Properties

Label 80.2.l.a.61.3
Level $80$
Weight $2$
Character 80.61
Analytic conductor $0.639$
Analytic rank $0$
Dimension $16$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [80,2,Mod(21,80)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(80, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("80.21");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.l (of order \(4\), degree \(2\), 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: \(0.638803216170\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 61.3
Root \(1.21331 + 0.726558i\) of defining polynomial
Character \(\chi\) \(=\) 80.61
Dual form 80.2.l.a.21.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.376912 + 1.36306i) q^{2} +(1.82762 + 1.82762i) q^{3} +(-1.71587 - 1.02751i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.18001 + 1.80230i) q^{6} -4.50961i q^{7} +(2.04729 - 1.95156i) q^{8} +3.68037i q^{9} +O(q^{10})\) \(q+(-0.376912 + 1.36306i) q^{2} +(1.82762 + 1.82762i) q^{3} +(-1.71587 - 1.02751i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-3.18001 + 1.80230i) q^{6} -4.50961i q^{7} +(2.04729 - 1.95156i) q^{8} +3.68037i q^{9} +(-0.697313 - 1.23035i) q^{10} +(-1.64080 + 1.64080i) q^{11} +(-1.25807 - 5.01385i) q^{12} +(1.51857 + 1.51857i) q^{13} +(6.14687 + 1.69972i) q^{14} -2.58464 q^{15} +(1.88845 + 3.52615i) q^{16} +1.45616 q^{17} +(-5.01657 - 1.38717i) q^{18} +(-2.67964 - 2.67964i) q^{19} +(1.93986 - 0.486749i) q^{20} +(8.24183 - 8.24183i) q^{21} +(-1.61808 - 2.85495i) q^{22} -2.37423i q^{23} +(7.30837 + 0.174953i) q^{24} -1.00000i q^{25} +(-2.64228 + 1.49754i) q^{26} +(-1.24345 + 1.24345i) q^{27} +(-4.63366 + 7.73792i) q^{28} +(0.924966 + 0.924966i) q^{29} +(0.974182 - 3.52303i) q^{30} -7.20435 q^{31} +(-5.51814 + 1.24503i) q^{32} -5.99752 q^{33} +(-0.548843 + 1.98483i) q^{34} +(3.18877 + 3.18877i) q^{35} +(3.78161 - 6.31505i) q^{36} +(-5.21123 + 5.21123i) q^{37} +(4.66251 - 2.64253i) q^{38} +5.55074i q^{39} +(-0.0676894 + 2.82762i) q^{40} +6.41166i q^{41} +(8.12768 + 14.3406i) q^{42} +(7.65800 - 7.65800i) q^{43} +(4.50135 - 1.12947i) q^{44} +(-2.60241 - 2.60241i) q^{45} +(3.23622 + 0.894875i) q^{46} -2.51027 q^{47} +(-2.99308 + 9.89582i) q^{48} -13.3366 q^{49} +(1.36306 + 0.376912i) q^{50} +(2.66130 + 2.66130i) q^{51} +(-1.04534 - 4.16603i) q^{52} +(1.50312 - 1.50312i) q^{53} +(-1.22623 - 2.16357i) q^{54} -2.32045i q^{55} +(-8.80078 - 9.23248i) q^{56} -9.79472i q^{57} +(-1.60942 + 0.912155i) q^{58} +(-5.31807 + 5.31807i) q^{59} +(4.43492 + 2.65574i) q^{60} +(-1.02169 - 1.02169i) q^{61} +(2.71541 - 9.81998i) q^{62} +16.5970 q^{63} +(0.382800 - 7.99084i) q^{64} -2.14759 q^{65} +(2.26054 - 8.17499i) q^{66} +(5.22745 + 5.22745i) q^{67} +(-2.49859 - 1.49622i) q^{68} +(4.33918 - 4.33918i) q^{69} +(-5.54838 + 3.14461i) q^{70} +1.92097i q^{71} +(7.18247 + 7.53478i) q^{72} +1.39412i q^{73} +(-5.13905 - 9.06740i) q^{74} +(1.82762 - 1.82762i) q^{75} +(1.84458 + 7.35129i) q^{76} +(7.39938 + 7.39938i) q^{77} +(-7.56600 - 2.09214i) q^{78} +5.06317 q^{79} +(-3.82870 - 1.15803i) q^{80} +6.49599 q^{81} +(-8.73949 - 2.41663i) q^{82} +(-2.44974 - 2.44974i) q^{83} +(-22.6105 + 5.67340i) q^{84} +(-1.02966 + 1.02966i) q^{85} +(7.55194 + 13.3247i) q^{86} +3.38097i q^{87} +(-0.157070 + 6.56133i) q^{88} -9.36007i q^{89} +(4.52813 - 2.56637i) q^{90} +(6.84817 - 6.84817i) q^{91} +(-2.43954 + 4.07388i) q^{92} +(-13.1668 - 13.1668i) q^{93} +(0.946152 - 3.42166i) q^{94} +3.78959 q^{95} +(-12.3605 - 7.80961i) q^{96} +18.6313 q^{97} +(5.02671 - 18.1785i) q^{98} +(-6.03876 - 6.03876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.376912 + 1.36306i −0.266517 + 0.963830i
