Properties

Label 552.2.b.c.413.10
Level $552$
Weight $2$
Character 552.413
Analytic conductor $4.408$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [552,2,Mod(413,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 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("552.413");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.b (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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 413.10
Character \(\chi\) \(=\) 552.413
Dual form 552.2.b.c.413.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32616 - 0.491215i) q^{2} +(1.50954 + 0.849295i) q^{3} +(1.51742 + 1.30286i) q^{4} +3.96539i q^{5} +(-1.58470 - 1.86781i) q^{6} +0.287329i q^{7} +(-1.37235 - 2.47319i) q^{8} +(1.55740 + 2.56408i) q^{9} +O(q^{10})\) \(q+(-1.32616 - 0.491215i) q^{2} +(1.50954 + 0.849295i) q^{3} +(1.51742 + 1.30286i) q^{4} +3.96539i q^{5} +(-1.58470 - 1.86781i) q^{6} +0.287329i q^{7} +(-1.37235 - 2.47319i) q^{8} +(1.55740 + 2.56408i) q^{9} +(1.94786 - 5.25875i) q^{10} +2.51457i q^{11} +(1.18408 + 3.25545i) q^{12} -4.58211i q^{13} +(0.141140 - 0.381045i) q^{14} +(-3.36779 + 5.98590i) q^{15} +(0.605098 + 3.95397i) q^{16} +3.13989 q^{17} +(-0.805843 - 4.16541i) q^{18} +5.13304 q^{19} +(-5.16636 + 6.01714i) q^{20} +(-0.244027 + 0.433734i) q^{21} +(1.23519 - 3.33473i) q^{22} +(-4.77034 + 0.493825i) q^{23} +(0.0288475 - 4.89889i) q^{24} -10.7243 q^{25} +(-2.25080 + 6.07663i) q^{26} +(0.173281 + 5.19326i) q^{27} +(-0.374351 + 0.435998i) q^{28} -4.88646 q^{29} +(7.40660 - 6.28397i) q^{30} +2.61622 q^{31} +(1.13979 - 5.54084i) q^{32} +(-2.13561 + 3.79583i) q^{33} +(-4.16400 - 1.54236i) q^{34} -1.13937 q^{35} +(-0.977432 + 5.91985i) q^{36} -3.22198 q^{37} +(-6.80725 - 2.52143i) q^{38} +(3.89157 - 6.91686i) q^{39} +(9.80714 - 5.44192i) q^{40} -5.33846i q^{41} +(0.536677 - 0.455332i) q^{42} -9.45753 q^{43} +(-3.27614 + 3.81565i) q^{44} +(-10.1676 + 6.17568i) q^{45} +(6.56882 + 1.68837i) q^{46} +4.95291i q^{47} +(-2.44467 + 6.48256i) q^{48} +6.91744 q^{49} +(14.2222 + 5.26795i) q^{50} +(4.73977 + 2.66669i) q^{51} +(5.96986 - 6.95297i) q^{52} -1.01064i q^{53} +(2.32121 - 6.97223i) q^{54} -9.97125 q^{55} +(0.710618 - 0.394317i) q^{56} +(7.74851 + 4.35947i) q^{57} +(6.48024 + 2.40030i) q^{58} +7.08582 q^{59} +(-12.9091 + 4.69533i) q^{60} +7.14363 q^{61} +(-3.46954 - 1.28513i) q^{62} +(-0.736736 + 0.447485i) q^{63} +(-4.23329 + 6.78817i) q^{64} +18.1699 q^{65} +(4.69674 - 3.98485i) q^{66} -4.13224 q^{67} +(4.76451 + 4.09084i) q^{68} +(-7.62040 - 3.30598i) q^{69} +(1.51099 + 0.559677i) q^{70} -7.87281i q^{71} +(4.20415 - 7.37056i) q^{72} +9.35254 q^{73} +(4.27287 + 1.58269i) q^{74} +(-16.1887 - 9.10811i) q^{75} +(7.78895 + 6.68765i) q^{76} -0.722509 q^{77} +(-8.55852 + 7.26129i) q^{78} +13.9945i q^{79} +(-15.6790 + 2.39945i) q^{80} +(-4.14904 + 7.98658i) q^{81} +(-2.62233 + 7.07967i) q^{82} +6.51283i q^{83} +(-0.935386 + 0.340220i) q^{84} +12.4509i q^{85} +(12.5422 + 4.64568i) q^{86} +(-7.37628 - 4.15005i) q^{87} +(6.21899 - 3.45088i) q^{88} +4.88399 q^{89} +(16.5175 - 3.19548i) q^{90} +1.31658 q^{91} +(-7.88197 - 5.46576i) q^{92} +(3.94928 + 2.22195i) q^{93} +(2.43294 - 6.56836i) q^{94} +20.3545i q^{95} +(6.42636 - 7.39607i) q^{96} -17.5303i q^{97} +(-9.17365 - 3.39795i) q^{98} +(-6.44756 + 3.91618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 12 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 12 q^{6} - 4 q^{9} + 16 q^{12} + 8 q^{16} + 20 q^{18} - 8 q^{24} - 144 q^{25} - 24 q^{31} + 40 q^{36} + 68 q^{39} - 24 q^{46} + 92 q^{48} - 160 q^{49} - 48 q^{52} - 32 q^{54} + 32 q^{55} - 40 q^{58} + 48 q^{64} + 72 q^{70} + 68 q^{72} - 8 q^{73} + 64 q^{78} + 12 q^{81} - 48 q^{82} + 92 q^{87} - 144 q^{94} + 68 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32616 0.491215i −0.937739 0.347342i
\(3\) 1.50954 + 0.849295i 0.871531 + 0.490341i
\(4\) 1.51742 + 1.30286i 0.758708 + 0.651431i
\(5\) 3.96539i 1.77338i 0.462368 + 0.886688i \(0.347000\pi\)
−0.462368 + 0.886688i \(0.653000\pi\)
\(6\) −1.58470 1.86781i −0.646952 0.762530i
\(7\) 0.287329i 0.108600i 0.998525 + 0.0543001i \(0.0172928\pi\)
−0.998525 + 0.0543001i \(0.982707\pi\)
\(8\) −1.37235 2.47319i −0.485200 0.874403i
\(9\) 1.55740 + 2.56408i 0.519132 + 0.854694i
\(10\) 1.94786 5.25875i 0.615967 1.66296i
\(11\) 2.51457i 0.758171i 0.925362 + 0.379086i \(0.123761\pi\)
−0.925362 + 0.379086i \(0.876239\pi\)
\(12\) 1.18408 + 3.25545i 0.341814 + 0.939768i
\(13\) 4.58211i 1.27085i −0.772163 0.635425i \(-0.780825\pi\)
0.772163 0.635425i \(-0.219175\pi\)
\(14\) 0.141140 0.381045i 0.0377214 0.101839i
\(15\) −3.36779 + 5.98590i −0.869559 + 1.54555i
\(16\) 0.605098 + 3.95397i 0.151275 + 0.988492i
\(17\) 3.13989 0.761535 0.380767 0.924671i \(-0.375660\pi\)
0.380767 + 0.924671i \(0.375660\pi\)
\(18\) −0.805843 4.16541i −0.189939 0.981796i
\(19\) 5.13304 1.17760 0.588800 0.808279i \(-0.299600\pi\)
0.588800 + 0.808279i \(0.299600\pi\)
\(20\) −5.16636 + 6.01714i −1.15523 + 1.34547i
\(21\) −0.244027 + 0.433734i −0.0532511 + 0.0946485i
\(22\) 1.23519 3.33473i 0.263344 0.710966i
\(23\) −4.77034 + 0.493825i −0.994685 + 0.102970i
\(24\) 0.0288475 4.89889i 0.00588846 0.999983i
\(25\) −10.7243 −2.14486
\(26\) −2.25080 + 6.07663i −0.441419 + 1.19172i
\(27\) 0.173281 + 5.19326i 0.0333479 + 0.999444i
\(28\) −0.374351 + 0.435998i −0.0707456 + 0.0823958i
\(29\) −4.88646 −0.907392 −0.453696 0.891156i \(-0.649895\pi\)
−0.453696 + 0.891156i \(0.649895\pi\)
\(30\) 7.40660 6.28397i 1.35225 1.14729i
\(31\) 2.61622 0.469887 0.234944 0.972009i \(-0.424509\pi\)
0.234944 + 0.972009i \(0.424509\pi\)
\(32\) 1.13979 5.54084i 0.201488 0.979491i
\(33\) −2.13561 + 3.79583i −0.371762 + 0.660769i
\(34\) −4.16400 1.54236i −0.714121 0.264513i
\(35\) −1.13937 −0.192589
\(36\) −0.977432 + 5.91985i −0.162905 + 0.986642i
\(37\) −3.22198 −0.529691 −0.264845 0.964291i \(-0.585321\pi\)
−0.264845 + 0.964291i \(0.585321\pi\)
\(38\) −6.80725 2.52143i −1.10428 0.409030i
\(39\) 3.89157 6.91686i 0.623149 1.10758i
\(40\) 9.80714 5.44192i 1.55065 0.860443i
\(41\) 5.33846i 0.833727i −0.908969 0.416864i \(-0.863129\pi\)
0.908969 0.416864i \(-0.136871\pi\)
\(42\) 0.536677 0.455332i 0.0828110 0.0702592i
\(43\) −9.45753 −1.44226 −0.721130 0.692800i \(-0.756377\pi\)
−0.721130 + 0.692800i \(0.756377\pi\)
\(44\) −3.27614 + 3.81565i −0.493896 + 0.575230i
\(45\) −10.1676 + 6.17568i −1.51569 + 0.920616i
\(46\) 6.56882 + 1.68837i 0.968520 + 0.248937i
\(47\) 4.95291i 0.722456i 0.932478 + 0.361228i \(0.117642\pi\)
−0.932478 + 0.361228i \(0.882358\pi\)
\(48\) −2.44467 + 6.48256i −0.352857 + 0.935677i
\(49\) 6.91744 0.988206
\(50\) 14.2222 + 5.26795i 2.01132 + 0.745000i
\(51\) 4.73977 + 2.66669i 0.663701 + 0.373412i
\(52\) 5.96986 6.95297i 0.827871 0.964203i
\(53\) 1.01064i 0.138822i −0.997588 0.0694112i \(-0.977888\pi\)
0.997588 0.0694112i \(-0.0221121\pi\)
\(54\) 2.32121 6.97223i 0.315877 0.948800i
\(55\) −9.97125 −1.34452
\(56\) 0.710618 0.394317i 0.0949604 0.0526929i
\(57\) 7.74851 + 4.35947i 1.02631 + 0.577426i
\(58\) 6.48024 + 2.40030i 0.850897 + 0.315175i
\(59\) 7.08582 0.922495 0.461247 0.887272i \(-0.347402\pi\)
0.461247 + 0.887272i \(0.347402\pi\)
\(60\) −12.9091 + 4.69533i −1.66656 + 0.606164i
\(61\) 7.14363 0.914648 0.457324 0.889300i \(-0.348808\pi\)
