645 0.166649i
\(765\) 0 0
\(766\) −27.3856 −0.989481
\(767\) −40.9442 15.6775i −1.47841 0.566082i
\(768\) 0 0
\(769\) 3.09729 + 11.5592i 0.111691 + 0.416837i 0.999018 0.0443040i \(-0.0141070\pi\)
−0.887327 + 0.461141i \(0.847440\pi\)
\(770\) −60.0145 28.6207i −2.16277 1.03142i
\(771\) 0 0
\(772\) −41.8368 41.8368i −1.50574 1.50574i
\(773\) 1.00730 + 0.269904i 0.0362299 + 0.00970777i 0.276888 0.960902i \(-0.410697\pi\)
−0.240659 + 0.970610i \(0.577363\pi\)
\(774\) 0 0
\(775\) 43.8623 + 43.8623i 1.57558 + 1.57558i
\(776\) −23.5734 + 13.6101i −0.846235 + 0.488574i
\(777\) 0 0
\(778\) −10.7958 40.2904i −0.387047 1.44448i
\(779\) 10.8258i 0.387875i
\(780\) 0 0
\(781\) −8.34771 −0.298704
\(782\) −3.65696 13.6480i −0.130773 0.488050i
\(783\) 0 0
\(784\) −9.32495 + 7.55319i −0.333034 + 0.269757i
\(785\) −13.2429 13.2429i −0.472660 0.472660i
\(786\) 0 0
\(787\) −12.4106 + 46.3169i −0.442389 + 1.65102i 0.280349 + 0.959898i \(0.409550\pi\)
−0.722738 + 0.691122i \(0.757117\pi\)
\(788\) −41.5834 + 41.5834i −1.48135 + 1.48135i
\(789\) 0 0
\(790\) −5.44390 + 9.42910i −0.193685 + 0.335472i
\(791\) −2.78921 7.87488i −0.0991730 0.279999i
\(792\) 0 0
\(793\) 7.73102 + 17.3249i 0.274537 + 0.615226i
\(794\) 5.95712i 0.211410i
\(795\) 0 0
\(796\) −60.7420 35.0694i −2.15294 1.24300i
\(797\) −22.8940 39.6535i −0.810946 1.40460i −0.912203 0.409739i \(-0.865620\pi\)
0.101257 0.994860i \(-0.467713\pi\)
\(798\) 0 0
\(799\) 1.30684 4.87720i 0.0462327 0.172543i
\(800\) 92.1834 + 24.7005i 3.25917 + 0.873293i
\(801\) 0 0
\(802\) −3.48001 6.02755i −0.122883 0.212840i
\(803\) −9.12732 + 15.8090i −0.322096 + 0.557887i
\(804\) 0 0
\(805\) −60.1652 + 4.73901i −2.12054 + 0.167028i
\(806\) 30.4910 + 22.1138i 1.07400 + 0.778926i
\(807\) 0 0
\(808\) −0.741108 2.76585i −0.0260721 0.0973023i
\(809\) 14.8591 25.7367i 0.522418 0.904855i −0.477241 0.878772i \(-0.658363\pi\)
0.999660 0.0260831i \(-0.00830344\pi\)
\(810\) 0 0
\(811\) −34.3752 + 34.3752i −1.20708 + 1.20708i −0.235107 + 0.971970i \(0.575544\pi\)
−0.971970 + 0.235107i \(0.924456\pi\)
\(812\) 4.01077 21.6480i 0.140750 0.759694i
\(813\) 0 0
\(814\) 16.7807 16.7807i 0.588164 0.588164i
\(815\) −2.32559 + 1.34268i −0.0814617 + 0.0470319i
\(816\) 0 0
\(817\) −21.4148 + 5.73807i −0.749207 + 0.200750i
\(818\) −6.76385 −0.236493
\(819\) 0 0
\(820\) 65.8733 2.30039
\(821\) 30.4555 8.16053i 1.06291 0.284805i 0.315330 0.948982i \(-0.397885\pi\)
0.747575 + 0.664177i \(0.231218\pi\)
\(822\) 0 0
\(823\) −1.78884 + 1.03279i −0.0623550 + 0.0360007i −0.530853 0.847464i \(-0.678129\pi\)
0.468498 + 0.883464i \(0.344795\pi\)
\(824\) −18.2784 + 18.2784i −0.636758 + 0.636758i
\(825\) 0 0
\(826\) −12.8574 + 69.3971i −0.447365 + 2.41463i
\(827\) −15.5395 + 15.5395i −0.540360 + 0.540360i −0.923634 0.383275i \(-0.874796\pi\)