\(3\) 1.82762 + 1.82762i 1.05518 + 1.05518i 0.998386 + 0.0567890i \(0.0180862\pi\)
0.0567890 + 0.998386i \(0.481914\pi\)
\(4\) −1.71587 1.02751i −0.857937 0.513754i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) −3.18001 + 1.80230i −1.29823 + 0.735788i
\(7\) 4.50961i 1.70447i −0.523158 0.852236i \(-0.675246\pi\)
0.523158 0.852236i \(-0.324754\pi\)
\(8\) 2.04729 1.95156i 0.723827 0.689982i
\(9\) 3.68037i 1.22679i
\(10\) −0.697313 1.23035i −0.220510 0.389070i
\(11\) −1.64080 + 1.64080i −0.494721 + 0.494721i −0.909790 0.415069i \(-0.863757\pi\)
0.415069 + 0.909790i \(0.363757\pi\)
\(12\) −1.25807 5.01385i −0.363174 1.44737i
\(13\) 1.51857 + 1.51857i 0.421176 + 0.421176i 0.885609 0.464432i \(-0.153742\pi\)
−0.464432 + 0.885609i \(0.653742\pi\)
\(14\) 6.14687 + 1.69972i 1.64282 + 0.454270i
\(15\) −2.58464 −0.667351
\(16\) 1.88845 + 3.52615i 0.472113 + 0.881538i
\(17\) 1.45616 0.353170 0.176585 0.984285i \(-0.443495\pi\)
0.176585 + 0.984285i \(0.443495\pi\)
\(18\) −5.01657 1.38717i −1.18242 0.326960i
\(19\) −2.67964 2.67964i −0.614752 0.614752i 0.329428 0.944181i \(-0.393144\pi\)
−0.944181 + 0.329428i \(0.893144\pi\)
\(20\) 1.93986 0.486749i 0.433767 0.108840i
\(21\) 8.24183 8.24183i 1.79852 1.79852i
\(22\) −1.61808 2.85495i −0.344975 0.608678i
\(23\) 2.37423i 0.495061i −0.968880 0.247530i \(-0.920381\pi\)
0.968880 0.247530i \(-0.0796190\pi\)
\(24\) 7.30837 + 0.174953i 1.49182 + 0.0357121i
\(25\) 1.00000i 0.200000i
\(26\) −2.64228 + 1.49754i −0.518193 + 0.293692i
\(27\) −1.24345 + 1.24345i −0.239303 + 0.239303i
\(28\) −4.63366 + 7.73792i −0.875679 + 1.46233i
\(29\) 0.924966 + 0.924966i 0.171762 + 0.171762i 0.787753 0.615991i \(-0.211244\pi\)
−0.615991 + 0.787753i \(0.711244\pi\)
\(30\) 0.974182 3.52303i 0.177860 0.643213i
\(31\) −7.20435 −1.29394 −0.646970 0.762515i \(-0.723964\pi\)
−0.646970 + 0.762515i \(0.723964\pi\)
\(32\) −5.51814 + 1.24503i −0.975479 + 0.220092i
\(33\) −5.99752 −1.04403
\(34\) −0.548843 + 1.98483i −0.0941259 + 0.340396i
\(35\) 3.18877 + 3.18877i 0.539001 + 0.539001i
\(36\) 3.78161 6.31505i 0.630268 1.05251i
\(37\) −5.21123 + 5.21123i −0.856720 + 0.856720i −0.990950 0.134230i \(-0.957144\pi\)
0.134230 + 0.990950i \(0.457144\pi\)
\(38\) 4.66251 2.64253i 0.756359 0.428675i
\(39\) 5.55074i 0.888830i
\(40\) −0.0676894 + 2.82762i −0.0107026 + 0.447086i
\(41\) 6.41166i 1.00133i 0.865640 + 0.500667i \(0.166912\pi\)
−0.865640 + 0.500667i \(0.833088\pi\)
\(42\) 8.12768 + 14.3406i 1.25413 + 2.21280i
\(43\) 7.65800 7.65800i 1.16783 1.16783i 0.185118 0.982716i \(-0.440733\pi\)
0.982716 0.185118i \(-0.0592669\pi\)
\(44\) 4.50135 1.12947i 0.678604 0.170275i
\(45\) −2.60241 2.60241i −0.387945 0.387945i
\(46\) 3.23622 + 0.894875i 0.477155 + 0.131942i
\(47\) −2.51027 −0.366161 −0.183081 0.983098i \(-0.558607\pi\)
−0.183081 + 0.983098i \(0.558607\pi\)
