Properties

Label 363.2.f.h.161.3
Level $363$
Weight $2$
Character 363.161
Analytic conductor $2.899$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $16$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,2,Mod(161,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.f (of order \(10\), degree \(4\), not 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: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: 16.0.26873856000000000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 2x^{14} - 8x^{10} - 16x^{8} - 32x^{6} + 128x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 161.3
Root \(0.294032 + 1.38331i\) of defining polynomial
Character \(\chi\) \(=\) 363.161
Dual form 363.2.f.h.239.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.98168 + 1.43977i) q^{2} +(-1.28716 + 1.15897i) q^{3} +(1.23607 + 3.80423i) q^{4} +(1.01807 + 1.40126i) q^{5} +(-4.21940 + 0.443477i) q^{6} +(-1.34500 + 0.437016i) q^{7} +(-1.51387 + 4.65921i) q^{8} +(0.313585 - 2.98357i) q^{9} +O(q^{10})\) \(q+(1.98168 + 1.43977i) q^{2} +(-1.28716 + 1.15897i) q^{3} +(1.23607 + 3.80423i) q^{4} +(1.01807 + 1.40126i) q^{5} +(-4.21940 + 0.443477i) q^{6} +(-1.34500 + 0.437016i) q^{7} +(-1.51387 + 4.65921i) q^{8} +(0.313585 - 2.98357i) q^{9} +4.24264i q^{10} +(-6.00000 - 3.46410i) q^{12} +(1.66251 - 2.28825i) q^{13} +(-3.29456 - 1.07047i) q^{14} +(-2.93444 - 0.623735i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(1.98168 - 1.43977i) q^{17} +(4.91709 - 5.46098i) q^{18} +(-2.68999 - 0.874032i) q^{19} +(-4.07230 + 5.60503i) q^{20} +(1.22474 - 2.12132i) q^{21} +8.66025i q^{23} +(-3.45127 - 7.75169i) q^{24} +(0.618034 - 1.90211i) q^{25} +(6.58911 - 2.14093i) q^{26} +(3.05422 + 4.20378i) q^{27} +(-3.32502 - 4.57649i) q^{28} +(1.51387 + 4.65921i) q^{29} +(-4.91709 - 5.46098i) q^{30} +(-2.42705 - 1.76336i) q^{31} +6.00000 q^{34} +(-1.98168 - 1.43977i) q^{35} +(11.7378 - 2.49494i) q^{36} +(0.927051 + 2.85317i) q^{37} +(-4.07230 - 5.60503i) q^{38} +(0.512083 + 4.87214i) q^{39} +(-8.06998 + 2.62210i) q^{40} +(3.02774 - 9.31841i) q^{41} +(5.48127 - 2.44042i) q^{42} -9.89949i q^{43} +(4.50000 - 2.59808i) q^{45} +(-12.4688 + 17.1618i) q^{46} +(6.58911 + 2.14093i) q^{47} +(1.44045 - 6.77681i) q^{48} +(-4.04508 + 2.93893i) q^{49} +(3.96336 - 2.87955i) q^{50} +(-0.882095 + 4.14993i) q^{51} +(10.7600 + 3.49613i) q^{52} +(-2.03615 + 2.80252i) q^{53} +12.7279i q^{54} -6.92820i q^{56} +(4.47544 - 1.99259i) q^{57} +(-3.70820 + 11.4127i) q^{58} +(1.64728 - 0.535233i) q^{59} +(-1.25434 - 11.9343i) q^{60} +(-1.66251 - 2.28825i) q^{61} +(-2.27080 - 6.98881i) q^{62} +(0.882095 + 4.14993i) q^{63} +(6.47214 + 4.70228i) q^{64} +4.89898 q^{65} -3.00000 q^{67} +(7.92672 + 5.75910i) q^{68} +(-10.0370 - 11.1472i) q^{69} +(-1.85410 - 5.70634i) q^{70} +(1.01807 + 1.40126i) q^{71} +(13.4263 + 5.97778i) q^{72} +(5.37999 - 1.74806i) q^{73} +(-2.27080 + 6.98881i) q^{74} +(1.40898 + 3.16461i) q^{75} -11.3137i q^{76} +(-6.00000 + 10.3923i) q^{78} +(5.81878 - 8.00886i) q^{79} +(-6.58911 - 2.14093i) q^{80} +(-8.80333 - 1.87121i) q^{81} +(19.4164 - 14.1068i) q^{82} +(-1.98168 + 1.43977i) q^{83} +(9.58385 + 2.03711i) q^{84} +(4.03499 + 1.31105i) q^{85} +(14.2530 - 19.6176i) q^{86} +(-7.34847 - 4.24264i) q^{87} -8.66025i q^{89} +(12.6582 + 1.33043i) q^{90} +(-1.23607 + 3.80423i) q^{91} +(-32.9456 + 10.7047i) q^{92} +(5.16769 - 0.543146i) q^{93} +(9.97505 + 13.7295i) q^{94} +(-1.51387 - 4.65921i) q^{95} +(-10.5172 - 7.64121i) q^{97} -12.2474 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 6 q^{3} - 16 q^{4} - 6 q^{9} - 96 q^{12} + 6 q^{15} - 16 q^{16} - 8 q^{25} - 12 q^{31} + 96 q^{34} - 24 q^{36} - 12 q^{37} + 12 q^{42} + 72 q^{45} + 24 q^{48} - 20 q^{49} + 48 q^{58} + 24 q^{60} + 32 q^{64} - 48 q^{67} - 30 q^{69} + 24 q^{70} + 12 q^{75} - 96 q^{78} + 18 q^{81} + 96 q^{82} + 16 q^{91} + 18 q^{93} - 52 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.98168 + 1.43977i 1.40126 + 1.01807i 0.994522 + 0.104528i \(0.0333333\pi\)
0.406737 + 0.913545i \(0.366667\pi\)
\(3\) −1.28716 + 1.15897i −0.743145 + 0.669131i
\(4\) 1.23607 + 3.80423i 0.618034 + 1.90211i
\(5\) 1.01807 + 1.40126i 0.455296 + 0.626662i 0.973525 0.228580i \(-0.0734083\pi\)
−0.518229 + 0.855242i \(0.673408\pi\)
\(6\) −4.21940 + 0.443477i −1.72256 + 0.181049i
\(7\) −1.34500 + 0.437016i −0.508361 + 0.165177i −0.551957 0.833873i \(-0.686119\pi\)
0.0435957 + 0.999049i \(0.486119\pi\)
\(8\) −1.51387 + 4.65921i −0.535233 + 1.64728i
\(9\) 0.313585 2.98357i 0.104528 0.994522i
\(10\) 4.24264i 1.34164i
\(11\) 0 0
\(12\) −6.00000 3.46410i −1.73205 1.00000i
\(13\) 1.66251 2.28825i 0.461097 0.634645i −0.513639 0.858006i \(-0.671703\pi\)
0.974736 + 0.223361i \(0.0717029\pi\)
\(14\) −3.29456 1.07047i −0.880507 0.286094i
\(15\) −2.93444 0.623735i −0.757670 0.161048i
\(16\) −3.23607 + 2.35114i −0.809017 + 0.587785i
\(17\) 1.98168 1.43977i 0.480628 0.349196i −0.320941 0.947099i \(-0.603999\pi\)
0.801569 + 0.597903i \(0.203999\pi\)
\(18\) 4.91709 5.46098i 1.15897 1.28716i
\(19\) −2.68999 0.874032i −0.617127 0.200517i −0.0162627 0.999868i \(-0.505177\pi\)
−0.600864 + 0.799351i \(0.705177\pi\)
\(20\) −4.07230 + 5.60503i −0.910593 + 1.25332i
\(21\) 1.22474 2.12132i 0.267261 0.462910i
\(22\) 0 0
\(23\) 8.66025i 1.80579i 0.429863 + 0.902894i \(0.358562\pi\)
−0.429863 + 0.902894i \(0.641438\pi\)
\(24\) −3.45127 7.75169i −0.704489 1.58231i
\(25\) 0.618034 1.90211i 0.123607 0.380423i
\(26\) 6.58911 2.14093i 1.29223 0.419871i
\(27\) 3.05422 + 4.20378i 0.587785 + 0.809017i
\(28\) −3.32502 4.57649i −0.628369 0.864876i
\(29\) 1.51387 + 4.65921i 0.281118 + 0.865193i 0.987535 + 0.157397i \(0.0503103\pi\)
−0.706417 + 0.707796i \(0.749690\pi\)
\(30\) −4.91709 5.46098i −0.897733 0.997033i
\(31\) −2.42705 1.76336i −0.435911 0.316708i 0.348097 0.937459i \(-0.386828\pi\)
−0.784008 + 0.620750i \(0.786828\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) −1.98168 1.43977i −0.334965 0.243366i
\(36\) 11.7378 2.49494i 1.95630 0.415823i
\(37\) 0.927051 + 2.85317i 0.152406 + 0.469058i 0.997889 0.0649448i \(-0.0206871\pi\)
−0.845483 + 0.534003i \(0.820687\pi\)
\(38\) −4.07230 5.60503i −0.660614 0.909257i
\(39\) 0.512083 + 4.87214i 0.0819989 + 0.780167i
\(40\) −8.06998 + 2.62210i −1.27598 + 0.414590i
\(41\) 3.02774 9.31841i 0.472853 1.45529i −0.375979 0.926628i \(-0.622693\pi\)
0.848832 0.528663i \(-0.177307\pi\)
\(42\) 5.48127 2.44042i 0.845779 0.376565i
\(43\) 9.89949i 1.50966i −0.655921 0.754829i \(-0.727720\pi\)
0.655921 0.754829i \(-0.272280\pi\)
\(44\) 0 0
\(45\) 4.50000 2.59808i 0.670820 0.387298i
\(46\) −12.4688 + 17.1618i −1.83843 + 2.53038i
\(47\) 6.58911 + 2.14093i 0.961121 + 0.312287i 0.747226 0.664570i \(-0.231385\pi\)
0.213895 + 0.976857i \(0.431385\pi\)
\(48\) 1.44045 6.77681i 0.207912 0.978148i
\(49\) −4.04508 + 2.93893i −0.577869 + 0.419847i
\(50\) 3.96336 2.87955i 0.560503 0.407230i
\(51\) −0.882095 + 4.14993i −0.123518 + 0.581106i
\(52\) 10.7600 + 3.49613i 1.49214 + 0.484826i
\(53\) −2.03615 + 2.80252i −0.279686 + 0.384955i −0.925630 0.378430i \(-0.876464\pi\)
0.645944 + 0.763385i \(0.276464\pi\)
\(54\) 12.7279i 1.73205i
\(55\) 0 0
\(56\) 6.92820i 0.925820i
\(57\) 4.47544 1.99259i 0.592787 0.263926i
\(58\) −3.70820 + 11.4127i −0.486911 + 1.49856i
\(59\) 1.64728 0.535233i 0.214457 0.0696814i −0.199818 0.979833i \(-0.564035\pi\)