0.383275 + 0.923634i \(0.374796\pi\)
\(828\) 0 0
\(829\) −7.58600 + 13.1393i −0.263473 + 0.456348i −0.967162 0.254159i \(-0.918201\pi\)
0.703690 + 0.710508i \(0.251535\pi\)
\(830\) −11.0460 41.2242i −0.383412 1.43091i
\(831\) 0 0
\(832\) 45.3418 + 4.72706i 1.57194 + 0.163881i
\(833\) −1.31380 8.28810i −0.0455205 0.287166i
\(834\) 0 0
\(835\) 35.9924 62.3406i 1.24557 2.15739i
\(836\) 7.44673 + 12.8981i 0.257550 + 0.446091i
\(837\) 0 0
\(838\) 71.1108 + 19.0541i 2.45648 + 0.658212i
\(839\) −14.3405 + 53.5194i −0.495088 + 1.84769i 0.0344471 + 0.999407i \(0.489033\pi\)
−0.529535 + 0.848288i \(0.677634\pi\)
\(840\) 0 0
\(841\) 10.1234 + 17.5343i 0.349084 + 0.604631i
\(842\) 49.0703 + 28.3308i 1.69108 + 0.976343i
\(843\) 0 0
\(844\) 30.7229i 1.05753i
\(845\) −46.2395 + 30.1390i −1.59069 + 1.03681i
\(846\) 0 0
\(847\) −9.27789 + 3.28615i −0.318792 + 0.112913i
\(848\) −9.48046 + 16.4206i −0.325560 + 0.563887i
\(849\) 0 0
\(850\) −24.2239 + 24.2239i −0.830873 + 0.830873i
\(851\) 5.57514 20.8067i 0.191113 0.713244i
\(852\) 0 0
\(853\) 31.2556 + 31.2556i 1.07017 + 1.07017i 0.997345 + 0.0728280i \(0.0232024\pi\)
0.0728280 + 0.997345i \(0.476798\pi\)
\(854\) 25.1679 17.2998i 0.861229 0.591988i
\(855\) 0 0
\(856\) 1.76279 + 6.57881i 0.0602508 + 0.224859i
\(857\) −4.67560 −0.159715 −0.0798577 0.996806i \(-0.525447\pi\)
−0.0798577 + 0.996806i \(0.525447\pi\)
\(858\) 0 0
\(859\) 4.70689i 0.160597i −0.996771 0.0802986i \(-0.974413\pi\)
0.996771 0.0802986i \(-0.0255874\pi\)
\(860\) 34.9151 + 130.305i 1.19060 + 4.44337i
\(861\) 0 0
\(862\) 33.3150 19.2344i 1.13471 0.655127i
\(863\) 31.1015 + 31.1015i 1.05871 + 1.05871i 0.998166 + 0.0605431i \(0.0192833\pi\)
0.0605431 + 0.998166i \(0.480717\pi\)
\(864\) 0 0
\(865\) −37.7848 10.1244i −1.28472 0.344240i
\(866\) −54.8070 54.8070i −1.86242 1.86242i
\(867\) 0 0
\(868\) 15.2537 31.9853i 0.517743 1.08565i
\(869\) −0.816302 3.04648i −0.0276912 0.103345i
\(870\) 0 0
\(871\) −2.43929 15.3177i −0.0826522 0.519019i
\(872\) 24.1845 0.818992
\(873\) 0 0
\(874\) 20.0322 + 11.5656i 0.677599 + 0.391212i
\(875\) 51.0725 + 74.3007i 1.72657 + 2.51182i
\(876\) 0 0
\(877\) 6.66722 24.8824i 0.225136 0.840220i −0.757214 0.653167i \(-0.773440\pi\)
0.982350 0.187052i \(-0.0598934\pi\)
\(878\) −10.6278 + 39.6633i −0.358669 + 1.33857i
\(879\) 0 0
\(880\) −17.0073 + 9.81918i −0.573316 + 0.331004i
\(881\) −9.58023 + 16.5935i −0.322766 + 0.559048i −0.981058 0.193716i \(-0.937946\pi\)
0.658291 + 0.752763i \(0.271279\pi\)
\(882\) 0 0
\(883\) 8.19989i 0.275948i −0.990436 0.137974i \(-0.955941\pi\)
0.990436 0.137974i \(-0.0440591\pi\)
\(884\) −7.13753 + 9.84137i −0.240061 + 0.331001i
\(885\) 0 0
\(886\) −64.6192 + 17.3147i −2.17092 + 0.581697i
