Properties

Label 675.2.ba.b.68.16
Level $675$
Weight $2$
Character 675.68
Analytic conductor $5.390$
Analytic rank $0$
Dimension $192$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(32,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([10, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.32");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.ba (of order \(36\), degree \(12\), 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 68.16
Character \(\chi\) \(=\) 675.68
Dual form 675.2.ba.b.407.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.52658 - 2.18018i) q^{2} +(-1.25829 + 1.19025i) q^{3} +(-1.73870 - 4.77703i) q^{4} +(0.674088 + 4.56031i) q^{6} +(-2.78918 + 1.30062i) q^{7} +(-7.92739 - 2.12414i) q^{8} +(0.166591 - 2.99537i) q^{9} +(-0.426793 - 0.508631i) q^{11} +(7.87366 + 3.94140i) q^{12} +(-0.384347 + 0.269123i) q^{13} +(-1.42232 + 8.06640i) q^{14} +(-8.94423 + 7.50510i) q^{16} +(-4.50051 + 1.20591i) q^{17} +(-6.27613 - 4.93586i) q^{18} +(-4.80938 + 2.77670i) q^{19} +(1.96154 - 4.95639i) q^{21} +(-1.76044 + 0.154018i) q^{22} +(-0.0280775 + 0.0602123i) q^{23} +(12.5032 - 6.76283i) q^{24} +1.24878i q^{26} +(3.35563 + 3.96733i) q^{27} +(11.0626 + 11.0626i) q^{28} +(-0.434735 - 2.46551i) q^{29} +(1.76652 - 0.642961i) q^{31} +(1.27781 + 14.6055i) q^{32} +(1.14243 + 0.132015i) q^{33} +(-4.24128 + 11.6528i) q^{34} +(-14.5986 + 4.41223i) q^{36} +(-0.656295 - 2.44933i) q^{37} +(-1.28820 + 14.7241i) q^{38} +(0.163296 - 0.796105i) q^{39} +(1.62695 + 0.286875i) q^{41} +(-7.81137 - 11.8428i) q^{42} +(-8.36925 - 0.732214i) q^{43} +(-1.68769 + 2.92316i) q^{44} +(0.0884111 + 0.153133i) q^{46} +(-1.73166 - 3.71355i) q^{47} +(2.32146 - 20.0895i) q^{48} +(1.58841 - 1.89299i) q^{49} +(4.22761 - 6.87413i) q^{51} +(1.95387 + 1.36812i) q^{52} +(7.52870 - 7.52870i) q^{53} +(13.7721 - 1.25944i) q^{54} +(24.8736 - 4.38589i) q^{56} +(2.74662 - 9.21828i) q^{57} +(-6.03890 - 2.81598i) q^{58} +(3.49452 + 2.93225i) q^{59} +(-5.84534 - 2.12753i) q^{61} +(1.29496 - 4.83286i) q^{62} +(3.43118 + 8.57130i) q^{63} +(13.5701 + 7.83468i) q^{64} +(2.03182 - 2.28917i) q^{66} +(-3.13881 - 4.48268i) q^{67} +(13.5857 + 19.4024i) q^{68} +(-0.0363384 - 0.109184i) q^{69} +(-5.33043 - 3.07752i) q^{71} +(-7.68321 + 23.3916i) q^{72} +(3.64803 - 13.6146i) q^{73} +(-6.34185 - 2.30824i) q^{74} +(21.6264 + 18.1467i) q^{76} +(1.85194 + 0.863572i) q^{77} +(-1.48637 - 1.57133i) q^{78} +(5.34198 - 0.941936i) q^{79} +(-8.94450 - 0.998001i) q^{81} +(3.10910 - 3.10910i) q^{82} +(-4.64599 - 3.25316i) q^{83} +(-27.0873 - 0.752663i) q^{84} +(-14.3727 + 17.1287i) q^{86} +(3.48160 + 2.58488i) q^{87} +(2.30295 + 4.93869i) q^{88} +(3.08131 + 5.33699i) q^{89} +(0.721988 - 1.25052i) q^{91} +(0.336454 + 0.0294359i) q^{92} +(-1.45751 + 2.91164i) q^{93} +(-10.7397 - 1.89370i) q^{94} +(-18.9921 - 16.8570i) q^{96} +(1.18828 - 13.5821i) q^{97} +(-1.70223 - 6.35281i) q^{98} +(-1.59464 + 1.19367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.52658 2.18018i 1.07945 1.54162i 0.262484 0.964936i \(-0.415458\pi\)
0.816969 0.576682i \(-0.195653\pi\)
\(3\) −1.25829 + 1.19025i −0.726474 + 0.687193i
\(4\) −1.73870 4.77703i −0.869348 2.38851i
\(5\) 0 0
\(6\) 0.674088 + 4.56031i 0.275195 + 1.86174i
\(7\) −2.78918 + 1.30062i −1.05421 + 0.491587i −0.870896 0.491468i \(-0.836461\pi\)
−0.183315 + 0.983054i \(0.558683\pi\)
\(8\) −7.92739 2.12414i −2.80276 0.750996i
\(9\) 0.166591 2.99537i 0.0555302 0.998457i
\(10\) 0 0
\(11\) −0.426793 0.508631i −0.128683 0.153358i 0.697856 0.716238i \(-0.254138\pi\)
−0.826538 + 0.562880i \(0.809693\pi\)
\(12\) 7.87366 + 3.94140i 2.27293 + 1.13778i
\(13\) −0.384347 + 0.269123i −0.106599 + 0.0746412i −0.625660 0.780096i \(-0.715170\pi\)
0.519062 + 0.854737i \(0.326282\pi\)
\(14\) −1.42232 + 8.06640i −0.380132 + 2.15584i
\(15\) 0 0
\(16\) −8.94423 + 7.50510i −2.23606 + 1.87627i
\(17\) −4.50051 + 1.20591i −1.09153 + 0.292476i −0.759313 0.650726i \(-0.774465\pi\)
−0.332221 + 0.943201i \(0.607798\pi\)
\(18\) −6.27613 4.93586i −1.47930 1.16339i
\(19\) −4.80938 + 2.77670i −1.10335 + 0.637018i −0.937098 0.349066i \(-0.886499\pi\)
−0.166249 + 0.986084i \(0.553166\pi\)
\(20\) 0 0
\(21\) 1.96154 4.95639i 0.428042 1.08157i
\(22\) −1.76044 + 0.154018i −0.375327 + 0.0328368i
\(23\) −0.0280775 + 0.0602123i −0.00585456 + 0.0125551i −0.909213 0.416331i \(-0.863316\pi\)
0.903359 + 0.428886i \(0.141094\pi\)
\(24\) 12.5032 6.76283i 2.55221 1.38046i
\(25\) 0 0
\(26\) 1.24878i 0.244906i
\(27\) 3.35563 + 3.96733i 0.645792 + 0.763513i
\(28\) 11.0626 + 11.0626i 2.09064 + 2.09064i
\(29\) −0.434735 2.46551i −0.0807283 0.457833i −0.998197 0.0600247i \(-0.980882\pi\)
0.917469 0.397808i \(-0.130229\pi\)
\(30\) 0 0
\(31\) 1.76652 0.642961i 0.317276 0.115479i −0.178473 0.983945i \(-0.557116\pi\)
0.495749 + 0.868466i \(0.334893\pi\)
\(32\) 1.27781 + 14.6055i 0.225888 + 2.58191i
\(33\) 1.14243 + 0.132015i 0.198871 + 0.0229808i
\(34\) −4.24128 + 11.6528i −0.727373 + 1.99844i
\(35\) 0 0
\(36\) −14.5986 + 4.41223i −2.43310 + 0.735372i
\(37\) −0.656295 2.44933i −0.107894 0.402667i 0.890763 0.454468i \(-0.150170\pi\)
−0.998657 + 0.0518010i \(0.983504\pi\)
\(38\) −1.28820 + 14.7241i −0.208973 + 2.38857i
\(39\) 0.163296 0.796105i 0.0261483 0.127479i
\(40\) 0 0
\(41\) 1.62695 + 0.286875i 0.254087 + 0.0448023i 0.299241 0.954178i \(-0.403267\pi\)
−0.0451539 + 0.998980i \(0.514378\pi\)
\(42\) −7.81137 11.8428i −1.20532 1.82738i
\(43\) −8.36925 0.732214i −1.27630 0.111662i −0.571224 0.820794i \(-0.693531\pi\)
−0.705075 + 0.709133i \(0.749087\pi\)
\(44\) −1.68769 + 2.92316i −0.254428 + 0.440682i
\(45\) 0 0
\(46\) 0.0884111 + 0.153133i 0.0130355 + 0.0225782i
\(47\) −1.73166 3.71355i −0.252588 0.541677i 0.738599 0.674145i \(-0.235488\pi\)
−0.991187 + 0.132468i \(0.957710\pi\)
\(48\) 2.32146 20.0895i 0.335075 2.89967i
\(49\) 1.58841 1.89299i 0.226916 0.270428i
\(50\) 0 0
\(51\) 4.22761 6.87413i 0.591984 0.962571i
\(52\) 1.95387 + 1.36812i 0.270953 + 0.189723i
\(53\) 7.52870 7.52870i 1.03415 1.03415i 0.0347509 0.999396i \(-0.488936\pi\)
0.999396 0.0347509i \(-0.0110638\pi\)
\(54\) 13.7721 1.25944i 1.87415 0.171388i
\(55\) 0 0
\(56\) 24.8736 4.38589i 3.32388 0.586089i
\(57\) 2.74662 9.21828i 0.363799 1.22099i
\(58\) −6.03890 2.81598i −0.792946 0.369757i
\(59\) 3.49452 + 2.93225i 0.454948 + 0.381747i 0.841268 0.540618i \(-0.181810\pi\)
−0.386320 + 0.922365i \(0.626254\pi\)
\(60\) 0 0
\(61\) −5.84534 2.12753i −0.748419 0.272402i −0.0604785 0.998169i \(-0.519263\pi\)
−0.687940 + 0.725767i \(0.741485\pi\)
\(62\) 1.29496 4.83286i 0.164460 0.613773i
\(63\) 3.43118 + 8.57130i 0.432288 + 1.07988i
\(64\) 13.5701 + 7.83468i 1.69626 + 0.979335i
\(65\) 0 0
\(66\) 2.03182 2.28917i 0.250100 0.281777i
\(67\) −3.13881 4.48268i −0.383466 0.547646i 0.580297 0.814405i \(-0.302936\pi\)
−0.963763 + 0.266758i \(0.914047\pi\)
\(68\) 13.5857 + 19.4024i 1.64751 + 2.35288i
\(69\) −0.0363384 0.109184i −0.00437462 0.0131442i
\(70\) 0 0
\(71\) −5.33043 3.07752i −0.632605 0.365235i 0.149155 0.988814i \(-0.452345\pi\)