\(48\) −2.99308 + 9.89582i −0.432015 + 1.42834i
\(49\) −13.3366 −1.90522
\(50\) 1.36306 + 0.376912i 0.192766 + 0.0533034i
\(51\) 2.66130 + 2.66130i 0.372657 + 0.372657i
\(52\) −1.04534 4.16603i −0.144962 0.577724i
\(53\) 1.50312 1.50312i 0.206470 0.206470i −0.596295 0.802765i \(-0.703361\pi\)
0.802765 + 0.596295i \(0.203361\pi\)
\(54\) −1.22623 2.16357i −0.166869 0.294425i
\(55\) 2.32045i 0.312889i
\(56\) −8.80078 9.23248i −1.17605 1.23374i
\(57\) 9.79472i 1.29734i
\(58\) −1.60942 + 0.912155i −0.211327 + 0.119772i
\(59\) −5.31807 + 5.31807i −0.692353 + 0.692353i −0.962749 0.270396i \(-0.912845\pi\)
0.270396 + 0.962749i \(0.412845\pi\)
\(60\) 4.43492 + 2.65574i 0.572546 + 0.342855i
\(61\) −1.02169 1.02169i −0.130815 0.130815i 0.638668 0.769483i \(-0.279486\pi\)
−0.769483 + 0.638668i \(0.779486\pi\)
\(62\) 2.71541 9.81998i 0.344857 1.24714i
\(63\) 16.5970 2.09103
\(64\) 0.382800 7.99084i 0.0478499 0.998855i
\(65\) −2.14759 −0.266375
\(66\) 2.26054 8.17499i 0.278253 1.00627i
\(67\) 5.22745 + 5.22745i 0.638635 + 0.638635i 0.950219 0.311584i \(-0.100859\pi\)
−0.311584 + 0.950219i \(0.600859\pi\)
\(68\) −2.49859 1.49622i −0.302998 0.181443i
\(69\) 4.33918 4.33918i 0.522376 0.522376i
\(70\) −5.54838 + 3.14461i −0.663158 + 0.375853i
\(71\) 1.92097i 0.227978i 0.993482 + 0.113989i \(0.0363628\pi\)
−0.993482 + 0.113989i \(0.963637\pi\)
\(72\) 7.18247 + 7.53478i 0.846462 + 0.887983i
\(73\) 1.39412i 0.163169i 0.996666 + 0.0815847i \(0.0259981\pi\)
−0.996666 + 0.0815847i \(0.974002\pi\)
\(74\) −5.13905 9.06740i −0.597403 1.05406i
\(75\) 1.82762 1.82762i 0.211035 0.211035i
\(76\) 1.84458 + 7.35129i 0.211587 + 0.843250i
\(77\) 7.39938 + 7.39938i 0.843237 + 0.843237i
\(78\) −7.56600 2.09214i −0.856681 0.236888i
\(79\) 5.06317 0.569651 0.284825 0.958579i \(-0.408064\pi\)
0.284825 + 0.958579i \(0.408064\pi\)
\(80\) −3.82870 1.15803i −0.428062 0.129471i
\(81\) 6.49599 0.721777
\(82\) −8.73949 2.41663i −0.965115 0.266872i
\(83\) −2.44974 2.44974i −0.268894 0.268894i 0.559761 0.828654i \(-0.310893\pi\)
−0.828654 + 0.559761i \(0.810893\pi\)
\(84\) −22.6105 + 5.67340i −2.46701 + 0.619019i
\(85\) −1.02966 + 1.02966i −0.111682 + 0.111682i
\(86\) 7.55194 + 13.3247i 0.814347 + 1.43684i
\(87\) 3.38097i 0.362478i
\(88\) −0.157070 + 6.56133i −0.0167437 + 0.699440i
\(89\) 9.36007i 0.992165i −0.868275 0.496083i \(-0.834771\pi\)
0.868275 0.496083i \(-0.165229\pi\)
\(90\) 4.52813 2.56637i 0.477307 0.270519i
\(91\) 6.84817 6.84817i 0.717883 0.717883i
\(92\) −2.43954 + 4.07388i −0.254340 + 0.424731i
\(93\) −13.1668 13.1668i −1.36533 1.36533i
\(94\) 0.946152 3.42166i 0.0975882 0.352917i
\(95\) 3.78959 0.388803
\(96\) −12.3605 7.80961i −1.26154 0.797065i
\(97\) 18.6313 1.89172 0.945859 0.324579i \(-0.105223\pi\)
0.945859 + 0.324579i \(0.105223\pi\)
\(98\) 5.02671 18.1785i 0.507774 1.83631i
\(99\) −6.03876 6.03876i −0.606918 0.606918i
\(100\) −1.02751 + 1.71587i −0.102751 + 0.171587i
\(101\) −4.84108 + 4.84108i −0.481705 + 0.481705i −0.905676 0.423971i \(-0.860636\pi\)
0.423971 + 0.905676i \(0.360636\pi\)
\(102\) −4.63059 + 2.62444i −0.458497 + 0.259858i
\(103\) 9.12540i 0.899153i 0.893242 + 0.449576i \(0.148425\pi\)
−0.893242 + 0.449576i \(0.851575\pi\)
\(104\) 6.07255 + 0.145369i 0.595463 + 0.0142546i