\(887\) −3.31720 1.91519i −0.111381 0.0643057i 0.443275 0.896386i \(-0.353817\pi\)
−0.554655 + 0.832080i \(0.687150\pi\)
\(888\) 0 0
\(889\) −13.4111 11.4526i −0.449792 0.384109i
\(890\) −11.9847 + 44.7276i −0.401729 + 1.49927i
\(891\) 0 0
\(892\) −30.6808 30.6808i −1.02727 1.02727i
\(893\) 4.13305 + 7.15866i 0.138307 + 0.239555i
\(894\) 0 0
\(895\) −11.1583 + 2.98986i −0.372982 + 0.0999401i
\(896\) −2.71840 34.5121i −0.0908154 1.15297i
\(897\) 0 0
\(898\) 43.3539 1.44674
\(899\) −3.64639 13.6085i −0.121614 0.453869i
\(900\) 0 0
\(901\) −6.62955 11.4827i −0.220862 0.382545i
\(902\) −23.0876 + 23.0876i −0.768732 + 0.768732i
\(903\) 0 0
\(904\) 5.43745 + 1.45696i 0.180847 + 0.0484578i
\(905\) −46.3914 + 46.3914i −1.54210 + 1.54210i
\(906\) 0 0
\(907\) 26.5418 + 15.3239i 0.881305 + 0.508821i 0.871088 0.491126i \(-0.163415\pi\)
0.0102163 + 0.999948i \(0.496748\pi\)
\(908\) 52.4716 14.0597i 1.74133 0.466588i
\(909\) 0 0
\(910\) 61.2199 + 64.3954i 2.02942 + 2.13469i
\(911\) 17.6785 0.585714 0.292857 0.956156i \(-0.405394\pi\)
0.292857 + 0.956156i \(0.405394\pi\)
\(912\) 0 0
\(913\) 10.7067 + 6.18149i 0.354339 + 0.204578i
\(914\) 15.4881 8.94204i 0.512300 0.295776i
\(915\) 0 0
\(916\) 48.4631 + 12.9857i 1.60127 + 0.429058i
\(917\) 4.72445 25.5000i 0.156015 0.842084i
\(918\) 0 0
\(919\) 6.76666 + 11.7202i 0.223212 + 0.386614i 0.955781 0.294078i \(-0.0950126\pi\)
−0.732570 + 0.680692i \(0.761679\pi\)
\(920\) 20.3330 35.2178i 0.670360 1.16110i
\(921\) 0 0
\(922\) −73.1348 −2.40856
\(923\) 10.4177 + 3.98892i 0.342902 + 0.131297i
\(924\) 0 0
\(925\) −50.4474 + 13.5173i −1.65870 + 0.444447i
\(926\) 2.57688 4.46329i 0.0846816 0.146673i
\(927\) 0 0
\(928\) −15.3269 15.3269i −0.503130 0.503130i
\(929\) 48.9198 + 13.1080i 1.60501 + 0.430060i 0.946549 0.322559i \(-0.104543\pi\)
0.658456 + 0.752619i \(0.271210\pi\)
\(930\) 0 0
\(931\) 11.1152 + 8.07346i 0.364285 + 0.264597i
\(932\) −35.0762 60.7538i −1.14896 1.99006i
\(933\) 0 0
\(934\) 26.0492 6.97987i 0.852357 0.228388i
\(935\) 13.7328i 0.449111i
\(936\) 0 0
\(937\) 24.1481i 0.788885i −0.918921 0.394443i \(-0.870938\pi\)
0.918921 0.394443i \(-0.129062\pi\)
\(938\) −23.5362 + 8.33631i −0.768484 + 0.272190i
\(939\) 0 0
\(940\) 43.5592 25.1489i 1.42074 0.820267i
\(941\) −11.0345 + 11.0345i −0.359716 + 0.359716i −0.863708 0.503992i \(-0.831864\pi\)
0.503992 + 0.863708i \(0.331864\pi\)
\(942\) 0 0
\(943\) −7.67049 + 28.6266i −0.249785 + 0.932212i
\(944\) 14.7403 + 14.7403i 0.479755 + 0.479755i
\(945\) 0 0
\(946\) −57.9071 33.4327i −1.88272 1.08699i
\(947\) 6.74864 + 25.1863i 0.219301 + 0.818444i 0.984608 + 0.174778i \(0.0559207\pi\)
−0.765307 + 0.643666i \(0.777413\pi\)
\(948\) 0 0
\(949\) 18.9448 15.3676i 0.614976 0.498855i
\(950\) 56.0833i 1.81958i
\(951\) 0 0
\(952\) 5.10375 + 2.43396i 0.165413 + 0.0788851i