−0.781760 + 0.623579i \(0.785678\pi\)
\(72\) −7.68321 + 23.3916i −0.905475 + 2.75673i
\(73\) 3.64803 13.6146i 0.426970 1.59347i −0.332613 0.943063i \(-0.607930\pi\)
0.759583 0.650410i \(-0.225403\pi\)
\(74\) −6.34185 2.30824i −0.737225 0.268328i
\(75\) 0 0
\(76\) 21.6264 + 18.1467i 2.48072 + 2.08157i
\(77\) 1.85194 + 0.863572i 0.211048 + 0.0984131i
\(78\) −1.48637 1.57133i −0.168298 0.177918i
\(79\) 5.34198 0.941936i 0.601020 0.105976i 0.135144 0.990826i \(-0.456850\pi\)
0.465876 + 0.884850i \(0.345739\pi\)
\(80\) 0 0
\(81\) −8.94450 0.998001i −0.993833 0.110889i
\(82\) 3.10910 3.10910i 0.343343 0.343343i
\(83\) −4.64599 3.25316i −0.509964 0.357081i 0.290099 0.956997i \(-0.406312\pi\)
−0.800063 + 0.599916i \(0.795201\pi\)
\(84\) −27.0873 0.752663i −2.95547 0.0821222i
\(85\) 0 0
\(86\) −14.3727 + 17.1287i −1.54984 + 1.84703i
\(87\) 3.48160 + 2.58488i 0.373267 + 0.277128i
\(88\) 2.30295 + 4.93869i 0.245495 + 0.526466i
\(89\) 3.08131 + 5.33699i 0.326619 + 0.565720i 0.981839 0.189718i \(-0.0607574\pi\)
−0.655220 + 0.755438i \(0.727424\pi\)
\(90\) 0 0
\(91\) 0.721988 1.25052i 0.0756849 0.131090i
\(92\) 0.336454 + 0.0294359i 0.0350778 + 0.00306891i
\(93\) −1.45751 + 2.91164i −0.151137 + 0.301923i
\(94\) −10.7397 1.89370i −1.10772 0.195320i
\(95\) 0 0
\(96\) −18.9921 16.8570i −1.93837 1.72046i
\(97\) 1.18828 13.5821i 0.120652 1.37906i −0.658669 0.752433i \(-0.728880\pi\)
0.779321 0.626625i \(-0.215564\pi\)
\(98\) −1.70223 6.35281i −0.171951 0.641731i
\(99\) −1.59464 + 1.19367i −0.160267 + 0.119968i
\(100\) 0 0
\(101\) −0.629841 + 1.73048i −0.0626716 + 0.172189i −0.967076 0.254487i \(-0.918093\pi\)
0.904405 + 0.426676i \(0.140316\pi\)
\(102\) −8.53305 19.7108i −0.844898 1.95166i
\(103\) 1.42347 + 16.2704i 0.140259 + 1.60317i 0.661627 + 0.749833i \(0.269866\pi\)
−0.521368 + 0.853332i \(0.674578\pi\)
\(104\) 3.61852 1.31704i 0.354826 0.129146i
\(105\) 0 0
\(106\) −4.92077 27.9071i −0.477947 2.71057i
\(107\) 10.4880 + 10.4880i 1.01391 + 1.01391i 0.999902 + 0.0140087i \(0.00445924\pi\)
0.0140087 + 0.999902i \(0.495541\pi\)
\(108\) 13.1176 22.9279i 1.26225 2.20624i
\(109\) 9.34913i 0.895484i −0.894163 0.447742i \(-0.852228\pi\)
0.894163 0.447742i \(-0.147772\pi\)
\(110\) 0 0
\(111\) 3.74113 + 2.30081i 0.355092 + 0.218383i
\(112\) 15.1858 32.5661i 1.43492 3.07721i
\(113\) −20.6993 + 1.81095i −1.94722 + 0.170360i −0.992064 0.125734i \(-0.959871\pi\)
−0.955159 + 0.296094i \(0.904316\pi\)
\(114\) −15.9045 20.0605i −1.48960 1.87884i
\(115\) 0 0
\(116\) −11.0219 + 6.36351i −1.02336 + 0.590837i
\(117\) 0.742094 + 1.19610i 0.0686066 + 0.110579i
\(118\) 11.7275 3.14237i 1.07960 0.289278i
\(119\) 10.9843 9.21693i 1.00693 0.844915i
\(120\) 0 0
\(121\) 1.83358 10.3987i 0.166689 0.945339i
\(122\) −13.5617 + 9.49604i −1.22782 + 0.859731i
\(123\) −2.38863 + 1.57551i −0.215375 + 0.142059i
\(124\) −6.14289 7.32081i −0.551648 0.657428i
\(125\) 0 0
\(126\) 23.9249 + 5.60417i 2.13140 + 0.499259i
\(127\) −7.35416 1.97054i −0.652576 0.174857i −0.0826829 0.996576i \(-0.526349\pi\)
−0.569893 + 0.821719i \(0.693016\pi\)
\(128\) 11.2214 5.23265i 0.991845 0.462505i
\(129\) 11.4025 9.04019i 1.00393 0.795945i
\(130\) 0 0
\(131\) 4.01388 + 11.0280i 0.350694 + 0.963524i 0.982148 + 0.188111i \(0.0602363\pi\)
−0.631454 + 0.775414i \(0.717541\pi\)
\(132\) −1.35570 5.68695i −0.117999 0.494986i
\(133\) 9.80281 13.9999i 0.850012 1.21394i
\(134\) −14.5647 −1.25820
\(135\) 0 0
\(136\) 38.2388 3.27895
\(137\) −3.85643 + 5.50755i −0.329477 + 0.470542i −0.949377 0.314139i \(-0.898284\pi\)
0.619900 + 0.784681i \(0.287173\pi\)
\(138\) −0.293514 0.0874536i −0.0249855 0.00744454i
\(139\) 0.519349 + 1.42690i 0.0440506 + 0.121028i 0.959767 0.280796i \(-0.0905985\pi\)
−0.915717 + 0.401824i \(0.868376\pi\)
\(140\) 0 0
\(141\) 6.59899 + 2.61161i 0.555735 + 0.219937i
\(142\) −14.8468 + 6.92320i −1.24592 + 0.580982i
\(143\) 0.300921 + 0.0806315i 0.0251643 + 0.00674274i
\(144\) 20.9905 + 28.0416i 1.74921 + 2.33680i
\(145\) 0 0
\(146\) −24.1133 28.7372i −1.99563 2.37830i
\(147\) 0.254462 + 4.27255i 0.0209876 + 0.352394i
\(148\) −10.5594 + 7.39377i −0.867978 + 0.607764i
\(149\) −3.69731 + 20.9685i −0.302895 + 1.71780i 0.330355 + 0.943857i \(0.392832\pi\)
−0.633250 + 0.773947i \(0.718280\pi\)
\(150\) 0 0
\(151\) 6.08208 5.10347i 0.494952 0.415314i −0.360845 0.932626i \(-0.617512\pi\)
0.855797 + 0.517312i \(0.173067\pi\)
\(152\) 44.0239 11.7962i 3.57081 0.956797i
\(153\) 2.86240 + 13.6816i 0.231411 + 1.10609i
\(154\) 4.70986 2.71924i 0.379531 0.219123i
\(155\) 0 0
\(156\) −4.08694 + 0.604116i −0.327217 + 0.0483680i
\(157\) 13.6200 1.19160i 1.08699 0.0950997i 0.470455 0.882424i \(-0.344090\pi\)
0.616539 + 0.787324i \(0.288534\pi\)
\(158\) 6.10136 13.0844i 0.485398 1.04094i
\(159\) −0.512227 + 18.4344i −0.0406223 + 1.46194i
\(160\) 0 0
\(161\) 0.204461i 0.0161138i
\(162\) −15.8303 + 17.9771i −1.24374 + 1.41241i
\(163\) −13.8462 13.8462i −1.08452 1.08452i −0.996082 0.0884330i \(-0.971814\pi\)
−0.0884330 0.996082i \(-0.528186\pi\)
\(164\) −1.45836 8.27077i −0.113879 0.645839i
\(165\) 0 0
\(166\) −14.1849 + 5.16289i −1.10096 + 0.400718i
\(167\) 1.91506 + 21.8892i 0.148192 + 1.69384i 0.598627 + 0.801028i \(0.295713\pi\)
−0.450435 + 0.892809i \(0.648731\pi\)
\(168\) −26.0779 + 35.1246i −2.01195 + 2.70992i
\(169\) −4.37097 + 12.0091i −0.336228 + 0.923779i
\(170\) 0 0
\(171\) 7.51604 + 14.8685i 0.574766 + 1.13702i
\(172\) 11.0538 + 41.2533i 0.842842 + 3.14553i
\(173\) 0.327061 3.73833i 0.0248660 0.284220i −0.973573 0.228374i \(-0.926659\pi\)
0.998439 0.0558456i \(-0.0177854\pi\)
\(174\) 10.9504 3.64450i 0.830149 0.276288i
\(175\) 0 0
\(176\) 7.63466 + 1.34620i 0.575484 + 0.101473i
\(177\) −7.88725 + 0.469743i −0.592842 + 0.0353081i
\(178\) 16.3394 + 1.42952i 1.22469 + 0.107147i
\(179\) 7.21345 12.4941i 0.539158 0.933850i −0.459791 0.888027i \(-0.652076\pi\)
0.998950 0.0458226i \(-0.0145909\pi\)
\(180\) 0 0
\(181\) −7.06370 12.2347i −0.525041 0.909397i −0.999575 0.0291599i \(-0.990717\pi\)
0.474534 0.880237i \(-0.342617\pi\)
\(182\) −1.62419 3.48308i −0.120393 0.258183i
\(183\) 9.88743 4.28039i 0.730900 0.316415i
\(184\) 0.350480 0.417686i 0.0258378 0.0307922i
\(185\) 0 0
\(186\) 4.12289 + 7.62247i 0.302305 + 0.558907i
\(187\) 2.53415 + 1.77443i 0.185315 + 0.129759i
\(188\) −14.7289 + 14.7289i −1.07422 + 1.07422i
\(189\) −14.5194 6.70121i −1.05613 0.487442i
\(190\) 0 0
\(191\) −2.54718 + 0.449136i −0.184307 + 0.0324983i −0.265040 0.964237i \(-0.585385\pi\)
0.0807326 + 0.996736i \(0.474274\pi\)
\(192\) −26.4003 + 6.29352i −1.90528 + 0.454195i
\(193\) 12.9195 + 6.02445i 0.929963 + 0.433649i 0.827740 0.561112i \(-0.189626\pi\)
0.102224 + 0.994761i \(0.467404\pi\)
\(194\) −27.7975 23.3248i −1.99574 1.67463i
\(195\) 0 0
\(196\) −11.8046 4.29654i −0.843189 0.306896i
\(197\) 2.16013 8.06170i 0.153903 0.574372i −0.845294 0.534301i \(-0.820575\pi\)
0.999197 0.0400711i \(-0.0127585\pi\)
\(198\) 0.168070 + 5.29882i 0.0119442 + 0.376571i
\(199\) −3.27312 1.88973i −0.232025 0.133960i 0.379481 0.925200i \(-0.376103\pi\)