\(105\) 11.6557i 1.13748i
\(106\) 1.48230 + 2.61539i 0.143974 + 0.254029i
\(107\) −10.1505 + 10.1505i −0.981290 + 0.981290i −0.999828 0.0185385i \(-0.994099\pi\)
0.0185385 + 0.999828i \(0.494099\pi\)
\(108\) 3.41127 0.855951i 0.328249 0.0823639i
\(109\) 1.35489 + 1.35489i 0.129775 + 0.129775i 0.769011 0.639236i \(-0.220749\pi\)
−0.639236 + 0.769011i \(0.720749\pi\)
\(110\) 3.16291 + 0.874603i 0.301572 + 0.0833902i
\(111\) −19.0483 −1.80798
\(112\) 15.9016 8.51618i 1.50256 0.804704i
\(113\) −2.56039 −0.240861 −0.120431 0.992722i \(-0.538428\pi\)
−0.120431 + 0.992722i \(0.538428\pi\)
\(114\) 13.3508 + 3.69175i 1.25042 + 0.345764i
\(115\) 1.67883 + 1.67883i 0.156552 + 0.156552i
\(116\) −0.636716 2.53754i −0.0591176 0.235604i
\(117\) −5.58891 + 5.58891i −0.516695 + 0.516695i
\(118\) −5.24441 9.25329i −0.482787 0.851835i
\(119\) 6.56670i 0.601969i
\(120\) −5.29151 + 5.04409i −0.483047 + 0.460460i
\(121\) 5.61553i 0.510503i
\(122\) 1.77772 1.00754i 0.160947 0.0912188i
\(123\) −11.7181 + 11.7181i −1.05658 + 1.05658i
\(124\) 12.3618 + 7.40253i 1.11012 + 0.664767i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) −6.25561 + 22.6228i −0.557294 + 2.01540i
\(127\) 13.7354 1.21882 0.609409 0.792856i \(-0.291407\pi\)
0.609409 + 0.792856i \(0.291407\pi\)
\(128\) 10.7477 + 3.53362i 0.949973 + 0.312331i
\(129\) 27.9918 2.46454
\(130\) 0.809451 2.92729i 0.0709935 0.256741i
\(131\) 5.20726 + 5.20726i 0.454960 + 0.454960i 0.896997 0.442037i \(-0.145744\pi\)
−0.442037 + 0.896997i \(0.645744\pi\)
\(132\) 10.2910 + 6.16250i 0.895716 + 0.536377i
\(133\) −12.0841 + 12.0841i −1.04783 + 1.04783i
\(134\) −9.09563 + 5.15505i −0.785743 + 0.445329i
\(135\) 1.75851i 0.151348i
\(136\) 2.98118 2.84179i 0.255634 0.243681i
\(137\) 22.7563i 1.94420i −0.234559 0.972102i \(-0.575365\pi\)
0.234559 0.972102i \(-0.424635\pi\)
\(138\) 4.27908 + 7.55006i 0.364260 + 0.642704i
\(139\) 6.28085 6.28085i 0.532734 0.532734i −0.388651 0.921385i \(-0.627059\pi\)
0.921385 + 0.388651i \(0.127059\pi\)
\(140\) −2.19505 8.74803i −0.185515 0.739343i
\(141\) −4.58782 4.58782i −0.386364 0.386364i
\(142\) −2.61841 0.724038i −0.219732 0.0607599i
\(143\) −4.98336 −0.416729
\(144\) −12.9775 + 6.95020i −1.08146 + 0.579184i
\(145\) −1.30810 −0.108632
\(146\) −1.90027 0.525460i −0.157268 0.0434874i
\(147\) −24.3741 24.3741i −2.01034 2.01034i
\(148\) 14.2964 3.58723i 1.17516 0.294869i
\(149\) −12.9574 + 12.9574i −1.06151 + 1.06151i −0.0635329 + 0.997980i \(0.520237\pi\)
−0.997980 + 0.0635329i \(0.979763\pi\)
\(150\) 1.80230 + 3.18001i 0.147158 + 0.259646i
\(151\) 14.3417i 1.16711i −0.812073 0.583555i \(-0.801661\pi\)
0.812073 0.583555i \(-0.198339\pi\)
\(152\) −10.7155 0.256515i −0.869142 0.0208061i
\(153\) 5.35920i 0.433266i
\(154\) −12.8747 + 7.29689i −1.03747 + 0.588001i
\(155\) 5.09425 5.09425i 0.409180 0.409180i
\(156\) 5.70343 9.52438i 0.456640 0.762560i
\(157\) −2.10564 2.10564i −0.168049 0.168049i 0.618073 0.786121i \(-0.287914\pi\)
−0.786121 + 0.618073i \(0.787914\pi\)
\(158\) −1.90837 + 6.90141i −0.151822 + 0.549047i
\(159\) 5.49426 0.435723
\(160\) 3.02155 4.78229i 0.238874 0.378073i
\(161\) −10.7068 −0.843817
\(162\) −2.44842 + 8.85444i −0.192366 + 0.695671i