0.457324 + 0.889300i \(0.348808\pi\)
\(62\) −3.46954 1.28513i −0.440632 0.163211i
\(63\) −0.736736 + 0.447485i −0.0928200 + 0.0563778i
\(64\) −4.23329 + 6.78817i −0.529161 + 0.848521i
\(65\) 18.1699 2.25369
\(66\) 4.69674 3.98485i 0.578128 0.490501i
\(67\) −4.13224 −0.504834 −0.252417 0.967619i \(-0.581225\pi\)
−0.252417 + 0.967619i \(0.581225\pi\)
\(68\) 4.76451 + 4.09084i 0.577782 + 0.496088i
\(69\) −7.62040 3.30598i −0.917388 0.397993i
\(70\) 1.51099 + 0.559677i 0.180598 + 0.0668942i
\(71\) 7.87281i 0.934331i −0.884170 0.467165i \(-0.845275\pi\)
0.884170 0.467165i \(-0.154725\pi\)
\(72\) 4.20415 7.37056i 0.495464 0.868628i
\(73\) 9.35254 1.09463 0.547316 0.836926i \(-0.315650\pi\)
0.547316 + 0.836926i \(0.315650\pi\)
\(74\) 4.27287 + 1.58269i 0.496712 + 0.183984i
\(75\) −16.1887 9.10811i −1.86931 1.05171i
\(76\) 7.78895 + 6.68765i 0.893454 + 0.767126i
\(77\) −0.722509 −0.0823376
\(78\) −8.55852 + 7.26129i −0.969061 + 0.822179i
\(79\) 13.9945i 1.57450i 0.616632 + 0.787252i \(0.288497\pi\)
−0.616632 + 0.787252i \(0.711503\pi\)
\(80\) −15.6790 + 2.39945i −1.75297 + 0.268267i
\(81\) −4.14904 + 7.98658i −0.461004 + 0.887398i
\(82\) −2.62233 + 7.07967i −0.289588 + 0.781818i
\(83\) 6.51283i 0.714876i 0.933937 + 0.357438i \(0.116350\pi\)
−0.933937 + 0.357438i \(0.883650\pi\)
\(84\) −0.935386 + 0.340220i −0.102059 + 0.0371211i
\(85\) 12.4509i 1.35049i
\(86\) 12.5422 + 4.64568i 1.35246 + 0.500957i
\(87\) −7.37628 4.15005i −0.790820 0.444932i
\(88\) 6.21899 3.45088i 0.662947 0.367865i
\(89\) 4.88399 0.517702 0.258851 0.965917i \(-0.416656\pi\)
0.258851 + 0.965917i \(0.416656\pi\)
\(90\) 16.5175 3.19548i 1.74109 0.336834i
\(91\) 1.31658 0.138015
\(92\) −7.88197 5.46576i −0.821752 0.569845i
\(93\) 3.94928 + 2.22195i 0.409521 + 0.230405i
\(94\) 2.43294 6.56836i 0.250939 0.677475i
\(95\) 20.3545i 2.08833i
\(96\) 6.42636 7.39607i 0.655888 0.754859i
\(97\) 17.5303i 1.77993i −0.456025 0.889967i \(-0.650727\pi\)
0.456025 0.889967i \(-0.349273\pi\)
\(98\) −9.17365 3.39795i −0.926679 0.343245i
\(99\) −6.44756 + 3.91618i −0.648004 + 0.393591i
\(100\) −16.2732 13.9723i −1.62732 1.39723i
\(101\) 11.8142 1.17556 0.587780 0.809021i \(-0.300002\pi\)
0.587780 + 0.809021i \(0.300002\pi\)
\(102\) −4.97579 5.86472i −0.492677 0.580693i
\(103\) 1.23502i 0.121690i −0.998147 0.0608449i \(-0.980621\pi\)
0.998147 0.0608449i \(-0.0193795\pi\)
\(104\) −11.3324 + 6.28828i −1.11123 + 0.616617i
\(105\) −1.71992 0.967664i −0.167847 0.0944343i
\(106\) −0.496443 + 1.34028i −0.0482188 + 0.130179i
\(107\) 17.1374i 1.65674i −0.560184 0.828368i \(-0.689269\pi\)
0.560184 0.828368i \(-0.310731\pi\)
\(108\) −6.50317 + 8.10610i −0.625768 + 0.780009i
\(109\) −11.6350 −1.11443 −0.557217 0.830367i \(-0.688131\pi\)
−0.557217 + 0.830367i \(0.688131\pi\)
\(110\) 13.2235 + 4.89803i 1.26081 + 0.467009i
\(111\) −4.86370 2.73641i −0.461642 0.259729i
\(112\) −1.13609 + 0.173862i −0.107350 + 0.0164285i
\(113\) 14.8510 1.39706 0.698532 0.715579i \(-0.253837\pi\)
0.698532 + 0.715579i \(0.253837\pi\)
\(114\) −8.13435 9.58755i −0.761851 0.897956i
\(115\) −1.95821 18.9163i −0.182604 1.76395i
\(116\) −7.41479 6.36638i −0.688446 0.591104i
\(117\) 11.7489 7.13616i 1.08619 0.659738i
\(118\) −9.39695 3.48066i −0.865059 0.320421i
\(119\) 0.902182i 0.0827029i
\(120\) 19.4260 + 0.114391i 1.77335 + 0.0104425i
\(121\) 4.67694 0.425177
\(122\) −9.47362 3.50906i −0.857701 0.317695i
\(123\) 4.53393 8.05859i 0.408810 0.726619i
\(124\) 3.96990 + 3.40858i 0.356507 + 0.306099i
\(125\) 22.6992i 2.03027i
\(126\) 1.19684 0.231542i 0.106623 0.0206274i
\(127\) 15.8942 1.41039 0.705193 0.709016i \(-0.250861\pi\)
0.705193 + 0.709016i \(0.250861\pi\)
\(128\) 8.94848 6.92276i 0.790942 0.611892i
\(129\) −14.2765 8.03223i −1.25697 0.707199i
\(130\) −24.0962 8.92531i −2.11338 0.782802i
\(131\) −3.61861 −0.316160 −0.158080 0.987426i \(-0.550530\pi\)
−0.158080 + 0.987426i \(0.550530\pi\)
\(132\) −8.18606 + 2.97744i −0.712505 + 0.259153i
\(133\) 1.47487i 0.127888i
\(134\) 5.48002 + 2.02982i 0.473402 + 0.175350i
\(135\) −20.5933 + 0.687125i −1.77239 + 0.0591383i
\(136\) −4.30904 7.76552i −0.369497 0.665888i
\(137\) −9.81893 −0.838888 −0.419444 0.907781i \(-0.637775\pi\)
−0.419444 + 0.907781i \(0.637775\pi\)
\(138\) 8.48194 + 8.12752i 0.722031 + 0.691861i
\(139\) 4.01764i 0.340772i 0.985377 + 0.170386i \(0.0545014\pi\)
−0.985377 + 0.170386i \(0.945499\pi\)
\(140\) −1.72890 1.48445i −0.146119 0.125459i
\(141\) −4.20648 + 7.47659i −0.354250 + 0.629643i
\(142\) −3.86724 + 10.4406i −0.324532 + 0.876158i
\(143\) 11.5220 0.963521
\(144\) −9.19592 + 7.70941i −0.766327 + 0.642451i
\(145\) 19.3767i 1.60915i
\(146\) −12.4030 4.59411i −1.02648 0.380211i
\(147\) 10.4421 + 5.87495i 0.861252 + 0.484558i
\(148\) −4.88909 4.19780i −0.401880 0.345057i
\(149\) 20.8517i 1.70824i −0.520079 0.854118i \(-0.674097\pi\)
0.520079 0.854118i \(-0.325903\pi\)
\(150\) 16.9949 + 20.0310i 1.38762 + 1.63552i
\(151\) −4.47289 −0.363999 −0.181999 0.983299i \(-0.558257\pi\)
−0.181999 + 0.983299i \(0.558257\pi\)
\(152\) −7.04435 12.6950i −0.571372 1.02970i
\(153\) 4.89005 + 8.05093i 0.395337 + 0.650879i
\(154\) 0.958165 + 0.354907i 0.0772111 + 0.0285993i
\(155\) 10.3743i 0.833287i
\(156\) 14.9168 5.42558i 1.19430 0.434394i
\(157\) 13.7855 1.10020 0.550101 0.835098i \(-0.314589\pi\)
0.550101 + 0.835098i \(0.314589\pi\)
\(158\) 6.87431 18.5590i 0.546891 1.47647i
\(159\) 0.858334 1.52560i 0.0680703 0.120988i
\(160\) 21.9716 + 4.51971i 1.73701 + 0.357315i
\(161\) −0.141890 1.37066i −0.0111825 0.108023i
\(162\) 9.42543 8.55343i 0.740532 0.672021i
\(163\) 15.5113i 1.21494i 0.794343 + 0.607470i \(0.207815\pi\)
−0.794343 + 0.607470i \(0.792185\pi\)
\(164\) 6.95528 8.10066i 0.543116 0.632555i
\(165\) −15.0520 8.46853i −1.17179 0.659274i
\(166\) 3.19920 8.63707i 0.248306 0.670366i
\(167\) 4.71846i 0.365125i −0.983194 0.182563i \(-0.941561\pi\)
0.983194 0.182563i \(-0.0584392\pi\)
\(168\) 1.40760 + 0.00828872i 0.108598 + 0.000639489i
\(169\) −7.99576 −0.615059
\(170\) 6.11606 16.5119i 0.469081 1.26640i
\(171\) 7.99417 + 13.1615i 0.611330 + 1.00649i
\(172\) −14.3510 12.3219i −1.09425 0.939533i
\(173\) 4.84055 0.368020 0.184010 0.982924i \(-0.441092\pi\)
0.184010 + 0.982924i \(0.441092\pi\)
\(174\) 7.74359 + 9.12698i 0.587040 + 0.691914i
\(175\) 3.08141i 0.232933i
\(176\) −9.94252 + 1.52156i −0.749446 + 0.114692i
\(177\) 10.6963 + 6.01795i 0.803983 + 0.452337i
\(178\) −6.47697 2.39909i −0.485469 0.179819i
\(179\) −7.69481 −0.575137 −0.287568 0.957760i \(-0.592847\pi\)
−0.287568 + 0.957760i \(0.592847\pi\)
\(180\) −23.4745 3.87590i −1.74969 0.288892i
\(181\) 9.72050 0.722519 0.361260 0.932465i \(-0.382347\pi\)
0.361260 + 0.932465i \(0.382347\pi\)
\(182\) −1.74599 0.646722i −0.129422 0.0479382i
\(183\) 10.7836 + 6.06705i 0.797144 + 0.448489i
\(184\) 7.76791 + 11.1202i 0.572658 + 0.819794i
\(185\) 12.7764i 0.939341i
\(186\) −4.14594 4.88661i −0.303995 0.358303i
\(187\) 7.89546i 0.577374i
\(188\) −6.45296 + 7.51562i −0.470630 + 0.548133i
\(189\) −1.49218 + 0.0497886i −0.108540 + 0.00362159i
\(190\) 9.99844 26.9934i 0.725363 1.95831i
\(191\) −22.9872 −1.66330 −0.831649 0.555301i \(-0.812603\pi\)
−0.831649 + 0.555301i \(0.812603\pi\)
\(192\) −12.1555 + 6.65167i −0.877245 + 0.480043i
\(193\) −3.01341 −0.216910 −0.108455 0.994101i \(-0.534590\pi\)