−0.611506 + 0.791240i \(0.709436\pi\)
\(200\) 0 0
\(201\) 9.28506 + 1.90454i 0.654917 + 0.134336i
\(202\) 2.81124 + 4.01487i 0.197798 + 0.282485i
\(203\) 4.41923 + 6.31132i 0.310169 + 0.442968i
\(204\) −40.1885 8.24340i −2.81376 0.577153i
\(205\) 0 0
\(206\) 37.6453 + 21.7345i 2.62287 + 1.51432i
\(207\) 0.175681 + 0.0941332i 0.0122107 + 0.00654271i
\(208\) 1.41790 5.29166i 0.0983134 0.366911i
\(209\) 3.46492 + 1.26113i 0.239674 + 0.0872341i
\(210\) 0 0
\(211\) −13.6392 11.4447i −0.938964 0.787885i 0.0384403 0.999261i \(-0.487761\pi\)
−0.977405 + 0.211376i \(0.932205\pi\)
\(212\) −49.0550 22.8747i −3.36911 1.57104i
\(213\) 10.3703 2.47214i 0.710558 0.169388i
\(214\) 38.8763 6.85495i 2.65753 0.468594i
\(215\) 0 0
\(216\) −18.1743 38.5784i −1.23660 2.62493i
\(217\) −4.09090 + 4.09090i −0.277708 + 0.277708i
\(218\) −20.3828 14.2722i −1.38049 0.966633i
\(219\) 11.6146 + 21.4733i 0.784842 + 1.45103i
\(220\) 0 0
\(221\) 1.40522 1.67468i 0.0945254 0.112651i
\(222\) 10.7273 4.64397i 0.719968 0.311683i
\(223\) 8.09113 + 17.3515i 0.541822 + 1.16194i 0.966516 + 0.256605i \(0.0826039\pi\)
−0.424694 + 0.905337i \(0.639618\pi\)
\(224\) −22.5602 39.0754i −1.50737 2.61083i
\(225\) 0 0
\(226\) −27.6508 + 47.8926i −1.83930 + 3.18577i
\(227\) −0.480953 0.0420779i −0.0319220 0.00279281i 0.0711836 0.997463i \(-0.477322\pi\)
−0.103106 + 0.994670i \(0.532878\pi\)
\(228\) −48.8115 + 2.90709i −3.23262 + 0.192526i
\(229\) −14.7979 2.60927i −0.977875 0.172426i −0.338203 0.941073i \(-0.609819\pi\)
−0.639672 + 0.768648i \(0.720930\pi\)
\(230\) 0 0
\(231\) −3.35814 + 1.11765i −0.220950 + 0.0735359i
\(232\) −1.79076 + 20.4685i −0.117569 + 1.34382i
\(233\) 0.143242 + 0.534587i 0.00938411 + 0.0350220i 0.970459 0.241266i \(-0.0775625\pi\)
−0.961075 + 0.276287i \(0.910896\pi\)
\(234\) 3.74056 + 0.208035i 0.244528 + 0.0135997i
\(235\) 0 0
\(236\) 7.93154 21.7917i 0.516299 1.41852i
\(237\) −5.60062 + 7.54355i −0.363800 + 0.490006i
\(238\) −3.32615 38.0181i −0.215602 2.46435i
\(239\) 5.32354 1.93761i 0.344351 0.125334i −0.164054 0.986451i \(-0.552457\pi\)
0.508406 + 0.861118i \(0.330235\pi\)
\(240\) 0 0
\(241\) 0.317967 + 1.80328i 0.0204821 + 0.116160i 0.993335 0.115266i \(-0.0367721\pi\)
−0.972853 + 0.231426i \(0.925661\pi\)
\(242\) −19.8720 19.8720i −1.27742 1.27742i
\(243\) 12.4426 9.39045i 0.798196 0.602397i
\(244\) 31.6225i 2.02442i
\(245\) 0 0
\(246\) −0.211532 + 7.61277i −0.0134868 + 0.485372i
\(247\) 1.10120 2.36153i 0.0700677 0.150261i
\(248\) −15.3696 + 1.34467i −0.975973 + 0.0853866i
\(249\) 9.71810 1.43649i 0.615859 0.0910340i
\(250\) 0 0
\(251\) −16.8470 + 9.72663i −1.06337 + 0.613939i −0.926364 0.376630i \(-0.877083\pi\)
−0.137011 + 0.990570i \(0.543749\pi\)
\(252\) 34.9796 31.2937i 2.20351 1.97132i
\(253\) 0.0426091 0.0114171i 0.00267881 0.000717786i
\(254\) −15.5228 + 13.0252i −0.973988 + 0.817273i
\(255\) 0 0
\(256\) 0.280392 1.59018i 0.0175245 0.0993864i
\(257\) 24.5109 17.1627i 1.52895 1.07058i 0.558428 0.829553i \(-0.311405\pi\)
0.970518 0.241027i \(-0.0774842\pi\)
\(258\) −2.30248 38.6600i −0.143346 2.40686i
\(259\) 5.01616 + 5.97802i 0.311689 + 0.371456i
\(260\) 0 0
\(261\) −7.45753 + 0.891463i −0.461609 + 0.0551802i
\(262\) 30.1706 + 8.08418i 1.86394 + 0.499442i
\(263\) −7.60797 + 3.54766i −0.469128 + 0.218758i −0.642782 0.766049i \(-0.722220\pi\)
0.173655 + 0.984807i \(0.444442\pi\)
\(264\) −8.77607 3.47321i −0.540130 0.213761i
\(265\) 0 0
\(266\) −15.5574 42.7437i −0.953888 2.62079i
\(267\) −10.2296 3.04794i −0.626039 0.186531i
\(268\) −15.9565 + 22.7882i −0.974696 + 1.39201i
\(269\) 2.21545 0.135079 0.0675393 0.997717i \(-0.478485\pi\)
0.0675393 + 0.997717i \(0.478485\pi\)
\(270\) 0 0
\(271\) −5.87725 −0.357017 −0.178509 0.983938i \(-0.557127\pi\)
−0.178509 + 0.983938i \(0.557127\pi\)
\(272\) 31.2031 44.5627i 1.89197 2.70201i
\(273\) 0.579966 + 2.43287i 0.0351011 + 0.147244i
\(274\) 6.12031 + 16.8154i 0.369741 + 1.01586i
\(275\) 0 0
\(276\) −0.458394 + 0.363427i −0.0275920 + 0.0218757i
\(277\) −10.2541 + 4.78156i −0.616108 + 0.287296i −0.705510 0.708700i \(-0.749282\pi\)
0.0894020 + 0.995996i \(0.471504\pi\)
\(278\) 3.90372 + 1.04600i 0.234130 + 0.0627348i
\(279\) −1.63162 5.39850i −0.0976826 0.323199i
\(280\) 0 0
\(281\) 13.9719 + 16.6511i 0.833496 + 0.993322i 0.999974 + 0.00727642i \(0.00231618\pi\)
−0.166478 + 0.986045i \(0.553239\pi\)
\(282\) 15.7676 10.4001i 0.938950 0.619320i
\(283\) −10.7514 + 7.52820i −0.639103 + 0.447505i −0.847685 0.530500i \(-0.822004\pi\)
0.208582 + 0.978005i \(0.433115\pi\)
\(284\) −5.43342 + 30.8145i −0.322414 + 1.82850i
\(285\) 0 0
\(286\) 0.635170 0.532971i 0.0375584 0.0315152i
\(287\) −4.91097 + 1.31589i −0.289885 + 0.0776745i
\(288\) 43.9617 1.39439i 2.59047 0.0821654i
\(289\) 4.07794 2.35440i 0.239879 0.138494i
\(290\) 0 0
\(291\) 14.6710 + 18.5046i 0.860029 + 1.08476i
\(292\) −71.3804 + 6.24497i −4.17722 + 0.365460i
\(293\) −1.80181 + 3.86399i −0.105263 + 0.225736i −0.951884 0.306460i \(-0.900855\pi\)
0.846621 + 0.532196i \(0.178633\pi\)
\(294\) 9.70336 + 5.96760i 0.565912 + 0.348037i
\(295\) 0 0
\(296\) 20.8108i 1.20960i
\(297\) 0.585751 3.40001i 0.0339887 0.197288i
\(298\) 40.0708 + 40.0708i 2.32124 + 2.32124i
\(299\) −0.00541301 0.0306987i −0.000313043 0.00177535i
\(300\) 0 0
\(301\) 24.2957 8.84290i 1.40038 0.509696i
\(302\) −1.84171 21.0508i −0.105978 1.21134i
\(303\) −1.26718 2.92711i −0.0727977 0.168158i
\(304\) 22.1768 60.9303i 1.27193 3.49459i
\(305\) 0 0
\(306\) 34.1980 + 14.6455i 1.95497 + 0.837225i
\(307\) 4.82189 + 17.9955i 0.275200 + 1.02706i 0.955707 + 0.294318i \(0.0950926\pi\)
−0.680508 + 0.732741i \(0.738241\pi\)
\(308\) 0.905354 10.3482i 0.0515873 0.589646i
\(309\) −21.1570 18.7785i −1.20358 1.06827i
\(310\) 0 0
\(311\) −8.07539 1.42391i −0.457913 0.0807425i −0.0600667 0.998194i \(-0.519131\pi\)
−0.397847 + 0.917452i \(0.630242\pi\)
\(312\) −2.98555 + 5.96418i −0.169023 + 0.337655i
\(313\) 18.9940 + 1.66176i 1.07360 + 0.0939283i 0.610222 0.792230i \(-0.291080\pi\)
0.463382 + 0.886158i \(0.346636\pi\)
\(314\) 18.1941 31.5131i 1.02675 1.77839i
\(315\) 0 0
\(316\) −13.7877 23.8811i −0.775621 1.34342i
\(317\) 7.17642 + 15.3899i 0.403068 + 0.864382i 0.998155 + 0.0607206i \(0.0193399\pi\)
−0.595087 + 0.803661i \(0.702882\pi\)
\(318\) 39.4082 + 29.2582i 2.20990 + 1.64072i
\(319\) −1.06849 + 1.27338i −0.0598241 + 0.0712956i
\(320\) 0 0
\(321\) −25.6803 0.713566i −1.43333 0.0398274i
\(322\) −0.445761 0.312125i −0.0248413 0.0173941i
\(323\) 18.2962 18.2962i 1.01803 1.01803i
\(324\) 10.7843 + 44.4633i 0.599127 + 2.47019i
\(325\) 0 0
\(326\) −51.3243 + 9.04986i −2.84259 + 0.501225i
\(327\) 11.1278 + 11.7639i 0.615371 + 0.650546i
\(328\) −12.2881 5.73003i −0.678497 0.316388i
\(329\) 9.65980 + 8.10554i 0.532562 + 0.446873i
\(330\) 0 0
\(331\) 13.3657 + 4.86470i 0.734643 + 0.267388i 0.682129 0.731232i \(-0.261054\pi\)
0.0525142 + 0.998620i \(0.483277\pi\)
\(332\) −7.46247 + 27.8503i −0.409556 + 1.52848i
\(333\) −7.44597 + 1.55781i −0.408037 + 0.0853676i
\(334\) 50.6458 + 29.2404i 2.77122 + 1.59996i