0.414275 + 0.910152i \(0.364035\pi\)
\(60\) −1.25434 11.9343i −0.161935 1.54071i
\(61\) −1.66251 2.28825i −0.212862 0.292980i 0.689213 0.724559i \(-0.257957\pi\)
−0.902075 + 0.431579i \(0.857957\pi\)
\(62\) −2.27080 6.98881i −0.288392 0.887580i
\(63\) 0.882095 + 4.14993i 0.111133 + 0.522842i
\(64\) 6.47214 + 4.70228i 0.809017 + 0.587785i
\(65\) 4.89898 0.607644
\(66\) 0 0
\(67\) −3.00000 −0.366508 −0.183254 0.983066i \(-0.558663\pi\)
−0.183254 + 0.983066i \(0.558663\pi\)
\(68\) 7.92672 + 5.75910i 0.961255 + 0.698393i
\(69\) −10.0370 11.1472i −1.20831 1.34196i
\(70\) −1.85410 5.70634i −0.221608 0.682038i
\(71\) 1.01807 + 1.40126i 0.120823 + 0.166299i 0.865144 0.501523i \(-0.167227\pi\)
−0.744321 + 0.667822i \(0.767227\pi\)
\(72\) 13.4263 + 5.97778i 1.58231 + 0.704489i
\(73\) 5.37999 1.74806i 0.629680 0.204595i 0.0232466 0.999730i \(-0.492600\pi\)
0.606433 + 0.795134i \(0.292600\pi\)
\(74\) −2.27080 + 6.98881i −0.263975 + 0.812433i
\(75\) 1.40898 + 3.16461i 0.162695 + 0.365418i
\(76\) 11.3137i 1.29777i
\(77\) 0 0
\(78\) −6.00000 + 10.3923i −0.679366 + 1.17670i
\(79\) 5.81878 8.00886i 0.654664 0.901067i −0.344627 0.938740i \(-0.611994\pi\)
0.999290 + 0.0376728i \(0.0119944\pi\)
\(80\) −6.58911 2.14093i −0.736685 0.239364i
\(81\) −8.80333 1.87121i −0.978148 0.207912i
\(82\) 19.4164 14.1068i 2.14418 1.55784i
\(83\) −1.98168 + 1.43977i −0.217518 + 0.158036i −0.691208 0.722655i \(-0.742921\pi\)
0.473691 + 0.880691i \(0.342921\pi\)
\(84\) 9.58385 + 2.03711i 1.04568 + 0.222267i
\(85\) 4.03499 + 1.31105i 0.437656 + 0.142203i
\(86\) 14.2530 19.6176i 1.53694 2.11542i
\(87\) −7.34847 4.24264i −0.787839 0.454859i
\(88\) 0 0
\(89\) 8.66025i 0.917985i −0.888440 0.458993i \(-0.848210\pi\)
0.888440 0.458993i \(-0.151790\pi\)
\(90\) 12.6582 + 1.33043i 1.33429 + 0.140240i
\(91\) −1.23607 + 3.80423i −0.129575 + 0.398791i
\(92\) −32.9456 + 10.7047i −3.43481 + 1.11604i
\(93\) 5.16769 0.543146i 0.535864 0.0563216i
\(94\) 9.97505 + 13.7295i 1.02885 + 1.41609i
\(95\) −1.51387 4.65921i −0.155320 0.478024i
\(96\) 0 0
\(97\) −10.5172 7.64121i −1.06786 0.775847i −0.0923353 0.995728i \(-0.529433\pi\)
−0.975527 + 0.219881i \(0.929433\pi\)
\(98\) −12.2474 −1.23718
\(99\) 0 0
\(100\) 8.00000 0.800000
\(101\) −9.90839 7.19887i −0.985922 0.716314i −0.0268978 0.999638i \(-0.508563\pi\)
−0.959024 + 0.283324i \(0.908563\pi\)
\(102\) −7.72299 + 6.95381i −0.764690 + 0.688530i
\(103\) −0.618034 1.90211i −0.0608967 0.187421i 0.915980 0.401224i \(-0.131415\pi\)
−0.976877 + 0.213803i \(0.931415\pi\)
\(104\) 8.14459 + 11.2101i 0.798643 + 1.09924i
\(105\) 4.21940 0.443477i 0.411771 0.0432789i
\(106\) −8.06998 + 2.62210i −0.783826 + 0.254680i
\(107\) 0.756934 2.32960i 0.0731756 0.225211i −0.907779 0.419449i \(-0.862223\pi\)
0.980954 + 0.194238i \(0.0622233\pi\)
\(108\) −12.2169 + 16.8151i −1.17557 + 1.61803i
\(109\) 18.3848i 1.76094i 0.474100 + 0.880471i \(0.342774\pi\)
−0.474100 + 0.880471i \(0.657226\pi\)
\(110\) 0 0
\(111\) −4.50000 2.59808i −0.427121 0.246598i
\(112\) 3.32502 4.57649i 0.314184 0.432438i
\(113\) −1.64728 0.535233i −0.154963 0.0503505i 0.230508 0.973070i \(-0.425961\pi\)
−0.385471 + 0.922720i \(0.625961\pi\)
\(114\) 11.7378 + 2.49494i 1.09934 + 0.233673i
\(115\) −12.1353 + 8.81678i −1.13162 + 0.822169i
\(116\) −15.8534 + 11.5182i −1.47195 + 1.06944i
\(117\) −6.30579 5.67776i −0.582971 0.524909i
\(118\) 4.03499 + 1.31105i 0.371451 + 0.120692i
\(119\) −2.03615 + 2.80252i −0.186653 + 0.256906i
\(120\) 7.34847 12.7279i 0.670820 1.16190i
\(121\) 0 0
\(122\) 6.92820i 0.627250i
\(123\) 6.90255 + 15.5034i 0.622382 + 1.39789i
\(124\) 3.70820 11.4127i 0.333007 1.02489i
\(125\) 11.5309 3.74663i 1.03136 0.335109i
\(126\) −4.22693 + 9.49384i −0.376565 + 0.845779i
\(127\) −1.66251 2.28825i −0.147524 0.203049i 0.728860 0.684663i \(-0.240051\pi\)
−0.876383 + 0.481614i \(0.840051\pi\)
\(128\) 6.05547 + 18.6368i 0.535233 + 1.64728i
\(129\) 11.4732 + 12.7423i 1.01016 + 1.12190i
\(130\) 9.70820 + 7.05342i 0.851466 + 0.618626i
\(131\) −12.2474 −1.07006 −0.535032 0.844832i \(-0.679701\pi\)
−0.535032 + 0.844832i \(0.679701\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) −5.94504 4.31932i −0.513573 0.373133i
\(135\) −2.78115 + 8.55951i −0.239364 + 0.736685i
\(136\) 3.70820 + 11.4127i 0.317976 + 0.978629i
\(137\) −9.16267 12.6113i −0.782819 1.07746i −0.994965 0.100220i \(-0.968045\pi\)
0.212146 0.977238i \(-0.431955\pi\)
\(138\) −3.84062 36.5411i −0.326935 3.11058i
\(139\) −14.7950 + 4.80718i −1.25489 + 0.407739i −0.859672 0.510847i \(-0.829332\pi\)
−0.395221 + 0.918586i \(0.629332\pi\)
\(140\) 3.02774 9.31841i 0.255890 0.787550i
\(141\) −10.9625 + 4.88084i −0.923213 + 0.411041i
\(142\) 4.24264i 0.356034i
\(143\) 0 0
\(144\) 6.00000 + 10.3923i 0.500000 + 0.866025i
\(145\) −4.98752 + 6.86474i −0.414191 + 0.570085i
\(146\) 13.1782 + 4.28187i 1.09064 + 0.354370i
\(147\) 1.80057 8.47101i 0.148508 0.698677i
\(148\) −9.70820 + 7.05342i −0.798009 + 0.579788i
\(149\) 1.98168 1.43977i 0.162345 0.117951i −0.503646 0.863910i \(-0.668009\pi\)
0.665992 + 0.745959i \(0.268009\pi\)
\(150\) −1.76419 + 8.29986i −0.144045 + 0.677681i
\(151\) −9.41498 3.05911i −0.766180 0.248947i −0.100251 0.994962i \(-0.531965\pi\)
−0.665929 + 0.746015i \(0.731965\pi\)
\(152\) 8.14459 11.2101i 0.660614 0.909257i
\(153\) −3.67423 6.36396i −0.297044 0.514496i
\(154\) 0 0
\(155\) 5.19615i 0.417365i
\(156\) −17.9018 + 7.97038i −1.43329 + 0.638141i
\(157\) 4.63525 14.2658i 0.369934 1.13854i −0.576900 0.816815i \(-0.695738\pi\)
0.946834 0.321724i \(-0.104262\pi\)
\(158\) 23.0619 7.49326i 1.83471 0.596132i
\(159\) −0.627171 5.96713i −0.0497379 0.473224i
\(160\) 0 0
\(161\) −3.78467 11.6480i −0.298274 0.917992i
\(162\) −14.7513 16.3829i −1.15897 1.28716i
\(163\) 8.09017 + 5.87785i 0.633671 + 0.460389i 0.857670 0.514200i \(-0.171911\pi\)
−0.223999 + 0.974589i \(0.571911\pi\)
\(164\) 39.1918 3.06037
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) −15.8534 11.5182i −1.22678 0.891304i −0.230131 0.973160i \(-0.573915\pi\)
−0.996644 + 0.0818552i \(0.973915\pi\)
\(168\) 8.02957 + 8.91774i 0.619495 + 0.688018i
\(169\) 1.54508 + 4.75528i 0.118853 + 0.365791i
\(170\) 6.10844 + 8.40755i 0.468496 + 0.644830i
\(171\) −3.45127 + 7.75169i −0.263926 + 0.592787i
\(172\) 37.6599 12.2364i 2.87154 0.933020i
\(173\) −0.756934 + 2.32960i −0.0575486 + 0.177116i −0.975699 0.219116i \(-0.929683\pi\)
0.918150 + 0.396233i \(0.129683\pi\)
\(174\) −8.45386 18.9877i −0.640886 1.43945i
\(175\) 2.82843i 0.213809i
\(176\) 0 0
\(177\) −1.50000 + 2.59808i −0.112747 + 0.195283i
\(178\) 12.4688 17.1618i 0.934577 1.28633i
\(179\) 14.8255 + 4.81710i 1.10811 + 0.360047i 0.805219 0.592978i \(-0.202048\pi\)
0.302892 + 0.953025i \(0.402048\pi\)
\(180\) 15.4460 + 13.9076i 1.15128 + 1.03661i
\(181\) 4.04508 2.93893i 0.300669 0.218449i −0.427213 0.904151i \(-0.640505\pi\)
0.727882 + 0.685702i \(0.240505\pi\)
\(182\) −7.92672 + 5.75910i −0.587567 + 0.426893i
\(183\) 4.79193 + 1.01856i 0.354229 + 0.0752938i
\(184\) −40.3499 13.1105i −2.97463 0.966517i
\(185\) −3.05422 + 4.20378i −0.224551 + 0.309068i
\(186\) 11.0227 + 6.36396i 0.808224 + 0.466628i
\(187\) 0 0
\(188\) 27.7128i 2.02116i
\(189\) −5.94504 4.31932i −0.432438 0.314184i
\(190\) 3.70820 11.4127i 0.269021 0.827963i
\(191\) −4.94183 + 1.60570i −0.357579 + 0.116184i −0.482297 0.876008i \(-0.660197\pi\)