−0.108455 + 0.994101i \(0.534590\pi\)
\(194\) −8.61116 + 23.2481i −0.618245 + 1.66911i
\(195\) 27.4281 + 15.4316i 1.96416 + 1.10508i
\(196\) 10.4966 + 9.01248i 0.749759 + 0.643748i
\(197\) −24.2018 −1.72431 −0.862154 0.506647i \(-0.830885\pi\)
−0.862154 + 0.506647i \(0.830885\pi\)
\(198\) 10.4742 2.02635i 0.744369 0.144006i
\(199\) 11.8884i 0.842748i 0.906887 + 0.421374i \(0.138452\pi\)
−0.906887 + 0.421374i \(0.861548\pi\)
\(200\) 14.7176 + 26.5232i 1.04069 + 1.87548i
\(201\) −6.23776 3.50949i −0.439978 0.247540i
\(202\) −15.6676 5.80333i −1.10237 0.408321i
\(203\) 1.40402i 0.0985430i
\(204\) 3.71787 + 10.2218i 0.260303 + 0.715666i
\(205\) 21.1691 1.47851
\(206\) −0.606658 + 1.63783i −0.0422679 + 0.114113i
\(207\) −8.69551 11.4625i −0.604380 0.796696i
\(208\) 18.1175 2.77263i 1.25622 0.192247i
\(209\) 12.9074i 0.892822i
\(210\) 1.80557 + 2.12813i 0.124596 + 0.146855i
\(211\) 12.3839i 0.852545i 0.904595 + 0.426273i \(0.140174\pi\)
−0.904595 + 0.426273i \(0.859826\pi\)
\(212\) 1.31673 1.53356i 0.0904333 0.105326i
\(213\) 6.68634 11.8843i 0.458141 0.814298i
\(214\) −8.41816 + 22.7270i −0.575454 + 1.55359i
\(215\) 37.5028i 2.55767i
\(216\) 12.6061 7.55555i 0.857736 0.514090i
\(217\) 0.751717i 0.0510299i
\(218\) 15.4300 + 5.71531i 1.04505 + 0.387089i
\(219\) 14.1180 + 7.94307i 0.954006 + 0.536743i
\(220\) −15.1305 12.9912i −1.02010 0.875864i
\(221\) 14.3873i 0.967796i
\(222\) 5.10589 + 6.01805i 0.342685 + 0.403905i
\(223\) −4.45336 −0.298219 −0.149110 0.988821i \(-0.547641\pi\)
−0.149110 + 0.988821i \(0.547641\pi\)
\(224\) 1.59204 + 0.327495i 0.106373 + 0.0218817i
\(225\) −16.7020 27.4980i −1.11347 1.83320i
\(226\) −19.6948 7.29503i −1.31008 0.485258i
\(227\) 15.4831i 1.02765i −0.857894 0.513826i \(-0.828228\pi\)
0.857894 0.513826i \(-0.171772\pi\)
\(228\) 6.07792 + 16.7104i 0.402520 + 1.10667i
\(229\) 25.4154 1.67950 0.839749 0.542975i \(-0.182702\pi\)
0.839749 + 0.542975i \(0.182702\pi\)
\(230\) −6.69505 + 26.0479i −0.441458 + 1.71755i
\(231\) −1.09065 0.613624i −0.0717597 0.0403735i
\(232\) 6.70595 + 12.0851i 0.440267 + 0.793427i
\(233\) 23.8892i 1.56503i 0.622631 + 0.782515i \(0.286064\pi\)
−0.622631 + 0.782515i \(0.713936\pi\)
\(234\) −19.0864 + 3.69247i −1.24771 + 0.241384i
\(235\) −19.6402 −1.28119
\(236\) 10.7521 + 9.23185i 0.699904 + 0.600942i
\(237\) −11.8855 + 21.1252i −0.772043 + 1.37223i
\(238\) 0.443165 1.19644i 0.0287261 0.0775537i
\(239\) 0.432286i 0.0279623i −0.999902 0.0139811i \(-0.995550\pi\)
0.999902 0.0139811i \(-0.00445048\pi\)
\(240\) −25.7059 9.69406i −1.65931 0.625749i
\(241\) 12.5532i 0.808620i 0.914622 + 0.404310i \(0.132488\pi\)
−0.914622 + 0.404310i \(0.867512\pi\)
\(242\) −6.20239 2.29739i −0.398705 0.147682i
\(243\) −13.0461 + 8.53227i −0.836907 + 0.547345i
\(244\) 10.8399 + 9.30717i 0.693951 + 0.595830i
\(245\) 27.4304i 1.75246i
\(246\) −9.97123 + 8.45987i −0.635742 + 0.539382i
\(247\) 23.5202i 1.49655i
\(248\) −3.59038 6.47040i −0.227990 0.410871i
\(249\) −5.53131 + 9.83134i −0.350533 + 0.623036i
\(250\) −11.1502 + 30.1028i −0.705199 + 1.90387i
\(251\) 4.72082i 0.297975i 0.988839 + 0.148988i \(0.0476015\pi\)
−0.988839 + 0.148988i \(0.952399\pi\)
\(252\) −1.70095 0.280845i −0.107150 0.0176916i
\(253\) −1.24176 11.9953i −0.0780686 0.754141i
\(254\) −21.0783 7.80749i −1.32257 0.489885i
\(255\) −10.5745 + 18.7950i −0.662199 + 1.17699i
\(256\) −15.2677 + 4.78508i −0.954232 + 0.299067i
\(257\) 9.92306i 0.618984i −0.950902 0.309492i \(-0.899841\pi\)
0.950902 0.309492i \(-0.100159\pi\)
\(258\) 14.9874 + 17.6649i 0.933073 + 1.09977i
\(259\) 0.925770i 0.0575245i
\(260\) 27.5712 + 23.6728i 1.70990 + 1.46813i
\(261\) −7.61015 12.5293i −0.471056 0.775543i
\(262\) 4.79887 + 1.77752i 0.296475 + 0.109815i
\(263\) 20.0077 1.23372 0.616862 0.787071i \(-0.288404\pi\)
0.616862 + 0.787071i \(0.288404\pi\)
\(264\) 12.3186 + 0.0725389i 0.758158 + 0.00446446i
\(265\) 4.00759 0.246184
\(266\) 0.724480 1.95592i 0.0444207 0.119925i
\(267\) 7.37256 + 4.14795i 0.451193 + 0.253850i
\(268\) −6.27033 5.38374i −0.383021 0.328864i
\(269\) 17.1022 1.04274 0.521370 0.853331i \(-0.325421\pi\)
0.521370 + 0.853331i \(0.325421\pi\)
\(270\) 27.6476 + 9.20451i 1.68258 + 0.560168i
\(271\) 9.11469 0.553678 0.276839 0.960916i \(-0.410713\pi\)
0.276839 + 0.960916i \(0.410713\pi\)
\(272\) 1.89994 + 12.4150i 0.115201 + 0.752771i
\(273\) 1.98742 + 1.11816i 0.120284 + 0.0676742i
\(274\) 13.0215 + 4.82321i 0.786658 + 0.291381i
\(275\) 26.9670i 1.62617i
\(276\) −7.25607 14.9449i −0.436764 0.899576i
\(277\) 19.2487i 1.15654i −0.815844 0.578272i \(-0.803727\pi\)
0.815844 0.578272i \(-0.196273\pi\)
\(278\) 1.97353 5.32804i 0.118364 0.319555i
\(279\) 4.07449 + 6.70821i 0.243933 + 0.401610i
\(280\) 1.56362 + 2.81788i 0.0934443 + 0.168400i
\(281\) −12.8707 −0.767799 −0.383900 0.923375i \(-0.625419\pi\)
−0.383900 + 0.923375i \(0.625419\pi\)
\(282\) 9.25110 7.84889i 0.550895 0.467395i
\(283\) −15.6946 −0.932947 −0.466473 0.884535i \(-0.654476\pi\)
−0.466473 + 0.884535i \(0.654476\pi\)
\(284\) 10.2572 11.9463i 0.608652 0.708884i
\(285\) −17.2870 + 30.7259i −1.02399 + 1.82004i
\(286\) −15.2801 5.65980i −0.903531 0.334671i
\(287\) 1.53390 0.0905430
\(288\) 15.9823 5.70676i 0.941764 0.336274i
\(289\) −7.14110 −0.420065
\(290\) −9.51813 + 25.6967i −0.558924 + 1.50896i
\(291\) 14.8884 26.4626i 0.872774 1.55127i
\(292\) 14.1917 + 12.1851i 0.830506 + 0.713078i
\(293\) 10.5441i 0.615991i −0.951388 0.307995i \(-0.900342\pi\)
0.951388 0.307995i \(-0.0996581\pi\)
\(294\) −10.9621 12.9205i −0.639322 0.753537i
\(295\) 28.0980i 1.63593i
\(296\) 4.42170 + 7.96856i 0.257006 + 0.463163i
\(297\) −13.0588 + 0.435726i −0.757749 + 0.0252834i
\(298\) −10.2427 + 27.6527i −0.593342 + 1.60188i
\(299\) 2.26276 + 21.8582i 0.130859 + 1.26409i
\(300\) −12.6984 34.9125i −0.733144 2.01567i
\(301\) 2.71742i 0.156630i
\(302\) 5.93178 + 2.19715i 0.341336 + 0.126432i
\(303\) 17.8340 + 10.0338i 1.02454 + 0.576425i
\(304\) 3.10599 + 20.2959i 0.178141 + 1.16405i
\(305\) 28.3273i 1.62202i
\(306\) −2.53026 13.0789i −0.144645 0.747672i
\(307\) 17.4478i 0.995800i −0.867234 0.497900i \(-0.834105\pi\)
0.867234 0.497900i \(-0.165895\pi\)
\(308\) −1.09635 0.941330i −0.0624701 0.0536373i
\(309\) 1.04889 1.86430i 0.0596694 0.106056i
\(310\) 5.09603 13.7581i 0.289435 0.781406i
\(311\) 22.5668i 1.27964i 0.768523 + 0.639822i \(0.220992\pi\)
−0.768523 + 0.639822i \(0.779008\pi\)
\(312\) −22.4473 0.132182i −1.27083 0.00748335i
\(313\) 20.9556i 1.18448i 0.805762 + 0.592239i \(0.201756\pi\)
−0.805762 + 0.592239i \(0.798244\pi\)
\(314\) −18.2818 6.77164i −1.03170 0.382146i
\(315\) −1.77445 2.92145i −0.0999791 0.164605i
\(316\) −18.2329 + 21.2355i −1.02568 + 1.19459i
\(317\) 18.7546 1.05336 0.526681 0.850063i \(-0.323436\pi\)
0.526681 + 0.850063i \(0.323436\pi\)
\(318\) −1.88769 + 1.60157i −0.105856 + 0.0898115i
\(319\) 12.2873i 0.687959i
\(320\) −26.9177 16.7866i −1.50475 0.938402i
\(321\) 14.5547 25.8695i 0.812366 1.44390i
\(322\) −0.485118 + 1.88741i −0.0270346 + 0.105181i
\(323\) 16.1172 0.896784
\(324\) −16.7012 + 6.71333i −0.927846 + 0.372963i
\(325\) 49.1400i 2.72580i
\(326\) 7.61939 20.5705i 0.421999 1.13930i
\(327\) −17.5635 9.88158i −0.971264 0.546453i
\(328\) −13.2030 + 7.32625i −0.729014 + 0.404525i