\(335\) 0 0
\(336\) 19.6537 + 59.0526i 1.07220 + 3.22158i
\(337\) 3.90887 + 5.58245i 0.212930 + 0.304095i 0.911382 0.411561i \(-0.135016\pi\)
−0.698452 + 0.715657i \(0.746128\pi\)
\(338\) 19.5094 + 27.8623i 1.06117 + 1.51551i
\(339\) 23.8902 26.9161i 1.29754 1.46188i
\(340\) 0 0
\(341\) −1.08097 0.624097i −0.0585377 0.0337968i
\(342\) 43.8897 + 6.31153i 2.37328 + 0.341288i
\(343\) 3.60734 13.4628i 0.194778 0.726922i
\(344\) 64.7910 + 23.5820i 3.49330 + 1.27146i
\(345\) 0 0
\(346\) −7.65094 6.41990i −0.411317 0.345136i
\(347\) 12.4642 + 5.81216i 0.669114 + 0.312013i 0.727327 0.686291i \(-0.240762\pi\)
−0.0582130 + 0.998304i \(0.518540\pi\)
\(348\) 6.29459 21.1260i 0.337425 1.13247i
\(349\) −26.3484 + 4.64594i −1.41040 + 0.248691i −0.826409 0.563070i \(-0.809620\pi\)
−0.583990 + 0.811761i \(0.698509\pi\)
\(350\) 0 0
\(351\) −2.35743 0.621756i −0.125830 0.0331869i
\(352\) 6.88345 6.88345i 0.366889 0.366889i
\(353\) 0.0387563 + 0.0271374i 0.00206279 + 0.00144438i 0.574607 0.818429i \(-0.305155\pi\)
−0.572545 + 0.819874i \(0.694044\pi\)
\(354\) −11.0164 + 17.9127i −0.585513 + 0.952049i
\(355\) 0 0
\(356\) 20.1375 23.9989i 1.06729 1.27194i
\(357\) −2.85097 + 24.6717i −0.150889 + 1.30576i
\(358\) −16.2274 34.7997i −0.857644 1.83922i
\(359\) 9.42597 + 16.3263i 0.497484 + 0.861667i 0.999996 0.00290290i \(-0.000924023\pi\)
−0.502512 + 0.864570i \(0.667591\pi\)
\(360\) 0 0
\(361\) 5.92010 10.2539i 0.311584 0.539680i
\(362\) −37.4571 3.27707i −1.96870 0.172239i
\(363\) 10.0700 + 15.2670i 0.528535 + 0.801312i
\(364\) −7.22909 1.27468i −0.378907 0.0668116i
\(365\) 0 0
\(366\) 5.76192 28.0907i 0.301180 1.46832i
\(367\) 1.72794 19.7504i 0.0901977 1.03096i −0.807357 0.590063i \(-0.799103\pi\)
0.897555 0.440902i \(-0.145341\pi\)
\(368\) −0.200768 0.749277i −0.0104658 0.0390588i
\(369\) 1.13033 4.82552i 0.0588427 0.251207i
\(370\) 0 0
\(371\) −11.2070 + 30.7909i −0.581836 + 1.59858i
\(372\) 16.4432 + 1.90011i 0.852538 + 0.0985160i
\(373\) −1.84840 21.1273i −0.0957063 1.09393i −0.880460 0.474120i \(-0.842766\pi\)
0.784754 0.619808i \(-0.212789\pi\)
\(374\) 7.73714 2.81609i 0.400078 0.145616i
\(375\) 0 0
\(376\) 5.83943 + 33.1170i 0.301145 + 1.70788i
\(377\) 0.830613 + 0.830613i 0.0427788 + 0.0427788i
\(378\) −36.7749 + 21.4250i −1.89150 + 1.10199i
\(379\) 4.95221i 0.254378i −0.991878 0.127189i \(-0.959405\pi\)
0.991878 0.127189i \(-0.0405955\pi\)
\(380\) 0 0
\(381\) 11.5991 6.27381i 0.594241 0.321417i
\(382\) −2.90926 + 6.23894i −0.148851 + 0.319212i
\(383\) 28.1753 2.46502i 1.43969 0.125957i 0.659596 0.751620i \(-0.270727\pi\)
0.780093 + 0.625663i \(0.215172\pi\)
\(384\) −7.89166 + 19.9406i −0.402720 + 1.01759i
\(385\) 0 0
\(386\) 32.8569 18.9699i 1.67237 0.965545i
\(387\) −3.58749 + 24.9470i −0.182362 + 1.26813i
\(388\) −66.9484 + 17.9388i −3.39879 + 0.910703i
\(389\) −22.5434 + 18.9162i −1.14300 + 0.959088i −0.999533 0.0305681i \(-0.990268\pi\)
−0.143463 + 0.989656i \(0.545824\pi\)
\(390\) 0 0
\(391\) 0.0537524 0.304845i 0.00271838 0.0154167i
\(392\) −16.6129 + 11.6325i −0.839080 + 0.587530i
\(393\) −18.1768 9.09894i −0.916898 0.458981i
\(394\) −14.2783 17.0163i −0.719332 0.857267i
\(395\) 0 0
\(396\) 8.47479 + 5.54221i 0.425874 + 0.278507i
\(397\) −18.9334 5.07320i −0.950242 0.254616i −0.249777 0.968303i \(-0.580357\pi\)
−0.700465 + 0.713687i \(0.747024\pi\)
\(398\) −9.11662 + 4.25115i −0.456975 + 0.213091i
\(399\) 4.32861 + 29.2837i 0.216702 + 1.46602i
\(400\) 0 0
\(401\) −0.0115561 0.0317502i −0.000577086 0.00158553i 0.939404 0.342813i \(-0.111380\pi\)
−0.939981 + 0.341227i \(0.889157\pi\)
\(402\) 18.3266 17.3356i 0.914047 0.864624i
\(403\) −0.505922 + 0.722531i −0.0252018 + 0.0359918i
\(404\) 9.36163 0.465759
\(405\) 0 0
\(406\) 20.5061 1.01770
\(407\) −0.965702 + 1.37917i −0.0478681 + 0.0683627i
\(408\) −48.1156 + 45.5139i −2.38207 + 2.25327i
\(409\) −3.01485 8.28322i −0.149075 0.409579i 0.842569 0.538589i \(-0.181042\pi\)
−0.991643 + 0.129010i \(0.958820\pi\)
\(410\) 0 0
\(411\) −1.70288 11.5202i −0.0839967 0.568251i
\(412\) 75.2490 35.0892i 3.70725 1.72872i
\(413\) −13.5606 3.63355i −0.667272 0.178795i
\(414\) 0.473417 0.239314i 0.0232672 0.0117616i
\(415\) 0 0
\(416\) −4.42180 5.26969i −0.216796 0.258368i
\(417\) −2.35187 1.17730i −0.115171 0.0576525i
\(418\) 8.03896 5.62894i 0.393198 0.275320i
\(419\) 5.75122 32.6168i 0.280966 1.59344i −0.438384 0.898788i \(-0.644449\pi\)
0.719350 0.694648i \(-0.244440\pi\)
\(420\) 0 0
\(421\) 12.7180 10.6716i 0.619835 0.520104i −0.277916 0.960605i \(-0.589644\pi\)
0.897752 + 0.440502i \(0.145199\pi\)
\(422\) −45.7728 + 12.2648i −2.22819 + 0.597040i
\(423\) −11.4119 + 4.56831i −0.554867 + 0.222119i
\(424\) −75.6750 + 43.6910i −3.67510 + 2.12182i
\(425\) 0 0
\(426\) 10.4413 26.3829i 0.505882 1.27826i
\(427\) 19.0708 1.66848i 0.922901 0.0807433i
\(428\) 31.8660 68.3368i 1.54030 3.30318i
\(429\) −0.474618 + 0.256714i −0.0229148 + 0.0123943i
\(430\) 0 0
\(431\) 14.4385i 0.695480i −0.937591 0.347740i \(-0.886949\pi\)
0.937591 0.347740i \(-0.113051\pi\)
\(432\) −59.7888 10.3004i −2.87659 0.495577i
\(433\) −16.4822 16.4822i −0.792085 0.792085i 0.189748 0.981833i \(-0.439233\pi\)
−0.981833 + 0.189748i \(0.939233\pi\)
\(434\) 2.67381 + 15.1640i 0.128347 + 0.727893i
\(435\) 0 0
\(436\) −44.6611 + 16.2553i −2.13888 + 0.778488i
\(437\) −0.0321562 0.367547i −0.00153824 0.0175821i
\(438\) 64.5461 + 7.45870i 3.08413 + 0.356390i
\(439\) 10.9388 30.0541i 0.522080 1.43440i −0.346121 0.938190i \(-0.612501\pi\)
0.868201 0.496213i \(-0.165277\pi\)
\(440\) 0 0
\(441\) −5.40560 5.07323i −0.257410 0.241582i
\(442\) −1.50592 5.62015i −0.0716291 0.267323i
\(443\) 1.56526 17.8910i 0.0743677 0.850027i −0.863798 0.503839i \(-0.831920\pi\)
0.938165 0.346188i \(-0.112524\pi\)
\(444\) 4.48633 21.8719i 0.212912 1.03799i
\(445\) 0 0
\(446\) 50.1811 + 8.84827i 2.37614 + 0.418978i
\(447\) −20.3055 30.7852i −0.960418 1.45609i
\(448\) −48.0392 4.20289i −2.26964 0.198568i
\(449\) 6.63475 11.4917i 0.313113 0.542328i −0.665921 0.746022i \(-0.731961\pi\)
0.979035 + 0.203694i \(0.0652947\pi\)
\(450\) 0 0
\(451\) −0.548456 0.949953i −0.0258258 0.0447316i
\(452\) 44.6407 + 95.7323i 2.09972 + 4.50287i
\(453\) −1.57860 + 13.6609i −0.0741689 + 0.641843i
\(454\) −0.825948 + 0.984327i −0.0387637 + 0.0461968i
\(455\) 0 0
\(456\) −41.3545 + 67.2427i −1.93660 + 3.14893i
\(457\) −6.59496 4.61784i −0.308499 0.216013i 0.409066 0.912505i \(-0.365855\pi\)
−0.717565 + 0.696491i \(0.754743\pi\)
\(458\) −28.2789 + 28.2789i −1.32138 + 1.32138i
\(459\) −19.8863 13.8084i −0.928213 0.644522i
\(460\) 0 0
\(461\) −14.1578 + 2.49640i −0.659393 + 0.116269i −0.493324 0.869846i \(-0.664218\pi\)
−0.166068 + 0.986114i \(0.553107\pi\)
\(462\) −2.68979 + 9.02752i −0.125140 + 0.419998i
\(463\) −18.8558 8.79261i −0.876304 0.408627i −0.0682032 0.997671i \(-0.521727\pi\)
−0.808101 + 0.589044i \(0.799504\pi\)
\(464\) 22.3922 + 18.7893i 1.03953 + 0.872272i
\(465\) 0 0
\(466\) 1.38417 + 0.503795i 0.0641202 + 0.0233378i
\(467\) 6.38314 23.8222i 0.295376 1.10236i −0.645542 0.763725i \(-0.723368\pi\)