\(163\) −5.34004 5.34004i −0.418265 0.418265i 0.466341 0.884605i \(-0.345572\pi\)
−0.884605 + 0.466341i \(0.845572\pi\)
\(164\) 6.58804 11.0016i 0.514439 0.859081i
\(165\) 4.24089 4.24089i 0.330153 0.330153i
\(166\) 4.26248 2.41581i 0.330833 0.187503i
\(167\) 16.0686i 1.24343i 0.783245 + 0.621714i \(0.213563\pi\)
−0.783245 + 0.621714i \(0.786437\pi\)
\(168\) 0.788969 32.9579i 0.0608702 2.54276i
\(169\) 8.38787i 0.645221i
\(170\) −1.01540 1.79158i −0.0778775 0.137408i
\(171\) 9.86207 9.86207i 0.754171 0.754171i
\(172\) −21.0088 + 5.27151i −1.60191 + 0.401949i
\(173\) 17.1133 + 17.1133i 1.30110 + 1.30110i 0.927649 + 0.373453i \(0.121826\pi\)
0.373453 + 0.927649i \(0.378174\pi\)
\(174\) −4.60847 1.27433i −0.349367 0.0966065i
\(175\) −4.50961 −0.340894
\(176\) −8.88430 2.68714i −0.669679 0.202551i
\(177\) −19.4388 −1.46111
\(178\) 12.7584 + 3.52792i 0.956279 + 0.264429i
\(179\) 1.04482 + 1.04482i 0.0780933 + 0.0780933i 0.745075 0.666981i \(-0.232414\pi\)
−0.666981 + 0.745075i \(0.732414\pi\)
\(180\) 1.79141 + 7.13942i 0.133524 + 0.532141i
\(181\) 11.9886 11.9886i 0.891104 0.891104i −0.103523 0.994627i \(-0.533012\pi\)
0.994627 + 0.103523i \(0.0330115\pi\)
\(182\) 6.75332 + 11.9156i 0.500589 + 0.883245i
\(183\) 3.73453i 0.276065i
\(184\) −4.63346 4.86074i −0.341583 0.358338i
\(185\) 7.36979i 0.541838i
\(186\) 22.9099 12.9844i 1.67983 0.952065i
\(187\) −2.38927 + 2.38927i −0.174721 + 0.174721i
\(188\) 4.30732 + 2.57933i 0.314143 + 0.188117i
\(189\) 5.60748 + 5.60748i 0.407884 + 0.407884i
\(190\) −1.42834 + 5.16544i −0.103623 + 0.374741i
\(191\) 0.0667471 0.00482965 0.00241483 0.999997i \(-0.499231\pi\)
0.00241483 + 0.999997i \(0.499231\pi\)
\(192\) 15.3038 13.9046i 1.10446 1.00348i
\(193\) −1.09895 −0.0791039 −0.0395520 0.999218i \(-0.512593\pi\)
−0.0395520 + 0.999218i \(0.512593\pi\)
\(194\) −7.02234 + 25.3956i −0.504175 + 1.82329i
\(195\) −3.92497 3.92497i −0.281073 0.281073i
\(196\) 22.8839 + 13.7034i 1.63456 + 0.978816i
\(197\) 11.9289 11.9289i 0.849899 0.849899i −0.140222 0.990120i \(-0.544782\pi\)
0.990120 + 0.140222i \(0.0447815\pi\)
\(198\) 10.5073 5.95512i 0.746720 0.423212i
\(199\) 11.0397i 0.782584i 0.920267 + 0.391292i \(0.127972\pi\)
−0.920267 + 0.391292i \(0.872028\pi\)
\(200\) −1.95156 2.04729i −0.137996 0.144765i
\(201\) 19.1076i 1.34774i
\(202\) −4.77403 8.42334i −0.335899 0.592664i
\(203\) 4.17123 4.17123i 0.292763 0.292763i
\(204\) −1.83195 7.30097i −0.128262 0.511170i
\(205\) −4.53373 4.53373i −0.316649 0.316649i
\(206\) −12.4385 3.43947i −0.866631 0.239639i
\(207\) 8.73803 0.607335
\(208\) −2.48696 + 8.22247i −0.172440 + 0.570126i
\(209\) 8.79353 0.608261
\(210\) −15.8875 4.39318i −1.09634 0.303158i
\(211\) −8.59737 8.59737i −0.591868 0.591868i 0.346268 0.938136i \(-0.387449\pi\)
−0.938136 + 0.346268i \(0.887449\pi\)
\(212\) −4.12364 + 1.03470i −0.283213 + 0.0710634i
\(213\) −3.51080 + 3.51080i −0.240556 + 0.240556i
\(214\) −10.0100 17.6617i −0.684266 1.20733i
\(215\) 10.8301i 0.738603i
\(216\) −0.119032 + 4.97238i −0.00809912 + 0.338328i
\(217\) 32.4888i 2.20548i
\(218\) −2.35748 + 1.33613i −0.159669 + 0.0904941i
\(219\) −2.54792 + 2.54792i −0.172172 + 0.172172i
\(220\) −2.38428 + 3.98159i −0.160748 + 0.268439i
\(221\) 2.21128 + 2.21128i 0.148747 + 0.148747i