0.124718 + 0.992192i \(0.460197\pi\)
\(192\) −13.7805 + 1.44839i −0.994522 + 0.104528i
\(193\) −8.31254 11.4412i −0.598350 0.823558i 0.397206 0.917729i \(-0.369980\pi\)
−0.995556 + 0.0941717i \(0.969980\pi\)
\(194\) −9.84014 30.2848i −0.706481 2.17432i
\(195\) −6.30579 + 5.67776i −0.451567 + 0.406593i
\(196\) −16.1803 11.7557i −1.15574 0.839693i
\(197\) 7.34847 0.523557 0.261778 0.965128i \(-0.415691\pi\)
0.261778 + 0.965128i \(0.415691\pi\)
\(198\) 0 0
\(199\) −18.0000 −1.27599 −0.637993 0.770042i \(-0.720235\pi\)
−0.637993 + 0.770042i \(0.720235\pi\)
\(200\) 7.92672 + 5.75910i 0.560503 + 0.407230i
\(201\) 3.86149 3.47690i 0.272369 0.245242i
\(202\) −9.27051 28.5317i −0.652271 2.00748i
\(203\) −4.07230 5.60503i −0.285819 0.393396i
\(204\) −16.8776 + 1.77391i −1.18167 + 0.124198i
\(205\) 16.1400 5.24419i 1.12726 0.366270i
\(206\) 1.51387 4.65921i 0.105476 0.324622i
\(207\) 25.8384 + 2.71573i 1.79590 + 0.188756i
\(208\) 11.3137i 0.784465i
\(209\) 0 0
\(210\) 9.00000 + 5.19615i 0.621059 + 0.358569i
\(211\) 3.32502 4.57649i 0.228904 0.315059i −0.679080 0.734064i \(-0.737621\pi\)
0.907984 + 0.419005i \(0.137621\pi\)
\(212\) −13.1782 4.28187i −0.905084 0.294080i
\(213\) −2.93444 0.623735i −0.201065 0.0427376i
\(214\) 4.85410 3.52671i 0.331820 0.241081i
\(215\) 13.8718 10.0784i 0.946046 0.687342i
\(216\) −24.2099 + 7.86629i −1.64728 + 0.535233i
\(217\) 4.03499 + 1.31105i 0.273913 + 0.0889997i
\(218\) −26.4699 + 36.4327i −1.79277 + 2.46754i
\(219\) −4.89898 + 8.48528i −0.331042 + 0.573382i
\(220\) 0 0
\(221\) 6.92820i 0.466041i
\(222\) −5.17691 11.6275i −0.347452 0.780389i
\(223\) −3.39919 + 10.4616i −0.227626 + 0.700562i 0.770388 + 0.637575i \(0.220063\pi\)
−0.998014 + 0.0629866i \(0.979937\pi\)
\(224\) 0 0
\(225\) −5.48127 2.44042i −0.365418 0.162695i
\(226\) −2.49376 3.43237i −0.165883 0.228318i
\(227\) 6.81241 + 20.9664i 0.452155 + 1.39159i 0.874443 + 0.485129i \(0.161227\pi\)
−0.422287 + 0.906462i \(0.638773\pi\)
\(228\) 13.1122 + 14.5626i 0.868379 + 0.964432i
\(229\) 7.28115 + 5.29007i 0.481152 + 0.349577i 0.801772 0.597631i \(-0.203891\pi\)
−0.320619 + 0.947208i \(0.603891\pi\)
\(230\) −36.7423 −2.42272
\(231\) 0 0
\(232\) −24.0000 −1.57568
\(233\) 19.8168 + 14.3977i 1.29824 + 0.943227i 0.999937 0.0112436i \(-0.00357902\pi\)
0.298304 + 0.954471i \(0.403579\pi\)
\(234\) −4.32136 20.3304i −0.282496 1.32904i
\(235\) 3.70820 + 11.4127i 0.241897 + 0.744481i
\(236\) 4.07230 + 5.60503i 0.265084 + 0.364857i
\(237\) 1.79229 + 17.0525i 0.116422 + 1.10768i
\(238\) −8.06998 + 2.62210i −0.523099 + 0.169965i
\(239\) −6.81241 + 20.9664i −0.440658 + 1.35621i 0.446518 + 0.894775i \(0.352664\pi\)
−0.887176 + 0.461431i \(0.847336\pi\)
\(240\) 10.9625 4.88084i 0.707629 0.315057i
\(241\) 2.82843i 0.182195i −0.995842 0.0910975i \(-0.970963\pi\)
0.995842 0.0910975i \(-0.0290375\pi\)
\(242\) 0 0
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 6.65003 9.15298i 0.425725 0.585960i
\(245\) −8.23639 2.67617i −0.526204 0.170974i
\(246\) −8.64273 + 40.6608i −0.551040 + 2.59244i
\(247\) −6.47214 + 4.70228i −0.411812 + 0.299199i
\(248\) 11.8901 8.63864i 0.755020 0.548554i
\(249\) 0.882095 4.14993i 0.0559005 0.262991i
\(250\) 28.2449 + 9.17734i 1.78637 + 0.580426i
\(251\) 9.16267 12.6113i 0.578342 0.796020i −0.415170 0.909744i \(-0.636278\pi\)
0.993512 + 0.113724i \(0.0362779\pi\)
\(252\) −14.6969 + 8.48528i −0.925820 + 0.534522i
\(253\) 0 0
\(254\) 6.92820i 0.434714i
\(255\) −6.71316 + 2.98889i −0.420394 + 0.187172i
\(256\) −9.88854 + 30.4338i −0.618034 + 1.90211i
\(257\) 9.88367 3.21140i 0.616526 0.200322i 0.0159289 0.999873i \(-0.494929\pi\)
0.600597 + 0.799552i \(0.294929\pi\)
\(258\) 4.39020 + 41.7699i 0.273322 + 2.60048i
\(259\) −2.49376 3.43237i −0.154955 0.213277i
\(260\) 6.05547 + 18.6368i 0.375544 + 1.15581i
\(261\) 14.3758 3.05567i 0.889838 0.189141i
\(262\) −24.2705 17.6336i −1.49944 1.08940i
\(263\) 12.2474 0.755210 0.377605 0.925967i \(-0.376748\pi\)
0.377605 + 0.925967i \(0.376748\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 7.92672 + 5.75910i 0.486018 + 0.353113i
\(267\) 10.0370 + 11.1472i 0.614252 + 0.682196i
\(268\) −3.70820 11.4127i −0.226515 0.697140i
\(269\) 10.1807 + 14.0126i 0.620731 + 0.854362i 0.997406 0.0719830i \(-0.0229327\pi\)
−0.376675 + 0.926345i \(0.622933\pi\)
\(270\) −17.8351 + 12.9580i −1.08541 + 0.788597i
\(271\) −5.37999 + 1.74806i −0.326811 + 0.106187i −0.467827 0.883820i \(-0.654963\pi\)
0.141016 + 0.990007i \(0.454963\pi\)
\(272\) −3.02774 + 9.31841i −0.183583 + 0.565012i
\(273\) −2.81795 6.32923i −0.170550 0.383062i
\(274\) 38.1838i 2.30677i
\(275\) 0 0
\(276\) 30.0000 51.9615i 1.80579 3.12772i
\(277\) −10.8063 + 14.8736i −0.649288 + 0.893668i −0.999068 0.0431639i \(-0.986256\pi\)
0.349780 + 0.936832i \(0.386256\pi\)
\(278\) −36.2401 11.7751i −2.17354 0.706225i
\(279\) −6.02218 + 6.68830i −0.360538 + 0.400418i
\(280\) 9.70820 7.05342i 0.580176 0.421523i
\(281\) −17.8351 + 12.9580i −1.06395 + 0.773007i −0.974816 0.223012i \(-0.928411\pi\)
−0.0891377 + 0.996019i \(0.528411\pi\)
\(282\) −28.7516 6.11133i −1.71213 0.363924i
\(283\) −18.8300 6.11822i −1.11932 0.363691i −0.309815 0.950797i \(-0.600267\pi\)
−0.809510 + 0.587106i \(0.800267\pi\)
\(284\) −4.07230 + 5.60503i −0.241646 + 0.332598i
\(285\) 7.34847 + 4.24264i 0.435286 + 0.251312i
\(286\) 0 0
\(287\) 13.8564i 0.817918i
\(288\) 0 0
\(289\) −3.39919 + 10.4616i −0.199952 + 0.615390i
\(290\) −19.7673 + 6.42280i −1.16078 + 0.377160i
\(291\) 22.3933 2.35363i 1.31272 0.137972i
\(292\) 13.3001 + 18.3060i 0.778327 + 1.07128i
\(293\) 1.51387 + 4.65921i 0.0884411 + 0.272194i 0.985489 0.169740i \(-0.0542927\pi\)
−0.897048 + 0.441934i \(0.854293\pi\)
\(294\) 15.7645 14.1944i 0.919403 0.827834i
\(295\) 2.42705 + 1.76336i 0.141308 + 0.102667i
\(296\) −14.6969 −0.854242
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 19.8168 + 14.3977i 1.14603 + 0.832643i
\(300\) −10.2973 + 9.27175i −0.594516 + 0.535304i
\(301\) 4.32624 + 13.3148i 0.249360 + 0.767452i
\(302\) −14.2530 19.6176i −0.820170 1.12887i
\(303\) 21.0970 2.21738i 1.21199 0.127385i
\(304\) 10.7600 3.49613i 0.617127 0.200517i
\(305\) 1.51387 4.65921i 0.0866838 0.266785i
\(306\) 1.88151 17.9014i 0.107559 1.02335i
\(307\) 2.82843i 0.161427i −0.996737 0.0807134i \(-0.974280\pi\)
0.996737 0.0807134i \(-0.0257199\pi\)
\(308\) 0 0
\(309\) 3.00000 + 1.73205i 0.170664 + 0.0985329i
\(310\) 7.48128 10.2971i 0.424908 0.584836i
\(311\) −16.4728 5.35233i −0.934086 0.303503i −0.197853 0.980232i \(-0.563397\pi\)
−0.736232 + 0.676729i \(0.763397\pi\)
\(312\) −23.4755 4.98988i −1.32904 0.282496i
\(313\) 26.6976 19.3969i 1.50904 1.09638i 0.542432 0.840099i \(-0.317503\pi\)
0.966603 0.256279i \(-0.0824966\pi\)
\(314\) 29.7252 21.5966i 1.67749 1.21877i
\(315\) −4.91709 + 5.46098i −0.277046 + 0.307691i
\(316\) 37.6599 + 12.2364i 2.11854 + 0.688354i
\(317\) −1.01807 + 1.40126i −0.0571807 + 0.0787025i −0.836650 0.547738i \(-0.815489\pi\)
0.779469 + 0.626441i \(0.215489\pi\)
\(318\) 7.34847 12.7279i 0.412082 0.713746i
\(319\) 0 0
\(320\) 13.8564i 0.774597i
\(321\) 1.72564 + 3.87585i 0.0963157 + 0.216329i
\(322\) 9.27051 28.5317i 0.516625 1.59001i
\(323\) −6.58911 + 2.14093i −0.366628 + 0.119125i
\(324\) −3.76302 35.8028i −0.209057 1.98904i
\(325\) −3.32502 4.57649i −0.184439 0.253858i
\(326\) 7.56934 + 23.2960i 0.419227 + 1.29025i