0.940918 0.338635i \(-0.109965\pi\)
\(468\) 4.42351 5.62465i 0.204477 0.260000i
\(469\) 14.5849 + 8.42062i 0.673470 + 0.388828i
\(470\) 0 0
\(471\) −15.7196 + 17.7106i −0.724322 + 0.816063i
\(472\) −21.4739 30.6679i −0.988418 1.41161i
\(473\) 3.19951 + 4.56937i 0.147113 + 0.210100i
\(474\) 7.89648 + 23.7262i 0.362698 + 1.08978i
\(475\) 0 0
\(476\) −63.1279 36.4469i −2.89346 1.67054i
\(477\) −21.2970 23.8055i −0.975125 1.08998i
\(478\) 3.90246 14.5642i 0.178494 0.666150i
\(479\) −25.2593 9.19362i −1.15412 0.420067i −0.307130 0.951668i \(-0.599368\pi\)
−0.846995 + 0.531601i \(0.821591\pi\)
\(480\) 0 0
\(481\) 0.911414 + 0.764768i 0.0415569 + 0.0348704i
\(482\) 4.41687 + 2.05962i 0.201183 + 0.0938132i
\(483\) 0.243361 + 0.257271i 0.0110733 + 0.0117063i
\(484\) −52.8631 + 9.32118i −2.40287 + 0.423690i
\(485\) 0 0
\(486\) −1.47818 41.4624i −0.0670516 1.88077i
\(487\) −1.39406 + 1.39406i −0.0631711 + 0.0631711i −0.737987 0.674815i \(-0.764223\pi\)
0.674815 + 0.737987i \(0.264223\pi\)
\(488\) 41.8191 + 29.2821i 1.89306 + 1.32554i
\(489\) 33.9029 + 0.942045i 1.53314 + 0.0426008i
\(490\) 0 0
\(491\) −15.2423 + 18.1651i −0.687875 + 0.819777i −0.991097 0.133143i \(-0.957493\pi\)
0.303222 + 0.952920i \(0.401938\pi\)
\(492\) 11.6794 + 8.67121i 0.526546 + 0.390928i
\(493\) 4.92970 + 10.5718i 0.222023 + 0.476129i
\(494\) −3.46749 6.00587i −0.156010 0.270217i
\(495\) 0 0
\(496\) −10.9747 + 19.0087i −0.492778 + 0.853516i
\(497\) 18.8702 + 1.65093i 0.846444 + 0.0740542i
\(498\) 11.7036 23.3801i 0.524451 1.04769i
\(499\) −30.8900 5.44673i −1.38282 0.243829i −0.567758 0.823196i \(-0.692189\pi\)
−0.815067 + 0.579366i \(0.803300\pi\)
\(500\) 0 0
\(501\) −28.4634 25.2636i −1.27165 1.12869i
\(502\) −4.51248 + 51.5779i −0.201402 + 2.30204i
\(503\) 1.59547 + 5.95437i 0.0711385 + 0.265492i 0.992330 0.123617i \(-0.0394495\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(504\) −8.99365 75.2363i −0.400609 3.35129i
\(505\) 0 0
\(506\) 0.0401548 0.110325i 0.00178510 0.00490452i
\(507\) −8.79397 20.3135i −0.390554 0.902156i
\(508\) 3.37332 + 38.5572i 0.149667 + 1.71070i
\(509\) −18.3832 + 6.69092i −0.814819 + 0.296570i −0.715613 0.698497i \(-0.753853\pi\)
−0.0992061 + 0.995067i \(0.531630\pi\)
\(510\) 0 0
\(511\) 7.53240 + 42.7184i 0.333214 + 1.88975i
\(512\) 14.4712 + 14.4712i 0.639545 + 0.639545i
\(513\) −27.1546 9.76284i −1.19890 0.431040i
\(514\) 79.6382i 3.51269i
\(515\) 0 0
\(516\) −63.0107 38.7518i −2.77389 1.70595i
\(517\) −1.14977 + 2.46569i −0.0505668 + 0.108441i
\(518\) 20.6907 1.81020i 0.909097 0.0795357i
\(519\) 4.03802 + 5.09319i 0.177250 + 0.223566i
\(520\) 0 0
\(521\) 1.02507 0.591824i 0.0449091 0.0259283i −0.477377 0.878698i \(-0.658413\pi\)
0.522286 + 0.852770i \(0.325079\pi\)
\(522\) −9.44094 + 17.6196i −0.413219 + 0.771190i
\(523\) −43.1925 + 11.5734i −1.88868 + 0.506069i −0.889926 + 0.456106i \(0.849244\pi\)
−0.998751 + 0.0499636i \(0.984089\pi\)
\(524\) 45.7023 38.3488i 1.99652 1.67528i
\(525\) 0 0
\(526\) −3.87963 + 22.0025i −0.169160 + 0.959354i
\(527\) −7.17489 + 5.02391i −0.312543 + 0.218845i
\(528\) −11.2089 + 7.39328i −0.487806 + 0.321751i
\(529\) 14.7813 + 17.6156i 0.642664 + 0.765897i
\(530\) 0 0
\(531\) 9.36533 9.97890i 0.406421 0.433047i
\(532\) −83.9219 22.4868i −3.63848 0.974927i
\(533\) −0.702518 + 0.327589i −0.0304294 + 0.0141895i
\(534\) −22.2613 + 17.6493i −0.963339 + 0.763762i
\(535\) 0 0
\(536\) 15.3607 + 42.2032i 0.663482 + 1.82290i
\(537\) 5.79449 + 24.3070i 0.250051 + 1.04892i
\(538\) 3.38206 4.83008i 0.145811 0.208240i
\(539\) −1.64076 −0.0706724
\(540\) 0 0
\(541\) −0.781277 −0.0335897 −0.0167949 0.999859i \(-0.505346\pi\)
−0.0167949 + 0.999859i \(0.505346\pi\)
\(542\) −8.97207 + 12.8134i −0.385383 + 0.550384i
\(543\) 23.4506 + 6.98719i 1.00636 + 0.299849i
\(544\) −23.3637 64.1912i −1.00171 2.75218i
\(545\) 0 0
\(546\) 6.18944 + 2.44953i 0.264884 + 0.104830i
\(547\) 10.0522 4.68743i 0.429802 0.200420i −0.195665 0.980671i \(-0.562686\pi\)
0.625467 + 0.780251i \(0.284909\pi\)
\(548\) 33.0149 + 8.84632i 1.41033 + 0.377896i
\(549\) −7.34652 + 17.1545i −0.313542 + 0.732137i
\(550\) 0 0
\(551\) 8.93677 + 10.6504i 0.380719 + 0.453724i
\(552\) 0.0561466 + 0.942732i 0.00238976 + 0.0401253i
\(553\) −13.6747 + 9.57510i −0.581505 + 0.407175i
\(554\) −5.22900 + 29.6551i −0.222159 + 1.25993i
\(555\) 0 0
\(556\) 5.91335 4.96189i 0.250782 0.210431i
\(557\) −13.0192 + 3.48849i −0.551642 + 0.147812i −0.523864 0.851802i \(-0.675510\pi\)
−0.0277782 + 0.999614i \(0.508843\pi\)
\(558\) −14.2605 4.68399i −0.603694 0.198289i
\(559\) 3.41375 1.97093i 0.144386 0.0833615i
\(560\) 0 0
\(561\) −5.30071 + 0.783531i −0.223796 + 0.0330807i
\(562\) 57.6316 5.04211i 2.43104 0.212689i
\(563\) −15.8881 + 34.0720i −0.669601 + 1.43596i 0.218277 + 0.975887i \(0.429956\pi\)
−0.887878 + 0.460078i \(0.847821\pi\)
\(564\) 1.00210 36.0644i 0.0421962 1.51858i
\(565\) 0 0
\(566\) 34.9323i 1.46831i
\(567\) 26.2458 8.84975i 1.10222 0.371654i
\(568\) 35.7193 + 35.7193i 1.49875 + 1.49875i
\(569\) −2.09817 11.8993i −0.0879598 0.498845i −0.996679 0.0814360i \(-0.974049\pi\)
0.908719 0.417409i \(-0.137062\pi\)
\(570\) 0 0
\(571\) 0.672547 0.244787i 0.0281452 0.0102440i −0.327909 0.944709i \(-0.606344\pi\)
0.356054 + 0.934465i \(0.384122\pi\)
\(572\) −0.138031 1.57770i −0.00577137 0.0659670i
\(573\) 2.67050 3.59693i 0.111562 0.150264i
\(574\) −4.62809 + 12.7156i −0.193173 + 0.530738i
\(575\) 0 0
\(576\) 25.7284 39.3422i 1.07202 1.63926i
\(577\) −9.67417 36.1045i −0.402741 1.50305i −0.808184 0.588930i \(-0.799549\pi\)
0.405443 0.914120i \(-0.367117\pi\)
\(578\) 1.09228 12.4848i 0.0454328 0.519300i
\(579\) −23.4271 + 7.79694i −0.973596 + 0.324030i
\(580\) 0 0
\(581\) 17.1896 + 3.03100i 0.713146 + 0.125747i
\(582\) 62.7398 3.73662i 2.60065 0.154888i
\(583\) −7.04253 0.616142i −0.291672 0.0255180i
\(584\) −57.8388 + 100.180i −2.39339 + 4.14547i
\(585\) 0 0
\(586\) 5.67358 + 9.82693i 0.234373 + 0.405947i
\(587\) −3.89170 8.34577i −0.160628 0.344467i 0.809478 0.587150i \(-0.199750\pi\)
−0.970106 + 0.242683i \(0.921972\pi\)
\(588\) 19.9677 8.64423i 0.823452 0.356482i
\(589\) −6.71056 + 7.99734i −0.276504 + 0.329525i
\(590\) 0 0
\(591\) 6.87740 + 12.7151i 0.282899 + 0.523028i
\(592\) 24.2525 + 16.9818i 0.996771 + 0.697946i
\(593\) 9.96484 9.96484i 0.409207 0.409207i −0.472255 0.881462i \(-0.656560\pi\)
0.881462 + 0.472255i \(0.156560\pi\)
\(594\) −6.51843 6.46741i −0.267454 0.265361i
\(595\) 0 0
\(596\) 106.595 18.7957i 4.36632 0.769900i
\(597\) 6.36780 1.51800i 0.260617 0.0621278i
\(598\) −0.0751920 0.0350626i −0.00307483 0.00143382i
\(599\) 5.73610 + 4.81316i 0.234371 + 0.196660i 0.752407 0.658698i \(-0.228893\pi\)
−0.518037 + 0.855358i \(0.673337\pi\)
\(600\) 0 0
\(601\) −20.4882 7.45708i −0.835730 0.304181i −0.111522 0.993762i \(-0.535572\pi\)
−0.724208 + 0.689581i \(0.757795\pi\)
\(602\) 17.8101 66.4682i 0.725886 2.70904i
\(603\) −13.9502 + 8.65512i −0.568095 + 0.352464i
\(604\) −34.9543 20.1809i −1.42227 0.821148i
\(605\) 0 0