\(329\) −1.42312 −0.0784589
\(330\) 15.8015 + 18.6244i 0.869842 + 1.02524i
\(331\) 20.0902i 1.10426i −0.833759 0.552129i \(-0.813815\pi\)
0.833759 0.552129i \(-0.186185\pi\)
\(332\) −8.48532 + 9.88266i −0.465692 + 0.542382i
\(333\) −5.01790 8.26143i −0.274979 0.452724i
\(334\) −2.31778 + 6.25744i −0.126823 + 0.342392i
\(335\) 16.3859i 0.895260i
\(336\) −1.86263 0.702425i −0.101615 0.0383204i
\(337\) 9.95962i 0.542535i −0.962504 0.271267i \(-0.912557\pi\)
0.962504 0.271267i \(-0.0874428\pi\)
\(338\) 10.6037 + 3.92764i 0.576764 + 0.213635i
\(339\) 22.4181 + 12.6129i 1.21758 + 0.685037i
\(340\) −16.2218 + 18.8932i −0.879750 + 1.02463i
\(341\) 6.57867i 0.356255i
\(342\) −4.13643 21.3812i −0.223672 1.15616i
\(343\) 3.99889i 0.215920i
\(344\) 12.9791 + 23.3902i 0.699785 + 1.26112i
\(345\) 13.1095 30.2179i 0.705792 1.62687i
\(346\) −6.41936 2.37775i −0.345107 0.127829i
\(347\) 23.9726 1.28691 0.643457 0.765482i \(-0.277500\pi\)
0.643457 + 0.765482i \(0.277500\pi\)
\(348\) −5.78594 15.9076i −0.310159 0.852738i
\(349\) 31.4645i 1.68425i −0.539279 0.842127i \(-0.681303\pi\)
0.539279 0.842127i \(-0.318697\pi\)
\(350\) −1.51364 + 4.08645i −0.0809072 + 0.218430i
\(351\) 23.7961 0.793991i 1.27014 0.0423801i
\(352\) 13.9328 + 2.86608i 0.742622 + 0.152763i
\(353\) 8.75860i 0.466173i −0.972456 0.233087i \(-0.925117\pi\)
0.972456 0.233087i \(-0.0748826\pi\)
\(354\) −11.2289 13.2350i −0.596810 0.703430i
\(355\) 31.2188 1.65692
\(356\) 7.41104 + 6.36317i 0.392784 + 0.337247i
\(357\) −0.766219 + 1.36188i −0.0405526 + 0.0720781i
\(358\) 10.2046 + 3.77981i 0.539328 + 0.199769i
\(359\) 13.0559 0.689066 0.344533 0.938774i \(-0.388037\pi\)
0.344533 + 0.938774i \(0.388037\pi\)
\(360\) 29.2271 + 16.6711i 1.54040 + 0.878645i
\(361\) 7.34811 0.386743
\(362\) −12.8910 4.77486i −0.677534 0.250961i
\(363\) 7.06001 + 3.97211i 0.370555 + 0.208481i
\(364\) 1.99779 + 1.71532i 0.104713 + 0.0899070i
\(365\) 37.0865i 1.94120i
\(366\) −11.3205 13.3429i −0.591734 0.697447i
\(367\) 9.05269i 0.472547i −0.971687 0.236273i \(-0.924074\pi\)
0.971687 0.236273i \(-0.0759261\pi\)
\(368\) −4.83909 18.5630i −0.252255 0.967661i
\(369\) 13.6883 8.31409i 0.712582 0.432814i
\(370\) −6.27597 + 16.9436i −0.326272 + 0.880857i
\(371\) 0.290387 0.0150761
\(372\) 3.09781 + 8.51698i 0.160614 + 0.441585i
\(373\) −24.9274 −1.29069 −0.645345 0.763891i \(-0.723286\pi\)
−0.645345 + 0.763891i \(0.723286\pi\)
\(374\) 3.87837 10.4707i 0.200546 0.541426i
\(375\) 19.2783 34.2652i 0.995526 1.76945i
\(376\) 12.2495 6.79714i 0.631718 0.350536i
\(377\) 22.3903i 1.15316i
\(378\) 2.00333 + 0.666952i 0.103040 + 0.0343043i
\(379\) −15.4021 −0.791152 −0.395576 0.918433i \(-0.629455\pi\)
−0.395576 + 0.918433i \(0.629455\pi\)
\(380\) −26.5191 + 30.8862i −1.36040 + 1.58443i
\(381\) 23.9929 + 13.4989i 1.22919 + 0.691569i
\(382\) 30.4848 + 11.2917i 1.55974 + 0.577733i
\(383\) 6.19991 0.316801 0.158400 0.987375i \(-0.449366\pi\)
0.158400 + 0.987375i \(0.449366\pi\)
\(384\) 19.3875 2.85025i 0.989365 0.145451i
\(385\) 2.86503i 0.146015i
\(386\) 3.99627 + 1.48023i 0.203405 + 0.0753419i
\(387\) −14.7291 24.2499i −0.748723 1.23269i
\(388\) 22.8396 26.6008i 1.15950 1.35045i
\(389\) 17.0295i 0.863428i 0.902010 + 0.431714i \(0.142091\pi\)
−0.902010 + 0.431714i \(0.857909\pi\)
\(390\) −28.7938 33.9379i −1.45803 1.71851i
\(391\) −14.9783 + 1.55056i −0.757487 + 0.0784149i
\(392\) −9.49318 17.1081i −0.479478 0.864090i
\(393\) −5.46243 3.07327i −0.275543 0.155026i
\(394\) 32.0955 + 11.8883i 1.61695 + 0.598924i
\(395\) −55.4936 −2.79219
\(396\) −14.8859 2.45782i −0.748043 0.123510i
\(397\) 0.151454i 0.00760127i −0.999993 0.00380063i \(-0.998790\pi\)
0.999993 0.00380063i \(-0.00120978\pi\)
\(398\) 5.83977 15.7660i 0.292721 0.790277i
\(399\) −1.25260 + 2.22637i −0.0627086 + 0.111458i
\(400\) −6.48927 42.4036i −0.324463 2.12018i
\(401\) −19.3398 −0.965786 −0.482893 0.875679i \(-0.660414\pi\)
−0.482893 + 0.875679i \(0.660414\pi\)
\(402\) 6.54837 + 7.71824i 0.326603 + 0.384951i
\(403\) 11.9878i 0.597156i
\(404\) 17.9271 + 15.3923i 0.891906 + 0.765796i
\(405\) −31.6699 16.4526i −1.57369 0.817534i
\(406\) −0.689677 + 1.86196i −0.0342281 + 0.0924076i
\(407\) 8.10190i 0.401596i
\(408\) 0.0905778 15.3820i 0.00448427 0.761522i
\(409\) −11.7458 −0.580792 −0.290396 0.956907i \(-0.593787\pi\)
−0.290396 + 0.956907i \(0.593787\pi\)
\(410\) −28.0736 10.3986i −1.38646 0.513549i
\(411\) −14.8220 8.33917i −0.731117 0.411341i
\(412\) 1.60906 1.87403i 0.0792725 0.0923269i
\(413\) 2.03596i 0.100183i
\(414\) 5.90113 + 19.4725i 0.290025 + 0.957019i
\(415\) −25.8259 −1.26774
\(416\) −25.3887 5.22265i −1.24479 0.256061i
\(417\) −3.41216 + 6.06477i −0.167094 + 0.296993i
\(418\) 6.34030 17.1173i 0.310114 0.837234i
\(419\) 5.42795i 0.265173i 0.991171 + 0.132586i \(0.0423282\pi\)
−0.991171 + 0.132586i \(0.957672\pi\)
\(420\) −1.34911 3.70917i −0.0658296 0.180989i
\(421\) 16.8191 0.819713 0.409857 0.912150i \(-0.365579\pi\)
0.409857 + 0.912150i \(0.365579\pi\)
\(422\) 6.08318 16.4231i 0.296125 0.799465i
\(423\) −12.6997 + 7.71364i −0.617479 + 0.375050i
\(424\) −2.49951 + 1.38696i −0.121387 + 0.0673567i
\(425\) −33.6732 −1.63339
\(426\) −14.7049 + 12.4761i −0.712456 + 0.604467i
\(427\) 2.05257i 0.0993310i
\(428\) 22.3277 26.0046i 1.07925 1.25698i
\(429\) 17.3929 + 9.78561i 0.839738 + 0.472454i
\(430\) −18.4219 + 49.7348i −0.888385 + 2.39843i
\(431\) −11.0468 −0.532106 −0.266053 0.963958i \(-0.585720\pi\)
−0.266053 + 0.963958i \(0.585720\pi\)
\(432\) −20.4291 + 3.82758i −0.982897 + 0.184155i
\(433\) 7.75165i 0.372520i 0.982500 + 0.186260i \(0.0596367\pi\)
−0.982500 + 0.186260i \(0.940363\pi\)
\(434\) 0.369255 0.996899i 0.0177248 0.0478527i
\(435\) 16.4565 29.2498i 0.789031 1.40242i
\(436\) −17.6552 15.1589i −0.845530 0.725978i
\(437\) −24.4863 + 2.53482i −1.17134 + 0.121257i
\(438\) −14.8210 17.4688i −0.708175 0.834690i
\(439\) −26.0172 −1.24173 −0.620866 0.783917i \(-0.713219\pi\)
−0.620866 + 0.783917i \(0.713219\pi\)
\(440\) 13.6841 + 24.6607i 0.652363 + 1.17565i
\(441\) 10.7732 + 17.7369i 0.513009 + 0.844614i
\(442\) −7.06727 + 19.0799i −0.336156 + 0.907540i
\(443\) −20.7333 −0.985068 −0.492534 0.870293i \(-0.663929\pi\)
−0.492534 + 0.870293i \(0.663929\pi\)
\(444\) −3.81508 10.4890i −0.181056 0.497786i
\(445\) 19.3669i 0.918080i
\(446\) 5.90588 + 2.18756i 0.279652 + 0.103584i
\(447\) 17.7092 31.4764i 0.837618 1.48878i
\(448\) −1.95044 1.21635i −0.0921496 0.0574670i
\(449\) 22.8916i 1.08032i −0.841561 0.540162i \(-0.818363\pi\)
0.841561 0.540162i \(-0.181637\pi\)
\(450\) 8.64212 + 44.6712i 0.407393 + 2.10582i
\(451\) 13.4239 0.632108
\(452\) 22.5351 + 19.3488i 1.05996 + 0.910091i
\(453\) −6.75199 3.79881i −0.317236 0.178483i
\(454\) −7.60556 + 20.5332i −0.356946 + 0.963669i
\(455\) 5.22073i 0.244752i
\(456\) 0.148075 25.1462i 0.00693426 1.17758i
\(457\) 15.4708i 0.723693i −0.932238 0.361846i \(-0.882146\pi\)
0.932238 0.361846i \(-0.117854\pi\)
\(458\) −33.7050 12.4844i −1.57493 0.583359i
\(459\) 0.544082 + 16.3063i 0.0253956 + 0.761111i
\(460\) 21.6739 31.2551i 1.01055 1.45728i
\(461\) −26.0194 −1.21185 −0.605923 0.795523i \(-0.707196\pi\)
−0.605923 + 0.795523i \(0.707196\pi\)
\(462\) 1.14496 + 1.34951i 0.0532685 + 0.0627849i
\(463\) −4.90636 −0.228018 −0.114009 0.993480i \(-0.536369\pi\)