\(953\) −2.70119 + 1.55953i −0.0875001 + 0.0505182i −0.543112 0.839661i \(-0.682754\pi\)
0.455612 + 0.890179i \(0.349421\pi\)
\(954\) 0 0
\(955\) −13.4327 3.59927i −0.434671 0.116470i
\(956\) 17.9786 + 4.81735i 0.581470 + 0.155804i
\(957\) 0 0
\(958\) −44.8518 + 25.8952i −1.44910 + 0.836636i
\(959\) 16.0394 + 7.64915i 0.517940 + 0.247004i
\(960\) 0 0
\(961\) 8.32384i 0.268511i
\(962\) −28.9604 + 12.9232i −0.933720 + 0.416661i
\(963\) 0 0
\(964\) 0.475429 + 1.77433i 0.0153126 + 0.0571472i
\(965\) −77.3469 44.6563i −2.48989 1.43754i
\(966\) 0 0
\(967\) 10.4152 + 10.4152i 0.334930 + 0.334930i 0.854455 0.519525i \(-0.173891\pi\)
−0.519525 + 0.854455i \(0.673891\pi\)
\(968\) 1.71654 6.40620i 0.0551715 0.205903i
\(969\) 0 0
\(970\) −100.561 + 100.561i −3.22881 + 3.22881i
\(971\) 17.7603 10.2539i 0.569955 0.329064i −0.187176 0.982326i \(-0.559934\pi\)
0.757131 + 0.653263i \(0.226600\pi\)
\(972\) 0 0
\(973\) 0.877861 0.310931i 0.0281429 0.00996798i
\(974\) 23.1919i 0.743117i
\(975\) 0 0
\(976\) 9.02035i 0.288734i
\(977\) −21.0235 + 5.63323i −0.672601 + 0.180223i −0.578926 0.815380i \(-0.696528\pi\)
−0.0936748 + 0.995603i \(0.529861\pi\)
\(978\) 0 0
\(979\) −6.70682 11.6166i −0.214351 0.371267i
\(980\) 49.1256 67.6339i 1.56926 2.16049i
\(981\) 0 0
\(982\) −23.1682 6.20790i −0.739327 0.198102i
\(983\) 4.97085 + 4.97085i 0.158546 + 0.158546i 0.781922 0.623376i \(-0.214240\pi\)
−0.623376 + 0.781922i \(0.714240\pi\)
\(984\) 0 0
\(985\) −44.3858 + 76.8784i −1.41425 + 2.44955i
\(986\) 7.51559 2.01380i 0.239345 0.0641323i
\(987\) 0 0
\(988\) −3.12997 19.6548i −0.0995775 0.625303i
\(989\) −60.6925 −1.92991
\(990\) 0 0
\(991\) −16.0062 + 27.7236i −0.508454 + 0.880668i 0.491498 + 0.870879i \(0.336449\pi\)
−0.999952 + 0.00978927i \(0.996884\pi\)
\(992\) −17.4438 30.2136i −0.553843 0.959283i
\(993\) 0 0
\(994\) 3.27137 17.6571i 0.103762 0.560049i
\(995\) −102.268 27.4027i −3.24212 0.868723i
\(996\) 0 0
\(997\) 38.9153 22.4677i 1.23246 0.711561i 0.264917 0.964271i \(-0.414655\pi\)
0.967542 + 0.252711i \(0.0813220\pi\)
\(998\) −56.8215 32.8059i −1.79865 1.03845i
\(999\) 0 0
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 819.2.fm.e.748.7 32
3.2 odd 2 273.2.by.d.202.2 yes 32
7.6 odd 2 819.2.fm.f.748.7 32
13.2 odd 12 819.2.fm.f.496.7 32
21.20 even 2 273.2.by.c.202.2 32
39.2 even 12 273.2.by.c.223.2 yes 32
91.41 even 12 inner 819.2.fm.e.496.7 32
273.41 odd 12 273.2.by.d.223.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.by.c.202.2 32 21.20 even 2
273.2.by.c.223.2 yes 32 39.2 even 12
273.2.by.d.202.2 yes 32 3.2 odd 2
273.2.by.d.223.2 yes 32 273.41 odd 12
819.2.fm.e.496.7 32 91.41 even 12 inner
819.2.fm.e.748.7 32 1.1 even 1 trivial
819.2.fm.f.496.7 32 13.2 odd 12
819.2.fm.f.748.7 32 7.6 odd 2