\(222\) 7.17951 25.9639i 0.481857 1.74259i
\(223\) −21.4238 −1.43465 −0.717323 0.696741i \(-0.754633\pi\)
−0.717323 + 0.696741i \(0.754633\pi\)
\(224\) 5.61460 + 24.8847i 0.375141 + 1.66268i
\(225\) 3.68037 0.245358
\(226\) 0.965041 3.48997i 0.0641936 0.232149i
\(227\) −8.06331 8.06331i −0.535181 0.535181i 0.386929 0.922110i \(-0.373536\pi\)
−0.922110 + 0.386929i \(0.873536\pi\)
\(228\) −10.0642 + 16.8065i −0.666515 + 1.11304i
\(229\) 4.63169 4.63169i 0.306071 0.306071i −0.537313 0.843383i \(-0.680560\pi\)
0.843383 + 0.537313i \(0.180560\pi\)
\(230\) −2.92112 + 1.65558i −0.192613 + 0.109166i
\(231\) 27.0465i 1.77953i
\(232\) 3.69880 + 0.0885445i 0.242838 + 0.00581323i
\(233\) 26.0672i 1.70772i −0.520502 0.853860i \(-0.674255\pi\)
0.520502 0.853860i \(-0.325745\pi\)
\(234\) −5.51150 9.72455i −0.360298 0.635714i
\(235\) 1.77503 1.77503i 0.115790 0.115790i
\(236\) 14.5895 3.66078i 0.949695 0.238296i
\(237\) 9.25353 + 9.25353i 0.601081 + 0.601081i
\(238\) 8.95082 + 2.47507i 0.580196 + 0.160435i
\(239\) 5.12209 0.331320 0.165660 0.986183i \(-0.447025\pi\)
0.165660 + 0.986183i \(0.447025\pi\)
\(240\) −4.88097 9.11383i −0.315066 0.588295i
\(241\) 11.4987 0.740695 0.370347 0.928893i \(-0.379239\pi\)
0.370347 + 0.928893i \(0.379239\pi\)
\(242\) −7.65432 2.11656i −0.492038 0.136058i
\(243\) 15.6025 + 15.6025i 1.00090 + 1.00090i
\(244\) 0.703301 + 2.80290i 0.0450242 + 0.179437i
\(245\) 9.43037 9.43037i 0.602484 0.602484i
\(246\) −11.5558 20.3891i −0.736769 1.29996i
\(247\) 8.13847i 0.517838i
\(248\) −14.7494 + 14.0598i −0.936588 + 0.892795i
\(249\) 8.95437i 0.567460i
\(250\) −1.23035 + 0.697313i −0.0778140 + 0.0441020i
\(251\) −19.8270 + 19.8270i −1.25147 + 1.25147i −0.296408 + 0.955061i \(0.595789\pi\)
−0.955061 + 0.296408i \(0.904211\pi\)
\(252\) −28.4784 17.0536i −1.79397 1.07427i
\(253\) 3.89564 + 3.89564i 0.244917 + 0.244917i
\(254\) −5.17703 + 18.7222i −0.324836 + 1.17473i
\(255\) −3.76365 −0.235689
\(256\) −8.86749 + 13.3179i −0.554218 + 0.832372i
\(257\) −24.2494 −1.51264 −0.756319 0.654203i \(-0.773004\pi\)
−0.756319 + 0.654203i \(0.773004\pi\)
\(258\) −10.5504 + 38.1545i −0.656842 + 2.37540i
\(259\) 23.5006 + 23.5006i 1.46026 + 1.46026i
\(260\) 3.68499 + 2.20666i 0.228533 + 0.136851i
\(261\) −3.40422 + 3.40422i −0.210716 + 0.210716i
\(262\) −9.06049 + 5.13514i −0.559759 + 0.317250i
\(263\) 22.5680i 1.39160i −0.718234 0.695802i \(-0.755049\pi\)
0.718234 0.695802i \(-0.244951\pi\)
\(264\) −12.2787 + 11.7045i −0.755700 + 0.720365i
\(265\) 2.12574i 0.130583i
\(266\) −11.9168 21.0261i −0.730664 1.28919i
\(267\) 17.1066 17.1066i 1.04691 1.04691i
\(268\) −3.59840 14.3409i −0.219807 0.876010i
\(269\) −5.10558 5.10558i −0.311293 0.311293i 0.534117 0.845410i \(-0.320644\pi\)
−0.845410 + 0.534117i \(0.820644\pi\)
\(270\) 2.39695 + 0.662802i 0.145874 + 0.0403369i
\(271\) 6.67920 0.405733 0.202866 0.979206i \(-0.434974\pi\)
0.202866 + 0.979206i \(0.434974\pi\)
\(272\) 2.74989 + 5.13464i 0.166736 + 0.311333i
\(273\) 25.0317 1.51498
\(274\) 31.0183 + 8.57713i 1.87388 + 0.518163i
\(275\) 1.64080 + 1.64080i 0.0989441 + 0.0989441i
\(276\) −11.9040 + 2.98695i −0.716539 + 0.179793i
\(277\) −11.8524 + 11.8524i −0.712141 + 0.712141i −0.966983 0.254842i \(-0.917977\pi\)