−0.114009 + 0.993480i \(0.536369\pi\)
\(464\) −2.95679 19.3209i −0.137265 0.896950i
\(465\) −8.81088 + 15.6604i −0.408595 + 0.726235i
\(466\) 11.7347 31.6809i 0.543600 1.46759i
\(467\) 42.0348i 1.94514i −0.232615 0.972569i \(-0.574728\pi\)
0.232615 0.972569i \(-0.425272\pi\)
\(468\) 27.1254 + 4.47870i 1.25387 + 0.207028i
\(469\) 1.18731i 0.0548250i
\(470\) 26.0461 + 9.64757i 1.20142 + 0.445009i
\(471\) 20.8097 + 11.7080i 0.958860 + 0.539474i
\(472\) −9.72425 17.5245i −0.447595 0.806632i
\(473\) 23.7816i 1.09348i
\(474\) 26.1391 22.1771i 1.20061 1.01863i
\(475\) −55.0484 −2.52579
\(476\) −1.17542 + 1.36898i −0.0538752 + 0.0627473i
\(477\) 2.59137 1.57397i 0.118651 0.0720671i
\(478\) −0.212346 + 0.573282i −0.00971246 + 0.0262213i
\(479\) 10.7256 0.490067 0.245033 0.969515i \(-0.421201\pi\)
0.245033 + 0.969515i \(0.421201\pi\)
\(480\) 29.3283 + 25.4830i 1.33865 + 1.16314i
\(481\) 14.7635i 0.673157i
\(482\) 6.16630 16.6475i 0.280867 0.758274i
\(483\) 0.949905 2.18956i 0.0432222 0.0996286i
\(484\) 7.09687 + 6.09341i 0.322585 + 0.276973i
\(485\) 69.5145 3.15649
\(486\) 21.4924 4.90674i 0.974916 0.222574i
\(487\) 23.2899 1.05537 0.527684 0.849441i \(-0.323061\pi\)
0.527684 + 0.849441i \(0.323061\pi\)
\(488\) −9.80359 17.6675i −0.443788 0.799771i
\(489\) −13.1737 + 23.4149i −0.595734 + 1.05886i
\(490\) 13.4742 36.3771i 0.608703 1.64335i
\(491\) 11.6656 0.526462 0.263231 0.964733i \(-0.415212\pi\)
0.263231 + 0.964733i \(0.415212\pi\)
\(492\) 17.3791 6.32115i 0.783510 0.284979i
\(493\) −15.3429 −0.691011
\(494\) −11.5535 + 31.1916i −0.519815 + 1.40338i
\(495\) −15.5292 25.5671i −0.697984 1.14916i
\(496\) 1.58307 + 10.3445i 0.0710820 + 0.464480i
\(497\) 2.26209 0.101469
\(498\) 12.1647 10.3209i 0.545114 0.462490i
\(499\) 6.95526i 0.311360i −0.987808 0.155680i \(-0.950243\pi\)
0.987808 0.155680i \(-0.0497569\pi\)
\(500\) 29.5739 34.4440i 1.32258 1.54038i
\(501\) 4.00736 7.12268i 0.179036 0.318218i
\(502\) 2.31894 6.26057i 0.103499 0.279423i
\(503\) 8.12303 0.362188 0.181094 0.983466i \(-0.442036\pi\)
0.181094 + 0.983466i \(0.442036\pi\)
\(504\) 2.11778 + 1.20798i 0.0943332 + 0.0538075i
\(505\) 46.8480i 2.08471i
\(506\) −4.24552 + 16.5178i −0.188737 + 0.734304i
\(507\) −12.0699 6.79076i −0.536042 0.301588i
\(508\) 24.1182 + 20.7080i 1.07007 + 0.918769i
\(509\) −19.3253 −0.856577 −0.428289 0.903642i \(-0.640883\pi\)
−0.428289 + 0.903642i \(0.640883\pi\)
\(510\) 23.2559 19.7310i 1.02979 0.873701i
\(511\) 2.68726i 0.118877i
\(512\) 22.5980 + 1.15394i 0.998699 + 0.0509974i
\(513\) 0.889456 + 26.6572i 0.0392704 + 1.17695i
\(514\) −4.87436 + 13.1596i −0.214999 + 0.580445i
\(515\) 4.89732 0.215802
\(516\) −11.1984 30.7885i −0.492984 1.35539i
\(517\) −12.4544 −0.547745
\(518\) −0.454752 + 1.22772i −0.0199807 + 0.0539430i
\(519\) 7.30699 + 4.11106i 0.320741 + 0.180455i
\(520\) −24.9355 44.9374i −1.09349 1.97064i
\(521\) 38.7398 1.69722 0.848611 0.529018i \(-0.177440\pi\)
0.848611 + 0.529018i \(0.177440\pi\)
\(522\) 3.93772 + 20.3541i 0.172349 + 0.890874i
\(523\) −39.4005 −1.72286 −0.861431 0.507874i \(-0.830432\pi\)
−0.861431 + 0.507874i \(0.830432\pi\)
\(524\) −5.49094 4.71456i −0.239873 0.205956i
\(525\) 2.61703 4.65150i 0.114216 0.203008i
\(526\) −26.5334 9.82806i −1.15691 0.428524i
\(527\) 8.21465 0.357836
\(528\) −16.3008 6.14729i −0.709403 0.267526i
\(529\) 22.5123 4.71143i 0.978795 0.204845i
\(530\) −5.31472 1.96859i −0.230857 0.0855101i
\(531\) 11.0354 + 18.1686i 0.478896 + 0.788451i
\(532\) −1.92156 + 2.23799i −0.0833100 + 0.0970294i
\(533\) −24.4614 −1.05954
\(534\) −7.73968 9.12237i −0.334929 0.394764i
\(535\) 67.9566 2.93802
\(536\) 5.67090 + 10.2198i 0.244945 + 0.441428i
\(537\) −11.6156 6.53516i −0.501249 0.282013i
\(538\) −22.6803 8.40086i −0.977817 0.362187i
\(539\) 17.3944i 0.749229i
\(540\) −32.1438 25.7876i −1.38325 1.10972i
\(541\) 20.8230i 0.895252i −0.894221 0.447626i \(-0.852270\pi\)
0.894221 0.447626i \(-0.147730\pi\)
\(542\) −12.0876 4.47728i −0.519206 0.192315i
\(543\) 14.6734 + 8.25558i 0.629698 + 0.354281i
\(544\) 3.57881 17.3976i 0.153440 0.745916i
\(545\) 46.1375i 1.97631i
\(546\) −2.08638 2.45911i −0.0892889 0.105240i
\(547\) 19.9002i 0.850870i 0.904989 + 0.425435i \(0.139879\pi\)
−0.904989 + 0.425435i \(0.860121\pi\)
\(548\) −14.8994 12.7927i −0.636471 0.546478i
\(549\) 11.1255 + 18.3169i 0.474823 + 0.781745i
\(550\) −13.2466 + 35.7627i −0.564838 + 1.52493i
\(551\) −25.0824 −1.06855
\(552\) 2.28158 + 23.3836i 0.0971107 + 0.995274i
\(553\) −4.02103 −0.170991
\(554\) −9.45527 + 25.5269i −0.401716 + 1.08454i
\(555\) 10.8510 19.2865i 0.460597 0.818665i
\(556\) −5.23443 + 6.09643i −0.221989 + 0.258546i
\(557\) 4.24687i 0.179946i 0.995944 + 0.0899728i \(0.0286780\pi\)
−0.995944 + 0.0899728i \(0.971322\pi\)
\(558\) −2.10827 10.8976i −0.0892500 0.461334i
\(559\) 43.3355i 1.83289i
\(560\) −0.689432 4.50504i −0.0291338 0.190373i
\(561\) −6.70558 + 11.9185i −0.283110 + 0.503199i
\(562\) 17.0686 + 6.32227i 0.719995 + 0.266689i
\(563\) 3.87933i 0.163494i 0.996653 + 0.0817471i \(0.0260500\pi\)
−0.996653 + 0.0817471i \(0.973950\pi\)
\(564\) −16.1240 + 5.86463i −0.678941 + 0.246945i
\(565\) 58.8900i 2.47752i
\(566\) 20.8136 + 7.70942i 0.874860 + 0.324051i
\(567\) −2.29478 1.19214i −0.0963716 0.0500652i
\(568\) −19.4709 + 10.8043i −0.816982 + 0.453338i
\(569\) −25.5810 −1.07241 −0.536205 0.844088i \(-0.680143\pi\)
−0.536205 + 0.844088i \(0.680143\pi\)
\(570\) 38.0184 32.2559i 1.59241 1.35105i
\(571\) 16.6589 0.697155 0.348577 0.937280i \(-0.386665\pi\)
0.348577 + 0.937280i \(0.386665\pi\)
\(572\) 17.4837 + 15.0116i 0.731031 + 0.627668i
\(573\) −34.7001 19.5230i −1.44962 0.815583i
\(574\) −2.03419 0.753473i −0.0849057 0.0314493i
\(575\) 51.1586 5.29594i 2.13346 0.220856i
\(576\) −23.9983 0.282641i −0.999931 0.0117767i
\(577\) −17.2222 −0.716971 −0.358485 0.933535i \(-0.616707\pi\)
−0.358485 + 0.933535i \(0.616707\pi\)
\(578\) 9.47026 + 3.50782i 0.393911 + 0.145906i
\(579\) −4.54885 2.55927i −0.189044 0.106360i
\(580\) 25.2452 29.4025i 1.04825 1.22087i
\(581\) −1.87133 −0.0776357
\(582\) −32.7433 + 27.7803i −1.35725 + 1.15153i
\(583\) 2.54133 0.105251
\(584\) −12.8350 23.1306i −0.531116 0.957150i
\(585\) 28.2977 + 46.5890i 1.16996 + 1.92622i
\(586\) −5.17940 + 13.9831i −0.213959 + 0.577638i
\(587\) 8.24485 0.340301 0.170151 0.985418i \(-0.445575\pi\)
0.170151 + 0.985418i \(0.445575\pi\)
\(588\) 8.19079 + 22.5194i 0.337782 + 0.928684i
\(589\) 13.4292 0.553340
\(590\) 13.8022 37.2626i 0.568227 1.53408i
\(591\) −36.5335 20.5545i −1.50279 0.845498i
\(592\) −1.94962 12.7396i −0.0801288 0.523595i
\(593\) 24.8805i 1.02172i 0.859664 + 0.510859i \(0.170673\pi\)
−0.859664 + 0.510859i \(0.829327\pi\)
\(594\) 17.5322 + 5.83685i 0.719353 + 0.239489i
\(595\) −3.57750 −0.146663
\(596\) 27.1669 31.6407i 1.11280 1.29605i
\(597\) −10.0968 + 17.9460i −0.413234 + 0.734481i
\(598\) 7.73631 30.0991i 0.316361 1.23084i
\(599\) 36.4718i 1.49020i 0.666955 + 0.745098i \(0.267597\pi\)
−0.666955 + 0.745098i \(0.732403\pi\)
\(600\) −0.309369 + 52.5373i −0.0126300 + 2.14483i
\(601\) −29.5759 −1.20642 −0.603212 0.797581i \(-0.706113\pi\)
−0.603212 + 0.797581i \(0.706113\pi\)
\(602\) −1.33484 + 3.60375i −0.0544040 + 0.146878i
\(603\) −6.43553 10.5954i −0.262075 0.431478i
\(604\) −6.78724 5.82756i −0.276169 0.237120i