\(327\) −21.3074 23.6642i −1.17830 1.30864i
\(328\) 38.8328 + 28.2137i 2.14418 + 1.55784i
\(329\) −9.79796 −0.540179
\(330\) 0 0
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) −7.92672 5.75910i −0.435035 0.316071i
\(333\) 8.80333 1.87121i 0.482419 0.102541i
\(334\) −14.8328 45.6507i −0.811616 2.49790i
\(335\) −3.05422 4.20378i −0.166870 0.229677i
\(336\) 1.02417 + 9.74428i 0.0558728 + 0.531594i
\(337\) 22.8649 7.42927i 1.24553 0.404698i 0.389215 0.921147i \(-0.372746\pi\)
0.856318 + 0.516449i \(0.172746\pi\)
\(338\) −3.78467 + 11.6480i −0.205859 + 0.633569i
\(339\) 2.74064 1.22021i 0.148851 0.0662727i
\(340\) 16.9706i 0.920358i
\(341\) 0 0
\(342\) −18.0000 + 10.3923i −0.973329 + 0.561951i
\(343\) 9.97505 13.7295i 0.538602 0.741322i
\(344\) 46.1238 + 14.9865i 2.48683 + 0.808019i
\(345\) 5.40170 25.4130i 0.290818 1.36819i
\(346\) −4.85410 + 3.52671i −0.260958 + 0.189597i
\(347\) 7.92672 5.75910i 0.425528 0.309164i −0.354330 0.935120i \(-0.615291\pi\)
0.779858 + 0.625956i \(0.215291\pi\)
\(348\) 7.05676 33.1994i 0.378282 1.77968i
\(349\) −9.41498 3.05911i −0.503972 0.163751i 0.0459869 0.998942i \(-0.485357\pi\)
−0.549959 + 0.835192i \(0.685357\pi\)
\(350\) −4.07230 + 5.60503i −0.217673 + 0.299602i
\(351\) 14.6969 0.784465
\(352\) 0 0
\(353\) 25.9808i 1.38282i 0.722464 + 0.691408i \(0.243009\pi\)
−0.722464 + 0.691408i \(0.756991\pi\)
\(354\) −6.71316 + 2.98889i −0.356800 + 0.158858i
\(355\) −0.927051 + 2.85317i −0.0492028 + 0.151431i
\(356\) 32.9456 10.7047i 1.74611 0.567346i
\(357\) −0.627171 5.96713i −0.0331934 0.315814i
\(358\) 22.4439 + 30.8913i 1.18619 + 1.63266i
\(359\) −7.56934 23.2960i −0.399494 1.22952i −0.925406 0.378978i \(-0.876276\pi\)
0.525911 0.850539i \(-0.323724\pi\)
\(360\) 5.29257 + 24.8996i 0.278943 + 1.31232i
\(361\) −8.89919 6.46564i −0.468378 0.340297i
\(362\) 12.2474 0.643712
\(363\) 0 0
\(364\) −16.0000 −0.838628
\(365\) 7.92672 + 5.75910i 0.414903 + 0.301445i
\(366\) 8.02957 + 8.91774i 0.419712 + 0.466138i
\(367\) −2.16312 6.65740i −0.112914 0.347513i 0.878592 0.477573i \(-0.158483\pi\)
−0.991506 + 0.130059i \(0.958483\pi\)
\(368\) −20.3615 28.0252i −1.06142 1.46091i
\(369\) −26.8526 11.9556i −1.39789 0.622382i
\(370\) −12.1050 + 3.93314i −0.629308 + 0.204474i
\(371\) 1.51387 4.65921i 0.0785961 0.241894i
\(372\) 8.45386 + 18.9877i 0.438312 + 0.984466i
\(373\) 32.5269i 1.68418i 0.539337 + 0.842090i \(0.318675\pi\)
−0.539337 + 0.842090i \(0.681325\pi\)
\(374\) 0 0
\(375\) −10.5000 + 18.1865i −0.542218 + 0.939149i
\(376\) −19.9501 + 27.4589i −1.02885 + 1.41609i
\(377\) 13.1782 + 4.28187i 0.678713 + 0.220527i
\(378\) −5.56231 17.1190i −0.286094 0.880507i
\(379\) −13.7533 + 9.99235i −0.706459 + 0.513273i −0.882029 0.471194i \(-0.843823\pi\)
0.175570 + 0.984467i \(0.443823\pi\)
\(380\) 15.8534 11.5182i 0.813264 0.590871i
\(381\) 4.79193 + 1.01856i 0.245498 + 0.0521822i
\(382\) −12.1050 3.93314i −0.619344 0.201237i
\(383\) 13.2350 18.2164i 0.676275 0.930813i −0.323607 0.946192i \(-0.604896\pi\)
0.999882 + 0.0153791i \(0.00489551\pi\)
\(384\) −29.3939 16.9706i −1.50000 0.866025i
\(385\) 0 0
\(386\) 34.6410i 1.76318i
\(387\) −29.5358 3.10434i −1.50139 0.157802i
\(388\) 16.0689 49.4549i 0.815774 2.51069i
\(389\) −21.4146 + 6.95803i −1.08576 + 0.352786i −0.796608 0.604496i \(-0.793375\pi\)
−0.289156 + 0.957282i \(0.593375\pi\)
\(390\) −20.6707 + 2.17258i −1.04670 + 0.110013i
\(391\) 12.4688 + 17.1618i 0.630575 + 0.867912i
\(392\) −7.56934 23.2960i −0.382309 1.17663i
\(393\) 15.7645 14.1944i 0.795213 0.716013i
\(394\) 14.5623 + 10.5801i 0.733638 + 0.533019i
\(395\) 17.1464 0.862730
\(396\) 0 0
\(397\) 32.0000 1.60603 0.803017 0.595956i \(-0.203227\pi\)
0.803017 + 0.595956i \(0.203227\pi\)
\(398\) −35.6702 25.9159i −1.78799 1.29905i
\(399\) −5.14866 + 4.63587i −0.257755 + 0.232084i
\(400\) 2.47214 + 7.60845i 0.123607 + 0.380423i
\(401\) 6.10844 + 8.40755i 0.305041 + 0.419853i 0.933827 0.357726i \(-0.116448\pi\)
−0.628786 + 0.777579i \(0.716448\pi\)
\(402\) 12.6582 1.33043i 0.631333 0.0663558i
\(403\) −8.06998 + 2.62210i −0.401994 + 0.130616i
\(404\) 15.1387 46.5921i 0.753177 2.31804i
\(405\) −6.34040 14.2408i −0.315057 0.707629i
\(406\) 16.9706i 0.842235i
\(407\) 0 0
\(408\) −18.0000 10.3923i −0.891133 0.514496i
\(409\) −10.8063 + 14.8736i −0.534337 + 0.735452i −0.987784 0.155831i \(-0.950194\pi\)
0.453446 + 0.891284i \(0.350194\pi\)
\(410\) 39.5347 + 12.8456i 1.95248 + 0.634399i
\(411\) 26.4100 + 5.61362i 1.30271 + 0.276899i
\(412\) 6.47214 4.70228i 0.318859 0.231665i
\(413\) −1.98168 + 1.43977i −0.0975120 + 0.0708466i
\(414\) 47.2934 + 42.5832i 2.32435 + 2.09285i
\(415\) −4.03499 1.31105i −0.198070 0.0643568i
\(416\) 0 0
\(417\) 13.4722 23.3345i 0.659736 1.14270i
\(418\) 0 0
\(419\) 6.92820i 0.338465i −0.985576 0.169232i \(-0.945871\pi\)
0.985576 0.169232i \(-0.0541289\pi\)
\(420\) 6.90255 + 15.5034i 0.336810 + 0.756488i
\(421\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(422\) 13.1782 4.28187i 0.641506 0.208438i
\(423\) 8.45386 18.9877i 0.411041 0.923213i
\(424\) −9.97505 13.7295i −0.484431 0.666762i
\(425\) −1.51387 4.65921i −0.0734334 0.226005i
\(426\) −4.91709 5.46098i −0.238234 0.264585i
\(427\) 3.23607 + 2.35114i 0.156604 + 0.113780i
\(428\) 9.79796 0.473602
\(429\) 0 0
\(430\) 42.0000 2.02542
\(431\) 5.94504 + 4.31932i 0.286362 + 0.208054i 0.721688 0.692219i \(-0.243367\pi\)
−0.435325 + 0.900273i \(0.643367\pi\)
\(432\) −19.7673 6.42280i −0.951057 0.309017i
\(433\) 1.54508 + 4.75528i 0.0742520 + 0.228524i 0.981294 0.192517i \(-0.0616649\pi\)
−0.907042 + 0.421041i \(0.861665\pi\)
\(434\) 6.10844 + 8.40755i 0.293215 + 0.403575i
\(435\) −1.53625 14.6164i −0.0736575 0.700804i
\(436\) −69.9398 + 22.7248i −3.34951 + 1.08832i
\(437\) 7.56934 23.2960i 0.362091 1.11440i
\(438\) −21.9251 + 9.76168i −1.04762 + 0.466431i
\(439\) 5.65685i 0.269987i −0.990846 0.134993i \(-0.956899\pi\)
0.990846 0.134993i \(-0.0431013\pi\)
\(440\) 0 0
\(441\) 7.50000 + 12.9904i 0.357143 + 0.618590i
\(442\) 9.97505 13.7295i 0.474465 0.653044i
\(443\) −24.7092 8.02850i −1.17397 0.381445i −0.343846 0.939026i \(-0.611730\pi\)
−0.830123 + 0.557581i \(0.811730\pi\)
\(444\) 4.32136 20.3304i 0.205083 0.964839i
\(445\) 12.1353 8.81678i 0.575266 0.417955i
\(446\) −21.7985 + 15.8375i −1.03219 + 0.749928i
\(447\) −0.882095 + 4.14993i −0.0417216 + 0.196285i
\(448\) −10.7600 3.49613i −0.508361 0.165177i
\(449\) −7.12652 + 9.80881i −0.336321 + 0.462906i −0.943362 0.331764i \(-0.892356\pi\)
0.607041 + 0.794670i \(0.292356\pi\)
\(450\) −7.34847 12.7279i −0.346410 0.600000i
\(451\) 0 0
\(452\) 6.92820i 0.325875i
\(453\) 15.6640 6.97408i 0.735961 0.327671i
\(454\) −16.6869 + 51.3571i −0.783156 + 2.41031i
\(455\) −6.58911 + 2.14093i −0.308902 + 0.100368i
\(456\) 2.50868 + 23.8685i 0.117480 + 1.11775i
\(457\) −18.2876 25.1707i −0.855457 1.17744i −0.982634 0.185556i \(-0.940591\pi\)
0.127177 0.991880i \(-0.459409\pi\)
\(458\) 6.81241 + 20.9664i 0.318323 + 0.979697i
\(459\) 12.1050 + 3.93314i 0.565012 + 0.183583i
\(460\) −48.5410 35.2671i −2.26324 1.64434i
\(461\) −4.89898 −0.228168 −0.114084 0.993471i \(-0.536393\pi\)
−0.114084 + 0.993471i \(0.536393\pi\)
\(462\) 0 0
\(463\) 19.0000 0.883005 0.441502 0.897260i \(-0.354446\pi\)
0.441502 + 0.897260i \(0.354446\pi\)
\(464\) −15.8534 11.5182i −0.735977 0.534719i