\(606\) −8.31607 1.70578i −0.337817 0.0692926i
\(607\) −13.1267 18.7469i −0.532796 0.760912i 0.459042 0.888415i \(-0.348193\pi\)
−0.991838 + 0.127503i \(0.959304\pi\)
\(608\) −46.7005 66.6953i −1.89396 2.70485i
\(609\) −13.0727 2.68146i −0.529734 0.108658i
\(610\) 0 0
\(611\) 1.66496 + 0.961264i 0.0673570 + 0.0388886i
\(612\) 60.3805 37.4619i 2.44074 1.51431i
\(613\) −3.87633 + 14.4667i −0.156564 + 0.584303i 0.842403 + 0.538848i \(0.181140\pi\)
−0.998966 + 0.0454549i \(0.985526\pi\)
\(614\) 46.5944 + 16.9590i 1.88040 + 0.684409i
\(615\) 0 0
\(616\) −12.8467 10.7796i −0.517607 0.434324i
\(617\) 0.430054 + 0.200538i 0.0173133 + 0.00807334i 0.431256 0.902230i \(-0.358071\pi\)
−0.413942 + 0.910303i \(0.635848\pi\)
\(618\) −73.2383 + 17.4591i −2.94608 + 0.702309i
\(619\) 10.1152 1.78359i 0.406565 0.0716885i 0.0333743 0.999443i \(-0.489375\pi\)
0.373191 + 0.927754i \(0.378264\pi\)
\(620\) 0 0
\(621\) −0.333100 + 0.0906578i −0.0133668 + 0.00363797i
\(622\) −15.4321 + 15.4321i −0.618770 + 0.618770i
\(623\) −15.5357 10.8782i −0.622425 0.435827i
\(624\) 4.51429 + 8.34610i 0.180716 + 0.334111i
\(625\) 0 0
\(626\) 32.6187 38.8735i 1.30371 1.55370i
\(627\) −5.86095 + 2.53727i −0.234064 + 0.101329i
\(628\) −29.3733 62.9913i −1.17212 2.51363i
\(629\) 5.90732 + 10.2318i 0.235540 + 0.407968i
\(630\) 0 0
\(631\) −6.48152 + 11.2263i −0.258025 + 0.446913i −0.965713 0.259613i \(-0.916405\pi\)
0.707688 + 0.706526i \(0.249738\pi\)
\(632\) −44.3488 3.88002i −1.76410 0.154339i
\(633\) 30.7842 1.83343i 1.22356 0.0728722i
\(634\) 44.5080 + 7.84797i 1.76764 + 0.311683i
\(635\) 0 0
\(636\) 88.9521 29.6048i 3.52718 1.17391i
\(637\) −0.101053 + 1.15504i −0.00400388 + 0.0457645i
\(638\) 1.14506 + 4.27341i 0.0453333 + 0.169186i
\(639\) −10.1063 + 15.4539i −0.399800 + 0.611347i
\(640\) 0 0
\(641\) 16.0051 43.9737i 0.632164 1.73686i −0.0428806 0.999080i \(-0.513653\pi\)
0.675045 0.737777i \(-0.264124\pi\)
\(642\) −40.7586 + 54.8982i −1.60861 + 2.16666i
\(643\) 1.93250 + 22.0886i 0.0762103 + 0.871088i 0.934043 + 0.357160i \(0.116255\pi\)
−0.857833 + 0.513928i \(0.828190\pi\)
\(644\) −0.976716 + 0.355496i −0.0384880 + 0.0140085i
\(645\) 0 0
\(646\) −11.9584 67.8196i −0.470498 2.66833i
\(647\) −23.9696 23.9696i −0.942341 0.942341i 0.0560849 0.998426i \(-0.482138\pi\)
−0.998426 + 0.0560849i \(0.982138\pi\)
\(648\) 68.7866 + 26.9109i 2.70219 + 1.05716i
\(649\) 3.02889i 0.118894i
\(650\) 0 0
\(651\) 0.278331 10.0167i 0.0109086 0.392587i
\(652\) −42.0693 + 90.2178i −1.64756 + 3.53320i
\(653\) −9.67068 + 0.846075i −0.378443 + 0.0331095i −0.274791 0.961504i \(-0.588609\pi\)
−0.103652 + 0.994614i \(0.533053\pi\)
\(654\) 42.6349 6.30213i 1.66716 0.246433i
\(655\) 0 0
\(656\) −16.7048 + 9.64453i −0.652214 + 0.376556i
\(657\) −40.1732 13.1953i −1.56731 0.514797i
\(658\) 32.4179 8.68636i 1.26378 0.338629i
\(659\) 15.9731 13.4030i 0.622224 0.522108i −0.276278 0.961078i \(-0.589101\pi\)
0.898502 + 0.438970i \(0.144657\pi\)
\(660\) 0 0
\(661\) −6.68365 + 37.9049i −0.259964 + 1.47433i 0.523038 + 0.852310i \(0.324799\pi\)
−0.783002 + 0.622020i \(0.786312\pi\)
\(662\) 31.0096 21.7132i 1.20522 0.843906i
\(663\) 0.225115 + 3.77980i 0.00874274 + 0.146795i
\(664\) 29.9205 + 35.6578i 1.16114 + 1.38379i
\(665\) 0 0
\(666\) −7.97054 + 18.6117i −0.308852 + 0.721187i
\(667\) 0.160660 + 0.0430488i 0.00622079 + 0.00166685i
\(668\) 101.236 47.2070i 3.91693 1.82649i
\(669\) −30.8337 12.2027i −1.19210 0.471784i
\(670\) 0 0
\(671\) 1.41262 + 3.88114i 0.0545335 + 0.149830i
\(672\) 74.8969 + 22.3158i 2.88921 + 0.860853i
\(673\) 11.8077 16.8631i 0.455153 0.650026i −0.524339 0.851510i \(-0.675687\pi\)
0.979492 + 0.201484i \(0.0645763\pi\)
\(674\) 18.1379 0.698646
\(675\) 0 0
\(676\) 64.9678 2.49876
\(677\) −13.0007 + 18.5670i −0.499659 + 0.713588i −0.987195 0.159515i \(-0.949007\pi\)
0.487536 + 0.873103i \(0.337896\pi\)
\(678\) −22.2116 93.1743i −0.853032 3.57834i
\(679\) 14.3508 + 39.4285i 0.550734 + 1.51313i
\(680\) 0 0
\(681\) 0.655262 0.519510i 0.0251097 0.0199077i
\(682\) −3.01082 + 1.40397i −0.115290 + 0.0537608i
\(683\) −7.91835 2.12172i −0.302987 0.0811852i 0.104122 0.994564i \(-0.466797\pi\)
−0.407110 + 0.913379i \(0.633463\pi\)
\(684\) 57.9589 61.7561i 2.21611 2.36130i
\(685\) 0 0
\(686\) −23.8444 28.4166i −0.910382 1.08495i
\(687\) 21.7258 14.3301i 0.828891 0.546726i
\(688\) 80.3518 56.2630i 3.06338 2.14500i
\(689\) −0.867490 + 4.91978i −0.0330487 + 0.187429i
\(690\) 0 0
\(691\) 2.09562 1.75844i 0.0797212 0.0668941i −0.602056 0.798454i \(-0.705652\pi\)
0.681777 + 0.731560i \(0.261207\pi\)
\(692\) −18.4268 + 4.93744i −0.700481 + 0.187693i
\(693\) 2.89523 5.40337i 0.109981 0.205257i
\(694\) 31.6991 18.3015i 1.20328 0.694715i
\(695\) 0 0
\(696\) −22.1094 27.8867i −0.838054 1.05704i
\(697\) −7.66804 + 0.670867i −0.290448 + 0.0254109i
\(698\) −30.0939 + 64.5366i −1.13907 + 2.44275i
\(699\) −0.816535 0.502171i −0.0308842 0.0189939i
\(700\) 0 0
\(701\) 45.2015i 1.70724i −0.520899 0.853618i \(-0.674403\pi\)
0.520899 0.853618i \(-0.325597\pi\)
\(702\) −4.95433 + 4.19045i −0.186989 + 0.158158i
\(703\) 9.95741 + 9.95741i 0.375551 + 0.375551i
\(704\) −1.80664 10.2459i −0.0680901 0.386158i
\(705\) 0 0
\(706\) 0.118329 0.0430682i 0.00445337 0.00162089i
\(707\) −0.493942 5.64579i −0.0185766 0.212332i
\(708\) 15.9575 + 36.8609i 0.599720 + 1.38532i
\(709\) 6.90171 18.9623i 0.259199 0.712144i −0.740018 0.672587i \(-0.765183\pi\)
0.999217 0.0395569i \(-0.0125946\pi\)
\(710\) 0 0
\(711\) −1.93152 16.1581i −0.0724378 0.605978i
\(712\) −13.0903 48.8536i −0.490579 1.83086i
\(713\) −0.0108853 + 0.124419i −0.000407656 + 0.00465953i
\(714\) 49.4365 + 43.8788i 1.85011 + 1.64212i
\(715\) 0 0
\(716\) −72.2265 12.7355i −2.69923 0.475947i
\(717\) −4.39231 + 8.77444i −0.164034 + 0.327688i
\(718\) 49.9836 + 4.37300i 1.86537 + 0.163199i
\(719\) −18.2157 + 31.5505i −0.679331 + 1.17664i 0.295852 + 0.955234i \(0.404396\pi\)
−0.975183 + 0.221402i \(0.928937\pi\)
\(720\) 0 0
\(721\) −25.1318 43.5295i −0.935957 1.62113i
\(722\) −13.3179 28.5603i −0.495640 1.06290i
\(723\) −2.54646 1.89059i −0.0947037 0.0703118i
\(724\) −46.1638 + 55.0159i −1.71566 + 2.04465i
\(725\) 0 0
\(726\) 48.6574 + 1.35202i 1.80585 + 0.0501782i
\(727\) −10.9561 7.67153i −0.406338 0.284521i 0.352485 0.935817i \(-0.385337\pi\)
−0.758824 + 0.651296i \(0.774226\pi\)
\(728\) −8.37976 + 8.37976i −0.310575 + 0.310575i
\(729\) −4.47945 + 26.6258i −0.165906 + 0.986142i
\(730\) 0 0
\(731\) 38.5489 6.79721i 1.42578 0.251404i
\(732\) −37.6388 39.7903i −1.39117 1.47069i
\(733\) 38.0568 + 17.7462i 1.40566 + 0.655470i 0.969656 0.244474i \(-0.0786152\pi\)
0.436005 + 0.899944i \(0.356393\pi\)
\(734\) −40.4216 33.9178i −1.49199 1.25193i
\(735\) 0 0
\(736\) −0.915308 0.333145i −0.0337387 0.0122799i
\(737\) −0.940413 + 3.50967i −0.0346406 + 0.129280i
\(738\) −8.79496 9.83085i −0.323747 0.361879i
\(739\) −34.0711 19.6709i −1.25332 0.723607i −0.281556 0.959545i \(-0.590850\pi\)
−0.971768 + 0.235938i \(0.924184\pi\)
\(740\) 0 0
\(741\) 1.42519 + 4.28220i 0.0523557 + 0.157310i