0.254842 + 0.966983i \(0.417977\pi\)
\(278\) 6.19386 + 10.9285i 0.371483 + 0.655448i
\(279\) 26.5147i 1.58739i
\(280\) 12.7514 + 0.305253i 0.762044 + 0.0182423i
\(281\) 0.477460i 0.0284829i −0.999899 0.0142414i \(-0.995467\pi\)
0.999899 0.0142414i \(-0.00453334\pi\)
\(282\) 7.98269 4.52428i 0.475362 0.269417i
\(283\) −0.482914 + 0.482914i −0.0287063 + 0.0287063i −0.721314 0.692608i \(-0.756462\pi\)
0.692608 + 0.721314i \(0.256462\pi\)
\(284\) 1.97382 3.29615i 0.117124 0.195591i
\(285\) 6.92591 + 6.92591i 0.410256 + 0.410256i
\(286\) 1.87829 6.79263i 0.111065 0.401656i
\(287\) 28.9141 1.70674
\(288\) −4.58217 20.3088i −0.270007 1.19671i
\(289\) −14.8796 −0.875271
\(290\) 0.493038 1.78302i 0.0289522 0.104703i
\(291\) 34.0508 + 34.0508i 1.99609 + 1.99609i
\(292\) 1.43247 2.39214i 0.0838290 0.139989i
\(293\) 7.46638 7.46638i 0.436190 0.436190i −0.454537 0.890728i \(-0.650195\pi\)
0.890728 + 0.454537i \(0.150195\pi\)
\(294\) 42.4103 24.0365i 2.47342 1.40184i
\(295\) 7.52088i 0.437883i
\(296\) −0.498857 + 20.8389i −0.0289955 + 1.21124i
\(297\) 4.08052i 0.236776i
\(298\) −12.7780 22.5456i −0.740207 1.30603i
\(299\) 3.60544 3.60544i 0.208508 0.208508i
\(300\) −5.01385 + 1.25807i −0.289475 + 0.0726347i
\(301\) −34.5346 34.5346i −1.99054 1.99054i
\(302\) 19.5486 + 5.40556i 1.12490 + 0.311055i
\(303\) −17.6953 −1.01657
\(304\) 4.38845 14.5092i 0.251695 0.832160i
\(305\) 1.44489 0.0827344
\(306\) −7.30492 2.01995i −0.417595 0.115473i
\(307\) 2.39349 + 2.39349i 0.136604 + 0.136604i 0.772102 0.635498i \(-0.219205\pi\)
−0.635498 + 0.772102i \(0.719205\pi\)
\(308\) −5.09348 20.2993i −0.290228 1.15666i
\(309\) −16.6777 + 16.6777i −0.948764 + 0.948764i
\(310\) 5.02369 + 8.86386i 0.285327 + 0.503433i
\(311\) 20.4404i 1.15907i −0.814948 0.579534i \(-0.803235\pi\)
0.814948 0.579534i \(-0.196765\pi\)
\(312\) 10.8326 + 11.3640i 0.613276 + 0.643359i
\(313\) 2.46975i 0.139598i 0.997561 + 0.0697992i \(0.0222359\pi\)
−0.997561 + 0.0697992i \(0.977764\pi\)
\(314\) 3.66376 2.07648i 0.206758 0.117182i
\(315\) −11.7359 + 11.7359i −0.661241 + 0.661241i
\(316\) −8.68776 5.20245i −0.488725 0.292660i
\(317\) −16.2241 16.2241i −0.911234 0.911234i 0.0851350 0.996369i \(-0.472868\pi\)
−0.996369 + 0.0851350i \(0.972868\pi\)
\(318\) −2.07085 + 7.48902i −0.116128 + 0.419963i
\(319\) −3.03537 −0.169948
\(320\) 5.37969 + 5.92105i 0.300734 + 0.330997i
\(321\) −37.1026 −2.07086
\(322\) 4.03553 14.5941i 0.224891 0.813296i
\(323\) −3.90198 3.90198i −0.217112 0.217112i
\(324\) −11.1463 6.67469i −0.619240 0.370816i
\(325\) 1.51857 1.51857i 0.0842353 0.0842353i
\(326\) 9.29154 5.26608i 0.514611 0.291661i
\(327\) 4.95246i 0.273871i
\(328\) 12.5128 + 13.1265i 0.690902 + 0.724792i
\(329\) 11.3204i 0.624111i
\(330\) 4.18215 + 7.37903i 0.230220 + 0.406202i
\(331\) 3.42340 3.42340i 0.188167 0.188167i −0.606736 0.794903i \(-0.707521\pi\)
0.794903 + 0.606736i \(0.207521\pi\)
\(332\) 1.68632 + 6.72057i 0.0925487 + 0.368839i
\(333\) −19.1792 19.1792i −1.05102 1.05102i
\(334\) −21.9025 6.05645i −1.19845 0.331394i
\(335\) −7.39273 −0.403908
\(336\) 44.6263 + 13.4976i 2.43456 + 0.736356i
\(337\) −5.40017 −0.294166 −0.147083 0.989124i \(-0.546988\pi\)
−0.147083 + 0.989124i \(0.546988\pi\)