\(465\) 6.02218 + 6.68830i 0.279272 + 0.310163i
\(466\) 18.5410 + 57.0634i 0.858896 + 2.64341i
\(467\) 15.2711 + 21.0189i 0.706663 + 0.972638i 0.999862 + 0.0165865i \(0.00527989\pi\)
−0.293200 + 0.956051i \(0.594720\pi\)
\(468\) 13.8051 31.0068i 0.638141 1.43329i
\(469\) 4.03499 1.31105i 0.186319 0.0605386i
\(470\) −9.08321 + 27.9552i −0.418977 + 1.28948i
\(471\) 10.5673 + 23.7346i 0.486917 + 1.09363i
\(472\) 8.48528i 0.390567i
\(473\) 0 0
\(474\) −21.0000 + 36.3731i −0.964562 + 1.67067i
\(475\) −3.32502 + 4.57649i −0.152562 + 0.209984i
\(476\) −13.1782 4.28187i −0.604023 0.196259i
\(477\) 7.72299 + 6.95381i 0.353611 + 0.318393i
\(478\) −43.6869 + 31.7404i −1.99819 + 1.45177i
\(479\) −23.7801 + 17.2773i −1.08654 + 0.789419i −0.978812 0.204761i \(-0.934358\pi\)
−0.107731 + 0.994180i \(0.534358\pi\)
\(480\) 0 0
\(481\) 8.06998 + 2.62210i 0.367960 + 0.119557i
\(482\) 4.07230 5.60503i 0.185488 0.255302i
\(483\) 18.3712 + 10.6066i 0.835917 + 0.482617i
\(484\) 0 0
\(485\) 22.5167i 1.02243i
\(486\) 37.9746 + 3.99129i 1.72256 + 0.181049i
\(487\) 8.34346 25.6785i 0.378078 1.16361i −0.563300 0.826252i \(-0.690469\pi\)
0.941378 0.337353i \(-0.109531\pi\)
\(488\) 13.1782 4.28187i 0.596550 0.193831i
\(489\) −17.2256 + 1.81049i −0.778970 + 0.0818730i
\(490\) −12.4688 17.1618i −0.563283 0.775293i
\(491\) 7.56934 + 23.2960i 0.341600 + 1.05134i 0.963379 + 0.268143i \(0.0864100\pi\)
−0.621780 + 0.783192i \(0.713590\pi\)
\(492\) −50.4463 + 45.4221i −2.27430 + 2.04779i
\(493\) 9.70820 + 7.05342i 0.437236 + 0.317670i
\(494\) −19.5959 −0.881662
\(495\) 0 0
\(496\) 12.0000 0.538816
\(497\) −1.98168 1.43977i −0.0888904 0.0645827i
\(498\) 7.72299 6.95381i 0.346075 0.311608i
\(499\) 1.85410 + 5.70634i 0.0830010 + 0.255451i 0.983941 0.178492i \(-0.0571219\pi\)
−0.900940 + 0.433943i \(0.857122\pi\)
\(500\) 28.5061 + 39.2352i 1.27483 + 1.75465i
\(501\) 33.7552 3.54781i 1.50807 0.158505i
\(502\) 36.3149 11.7994i 1.62081 0.526634i
\(503\) −6.81241 + 20.9664i −0.303750 + 0.934847i 0.676390 + 0.736543i \(0.263543\pi\)
−0.980141 + 0.198304i \(0.936457\pi\)
\(504\) −20.6707 2.17258i −0.920748 0.0967746i
\(505\) 21.2132i 0.943975i
\(506\) 0 0
\(507\) −7.50000 4.33013i −0.333087 0.192308i
\(508\) 6.65003 9.15298i 0.295047 0.406098i
\(509\) −28.0037 9.09896i −1.24124 0.403304i −0.386468 0.922303i \(-0.626305\pi\)
−0.854775 + 0.518998i \(0.826305\pi\)
\(510\) −17.6067 3.74241i −0.779636 0.165717i
\(511\) −6.47214 + 4.70228i −0.286310 + 0.208017i
\(512\) −31.7069 + 23.0364i −1.40126 + 1.01807i
\(513\) −4.54160 13.9776i −0.200517 0.617127i
\(514\) 24.2099 + 7.86629i 1.06785 + 0.346967i
\(515\) 2.03615 2.80252i 0.0897234 0.123494i
\(516\) −34.2929 + 59.3970i −1.50966 + 2.61481i
\(517\) 0 0
\(518\) 10.3923i 0.456612i
\(519\) −1.72564 3.87585i −0.0757471 0.170131i
\(520\) −7.41641 + 22.8254i −0.325231 + 1.00096i
\(521\) −37.8874 + 12.3104i −1.65988 + 0.539327i −0.980846 0.194783i \(-0.937600\pi\)
−0.679031 + 0.734110i \(0.737600\pi\)
\(522\) 32.8876 + 14.6425i 1.43945 + 0.640886i
\(523\) 16.6251 + 22.8825i 0.726964 + 1.00058i 0.999264 + 0.0383675i \(0.0122157\pi\)
−0.272300 + 0.962212i \(0.587784\pi\)
\(524\) −15.1387 46.5921i −0.661336 2.03538i
\(525\) −3.27806 3.64065i −0.143066 0.158891i
\(526\) 24.2705 + 17.6336i 1.05824 + 0.768860i
\(527\) −7.34847 −0.320104
\(528\) 0 0
\(529\) −52.0000 −2.26087
\(530\) −11.8901 8.63864i −0.516472 0.375239i
\(531\) −1.08034 5.08260i −0.0468828 0.220566i
\(532\) 4.94427 + 15.2169i 0.214361 + 0.659736i
\(533\) −16.2892 22.4201i −0.705563 0.971124i
\(534\) 3.84062 + 36.5411i 0.166200 + 1.58129i
\(535\) 4.03499 1.31105i 0.174448 0.0566816i
\(536\) 4.54160 13.9776i 0.196167 0.603741i
\(537\) −24.6657 + 10.9819i −1.06440 + 0.473904i
\(538\) 42.4264i 1.82913i
\(539\) 0 0
\(540\) −36.0000 −1.54919
\(541\) 8.31254 11.4412i 0.357384 0.491897i −0.592034 0.805913i \(-0.701675\pi\)
0.949418 + 0.314016i \(0.101675\pi\)
\(542\) −13.1782 4.28187i −0.566053 0.183922i
\(543\) −1.80057 + 8.47101i −0.0772698 + 0.363526i
\(544\) 0 0
\(545\) −25.7618 + 18.7171i −1.10352 + 0.801751i
\(546\) 3.52838 16.5997i 0.151001 0.710402i
\(547\) 13.4500 + 4.37016i 0.575079 + 0.186855i 0.582095 0.813121i \(-0.302233\pi\)
−0.00701574 + 0.999975i \(0.502233\pi\)
\(548\) 36.6507 50.4453i 1.56564 2.15492i
\(549\) −7.34847 + 4.24264i −0.313625 + 0.181071i
\(550\) 0 0
\(551\) 13.8564i 0.590303i
\(552\) 67.1316 29.8889i 2.85731 1.27216i
\(553\) −4.32624 + 13.3148i −0.183970 + 0.566203i
\(554\) −42.8292 + 13.9161i −1.81964 + 0.591237i
\(555\) −0.940756 8.95070i −0.0399329 0.379936i
\(556\) −36.5752 50.3414i −1.55113 2.13495i
\(557\) −9.84014 30.2848i −0.416940 1.28321i −0.910504 0.413500i \(-0.864306\pi\)
0.493564 0.869710i \(-0.335694\pi\)
\(558\) −21.5637 + 4.58350i −0.912863 + 0.194035i
\(559\) −22.6525 16.4580i −0.958098 0.696099i
\(560\) 9.79796 0.414039
\(561\) 0 0
\(562\) −54.0000 −2.27785
\(563\) 3.96336 + 2.87955i 0.167036 + 0.121358i 0.668163 0.744015i \(-0.267081\pi\)
−0.501127 + 0.865374i \(0.667081\pi\)
\(564\) −32.1183 35.6710i −1.35242 1.50202i
\(565\) −0.927051 2.85317i −0.0390013 0.120034i
\(566\) −28.5061 39.2352i −1.19820 1.64918i
\(567\) 12.6582 1.33043i 0.531594 0.0558728i
\(568\) −8.06998 + 2.62210i −0.338609 + 0.110021i
\(569\) −9.08321 + 27.9552i −0.380788 + 1.17194i 0.558702 + 0.829368i \(0.311299\pi\)
−0.939490 + 0.342576i \(0.888701\pi\)
\(570\) 8.45386 + 18.9877i 0.354093 + 0.795307i
\(571\) 19.7990i 0.828562i −0.910149 0.414281i \(-0.864033\pi\)
0.910149 0.414281i \(-0.135967\pi\)
\(572\) 0 0
\(573\) 4.50000 7.79423i 0.187990 0.325609i
\(574\) −19.9501 + 27.4589i −0.832701 + 1.14611i
\(575\) 16.4728 + 5.35233i 0.686963 + 0.223208i
\(576\) 16.0591 17.8355i 0.669131 0.743145i
\(577\) −2.42705 + 1.76336i −0.101039 + 0.0734095i −0.637158 0.770733i \(-0.719890\pi\)
0.536118 + 0.844143i \(0.319890\pi\)
\(578\) −21.7985 + 15.8375i −0.906697 + 0.658754i
\(579\) 23.9596 + 5.09278i 0.995728 + 0.211649i
\(580\) −32.2799 10.4884i −1.34035 0.435506i
\(581\) 2.03615 2.80252i 0.0844736 0.116268i
\(582\) 47.7650 + 27.5772i 1.97993 + 1.14311i
\(583\) 0 0
\(584\) 27.7128i 1.14676i
\(585\) 1.53625 14.6164i 0.0635161 0.604315i
\(586\) −3.70820 + 11.4127i −0.153184 + 0.471453i
\(587\) 26.3565 8.56373i 1.08785 0.353463i 0.290433 0.956895i \(-0.406201\pi\)
0.797414 + 0.603432i \(0.206201\pi\)
\(588\) 34.4512 3.62097i 1.42075 0.149326i
\(589\) 4.98752 + 6.86474i 0.205507 + 0.282857i
\(590\) 2.27080 + 6.98881i 0.0934874 + 0.287725i
\(591\) −9.45869 + 8.51664i −0.389078 + 0.350328i
\(592\) −9.70820 7.05342i −0.399005 0.289894i
\(593\) −19.5959 −0.804708 −0.402354 0.915484i \(-0.631808\pi\)
−0.402354 + 0.915484i \(0.631808\pi\)
\(594\) 0 0
\(595\) −6.00000 −0.245976
\(596\) 7.92672 + 5.75910i 0.324691 + 0.235902i
\(597\) 23.1690 20.8614i 0.948243 0.853801i
\(598\) 18.5410 + 57.0634i 0.758199 + 2.33350i
\(599\) 12.2169 + 16.8151i 0.499168 + 0.687046i 0.982046 0.188641i \(-0.0604084\pi\)
−0.482878 + 0.875688i \(0.660408\pi\)
\(600\) −16.8776 + 1.77391i −0.689025 + 0.0724194i
\(601\) 1.34500 0.437016i 0.0548636 0.0178263i −0.281457 0.959574i \(-0.590818\pi\)
0.336320 + 0.941748i \(0.390818\pi\)
\(602\) −10.5971 + 32.6144i −0.431905 + 1.32927i
\(603\) −0.940756 + 8.95070i −0.0383106 + 0.364501i
\(604\) 39.5980i 1.61122i
\(605\) 0 0
\(606\) 45.0000 + 25.9808i 1.82800 + 1.05540i