\(605\) 18.5459i 0.753998i
\(606\) −18.7220 22.0667i −0.760531 0.896400i
\(607\) −6.98238 −0.283406 −0.141703 0.989909i \(-0.545258\pi\)
−0.141703 + 0.989909i \(0.545258\pi\)
\(608\) 5.85059 28.4413i 0.237273 1.15345i
\(609\) 1.19243 2.11942i 0.0483197 0.0858833i
\(610\) 13.9148 37.5666i 0.563393 1.52103i
\(611\) 22.6948 0.918133
\(612\) −3.06903 + 18.5877i −0.124058 + 0.751362i
\(613\) 34.1148 1.37788 0.688942 0.724817i \(-0.258076\pi\)
0.688942 + 0.724817i \(0.258076\pi\)
\(614\) −8.57064 + 23.1387i −0.345883 + 0.933800i
\(615\) 31.9555 + 17.9788i 1.28857 + 0.724975i
\(616\) 0.991538 + 1.78690i 0.0399502 + 0.0719962i
\(617\) −39.6240 −1.59520 −0.797602 0.603184i \(-0.793898\pi\)
−0.797602 + 0.603184i \(0.793898\pi\)
\(618\) −2.30678 + 1.95713i −0.0927921 + 0.0787274i
\(619\) −14.2721 −0.573645 −0.286822 0.957984i \(-0.592599\pi\)
−0.286822 + 0.957984i \(0.592599\pi\)
\(620\) −13.5163 + 15.7422i −0.542829 + 0.632221i
\(621\) −3.39117 24.6881i −0.136083 0.990697i
\(622\) 11.0851 29.9272i 0.444473 1.19997i
\(623\) 1.40331i 0.0562226i
\(624\) 29.7038 + 11.2017i 1.18910 + 0.448429i
\(625\) 36.3894 1.45558
\(626\) 10.2937 27.7905i 0.411418 1.11073i
\(627\) −10.9622 + 19.4842i −0.437787 + 0.778122i
\(628\) 20.9183 + 17.9606i 0.834732 + 0.716706i
\(629\) −10.1167 −0.403378
\(630\) 0.918156 + 4.74595i 0.0365802 + 0.189083i
\(631\) 1.61081i 0.0641255i 0.999486 + 0.0320627i \(0.0102076\pi\)
−0.999486 + 0.0320627i \(0.989792\pi\)
\(632\) 34.6110 19.2054i 1.37675 0.763950i
\(633\) −10.5176 + 18.6940i −0.418038 + 0.743020i
\(634\) −24.8716 9.21254i −0.987779 0.365877i
\(635\) 63.0268i 2.50114i
\(636\) 3.29010 1.19668i 0.130461 0.0474514i
\(637\) 31.6965i 1.25586i
\(638\) −6.03573 + 16.2950i −0.238957 + 0.645125i
\(639\) 20.1865 12.2611i 0.798567 0.485041i
\(640\) 27.4515 + 35.4842i 1.08511 + 1.40264i
\(641\) 0.197384 0.00779619 0.00389810 0.999992i \(-0.498759\pi\)
0.00389810 + 0.999992i \(0.498759\pi\)
\(642\) −32.0094 + 27.1577i −1.26331 + 1.07183i
\(643\) −38.0575 −1.50084 −0.750421 0.660961i \(-0.770149\pi\)
−0.750421 + 0.660961i \(0.770149\pi\)
\(644\) 1.57047 2.26472i 0.0618853 0.0892425i
\(645\) 31.8509 56.6118i 1.25413 2.22909i
\(646\) −21.3740 7.91700i −0.840949 0.311490i
\(647\) 41.6702i 1.63822i 0.573634 + 0.819112i \(0.305533\pi\)
−0.573634 + 0.819112i \(0.694467\pi\)
\(648\) 25.4462 0.699071i 0.999623 0.0274621i
\(649\) 17.8178i 0.699409i
\(650\) 24.1383 65.1677i 0.946783 2.55609i
\(651\) −0.638430 + 1.13474i −0.0250220 + 0.0444741i
\(652\) −20.2091 + 23.5371i −0.791449 + 0.921784i
\(653\) −35.8779 −1.40401 −0.702005 0.712172i \(-0.747711\pi\)
−0.702005 + 0.712172i \(0.747711\pi\)
\(654\) 18.4381 + 21.7320i 0.720986 + 0.849790i
\(655\) 14.3492i 0.560670i
\(656\) 21.1081 3.23029i 0.824133 0.126122i
\(657\) 14.5656 + 23.9807i 0.568258 + 0.935576i
\(658\) 1.88728 + 0.699056i 0.0735739 + 0.0272520i
\(659\) 24.0238i 0.935836i 0.883772 + 0.467918i \(0.154996\pi\)
−0.883772 + 0.467918i \(0.845004\pi\)
\(660\) −11.8067 32.4609i −0.459576 1.26354i
\(661\) −1.96209 −0.0763164 −0.0381582 0.999272i \(-0.512149\pi\)
−0.0381582 + 0.999272i \(0.512149\pi\)
\(662\) −9.86862 + 26.6429i −0.383555 + 1.03551i
\(663\) 12.2191 21.7182i 0.474550 0.843464i
\(664\) 16.1074 8.93790i 0.625089 0.346858i
\(665\) −5.84845 −0.226793
\(666\) 2.59641 + 13.4209i 0.100609 + 0.520048i
\(667\) 23.3101 2.41306i 0.902569 0.0934339i
\(668\) 6.14750 7.15986i 0.237854 0.277023i
\(669\) −6.72251 3.78222i −0.259907 0.146229i
\(670\) −8.04903 + 21.7304i −0.310961 + 0.839520i
\(671\) 17.9632i 0.693460i
\(672\) 2.12511 + 1.84648i 0.0819778 + 0.0712296i
\(673\) −21.9447 −0.845907 −0.422953 0.906151i \(-0.639007\pi\)
−0.422953 + 0.906151i \(0.639007\pi\)
\(674\) −4.89232 + 13.2081i −0.188445 + 0.508756i
\(675\) −1.85832 55.6942i −0.0715266 2.14367i
\(676\) −12.1329 10.4174i −0.466650 0.400668i
\(677\) 16.4455i 0.632052i −0.948750 0.316026i \(-0.897651\pi\)
0.948750 0.316026i \(-0.102349\pi\)
\(678\) −23.5344 27.7388i −0.903833 1.06530i
\(679\) 5.03697 0.193301
\(680\) 30.7933 17.0870i 1.18087 0.655257i
\(681\) 13.1498 23.3724i 0.503900 0.895631i
\(682\) 3.23154 8.72439i 0.123742 0.334074i
\(683\) 49.6858 1.90118 0.950588 0.310457i \(-0.100482\pi\)
0.950588 + 0.310457i \(0.100482\pi\)
\(684\) −5.01720 + 30.3868i −0.191837 + 1.16187i
\(685\) 38.9359i 1.48766i
\(686\) 1.96431 5.30318i 0.0749979 0.202476i
\(687\) 38.3655 + 21.5852i 1.46373 + 0.823526i
\(688\) −5.72273 37.3948i −0.218177 1.42566i
\(689\) −4.63088 −0.176422
\(690\) −32.2288 + 33.6342i −1.22693 + 1.28043i
\(691\) 4.13168i 0.157177i 0.996907 + 0.0785883i \(0.0250412\pi\)
−0.996907 + 0.0785883i \(0.974959\pi\)
\(692\) 7.34513 + 6.30658i 0.279220 + 0.239740i
\(693\) −1.12523 1.85257i −0.0427440 0.0703734i
\(694\) −31.7915 11.7757i −1.20679 0.446999i
\(695\) −15.9315 −0.604316
\(696\) −0.140962 + 23.9382i −0.00534315 + 0.907377i
\(697\) 16.7622i 0.634912i
\(698\) −15.4558 + 41.7270i −0.585012 + 1.57939i
\(699\) −20.2889 + 36.0615i −0.767398 + 1.36397i
\(700\) 4.01465 4.67578i 0.151740 0.176728i
\(701\) 14.0993i 0.532522i −0.963901 0.266261i \(-0.914212\pi\)
0.963901 0.266261i \(-0.0857882\pi\)
\(702\) −31.9475 10.6361i −1.20578 0.401432i
\(703\) −16.5386 −0.623764
\(704\) −17.0693 10.6449i −0.643324 0.401195i
\(705\) −29.6476 16.6803i −1.11659 0.628218i
\(706\) −4.30236 + 11.6153i −0.161921 + 0.437149i
\(707\) 3.39457i 0.127666i
\(708\) 8.39016 + 23.0675i 0.315321 + 0.866931i
\(709\) −7.17494 −0.269461 −0.134730 0.990882i \(-0.543017\pi\)
−0.134730 + 0.990882i \(0.543017\pi\)
\(710\) −41.4012 15.3351i −1.55376 0.575517i
\(711\) −35.8830 + 21.7950i −1.34572 + 0.817375i
\(712\) −6.70256 12.0790i −0.251189 0.452680i
\(713\) −12.4803 + 1.29196i −0.467390 + 0.0483841i
\(714\) 1.68510 1.42969i 0.0630634 0.0535048i
\(715\) 45.6894i 1.70869i
\(716\) −11.6762 10.0253i −0.436361 0.374662i
\(717\) 0.367139 0.652552i 0.0137110 0.0243700i
\(718\) −17.3143 6.41327i −0.646164 0.239341i
\(719\) 0.624362i 0.0232848i −0.999932 0.0116424i \(-0.996294\pi\)
0.999932 0.0116424i \(-0.00370597\pi\)
\(720\) −30.5708 36.4654i −1.13931 1.35899i
\(721\) 0.354856 0.0132155
\(722\) −9.74479 3.60950i −0.362663 0.134332i
\(723\) −10.6613 + 18.9494i −0.396499 + 0.704737i
\(724\) 14.7500 + 12.6645i 0.548181 + 0.470672i
\(725\) 52.4039 1.94623
\(726\) −7.41157 8.73564i −0.275069 0.324210i
\(727\) 40.0473i 1.48527i −0.669695 0.742636i \(-0.733575\pi\)
0.669695 0.742636i \(-0.266425\pi\)
\(728\) −1.80681 3.25613i −0.0669647 0.120680i
\(729\) −26.9399 + 1.79978i −0.997776 + 0.0666586i
\(730\) 18.2174 49.1827i 0.674258 1.82033i
\(731\) −29.6956 −1.09833
\(732\) 8.45861 + 23.2557i 0.312639 + 0.859557i
\(733\) −13.8789 −0.512627 −0.256314 0.966594i \(-0.582508\pi\)
−0.256314 + 0.966594i \(0.582508\pi\)
\(734\) −4.44682 + 12.0053i −0.164135 + 0.443125i
\(735\) −23.2965 + 41.4071i −0.859303 + 1.52732i
\(736\) −2.70098 + 26.9945i −0.0995594 + 0.995032i
\(737\) 10.3908i 0.382750i
\(738\) −22.2369 + 4.30196i −0.818550 + 0.158357i
\(739\) 37.4827i 1.37882i 0.724369 + 0.689412i \(0.242131\pi\)
−0.724369 + 0.689412i \(0.757869\pi\)
\(740\) 16.6459 19.3871i 0.611916 0.712685i
\(741\) 19.9756 35.5045i 0.733821 1.30429i
\(742\) −0.385101 0.142643i −0.0141375 0.00523657i
\(743\) −3.58471 −0.131510 −0.0657552 0.997836i \(-0.520946\pi\)