\(742\) 50.0213 + 71.4378i 1.83634 + 2.62256i
\(743\) −7.43173 10.6136i −0.272644 0.389376i 0.659358 0.751829i \(-0.270828\pi\)
−0.932002 + 0.362453i \(0.881939\pi\)
\(744\) 17.7390 19.9858i 0.650342 0.732714i
\(745\) 0 0
\(746\) −48.8829 28.2225i −1.78973 1.03330i
\(747\) −10.5184 + 13.3745i −0.384848 + 0.489349i
\(748\) 4.07039 15.1909i 0.148828 0.555434i
\(749\) −42.8937 15.6120i −1.56730 0.570451i
\(750\) 0 0
\(751\) 30.6700 + 25.7352i 1.11916 + 0.939089i 0.998562 0.0536119i \(-0.0170734\pi\)
0.120601 + 0.992701i \(0.461518\pi\)
\(752\) 43.3589 + 20.2186i 1.58114 + 0.737296i
\(753\) 9.62128 32.2912i 0.350619 1.17676i
\(754\) 3.07888 0.542889i 0.112126 0.0197709i
\(755\) 0 0
\(756\) −6.76700 + 81.0112i −0.246113 + 2.94635i
\(757\) −0.846964 + 0.846964i −0.0307834 + 0.0307834i −0.722331 0.691548i \(-0.756929\pi\)
0.691548 + 0.722331i \(0.256929\pi\)
\(758\) −10.7967 7.55993i −0.392154 0.274589i
\(759\) −0.0400255 + 0.0650817i −0.00145283 + 0.00236232i
\(760\) 0 0
\(761\) −3.25980 + 3.88488i −0.118168 + 0.140827i −0.821885 0.569653i \(-0.807078\pi\)
0.703718 + 0.710480i \(0.251522\pi\)
\(762\) 4.02893 34.8656i 0.145953 1.26305i
\(763\) 12.1596 + 26.0764i 0.440208 + 0.944029i
\(764\) 6.57430 + 11.3870i 0.237850 + 0.411968i
\(765\) 0 0
\(766\) 37.6375 65.1901i 1.35990 2.35542i
\(767\) −2.13224 0.186547i −0.0769909 0.00673583i
\(768\) 1.53991 + 2.33465i 0.0555666 + 0.0842444i
\(769\) −26.0795 4.59852i −0.940451 0.165827i −0.317651 0.948208i \(-0.602894\pi\)
−0.622800 + 0.782381i \(0.714005\pi\)
\(770\) 0 0
\(771\) −10.4138 + 50.7698i −0.375045 + 1.82843i
\(772\) 6.31593 72.1914i 0.227315 2.59822i
\(773\) 2.81189 + 10.4941i 0.101137 + 0.377447i 0.997878 0.0651074i \(-0.0207390\pi\)
−0.896742 + 0.442555i \(0.854072\pi\)
\(774\) 48.9124 + 45.9049i 1.75812 + 1.65002i
\(775\) 0 0
\(776\) −38.2703 + 105.147i −1.37383 + 3.77455i
\(777\) −13.4271 1.55159i −0.481696 0.0556629i
\(778\) 6.82635 + 78.0256i 0.244737 + 2.79735i
\(779\) −8.62118 + 3.13785i −0.308886 + 0.112425i
\(780\) 0 0
\(781\) 0.709661 + 4.02469i 0.0253937 + 0.144015i
\(782\) −0.582559 0.582559i −0.0208323 0.0208323i
\(783\) 8.32267 9.99807i 0.297428 0.357302i
\(784\) 28.8525i 1.03045i
\(785\) 0 0
\(786\) −47.5856 + 25.7384i −1.69732 + 0.918058i
\(787\) −3.36829 + 7.22332i −0.120067 + 0.257484i −0.957151 0.289591i \(-0.906481\pi\)
0.837084 + 0.547074i \(0.184259\pi\)
\(788\) −42.2668 + 3.69786i −1.50569 + 0.131731i
\(789\) 5.35043 13.5194i 0.190480 0.481303i
\(790\) 0 0
\(791\) 55.3786 31.9729i 1.96904 1.13682i
\(792\) 15.1769 6.07544i 0.539286 0.215882i
\(793\) 2.81921 0.755404i 0.100113 0.0268252i
\(794\) −39.9638 + 33.5336i −1.41826 + 1.19006i
\(795\) 0 0
\(796\) −3.33636 + 18.9215i −0.118254 + 0.670653i
\(797\) 0.621792 0.435383i 0.0220250 0.0154221i −0.562512 0.826789i \(-0.690165\pi\)
0.584537 + 0.811367i \(0.301276\pi\)
\(798\) 70.4517 + 35.2667i 2.49396 + 1.24843i
\(799\) 12.2715 + 14.6246i 0.434136 + 0.517383i
\(800\) 0 0
\(801\) 16.4996 8.34059i 0.582984 0.294700i
\(802\) −0.0868625 0.0232747i −0.00306722 0.000821859i
\(803\) −8.48179 + 3.95512i −0.299316 + 0.139573i
\(804\) −7.04587 47.6664i −0.248489 1.68106i
\(805\) 0 0
\(806\) 0.802918 + 2.20600i 0.0282816 + 0.0777030i
\(807\) −2.78768 + 2.63695i −0.0981311 + 0.0928251i
\(808\) 8.66877 12.3803i 0.304966 0.435537i
\(809\) 3.88327 0.136528 0.0682642 0.997667i \(-0.478254\pi\)
0.0682642 + 0.997667i \(0.478254\pi\)
\(810\) 0 0
\(811\) −22.9810 −0.806974 −0.403487 0.914985i \(-0.632202\pi\)
−0.403487 + 0.914985i \(0.632202\pi\)
\(812\) 22.4656 32.0843i 0.788390 1.12594i
\(813\) 7.39528 6.99542i 0.259364 0.245340i
\(814\) 1.53261 + 4.21081i 0.0537179 + 0.147589i
\(815\) 0 0
\(816\) 13.7783 + 93.2125i 0.482337 + 3.26309i
\(817\) 42.2840 19.7174i 1.47933 0.689824i
\(818\) −22.6613 6.07207i −0.792333 0.212305i
\(819\) −3.62550 2.37095i −0.126685 0.0828476i
\(820\) 0 0
\(821\) −1.59034 1.89529i −0.0555031 0.0661461i 0.737579 0.675261i \(-0.235969\pi\)
−0.793082 + 0.609115i \(0.791525\pi\)
\(822\) −27.7157 13.8739i −0.966697 0.483909i
\(823\) −26.9245 + 18.8527i −0.938528 + 0.657164i −0.939396 0.342835i \(-0.888613\pi\)
0.000867529 1.00000i \(0.499724\pi\)
\(824\) 23.2761 132.005i 0.810860 4.59862i
\(825\) 0 0
\(826\) −28.6230 + 24.0176i −0.995923 + 0.835678i
\(827\) −8.32126 + 2.22968i −0.289359 + 0.0775334i −0.400579 0.916262i \(-0.631191\pi\)
0.111220 + 0.993796i \(0.464524\pi\)
\(828\) 0.144222 1.00290i 0.00501205 0.0348532i
\(829\) 7.38409 4.26321i 0.256460 0.148067i −0.366259 0.930513i \(-0.619361\pi\)
0.622719 + 0.782446i \(0.286028\pi\)
\(830\) 0 0
\(831\) 7.21135 18.2216i 0.250159 0.632099i
\(832\) −7.32410 + 0.640776i −0.253918 + 0.0222149i
\(833\) −4.86588 + 10.4349i −0.168593 + 0.361548i
\(834\) −6.15702 + 3.33025i −0.213200 + 0.115317i
\(835\) 0 0
\(836\) 18.7448i 0.648301i
\(837\) 8.47863 + 4.85083i 0.293064 + 0.167669i
\(838\) −62.3307 62.3307i −2.15318 2.15318i
\(839\) −8.06541 45.7412i −0.278449 1.57916i −0.727789 0.685802i \(-0.759452\pi\)
0.449340 0.893361i \(-0.351659\pi\)
\(840\) 0 0
\(841\) 21.3614 7.77490i 0.736599 0.268100i
\(842\) −3.85112 44.0185i −0.132718 1.51698i
\(843\) −37.3998 4.32178i −1.28812 0.148850i
\(844\) −30.9571 + 85.0539i −1.06559 + 2.92768i
\(845\) 0 0
\(846\) −7.46146 + 31.8539i −0.256530 + 1.09516i
\(847\) 8.41058 + 31.3887i 0.288991 + 1.07853i
\(848\) −10.8348 + 123.842i −0.372068 + 4.25276i
\(849\) 4.56789 22.2695i 0.156770 0.764288i
\(850\) 0 0
\(851\) 0.165907 + 0.0292538i 0.00568721 + 0.00100281i
\(852\) −29.8402 45.2407i −1.02231 1.54992i
\(853\) −20.6498 1.80662i −0.707035 0.0618575i −0.272034 0.962288i \(-0.587696\pi\)
−0.435001 + 0.900430i \(0.643252\pi\)
\(854\) 25.4755 44.1248i 0.871752 1.50992i
\(855\) 0 0
\(856\) −60.8644 105.420i −2.08030 3.60319i
\(857\) 1.85929 + 3.98725i 0.0635120 + 0.136202i 0.935502 0.353322i \(-0.114948\pi\)
−0.871990 + 0.489524i \(0.837170\pi\)
\(858\) −0.164858 + 1.42665i −0.00562814 + 0.0487049i
\(859\) 27.5782 32.8664i 0.940956 1.12139i −0.0514862 0.998674i \(-0.516396\pi\)
0.992442 0.122714i \(-0.0391598\pi\)
\(860\) 0 0
\(861\) 4.61318 7.50107i 0.157217 0.255636i
\(862\) −31.4786 22.0415i −1.07217 0.750738i
\(863\) 29.7115 29.7115i 1.01139 1.01139i 0.0114553 0.999934i \(-0.496354\pi\)
0.999934 0.0114553i \(-0.00364642\pi\)
\(864\) −53.6570 + 54.0802i −1.82545 + 1.83985i
\(865\) 0 0
\(866\) −61.0955 + 10.7728i −2.07611 + 0.366074i
\(867\) −2.32890 + 7.81631i −0.0790936 + 0.265456i
\(868\) 26.6552 + 12.4295i 0.904736 + 0.421885i
\(869\) −2.75902 2.31509i −0.0935932 0.0785340i
\(870\) 0 0
\(871\) 2.41278 + 0.878181i 0.0817540 + 0.0297560i
\(872\) −19.8588 + 74.1142i −0.672505 + 2.50982i
\(873\) −40.4856 5.82201i −1.37023 0.197045i
\(874\) −0.850406 0.490982i −0.0287654 0.0166077i
\(875\) 0 0
\(876\) 82.3842 92.8188i 2.78350 3.13606i
\(877\) −6.63310 9.47306i −0.223984 0.319882i 0.691394 0.722478i \(-0.256997\pi\)
−0.915378 + 0.402596i \(0.868108\pi\)
\(878\) −48.8243 69.7284i −1.64774 2.35322i
\(879\) −2.33193 7.00662i −0.0786540 0.236328i