\(607\) 5.81878 8.00886i 0.236177 0.325070i −0.674433 0.738336i \(-0.735612\pi\)
0.910610 + 0.413266i \(0.135612\pi\)
\(608\) 0 0
\(609\) 11.7378 + 2.49494i 0.475638 + 0.101100i
\(610\) 9.70820 7.05342i 0.393074 0.285585i
\(611\) 15.8534 11.5182i 0.641361 0.465976i
\(612\) 19.6683 21.8439i 0.795046 0.882988i
\(613\) 10.7600 + 3.49613i 0.434591 + 0.141207i 0.518139 0.855297i \(-0.326625\pi\)
−0.0835475 + 0.996504i \(0.526625\pi\)
\(614\) 4.07230 5.60503i 0.164344 0.226201i
\(615\) −14.6969 + 25.4558i −0.592638 + 1.02648i
\(616\) 0 0
\(617\) 10.3923i 0.418378i 0.977875 + 0.209189i \(0.0670825\pi\)
−0.977875 + 0.209189i \(0.932918\pi\)
\(618\) 3.45127 + 7.75169i 0.138831 + 0.311819i
\(619\) −7.72542 + 23.7764i −0.310511 + 0.955655i 0.667052 + 0.745011i \(0.267556\pi\)
−0.977563 + 0.210643i \(0.932444\pi\)
\(620\) 19.7673 6.42280i 0.793875 0.257946i
\(621\) −36.4058 + 26.4503i −1.46091 + 1.06142i
\(622\) −24.9376 34.3237i −0.999907 1.37625i
\(623\) 3.78467 + 11.6480i 0.151630 + 0.466668i
\(624\) −13.1122 14.5626i −0.524909 0.582971i
\(625\) 8.89919 + 6.46564i 0.355967 + 0.258626i
\(626\) 80.8332 3.23074
\(627\) 0 0
\(628\) 60.0000 2.39426
\(629\) 5.94504 + 4.31932i 0.237044 + 0.172223i
\(630\) −17.6067 + 3.74241i −0.701466 + 0.149101i
\(631\) −12.0517 37.0912i −0.479769 1.47658i −0.839416 0.543489i \(-0.817103\pi\)
0.359647 0.933088i \(-0.382897\pi\)
\(632\) 28.5061 + 39.2352i 1.13391 + 1.56069i
\(633\) 1.02417 + 9.74428i 0.0407069 + 0.387301i
\(634\) −4.03499 + 1.31105i −0.160250 + 0.0520684i
\(635\) 1.51387 4.65921i 0.0600760 0.184895i
\(636\) 21.9251 9.76168i 0.869386 0.387076i
\(637\) 14.1421i 0.560332i
\(638\) 0 0
\(639\) 4.50000 2.59808i 0.178017 0.102778i
\(640\) −19.9501 + 27.4589i −0.788597 + 1.08541i
\(641\) 8.23639 + 2.67617i 0.325318 + 0.105702i 0.467123 0.884192i \(-0.345291\pi\)
−0.141805 + 0.989895i \(0.545291\pi\)
\(642\) −2.16068 + 10.1652i −0.0852753 + 0.401189i
\(643\) −5.66312 + 4.11450i −0.223332 + 0.162260i −0.693825 0.720144i \(-0.744076\pi\)
0.470493 + 0.882403i \(0.344076\pi\)
\(644\) 39.6336 28.7955i 1.56178 1.13470i
\(645\) −6.17466 + 29.0495i −0.243127 + 1.14382i
\(646\) −16.1400 5.24419i −0.635018 0.206330i
\(647\) −17.3073 + 23.8214i −0.680418 + 0.936516i −0.999939 0.0110637i \(-0.996478\pi\)
0.319520 + 0.947579i \(0.396478\pi\)
\(648\) 22.0454 38.1838i 0.866025 1.50000i
\(649\) 0 0
\(650\) 13.8564i 0.543493i
\(651\) −6.71316 + 2.98889i −0.263110 + 0.117144i
\(652\) −12.3607 + 38.0423i −0.484082 + 1.48985i
\(653\) 1.64728 0.535233i 0.0644630 0.0209453i −0.276608 0.960983i \(-0.589210\pi\)
0.341071 + 0.940038i \(0.389210\pi\)
\(654\) −8.15322 77.5727i −0.318816 3.03333i
\(655\) −12.4688 17.1618i −0.487197 0.670569i
\(656\) 12.1109 + 37.2737i 0.472853 + 1.45529i
\(657\) −3.52838 16.5997i −0.137655 0.647617i
\(658\) −19.4164 14.1068i −0.756930 0.549942i
\(659\) −36.7423 −1.43128 −0.715639 0.698470i \(-0.753865\pi\)
−0.715639 + 0.698470i \(0.753865\pi\)
\(660\) 0 0
\(661\) 15.0000 0.583432 0.291716 0.956505i \(-0.405774\pi\)
0.291716 + 0.956505i \(0.405774\pi\)
\(662\) 9.90839 + 7.19887i 0.385101 + 0.279792i
\(663\) 8.02957 + 8.91774i 0.311843 + 0.346336i
\(664\) −3.70820 11.4127i −0.143906 0.442898i
\(665\) 4.07230 + 5.60503i 0.157917 + 0.217354i
\(666\) 20.1395 + 8.96668i 0.780389 + 0.347452i
\(667\) −40.3499 + 13.1105i −1.56235 + 0.507640i
\(668\) 24.2219 74.5473i 0.937173 2.88432i
\(669\) −7.74937 17.4054i −0.299608 0.672931i
\(670\) 12.7279i 0.491723i
\(671\) 0 0
\(672\) 0 0
\(673\) −19.1188 + 26.3148i −0.736977 + 1.01436i 0.261810 + 0.965119i \(0.415681\pi\)
−0.998787 + 0.0492424i \(0.984319\pi\)
\(674\) 56.0075 + 18.1979i 2.15733 + 0.700958i
\(675\) 9.88367 3.21140i 0.380423 0.123607i
\(676\) −16.1803 + 11.7557i −0.622321 + 0.452143i
\(677\) 33.6885 24.4762i 1.29476 0.940695i 0.294866 0.955539i \(-0.404725\pi\)
0.999890 + 0.0148435i \(0.00472501\pi\)
\(678\) 7.18789 + 1.52783i 0.276049 + 0.0586761i
\(679\) 17.4850 + 5.68121i 0.671011 + 0.218025i
\(680\) −12.2169 + 16.8151i −0.468496 + 0.644830i
\(681\) −33.0681 19.0919i −1.26717 0.731603i
\(682\) 0 0
\(683\) 45.0333i 1.72315i −0.507628 0.861576i \(-0.669478\pi\)
0.507628 0.861576i \(-0.330522\pi\)
\(684\) −33.7552 3.54781i −1.29066 0.135654i
\(685\) 8.34346 25.6785i 0.318787 0.981126i
\(686\) 39.5347 12.8456i 1.50944 0.490447i
\(687\) −15.5031 + 1.62944i −0.591479 + 0.0621669i
\(688\) 23.2751 + 32.0354i 0.887355 + 1.22134i
\(689\) 3.02774 + 9.31841i 0.115348 + 0.355003i
\(690\) 47.2934 42.5832i 1.80043 1.62112i
\(691\) −4.04508 2.93893i −0.153882 0.111802i 0.508180 0.861251i \(-0.330319\pi\)
−0.662062 + 0.749449i \(0.730319\pi\)
\(692\) −9.79796 −0.372463
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) −21.7985 15.8375i −0.826863 0.600751i
\(696\) 30.8920 27.8152i 1.17096 1.05433i
\(697\) −7.41641 22.8254i −0.280916 0.864572i
\(698\) −14.2530 19.6176i −0.539485 0.742538i
\(699\) −42.1940 + 4.43477i −1.59592 + 0.167738i
\(700\) −10.7600 + 3.49613i −0.406689 + 0.132141i
\(701\) −8.32627 + 25.6256i −0.314479 + 0.967867i 0.661489 + 0.749955i \(0.269925\pi\)
−0.975968 + 0.217912i \(0.930075\pi\)
\(702\) 29.1246 + 21.1603i 1.09924 + 0.798643i
\(703\) 8.48528i 0.320028i
\(704\) 0 0
\(705\) −18.0000 10.3923i −0.677919 0.391397i
\(706\) −37.4064 + 51.4855i −1.40781 + 1.93768i
\(707\) 16.4728 + 5.35233i 0.619523 + 0.201295i
\(708\) −11.7378 2.49494i −0.441132 0.0937656i
\(709\) −2.42705 + 1.76336i −0.0911498 + 0.0662242i −0.632427 0.774620i \(-0.717941\pi\)
0.541277 + 0.840844i \(0.317941\pi\)
\(710\) −5.94504 + 4.31932i −0.223113 + 0.162101i
\(711\) −22.0703 19.8722i −0.827700 0.745264i
\(712\) 40.3499 + 13.1105i 1.51218 + 0.491336i
\(713\) 15.2711 21.0189i 0.571908 0.787163i
\(714\) 7.34847 12.7279i 0.275010 0.476331i
\(715\) 0 0
\(716\) 62.3538i 2.33027i
\(717\) −15.5307 34.8826i −0.580006 1.30271i
\(718\) 18.5410 57.0634i 0.691945 2.12959i
\(719\) 11.5309 3.74663i 0.430032 0.139726i −0.0860002 0.996295i \(-0.527409\pi\)
0.516032 + 0.856569i \(0.327409\pi\)
\(720\) −8.45386 + 18.9877i −0.315057 + 0.707629i
\(721\) 1.66251 + 2.28825i 0.0619150 + 0.0852187i
\(722\) −8.32627 25.6256i −0.309872 0.953687i
\(723\) 3.27806 + 3.64065i 0.121912 + 0.135397i
\(724\) 16.1803 + 11.7557i 0.601338 + 0.436897i
\(725\) 9.79796 0.363887
\(726\) 0 0
\(727\) −3.00000 −0.111264 −0.0556319 0.998451i \(-0.517717\pi\)
−0.0556319 + 0.998451i \(0.517717\pi\)
\(728\) −15.8534 11.5182i −0.587567 0.426893i
\(729\) −8.34346 + 25.6785i −0.309017 + 0.951057i
\(730\) 7.41641 + 22.8254i 0.274494 + 0.844804i
\(731\) −14.2530 19.6176i −0.527168 0.725584i
\(732\) 2.04833 + 19.4886i 0.0757085 + 0.720318i
\(733\) −34.9699 + 11.3624i −1.29164 + 0.419680i −0.872667 0.488316i \(-0.837611\pi\)
−0.418977 + 0.907997i \(0.637611\pi\)
\(734\) 5.29854 16.3072i 0.195573 0.601911i
\(735\) 13.7032 6.10105i 0.505449 0.225041i
\(736\) 0 0
\(737\) 0 0
\(738\) −36.0000 62.3538i −1.32518 2.29528i
\(739\) 30.7564 42.3325i 1.13139 1.55723i 0.345994 0.938237i \(-0.387542\pi\)
0.785398 0.618991i \(-0.212458\pi\)
\(740\) −19.7673 6.42280i −0.726662 0.236107i
\(741\) 2.88091 13.5536i 0.105833 0.497904i
\(742\) 9.70820 7.05342i 0.356399 0.258939i
\(743\) −11.8901 + 8.63864i −0.436204 + 0.316921i −0.784125 0.620603i \(-0.786888\pi\)
0.347921 + 0.937524i \(0.386888\pi\)
\(744\) −5.29257 + 24.8996i −0.194035 + 0.912863i