−0.0657552 + 0.997836i \(0.520946\pi\)
\(744\) 0.0754714 12.8166i 0.00276691 0.469879i
\(745\) 82.6851 3.02935
\(746\) 33.0577 + 12.2447i 1.21033 + 0.448310i
\(747\) −16.6994 + 10.1430i −0.611000 + 0.371115i
\(748\) −10.2867 + 11.9807i −0.376119 + 0.438058i
\(749\) 4.92408 0.179922
\(750\) −42.3977 + 35.9714i −1.54815 + 1.31349i
\(751\) 31.3303i 1.14326i −0.820512 0.571630i \(-0.806311\pi\)
0.820512 0.571630i \(-0.193689\pi\)
\(752\) −19.5836 + 2.99700i −0.714142 + 0.109289i
\(753\) −4.00937 + 7.12624i −0.146109 + 0.259695i
\(754\) 10.9985 29.6932i 0.400540 1.08136i
\(755\) 17.7368i 0.645507i
\(756\) −2.32912 1.86855i −0.0847092 0.0679585i
\(757\) −23.5815 −0.857085 −0.428543 0.903522i \(-0.640973\pi\)
−0.428543 + 0.903522i \(0.640973\pi\)
\(758\) 20.4257 + 7.56574i 0.741894 + 0.274800i
\(759\) 8.31311 19.1620i 0.301747 0.695537i
\(760\) 50.3405 27.9336i 1.82604 1.01326i
\(761\) 33.9195i 1.22958i −0.788690 0.614791i \(-0.789240\pi\)
0.788690 0.614791i \(-0.210760\pi\)
\(762\) −25.1876 29.6874i −0.912452 1.07546i
\(763\) 3.34309i 0.121028i
\(764\) −34.8812 29.9492i −1.26196 1.08352i
\(765\) −31.9251 + 19.3909i −1.15425 + 0.701081i
\(766\) −8.22209 3.04549i −0.297076 0.110038i
\(767\) 32.4680i 1.17235i
\(768\) −27.1111 5.74355i −0.978287 0.207252i
\(769\) 33.4521i 1.20631i −0.797623 0.603156i \(-0.793910\pi\)
0.797623 0.603156i \(-0.206090\pi\)
\(770\) −1.40735 + 3.79950i −0.0507173 + 0.136924i
\(771\) 8.42761 14.9792i 0.303513 0.539463i
\(772\) −4.57259 3.92606i −0.164571 0.141302i
\(773\) 8.93447i 0.321350i −0.987007 0.160675i \(-0.948633\pi\)
0.987007 0.160675i \(-0.0513672\pi\)
\(774\) 7.62129 + 39.3945i 0.273941 + 1.41600i
\(775\) −28.0572 −1.00784
\(776\) −43.3557 + 24.0578i −1.55638 + 0.863625i
\(777\) 0.786252 1.39748i 0.0282066 0.0501344i
\(778\) 8.36513 22.5838i 0.299905 0.809670i
\(779\) 27.4025i 0.981797i
\(780\) 21.5145 + 59.1511i 0.770344 + 2.11795i
\(781\) 19.7967 0.708383
\(782\) 20.6254 + 5.30130i 0.737561 + 0.189574i
\(783\) −0.846728 25.3767i −0.0302596 0.906888i
\(784\) 4.18573 + 27.3513i 0.149490 + 0.976833i
\(785\) 54.6649i 1.95107i
\(786\) 5.73443 + 6.75889i 0.204540 + 0.241081i
\(787\) 53.3309 1.90104 0.950521 0.310661i \(-0.100550\pi\)
0.950521 + 0.310661i \(0.100550\pi\)
\(788\) −36.7242 31.5316i −1.30825 1.12327i
\(789\) 30.2023 + 16.9924i 1.07523 + 0.604946i
\(790\) 73.5936 + 27.2593i 2.61834 + 0.969843i
\(791\) 4.26712i 0.151721i
\(792\) 18.5338 + 10.5716i 0.658569 + 0.375647i
\(793\) 32.7329i 1.16238i
\(794\) −0.0743966 + 0.200853i −0.00264024 + 0.00712800i
\(795\) 6.04960 + 3.40363i 0.214557 + 0.120714i
\(796\) −15.4890 + 18.0397i −0.548992 + 0.639399i
\(797\) 27.1714i 0.962460i 0.876594 + 0.481230i \(0.159810\pi\)
−0.876594 + 0.481230i \(0.840190\pi\)
\(798\) 2.75478 2.33724i 0.0975182 0.0827372i
\(799\) 15.5516i 0.550175i
\(800\) −12.2235 + 59.4217i −0.432165 + 2.10087i
\(801\) 7.60630 + 12.5230i 0.268756 + 0.442477i
\(802\) 25.6478 + 9.50002i 0.905655 + 0.335458i
\(803\) 23.5176i 0.829919i
\(804\) −4.89289 13.4523i −0.172559 0.474426i
\(805\) 5.43519 0.562651i 0.191565 0.0198308i
\(806\) −5.88860 + 15.8978i −0.207417 + 0.559976i
\(807\) 25.8164 + 14.5248i 0.908780 + 0.511298i
\(808\) −16.2133 29.2188i −0.570382 1.02791i
\(809\) 16.9102i 0.594532i −0.954795 0.297266i \(-0.903925\pi\)
0.954795 0.297266i \(-0.0960747\pi\)
\(810\) 33.9177 + 37.3755i 1.19175 + 1.31324i
\(811\) 9.29547i 0.326408i 0.986592 + 0.163204i \(0.0521829\pi\)
−0.986592 + 0.163204i \(0.947817\pi\)
\(812\) 1.82925 2.13048i 0.0641940 0.0747654i
\(813\) 13.7590 + 7.74107i 0.482548 + 0.271491i
\(814\) −3.97978 + 10.7444i −0.139491 + 0.376592i
\(815\) −61.5084 −2.15454
\(816\) −7.67598 + 20.3545i −0.268713 + 0.712551i
\(817\) −48.5459 −1.69841
\(818\) 15.5768 + 5.76971i 0.544631 + 0.201733i
\(819\) 2.05043 + 3.37581i 0.0716478 + 0.117960i
\(820\) 32.1223 + 27.5804i 1.12176 + 0.963149i
\(821\) −22.0273 −0.768759 −0.384380 0.923175i \(-0.625585\pi\)
−0.384380 + 0.923175i \(0.625585\pi\)
\(822\) 15.5601 + 18.3399i 0.542720 + 0.639678i
\(823\) 35.3900 1.23362 0.616808 0.787113i \(-0.288425\pi\)
0.616808 + 0.787113i \(0.288425\pi\)
\(824\) −3.05442 + 1.69488i −0.106406 + 0.0590439i
\(825\) 22.9030 40.7077i 0.797379 1.41726i
\(826\) 1.00010 2.70002i 0.0347978 0.0939456i
\(827\) 6.38502i 0.222029i −0.993819 0.111014i \(-0.964590\pi\)
0.993819 0.111014i \(-0.0354100\pi\)
\(828\) 1.73931 28.7224i 0.0604452 0.998172i
\(829\) 21.0446i 0.730908i 0.930829 + 0.365454i \(0.119086\pi\)
−0.930829 + 0.365454i \(0.880914\pi\)
\(830\) 34.2493 + 12.6861i 1.18881 + 0.440340i
\(831\) 16.3479 29.0566i 0.567101 1.00796i
\(832\) 31.1042 + 19.3974i 1.07834 + 0.672484i
\(833\) 21.7200 0.752553
\(834\) 7.50419 6.36677i 0.259849 0.220463i
\(835\) 18.7105 0.647504
\(836\) −16.8165 + 19.5859i −0.581612 + 0.677391i
\(837\) 0.453340 + 13.5867i 0.0156697 + 0.469626i
\(838\) 2.66629 7.19834i 0.0921055 0.248663i
\(839\) 9.43913 0.325875 0.162937 0.986636i \(-0.447903\pi\)
0.162937 + 0.986636i \(0.447903\pi\)
\(840\) −0.0328680 + 5.58167i −0.00113405 + 0.192586i
\(841\) −5.12253 −0.176639
\(842\) −22.3049 8.26180i −0.768677 0.284721i
\(843\) −19.4287 10.9310i −0.669161 0.376483i
\(844\) −16.1346 + 18.7916i −0.555375 + 0.646833i
\(845\) 31.7063i 1.09073i
\(846\) 20.6309 3.99127i 0.709304 0.137223i
\(847\) 1.34382i 0.0461743i
\(848\) 3.99605 0.611538i 0.137225 0.0210003i
\(849\) −23.6915 13.3293i −0.813092 0.457462i
\(850\) 44.6561 + 16.5408i 1.53169 + 0.567344i
\(851\) 15.3700 1.59110i 0.526875 0.0545421i
\(852\) 25.6295 9.32202i 0.878054 0.319367i
\(853\) 1.79992i 0.0616279i 0.999525 + 0.0308140i \(0.00980994\pi\)
−0.999525 + 0.0308140i \(0.990190\pi\)
\(854\) 1.00826 2.72205i 0.0345018 0.0931465i
\(855\) −52.1906 + 31.7000i −1.78488 + 1.08412i
\(856\) −42.3840 + 23.5186i −1.44866 + 0.803849i
\(857\) 53.5766i 1.83014i −0.403292 0.915072i \(-0.632134\pi\)
0.403292 0.915072i \(-0.367866\pi\)
\(858\) −18.2590 21.5210i −0.623352 0.734714i
\(859\) 56.7146i 1.93508i −0.252723 0.967539i \(-0.581326\pi\)
0.252723 0.967539i \(-0.418674\pi\)
\(860\) 48.8610 56.9073i 1.66615 1.94052i
\(861\) 2.31547 + 1.30273i 0.0789110 + 0.0443969i
\(862\) 14.6499 + 5.42636i 0.498976 + 0.184822i
\(863\) 53.0626i 1.80627i −0.429355 0.903136i \(-0.641259\pi\)
0.429355 0.903136i \(-0.358741\pi\)
\(864\) 28.9725 + 4.95911i 0.985665 + 0.168712i
\(865\) 19.1947i 0.652639i
\(866\) 3.80773 10.2799i 0.129392 0.349327i
\(867\) −10.7797 6.06490i −0.366099 0.205975i
\(868\) −0.979384 + 1.14067i −0.0332425 + 0.0387168i
\(869\) −35.1901 −1.19374
\(870\) −36.1920 + 30.7063i −1.22702 + 1.04104i
\(871\) 18.9344i 0.641567i
\(872\) 15.9674 + 28.7756i 0.540724 + 0.974465i
\(873\) 44.9492 27.3016i 1.52130 0.924020i
\(874\) 33.7180 + 8.66648i 1.14053 + 0.293148i
\(875\) 6.52213 0.220488
\(876\) 11.0741 + 30.4467i 0.374160 + 1.02870i
\(877\) 35.9210i 1.21296i 0.795097 + 0.606482i \(0.207420\pi\)
−0.795097 + 0.606482i \(0.792580\pi\)
\(878\) 34.5030 + 12.7800i 1.16442 + 0.431305i
\(879\) 8.95502 15.9166i 0.302045 0.536855i
\(880\) −6.03359 39.4260i −0.203392 1.32905i
\(881\) 4.80430 0.161861 0.0809305 0.996720i \(-0.474211\pi\)
0.0809305 + 0.996720i \(0.474211\pi\)
\(882\) −5.57437 28.8140i −0.187699 0.970217i