\(880\) 0 0
\(881\) 12.7653 + 7.37007i 0.430075 + 0.248304i 0.699379 0.714751i \(-0.253460\pi\)
−0.269304 + 0.963055i \(0.586794\pi\)
\(882\) −19.3126 + 4.04050i −0.650289 + 0.136051i
\(883\) −4.11349 + 15.3517i −0.138430 + 0.516627i 0.861530 + 0.507706i \(0.169506\pi\)
−0.999960 + 0.00892106i \(0.997160\pi\)
\(884\) −10.4432 3.80103i −0.351244 0.127842i
\(885\) 0 0
\(886\) −36.6160 30.7245i −1.23014 1.03221i
\(887\) 6.76369 + 3.15396i 0.227102 + 0.105900i 0.532839 0.846216i \(-0.321125\pi\)
−0.305737 + 0.952116i \(0.598903\pi\)
\(888\) −24.7702 26.1861i −0.831232 0.878747i
\(889\) 23.0750 4.06875i 0.773911 0.136461i
\(890\) 0 0
\(891\) 3.30983 + 4.97539i 0.110883 + 0.166682i
\(892\) 68.8206 68.8206i 2.30428 2.30428i
\(893\) 18.6396 + 13.0516i 0.623750 + 0.436755i
\(894\) −98.1150 2.72628i −3.28146 0.0911803i
\(895\) 0 0
\(896\) −24.4930 + 29.1896i −0.818253 + 0.975156i
\(897\) 0.0433504 + 0.0321851i 0.00144743 + 0.00107463i
\(898\) −14.9255 32.0079i −0.498072 1.06812i
\(899\) −2.35319 4.07585i −0.0784834 0.135937i
\(900\) 0 0
\(901\) −24.8041 + 42.9619i −0.826344 + 1.43127i
\(902\) −2.90833 0.254446i −0.0968367 0.00847211i
\(903\) −20.0457 + 40.0450i −0.667080 + 1.33261i
\(904\) 167.938 + 29.6120i 5.58553 + 0.984880i
\(905\) 0 0
\(906\) 27.3733 + 24.2960i 0.909415 + 0.807180i
\(907\) −1.42792 + 16.3212i −0.0474134 + 0.541937i 0.934928 + 0.354838i \(0.115464\pi\)
−0.982341 + 0.187099i \(0.940092\pi\)
\(908\) 0.635223 + 2.37069i 0.0210806 + 0.0786740i
\(909\) 5.07849 + 2.17489i 0.168443 + 0.0721365i
\(910\) 0 0
\(911\) −0.825532 + 2.26813i −0.0273511 + 0.0751465i −0.952617 0.304173i \(-0.901620\pi\)
0.925266 + 0.379320i \(0.123842\pi\)
\(912\) 44.6177 + 103.064i 1.47744 + 3.41279i
\(913\) 0.328216 + 3.75152i 0.0108624 + 0.124157i
\(914\) −20.1354 + 7.32869i −0.666020 + 0.242412i
\(915\) 0 0
\(916\) 13.2645 + 75.2269i 0.438273 + 2.48557i
\(917\) −25.5387 25.5387i −0.843361 0.843361i
\(918\) −60.4628 + 22.2760i −1.99557 + 0.735218i
\(919\) 5.68243i 0.187446i 0.995598 + 0.0937230i \(0.0298768\pi\)
−0.995598 + 0.0937230i \(0.970123\pi\)
\(920\) 0 0
\(921\) −27.4866 16.9043i −0.905714 0.557017i
\(922\) −16.1703 + 34.6774i −0.532541 + 1.14204i
\(923\) 2.87697 0.251702i 0.0946965 0.00828487i
\(924\) 11.1778 + 14.0987i 0.367724 + 0.463813i
\(925\) 0 0
\(926\) −47.9543 + 27.6864i −1.57588 + 0.909832i
\(927\) 48.9729 1.55334i 1.60848 0.0510183i
\(928\) 35.4544 9.49998i 1.16385 0.311852i
\(929\) 31.5686 26.4892i 1.03573 0.869082i 0.0442093 0.999022i \(-0.485923\pi\)
0.991522 + 0.129941i \(0.0414787\pi\)
\(930\) 0 0
\(931\) −2.38300 + 13.5147i −0.0780996 + 0.442925i
\(932\) 2.30468 1.61376i 0.0754924 0.0528604i
\(933\) 11.8560 7.82008i 0.388148 0.256018i
\(934\) −42.1923 50.2828i −1.38057 1.64530i
\(935\) 0 0
\(936\) −3.34220 11.0582i −0.109243 0.361450i
\(937\) −7.80116 2.09031i −0.254853 0.0682876i 0.129131 0.991628i \(-0.458781\pi\)
−0.383983 + 0.923340i \(0.625448\pi\)
\(938\) 40.6235 18.9430i 1.32640 0.618512i
\(939\) −25.8779 + 20.5167i −0.844493 + 0.669538i
\(940\) 0 0
\(941\) 17.0461 + 46.8337i 0.555686 + 1.52673i 0.825833 + 0.563915i \(0.190706\pi\)
−0.270147 + 0.962819i \(0.587072\pi\)
\(942\) 14.6151 + 61.3082i 0.476186 + 1.99753i
\(943\) −0.0629540 + 0.0899076i −0.00205006 + 0.00292780i
\(944\) −53.2626 −1.73355
\(945\) 0 0
\(946\) 14.8463 0.482696
\(947\) 27.9030 39.8496i 0.906726 1.29494i −0.0484276 0.998827i \(-0.515421\pi\)
0.955153 0.296112i \(-0.0956901\pi\)
\(948\) 45.7735 + 13.6384i 1.48666 + 0.442955i
\(949\) 2.26190 + 6.21452i 0.0734244 + 0.201732i
\(950\) 0 0
\(951\) −27.3479 10.8232i −0.886816 0.350966i
\(952\) −106.655 + 49.7340i −3.45671 + 1.61189i
\(953\) 48.5541 + 13.0100i 1.57282 + 0.421436i 0.936694 0.350148i \(-0.113869\pi\)
0.636127 + 0.771584i \(0.280535\pi\)
\(954\) −84.4117 + 10.0905i −2.73293 + 0.326691i
\(955\) 0 0
\(956\) −18.5120 22.0618i −0.598722 0.713529i
\(957\) −0.171171 2.87406i −0.00553318 0.0929051i
\(958\) −58.6039 + 41.0349i −1.89341 + 1.32578i
\(959\) 3.59307 20.3773i 0.116026 0.658017i
\(960\) 0 0
\(961\) −21.0402 + 17.6548i −0.678716 + 0.569510i
\(962\) 3.05867 0.819569i 0.0986156 0.0264240i
\(963\) 33.1626 29.6682i 1.06865 0.956043i
\(964\) 8.06148 4.65430i 0.259643 0.149905i
\(965\) 0 0
\(966\) 0.932406 0.137825i 0.0299997 0.00443444i
\(967\) 49.5607 4.33600i 1.59377 0.139436i 0.744581 0.667533i \(-0.232650\pi\)
0.849185 + 0.528096i \(0.177094\pi\)
\(968\) −36.6238 + 78.5400i −1.17713 + 2.52437i
\(969\) −1.24481 + 44.7991i −0.0399891 + 1.43916i
\(970\) 0 0
\(971\) 40.2818i 1.29270i −0.763039 0.646352i \(-0.776294\pi\)
0.763039 0.646352i \(-0.223706\pi\)
\(972\) −66.4924 43.1118i −2.13275 1.38281i
\(973\) −3.30441 3.30441i −0.105934 0.105934i
\(974\) 0.911162 + 5.16745i 0.0291955 + 0.165576i
\(975\) 0 0
\(976\) 68.2493 24.8407i 2.18461 0.795132i
\(977\) −3.30670 37.7958i −0.105791 1.20919i −0.844644 0.535328i \(-0.820188\pi\)
0.738854 0.673866i \(-0.235367\pi\)
\(978\) 53.8093 72.4763i 1.72063 2.31754i
\(979\) 1.39948 3.84504i 0.0447276 0.122888i
\(980\) 0 0
\(981\) −28.0041 1.55748i −0.894102 0.0497264i
\(982\) 16.3345 + 60.9612i 0.521255 + 1.94535i
\(983\) −3.12235 + 35.6886i −0.0995874 + 1.13829i 0.767811 + 0.640676i \(0.221346\pi\)
−0.867399 + 0.497614i \(0.834210\pi\)
\(984\) 22.2822 7.41591i 0.710330 0.236411i
\(985\) 0 0
\(986\) 30.5739 + 5.39101i 0.973672 + 0.171685i
\(987\) −21.8025 + 1.29850i −0.693981 + 0.0413316i
\(988\) −13.1958 1.15448i −0.419813 0.0367289i
\(989\) 0.279076 0.483373i 0.00887409 0.0153704i
\(990\) 0 0
\(991\) 21.8850 + 37.9060i 0.695201 + 1.20412i 0.970113 + 0.242654i \(0.0780179\pi\)
−0.274912 + 0.961469i \(0.588649\pi\)
\(992\) 11.6480 + 24.9793i 0.369826 + 0.793094i
\(993\) −22.6081 + 9.78732i −0.717447 + 0.310591i
\(994\) 32.4061 38.6201i 1.02786 1.22495i
\(995\) 0 0
\(996\) −23.7590 43.9260i −0.752833 1.39185i
\(997\) 19.9603 + 13.9764i 0.632150 + 0.442636i 0.845233 0.534398i \(-0.179462\pi\)
−0.213083 + 0.977034i \(0.568351\pi\)
\(998\) −59.0307 + 59.0307i −1.86859 + 1.86859i
\(999\) 7.51500 10.8228i 0.237764 0.342418i
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 675.2.ba.b.68.16 192
5.2 odd 4 inner 675.2.ba.b.257.16 192
5.3 odd 4 135.2.q.a.122.1 yes 192
5.4 even 2 135.2.q.a.68.1 yes 192
15.8 even 4 405.2.r.a.152.16 192
15.14 odd 2 405.2.r.a.233.16 192
27.2 odd 18 inner 675.2.ba.b.218.16 192
135.2 even 36 inner 675.2.ba.b.407.16 192
135.29 odd 18 135.2.q.a.83.1 yes 192
135.79 even 18 405.2.r.a.8.16 192
135.83 even 36 135.2.q.a.2.1 192
135.133 odd 36 405.2.r.a.332.16 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.2.q.a.2.1 192 135.83 even 36
135.2.q.a.68.1 yes 192 5.4 even 2
135.2.q.a.83.1 yes 192 135.29 odd 18
135.2.q.a.122.1 yes 192 5.3 odd 4
405.2.r.a.8.16 192 135.79 even 18
405.2.r.a.152.16 192 15.8 even 4
405.2.r.a.233.16 192 15.14 odd 2
405.2.r.a.332.16 192 135.133 odd 36
675.2.ba.b.68.16 192 1.1 even 1 trivial
675.2.ba.b.218.16 192 27.2 odd 18 inner
675.2.ba.b.257.16 192 5.2 odd 4 inner
675.2.ba.b.407.16 192 135.2 even 36 inner