\(745\) 4.03499 + 1.31105i 0.147831 + 0.0480331i
\(746\) −46.8314 + 64.4579i −1.71462 + 2.35997i
\(747\) 3.67423 + 6.36396i 0.134433 + 0.232845i
\(748\) 0 0
\(749\) 3.46410i 0.126576i
\(750\) −46.9921 + 20.9222i −1.71591 + 0.763972i
\(751\) 8.34346 25.6785i 0.304457 0.937023i −0.675422 0.737431i \(-0.736039\pi\)
0.979879 0.199591i \(-0.0639615\pi\)
\(752\) −26.3565 + 8.56373i −0.961121 + 0.312287i
\(753\) 2.82227 + 26.8521i 0.102849 + 0.978545i
\(754\) 19.9501 + 27.4589i 0.726540 + 0.999996i
\(755\) −5.29854 16.3072i −0.192834 0.593481i
\(756\) 9.08321 27.9552i 0.330353 1.01672i
\(757\) 24.2705 + 17.6336i 0.882127 + 0.640903i 0.933813 0.357761i \(-0.116460\pi\)
−0.0516866 + 0.998663i \(0.516460\pi\)
\(758\) −41.6413 −1.51248
\(759\) 0 0
\(760\) 24.0000 0.870572
\(761\) −19.8168 14.3977i −0.718358 0.521918i 0.167501 0.985872i \(-0.446430\pi\)
−0.885859 + 0.463954i \(0.846430\pi\)
\(762\) 8.02957 + 8.91774i 0.290881 + 0.323056i
\(763\) −8.03444 24.7275i −0.290866 0.895194i
\(764\) −12.2169 16.8151i −0.441991 0.608349i
\(765\) 5.17691 11.6275i 0.187172 0.420394i
\(766\) 52.4549 17.0436i 1.89527 0.615811i
\(767\) 1.51387 4.65921i 0.0546626 0.168234i
\(768\) −22.5436 50.6338i −0.813473 1.82709i
\(769\) 14.1421i 0.509978i 0.966944 + 0.254989i \(0.0820719\pi\)
−0.966944 + 0.254989i \(0.917928\pi\)
\(770\) 0 0
\(771\) −9.00000 + 15.5885i −0.324127 + 0.561405i
\(772\) 33.2502 45.7649i 1.19670 1.64712i
\(773\) −3.29456 1.07047i −0.118497 0.0385020i 0.249168 0.968460i \(-0.419843\pi\)
−0.367665 + 0.929958i \(0.619843\pi\)
\(774\) −54.0609 48.6767i −1.94318 1.74965i
\(775\) −4.85410 + 3.52671i −0.174364 + 0.126683i
\(776\) 51.5236 37.4341i 1.84959 1.34381i
\(777\) 7.18789 + 1.52783i 0.257864 + 0.0548107i
\(778\) −52.4549 17.0436i −1.88060 0.611044i
\(779\) −16.2892 + 22.4201i −0.583621 + 0.803285i
\(780\) −29.3939 16.9706i −1.05247 0.607644i
\(781\) 0 0
\(782\) 51.9615i 1.85814i
\(783\) −14.9626 + 20.5942i −0.534719 + 0.735977i
\(784\) 6.18034 19.0211i 0.220726 0.679326i
\(785\) 24.7092 8.02850i 0.881908 0.286549i
\(786\) 51.6769 5.43146i 1.84325 0.193734i
\(787\) 16.6251 + 22.8825i 0.592620 + 0.815671i 0.995008 0.0997979i \(-0.0318196\pi\)
−0.402388 + 0.915469i \(0.631820\pi\)
\(788\) 9.08321 + 27.9552i 0.323576 + 0.995864i
\(789\) −15.7645 + 14.1944i −0.561230 + 0.505334i
\(790\) 33.9787 + 24.6870i 1.20891 + 0.878323i
\(791\) 2.44949 0.0870938
\(792\) 0 0
\(793\) −8.00000 −0.284088
\(794\) 63.4137 + 46.0728i 2.25047 + 1.63506i
\(795\) 7.72299 6.95381i 0.273906 0.246626i
\(796\) −22.2492 68.4761i −0.788603 2.42707i
\(797\) −19.3434 26.6239i −0.685179 0.943067i 0.314803 0.949157i \(-0.398062\pi\)
−0.999981 + 0.00608970i \(0.998062\pi\)
\(798\) −16.8776 + 1.77391i −0.597460 + 0.0627956i
\(799\) 16.1400 5.24419i 0.570991 0.185526i
\(800\) 0 0
\(801\) −25.8384 2.71573i −0.912956 0.0959556i
\(802\) 25.4558i 0.898877i
\(803\) 0 0
\(804\) 18.0000 + 10.3923i 0.634811 + 0.366508i
\(805\) 12.4688 17.1618i 0.439468 0.604875i
\(806\) −19.7673 6.42280i −0.696275 0.226233i
\(807\) −29.3444 6.23735i −1.03297 0.219565i
\(808\) 48.5410 35.2671i 1.70767 1.24069i
\(809\) 39.6336 28.7955i 1.39344 1.01240i 0.397965 0.917401i \(-0.369717\pi\)
0.995478 0.0949943i \(-0.0302833\pi\)
\(810\) 7.93885 37.3494i 0.278943 1.31232i
\(811\) 14.7950 + 4.80718i 0.519522 + 0.168803i 0.557028 0.830494i \(-0.311942\pi\)
−0.0375066 + 0.999296i \(0.511942\pi\)
\(812\) 16.2892 22.4201i 0.571638 0.786793i
\(813\) 4.89898 8.48528i 0.171815 0.297592i
\(814\) 0 0
\(815\) 17.3205i 0.606711i
\(816\) −6.90255 15.5034i −0.241638 0.542727i
\(817\) −8.65248 + 26.6296i −0.302712 + 0.931651i
\(818\) −42.8292 + 13.9161i −1.49749 + 0.486564i
\(819\) 10.9625 + 4.88084i 0.383062 + 0.170550i
\(820\) 39.9002 + 54.9179i 1.39337 + 1.91782i
\(821\) 9.84014 + 30.2848i 0.343423 + 1.05695i 0.962422 + 0.271557i \(0.0875384\pi\)
−0.618999 + 0.785392i \(0.712462\pi\)
\(822\) 44.2538 + 49.1488i 1.54353 + 1.71426i
\(823\) −25.0795 18.2213i −0.874217 0.635156i 0.0574979 0.998346i \(-0.481688\pi\)
−0.931715 + 0.363190i \(0.881688\pi\)
\(824\) 9.79796 0.341328
\(825\) 0 0
\(826\) −6.00000 −0.208767
\(827\) 3.96336 + 2.87955i 0.137819 + 0.100132i 0.654559 0.756011i \(-0.272854\pi\)
−0.516739 + 0.856143i \(0.672854\pi\)
\(828\) 21.6068 + 101.652i 0.750889 + 3.53265i
\(829\) 9.57953 + 29.4828i 0.332711 + 1.02398i 0.967839 + 0.251571i \(0.0809473\pi\)
−0.635128 + 0.772407i \(0.719053\pi\)
\(830\) −6.10844 8.40755i −0.212027 0.291830i
\(831\) −3.32854 31.6689i −0.115466 1.09858i
\(832\) 21.5200 6.99226i 0.746070 0.242413i
\(833\) −3.78467 + 11.6480i −0.131131 + 0.403580i
\(834\) 60.2940 26.8446i 2.08781 0.929553i
\(835\) 33.9411i 1.17458i
\(836\) 0 0
\(837\) 15.5885i 0.538816i
\(838\) 9.97505 13.7295i 0.344582 0.474277i
\(839\) −44.4765 14.4513i −1.53550 0.498914i −0.585369 0.810767i \(-0.699050\pi\)
−0.950130 + 0.311853i \(0.899050\pi\)
\(840\) −4.32136 + 20.3304i −0.149101 + 0.701466i
\(841\) 4.04508 2.93893i 0.139486 0.101342i
\(842\) 0 0
\(843\) 7.93885 37.3494i 0.273429 1.28638i
\(844\) 21.5200 + 6.99226i 0.740747 + 0.240683i
\(845\) −5.09037 + 7.00629i −0.175114 + 0.241024i
\(846\) 44.0908 25.4558i 1.51587 0.875190i
\(847\) 0 0
\(848\) 13.8564i 0.475831i
\(849\) 31.3281 13.9482i 1.07518 0.478700i
\(850\) 3.70820 11.4127i 0.127190 0.391452i
\(851\) −24.7092 + 8.02850i −0.847020 + 0.275213i
\(852\) −1.25434 11.9343i −0.0429730 0.408861i
\(853\) 34.0814 + 46.9090i 1.16693 + 1.60613i 0.681398 + 0.731913i \(0.261372\pi\)
0.485528 + 0.874221i \(0.338628\pi\)
\(854\) 3.02774 + 9.31841i 0.103607 + 0.318870i
\(855\) −14.3758 + 3.05567i −0.491641 + 0.104502i
\(856\) 9.70820 + 7.05342i 0.331820 + 0.241081i
\(857\) −19.5959 −0.669384 −0.334692 0.942328i \(-0.608632\pi\)
−0.334692 + 0.942328i \(0.608632\pi\)
\(858\) 0 0
\(859\) 25.0000 0.852989 0.426494 0.904490i \(-0.359748\pi\)
0.426494 + 0.904490i \(0.359748\pi\)
\(860\) 55.4870 + 40.3137i 1.89209 + 1.37468i
\(861\) −16.0591 17.8355i −0.547294 0.607831i
\(862\) 5.56231 + 17.1190i 0.189453 + 0.583076i
\(863\) 12.2169 + 16.8151i 0.415868 + 0.572393i 0.964637 0.263581i \(-0.0849036\pi\)
−0.548770 + 0.835974i \(0.684904\pi\)
\(864\) 0 0
\(865\) −4.03499 + 1.31105i −0.137194 + 0.0445770i
\(866\) −3.78467 + 11.6480i −0.128608 + 0.395816i
\(867\) −7.74937 17.4054i −0.263183 0.591118i
\(868\) 16.9706i 0.576018i
\(869\) 0 0
\(870\) 18.0000 31.1769i 0.610257 1.05700i
\(871\) −4.98752 + 6.86474i −0.168996 + 0.232603i
\(872\) −85.6585 27.8321i −2.90076 0.942515i
\(873\) −26.0961 + 28.9826i −0.883219 + 0.980914i
\(874\) 48.5410 35.2671i 1.64192 1.19293i
\(875\) −13.8718 + 10.0784i −0.468951 + 0.340713i
\(876\) −38.3354 8.14844i −1.29523 0.275310i
\(877\) −26.8999 8.74032i −0.908346 0.295140i −0.182669 0.983175i \(-0.558474\pi\)
−0.725678 + 0.688035i \(0.758474\pi\)
\(878\) 8.14459 11.2101i 0.274867 0.378321i
\(879\) −7.34847 4.24264i −0.247858 0.143101i
\(880\) 0 0
\(881\) 1.73205i 0.0583543i 0.999574 + 0.0291771i \(0.00928869\pi\)
−0.999574 + 0.0291771i \(0.990711\pi\)
\(882\) −3.84062 + 36.5411i −0.129320 + 1.23040i
\(883\) 1.85410 5.70634i 0.0623955 0.192034i −0.915000 0.403455i \(-0.867809\pi\)
0.977395 + 0.211421i \(0.0678092\pi\)
\(884\) 26.3565 8.56373i 0.886463 0.288029i
\(885\) −5.16769 + 0.543146i −0.173710 + 0.0182576i
\(886\) −37.4064 51.4855i −1.25669 1.72969i