\(883\) 25.0771i 0.843911i −0.906617 0.421955i \(-0.861344\pi\)
0.906617 0.421955i \(-0.138656\pi\)
\(884\) 18.7447 21.8315i 0.630453 0.734274i
\(885\) −23.8635 + 42.4150i −0.802164 + 1.42576i
\(886\) 27.4957 + 10.1845i 0.923736 + 0.342155i
\(887\) 28.7995i 0.966993i 0.875346 + 0.483496i \(0.160633\pi\)
−0.875346 + 0.483496i \(0.839367\pi\)
\(888\) −0.0929460 + 15.7842i −0.00311906 + 0.529682i
\(889\) 4.56688i 0.153168i
\(890\) 9.51333 25.6837i 0.318888 0.860920i
\(891\) −20.0828 10.4330i −0.672799 0.349520i
\(892\) −6.75760 5.80212i −0.226261 0.194269i
\(893\) 25.4235i 0.850764i
\(894\) −38.9470 + 33.0437i −1.30258 + 1.10515i
\(895\) 30.5129i 1.01993i
\(896\) 1.98911 + 2.57116i 0.0664516 + 0.0858965i
\(897\) −15.1484 + 34.9175i −0.505789 + 1.16586i
\(898\) −11.2447 + 30.3581i −0.375241 + 1.01306i
\(899\) −12.7841 −0.426372
\(900\) 10.4823 63.4864i 0.349410 2.11621i
\(901\) 3.17330i 0.105718i
\(902\) −17.8023 6.59403i −0.592752 0.219557i
\(903\) 2.30790 4.10205i 0.0768020 0.136508i
\(904\) −20.3808 36.7292i −0.677856 1.22160i
\(905\) 38.5456i 1.28130i
\(906\) 7.08821 + 8.35451i 0.235490 + 0.277560i
\(907\) −22.7801 −0.756402 −0.378201 0.925723i \(-0.623457\pi\)
−0.378201 + 0.925723i \(0.623457\pi\)
\(908\) 20.1724 23.4944i 0.669445 0.779688i
\(909\) 18.3994 + 30.2926i 0.610270 + 1.00474i
\(910\) 2.56450 6.92354i 0.0850125 0.229513i
\(911\) −7.35787 −0.243777 −0.121889 0.992544i \(-0.538895\pi\)
−0.121889 + 0.992544i \(0.538895\pi\)
\(912\) −12.5486 + 33.2753i −0.415525 + 1.10185i
\(913\) −16.3769 −0.541998
\(914\) −7.59948 + 20.5168i −0.251369 + 0.678635i
\(915\) −24.0582 + 42.7610i −0.795340 + 1.41364i
\(916\) 38.5657 + 33.1128i 1.27425 + 1.09408i
\(917\) 1.03973i 0.0343350i
\(918\) 7.28834 21.8920i 0.240551 0.722544i
\(919\) 48.0916i 1.58640i −0.608964 0.793198i \(-0.708415\pi\)
0.608964 0.793198i \(-0.291585\pi\)
\(920\) −44.0961 + 30.8028i −1.45380 + 1.01554i
\(921\) 14.8184 26.3381i 0.488281 0.867870i
\(922\) 34.5060 + 12.7811i 1.13639 + 0.420924i
\(923\) −36.0741 −1.18739
\(924\) −0.855507 2.35209i −0.0281441 0.0773782i
\(925\) 34.5536 1.13611
\(926\) 6.50663 + 2.41008i 0.213821 + 0.0792001i
\(927\) 3.16668 1.92341i 0.104007 0.0631730i
\(928\) −5.56953 + 27.0751i −0.182829 + 0.888783i
\(929\) 31.4154i 1.03071i −0.856978 0.515353i \(-0.827661\pi\)
0.856978 0.515353i \(-0.172339\pi\)
\(930\) 19.3773 16.4403i 0.635407 0.539097i
\(931\) 35.5075 1.16371
\(932\) −31.1243 + 36.2498i −1.01951 + 1.18740i
\(933\) −19.1658 + 34.0653i −0.627461 + 1.11525i
\(934\) −20.6481 + 55.7450i −0.675627 + 1.82403i
\(935\) −31.3086 −1.02390
\(936\) −33.7727 19.2639i −1.10390 0.629661i
\(937\) 25.0673i 0.818914i 0.912329 + 0.409457i \(0.134282\pi\)
−0.912329 + 0.409457i \(0.865718\pi\)
\(938\) −0.583226 + 1.57457i −0.0190430 + 0.0514116i
\(939\) −17.7974 + 31.6331i −0.580798 + 1.03231i
\(940\) −29.8024 25.5885i −0.972046 0.834605i
\(941\) 12.8371i 0.418479i 0.977864 + 0.209239i \(0.0670988\pi\)
−0.977864 + 0.209239i \(0.932901\pi\)
\(942\) −21.8459 25.7487i −0.711778 0.838938i
\(943\) 2.63626 + 25.4663i 0.0858486 + 0.829296i
\(944\) 4.28762 + 28.0171i 0.139550 + 0.911879i
\(945\) −0.197431 5.91706i −0.00642243 0.192482i
\(946\) −11.6819 + 31.5383i −0.379811 + 1.02540i
\(947\) −20.8801 −0.678512 −0.339256 0.940694i \(-0.610175\pi\)
−0.339256 + 0.940694i \(0.610175\pi\)
\(948\) −45.5584 + 16.5706i −1.47967 + 0.538187i
\(949\) 42.8544i 1.39111i
\(950\) 73.0031 + 27.0406i 2.36853 + 0.877313i
\(951\) 28.3107 + 15.9282i 0.918038 + 0.516507i
\(952\) 2.23126 1.23811i 0.0723156 0.0401275i
\(953\) −8.76117 −0.283802 −0.141901 0.989881i \(-0.545322\pi\)
−0.141901 + 0.989881i \(0.545322\pi\)
\(954\) −4.20974 + 0.814420i −0.136295 + 0.0263678i
\(955\) 91.1534i 2.94965i
\(956\) 0.563210 0.655958i 0.0182155 0.0212152i
\(957\) 10.4356 18.5482i 0.337334 0.599577i
\(958\) −14.2239 5.26859i −0.459554 0.170220i
\(959\) 2.82127i 0.0911034i
\(960\) −26.3765 48.2012i −0.851297 1.55569i
\(961\) −24.1554 −0.779206
\(962\) 7.25205 19.5788i 0.233816 0.631246i
\(963\) 43.9418 26.6897i 1.41600 0.860065i
\(964\) −16.3550 + 19.0483i −0.526760 + 0.613506i
\(965\) 11.9493i 0.384663i
\(966\) −2.33528 + 2.43711i −0.0751362 + 0.0784127i
\(967\) −41.0937 −1.32148 −0.660742 0.750613i \(-0.729758\pi\)
−0.660742 + 0.750613i \(0.729758\pi\)
\(968\) −6.41842 11.5669i −0.206296 0.371776i
\(969\) 24.3294 + 13.6882i 0.781574 + 0.439730i
\(970\) −92.1876 34.1466i −2.95997 1.09638i
\(971\) 33.2061i 1.06563i 0.846231 + 0.532817i \(0.178867\pi\)
−0.846231 + 0.532817i \(0.821133\pi\)
\(972\) −30.9127 4.05026i −0.991525 0.129912i
\(973\) −1.15439 −0.0370079
\(974\) −30.8862 11.4404i −0.989659 0.366573i
\(975\) −41.7344 + 74.1786i −1.33657 + 2.37562i
\(976\) 4.32260 + 28.2457i 0.138363 + 0.904122i
\(977\) 16.4427 0.526049 0.263025 0.964789i \(-0.415280\pi\)
0.263025 + 0.964789i \(0.415280\pi\)
\(978\) 28.9722 24.5808i 0.926428 0.786008i
\(979\) 12.2811i 0.392507i
\(980\) −35.7380 + 41.6232i −1.14161 + 1.32961i
\(981\) −18.1204 29.8332i −0.578538 0.952501i
\(982\) −15.4705 5.73033i −0.493684 0.182862i
\(983\) −14.9568 −0.477049 −0.238525 0.971136i \(-0.576664\pi\)
−0.238525 + 0.971136i \(0.576664\pi\)
\(984\) −26.1525 0.154001i −0.833713 0.00490937i
\(985\) 95.9696i 3.05785i
\(986\) 20.3472 + 7.53668i 0.647988 + 0.240017i
\(987\) −2.14824 1.20865i −0.0683793 0.0384716i
\(988\) 30.6436 35.6899i 0.974901 1.13545i
\(989\) 45.1156 4.67036i 1.43459 0.148509i
\(990\) 8.03526 + 41.5343i 0.255377 + 1.32005i
\(991\) 0.819062 0.0260184 0.0130092 0.999915i \(-0.495859\pi\)
0.0130092 + 0.999915i \(0.495859\pi\)
\(992\) 2.98194 14.4961i 0.0946768 0.460250i
\(993\) 17.0625 30.3269i 0.541463 0.962395i
\(994\) −2.99990 1.11117i −0.0951510 0.0352442i
\(995\) −47.1422 −1.49451
\(996\) −21.2022 + 7.71169i −0.671817 + 0.244354i
\(997\) 44.2375i 1.40102i 0.713644 + 0.700508i \(0.247043\pi\)
−0.713644 + 0.700508i \(0.752957\pi\)
\(998\) −3.41653 + 9.22381i −0.108148 + 0.291975i
\(999\) −0.558307 16.7326i −0.0176641 0.529396i
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 552.2.b.c.413.10 yes 80
3.2 odd 2 inner 552.2.b.c.413.71 yes 80
4.3 odd 2 2208.2.b.c.689.14 80
8.3 odd 2 2208.2.b.c.689.67 80
8.5 even 2 inner 552.2.b.c.413.69 yes 80
12.11 even 2 2208.2.b.c.689.65 80
23.22 odd 2 inner 552.2.b.c.413.9 80
24.5 odd 2 inner 552.2.b.c.413.12 yes 80
24.11 even 2 2208.2.b.c.689.16 80
69.68 even 2 inner 552.2.b.c.413.72 yes 80
92.91 even 2 2208.2.b.c.689.13 80
184.45 odd 2 inner 552.2.b.c.413.70 yes 80
184.91 even 2 2208.2.b.c.689.68 80
276.275 odd 2 2208.2.b.c.689.66 80
552.275 odd 2 2208.2.b.c.689.15 80
552.413 even 2 inner 552.2.b.c.413.11 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.b.c.413.9 80 23.22 odd 2 inner
552.2.b.c.413.10 yes 80 1.1 even 1 trivial
552.2.b.c.413.11 yes 80 552.413 even 2 inner
552.2.b.c.413.12 yes 80 24.5 odd 2 inner
552.2.b.c.413.69 yes 80 8.5 even 2 inner
552.2.b.c.413.70 yes 80 184.45 odd 2 inner
552.2.b.c.413.71 yes 80 3.2 odd 2 inner
552.2.b.c.413.72 yes 80 69.68 even 2 inner
2208.2.b.c.689.13 80 92.91 even 2
2208.2.b.c.689.14 80 4.3 odd 2
2208.2.b.c.689.15 80 552.275 odd 2
2208.2.b.c.689.16 80 24.11 even 2
2208.2.b.c.689.65 80 12.11 even 2
2208.2.b.c.689.66 80 276.275 odd 2
2208.2.b.c.689.67 80 8.3 odd 2
2208.2.b.c.689.68 80 184.91 even 2