\(887\) 6.81241 + 20.9664i 0.228738 + 0.703984i 0.997891 + 0.0649184i \(0.0206787\pi\)
−0.769152 + 0.639065i \(0.779321\pi\)
\(888\) 18.9174 17.0333i 0.634826 0.571600i
\(889\) 3.23607 + 2.35114i 0.108534 + 0.0788547i
\(890\) 36.7423 1.23161
\(891\) 0 0
\(892\) −44.0000 −1.47323
\(893\) −15.8534 11.5182i −0.530515 0.385442i
\(894\) −7.72299 + 6.95381i −0.258295 + 0.232570i
\(895\) 8.34346 + 25.6785i 0.278891 + 0.858338i
\(896\) −16.2892 22.4201i −0.544183 0.749004i
\(897\) −42.1940 + 4.43477i −1.40882 + 0.148073i
\(898\) −28.2449 + 9.17734i −0.942546 + 0.306252i
\(899\) 4.54160 13.9776i 0.151471 0.466180i
\(900\) 2.50868 23.8685i 0.0836228 0.795618i
\(901\) 8.48528i 0.282686i
\(902\) 0 0
\(903\) −21.0000 12.1244i −0.698836 0.403473i
\(904\) 4.98752 6.86474i 0.165883 0.228318i
\(905\) 8.23639 + 2.67617i 0.273787 + 0.0889588i
\(906\) 41.0822 + 8.73229i 1.36486 + 0.290111i
\(907\) −17.7984 + 12.9313i −0.590985 + 0.429376i −0.842668 0.538434i \(-0.819016\pi\)
0.251682 + 0.967810i \(0.419016\pi\)
\(908\) −71.3404 + 51.8319i −2.36752 + 1.72010i
\(909\) −24.5854 + 27.3049i −0.815447 + 0.905646i
\(910\) −16.1400 5.24419i −0.535035 0.173843i
\(911\) 2.03615 2.80252i 0.0674606 0.0928515i −0.773954 0.633242i \(-0.781724\pi\)
0.841414 + 0.540391i \(0.181724\pi\)
\(912\) −9.79796 + 16.9706i −0.324443 + 0.561951i
\(913\) 0 0
\(914\) 76.2102i 2.52081i
\(915\) 3.45127 + 7.75169i 0.114096 + 0.256263i
\(916\) −11.1246 + 34.2380i −0.367568 + 1.13126i
\(917\) 16.4728 5.35233i 0.543979 0.176750i
\(918\) 18.3253 + 25.2227i 0.604826 + 0.832472i
\(919\) −4.15627 5.72061i −0.137103 0.188706i 0.734945 0.678127i \(-0.237208\pi\)
−0.872047 + 0.489421i \(0.837208\pi\)
\(920\) −22.7080 69.8881i −0.748661 2.30414i
\(921\) 3.27806 + 3.64065i 0.108016 + 0.119964i
\(922\) −9.70820 7.05342i −0.319723 0.232292i
\(923\) 4.89898 0.161252
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) 37.6519 + 27.3557i 1.23732 + 0.898964i
\(927\) −5.86889 + 1.24747i −0.192759 + 0.0409723i
\(928\) 0 0
\(929\) 26.4699 + 36.4327i 0.868450 + 1.19532i 0.979488 + 0.201503i \(0.0645825\pi\)
−0.111038 + 0.993816i \(0.535418\pi\)
\(930\) 2.30437 + 21.9246i 0.0755634 + 0.718937i
\(931\) 13.4500 4.37016i 0.440805 0.143226i
\(932\) −30.2774 + 93.1841i −0.991768 + 3.05235i
\(933\) 27.4064 12.2021i 0.897244 0.399479i
\(934\) 63.6396i 2.08235i
\(935\) 0 0
\(936\) 36.0000 20.7846i 1.17670 0.679366i
\(937\) −33.2502 + 45.7649i −1.08624 + 1.49507i −0.233769 + 0.972292i \(0.575106\pi\)
−0.852466 + 0.522782i \(0.824894\pi\)
\(938\) 9.88367 + 3.21140i 0.322713 + 0.104856i
\(939\) −11.8837 + 55.9086i −0.387811 + 1.82451i
\(940\) −38.8328 + 28.2137i −1.26659 + 0.920229i
\(941\) −5.94504 + 4.31932i −0.193803 + 0.140806i −0.680455 0.732790i \(-0.738218\pi\)
0.486652 + 0.873596i \(0.338218\pi\)
\(942\) −13.2314 + 62.2489i −0.431103 + 2.02818i
\(943\) 80.6998 + 26.2210i 2.62795 + 0.853872i
\(944\) −4.07230 + 5.60503i −0.132542 + 0.182428i
\(945\) 12.7279i 0.414039i
\(946\) 0 0
\(947\) 50.2295i 1.63224i 0.577883 + 0.816119i \(0.303879\pi\)
−0.577883 + 0.816119i \(0.696121\pi\)
\(948\) −62.6562 + 27.8963i −2.03498 + 0.906030i
\(949\) 4.94427 15.2169i 0.160498 0.493962i
\(950\) −13.1782 + 4.28187i −0.427558 + 0.138922i
\(951\) −0.313585 2.98357i −0.0101687 0.0967487i
\(952\) −9.97505 13.7295i −0.323293 0.444975i
\(953\) −2.27080 6.98881i −0.0735585 0.226390i 0.907517 0.420015i \(-0.137975\pi\)
−0.981075 + 0.193626i \(0.937975\pi\)
\(954\) 5.29257 + 24.8996i 0.171353 + 0.806153i
\(955\) −7.28115 5.29007i −0.235613 0.171183i
\(956\) −88.1816 −2.85200
\(957\) 0 0
\(958\) −72.0000 −2.32621
\(959\) 17.8351 + 12.9580i 0.575926 + 0.418435i
\(960\) −16.0591 17.8355i −0.518306 0.575638i
\(961\) −6.79837 20.9232i −0.219302 0.674943i
\(962\) 12.2169 + 16.8151i 0.393888 + 0.542141i
\(963\) −6.71316 2.98889i −0.216329 0.0963157i
\(964\) 10.7600 3.49613i 0.346555 0.112603i
\(965\) 7.56934 23.2960i 0.243666 0.749926i
\(966\) 21.1347 + 47.4692i 0.679996 + 1.52730i
\(967\) 31.1127i 1.00052i −0.865876 0.500258i \(-0.833238\pi\)
0.865876 0.500258i \(-0.166762\pi\)
\(968\) 0 0
\(969\) 6.00000 10.3923i 0.192748 0.333849i
\(970\) 32.4189 44.6208i 1.04091 1.43269i
\(971\) 37.8874 + 12.3104i 1.21586 + 0.395058i 0.845574 0.533858i \(-0.179258\pi\)
0.370290 + 0.928916i \(0.379258\pi\)
\(972\) 46.3379 + 41.7229i 1.48629 + 1.33826i
\(973\) 17.7984 12.9313i 0.570590 0.414558i
\(974\) 53.5053 38.8739i 1.71442 1.24560i
\(975\) 9.58385 + 2.03711i 0.306929 + 0.0652397i
\(976\) 10.7600 + 3.49613i 0.344418 + 0.111908i
\(977\) −21.3796 + 29.4264i −0.683992 + 0.941435i −0.999973 0.00733075i \(-0.997667\pi\)
0.315981 + 0.948766i \(0.397667\pi\)
\(978\) −36.7423 21.2132i −1.17489 0.678323i
\(979\) 0 0
\(980\) 34.6410i 1.10657i
\(981\) 54.8522 + 5.76520i 1.75130 + 0.184069i
\(982\) −18.5410 + 57.0634i −0.591668 + 1.82097i
\(983\) 1.64728 0.535233i 0.0525400 0.0170713i −0.282629 0.959229i \(-0.591207\pi\)
0.335169 + 0.942158i \(0.391207\pi\)
\(984\) −82.6830 + 8.69033i −2.63584 + 0.277038i
\(985\) 7.48128 + 10.2971i 0.238374 + 0.328093i
\(986\) 9.08321 + 27.9552i 0.289268 + 0.890276i
\(987\) 12.6116 11.3555i 0.401431 0.361450i
\(988\) −25.8885 18.8091i −0.823624 0.598398i
\(989\) 85.7321 2.72612
\(990\) 0 0
\(991\) 18.0000 0.571789 0.285894 0.958261i \(-0.407709\pi\)
0.285894 + 0.958261i \(0.407709\pi\)
\(992\) 0 0
\(993\) −6.43582 + 5.79484i −0.204235 + 0.183894i
\(994\) −1.85410 5.70634i −0.0588085 0.180994i
\(995\) −18.3253 25.2227i −0.580952 0.799612i
\(996\) 16.8776 1.77391i 0.534787 0.0562084i
\(997\) 1.34500 0.437016i 0.0425965 0.0138404i −0.287641 0.957738i \(-0.592871\pi\)
0.330238 + 0.943898i \(0.392871\pi\)
\(998\) −4.54160 + 13.9776i −0.143762 + 0.442454i
\(999\) −9.16267 + 12.6113i −0.289894 + 0.399005i
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 363.2.f.h.161.3 16
3.2 odd 2 inner 363.2.f.h.161.2 16
11.2 odd 10 inner 363.2.f.h.215.3 16
11.3 even 5 inner 363.2.f.h.239.4 16
11.4 even 5 inner 363.2.f.h.233.2 16
11.5 even 5 363.2.d.c.362.1 4
11.6 odd 10 363.2.d.c.362.3 yes 4
11.7 odd 10 inner 363.2.f.h.233.4 16
11.8 odd 10 inner 363.2.f.h.239.2 16
11.9 even 5 inner 363.2.f.h.215.1 16
11.10 odd 2 inner 363.2.f.h.161.1 16
33.2 even 10 inner 363.2.f.h.215.2 16
33.5 odd 10 363.2.d.c.362.4 yes 4
33.8 even 10 inner 363.2.f.h.239.3 16
33.14 odd 10 inner 363.2.f.h.239.1 16
33.17 even 10 363.2.d.c.362.2 yes 4
33.20 odd 10 inner 363.2.f.h.215.4 16
33.26 odd 10 inner 363.2.f.h.233.3 16
33.29 even 10 inner 363.2.f.h.233.1 16
33.32 even 2 inner 363.2.f.h.161.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.2.d.c.362.1 4 11.5 even 5
363.2.d.c.362.2 yes 4 33.17 even 10
363.2.d.c.362.3 yes 4 11.6 odd 10
363.2.d.c.362.4 yes 4 33.5 odd 10
363.2.f.h.161.1 16 11.10 odd 2 inner
363.2.f.h.161.2 16 3.2 odd 2 inner
363.2.f.h.161.3 16 1.1 even 1 trivial
363.2.f.h.161.4 16 33.32 even 2 inner
363.2.f.h.215.1 16 11.9 even 5 inner
363.2.f.h.215.2 16 33.2 even 10 inner
363.2.f.h.215.3 16 11.2 odd 10 inner
363.2.f.h.215.4 16 33.20 odd 10 inner
363.2.f.h.233.1 16 33.29 even 10 inner
363.2.f.h.233.2 16 11.4 even 5 inner
363.2.f.h.233.3 16 33.26 odd 10 inner
363.2.f.h.233.4 16 11.7 odd 10 inner
363.2.f.h.239.1 16 33.14 odd 10 inner
363.2.f.h.239.2 16 11.8 odd 10 inner
363.2.f.h.239.3 16 33.8 even 10 inner
363.2.f.h.239.4 16 11.3 even 5 inner