\(338\) 11.4332 + 3.16149i 0.621883 + 0.171962i
\(339\) −4.67941 4.67941i −0.254151 0.254151i
\(340\) 2.82475 0.708783i 0.153194 0.0384392i
\(341\) 11.8209 11.8209i 0.640139 0.640139i
\(342\) 9.72548 + 17.1597i 0.525894 + 0.927893i
\(343\) 28.5754i 1.54292i
\(344\) 0.733080 30.6232i 0.0395250 1.65109i
\(345\) 6.13653i 0.330379i
\(346\) −29.7767 + 16.8763i −1.60081 + 0.907276i
\(347\) −4.07531 + 4.07531i −0.218774 + 0.218774i −0.807982 0.589208i \(-0.799440\pi\)
0.589208 + 0.807982i \(0.299440\pi\)
\(348\) 3.47397 5.80132i 0.186224 0.310983i
\(349\) 1.55681 + 1.55681i 0.0833339 + 0.0833339i 0.747545 0.664211i \(-0.231232\pi\)
−0.664211 + 0.747545i \(0.731232\pi\)
\(350\) 1.69972 6.14687i 0.0908541 0.328564i
\(351\) −3.77655 −0.201577
\(352\) 7.01133 11.0970i 0.373705 0.591474i
\(353\) 1.34919 0.0718103 0.0359052 0.999355i \(-0.488569\pi\)
0.0359052 + 0.999355i \(0.488569\pi\)
\(354\) 7.32670 26.4963i 0.389410 1.40826i
\(355\) −1.35833 1.35833i −0.0720929 0.0720929i
\(356\) −9.61755 + 16.0607i −0.509729 + 0.851216i
\(357\) 12.0014 12.0014i 0.635182 0.635182i
\(358\) −1.81795 + 1.03035i −0.0960819 + 0.0544555i
\(359\) 23.2192i 1.22546i −0.790291 0.612732i \(-0.790071\pi\)
0.790291 0.612732i \(-0.209929\pi\)
\(360\) −10.4067 0.249122i −0.548480 0.0131299i
\(361\) 4.63903i 0.244159i
\(362\) 11.8225 + 20.8598i 0.621379 + 1.09637i
\(363\) −10.2630 + 10.2630i −0.538670 + 0.538670i
\(364\) −18.7871 + 4.71405i −0.984714 + 0.247083i
\(365\) −0.985792 0.985792i −0.0515987 0.0515987i
\(366\) 5.09040 + 1.40759i 0.266080 + 0.0735759i
\(367\) −5.16452 −0.269586 −0.134793 0.990874i \(-0.543037\pi\)
−0.134793 + 0.990874i \(0.543037\pi\)
\(368\) 8.37189 4.48362i 0.436415 0.233725i
\(369\) −23.5973 −1.22843
\(370\) 10.0455 + 2.77776i 0.522239 + 0.144409i
\(371\) −6.77849 6.77849i −0.351922 0.351922i
\(372\) 9.06359 + 36.1216i 0.469925 + 1.87282i
\(373\) 18.5056 18.5056i 0.958185 0.958185i −0.0409750 0.999160i \(-0.513046\pi\)
0.999160 + 0.0409750i \(0.0130464\pi\)
\(374\) −2.35618 4.15727i −0.121835 0.214967i
\(375\) 2.58464i 0.133470i
\(376\) −5.13926 + 4.89896i −0.265037 + 0.252645i
\(377\) 2.80926i 0.144684i
\(378\) −9.75687 + 5.52982i −0.501839 + 0.284423i
\(379\) −13.5254 + 13.5254i −0.694754 + 0.694754i −0.963274 0.268520i \(-0.913465\pi\)
0.268520 + 0.963274i \(0.413465\pi\)
\(380\) −6.50246 3.89383i −0.333569 0.199749i
\(381\) 25.1030 + 25.1030i 1.28607 + 1.28607i
\(382\) −0.0251578 + 0.0909805i −0.00128718 + 0.00465497i
\(383\) 21.9051 1.11930 0.559650 0.828729i \(-0.310936\pi\)
0.559650 + 0.828729i \(0.310936\pi\)
\(384\) 13.1846 + 26.1008i 0.672825 + 1.33195i
\(385\) −10.4643 −0.533310
\(386\) 0.414206 1.49793i 0.0210825 0.0762427i
\(387\) 28.1843 + 28.1843i 1.43269 + 1.43269i
\(388\) −31.9689 19.1438i −1.62298 0.971878i
\(389\) 4.48844 4.48844i 0.227573 0.227573i −0.584105 0.811678i \(-0.698554\pi\)
0.811678 + 0.584105i \(0.198554\pi\)
\(390\) 6.82934 3.87061i 0.345817 0.195996i
\(391\) 3.45725i 0.174841i
\(392\) −27.3038 + 26.0271i −1.37905 + 1.31457i
\(393\) 19.0337i 0.960126i
\(394\) 11.7637 + 20.7560i 0.592646 + 1.04567i
\(395\) −3.58020 + 3.58020i −0.180139 + 0.180139i
\(396\) 4.15688 + 16.5666i 0.208891 + 0.832504i
\(397\) 11.7892 + 11.7892i 0.591682 + 0.591682i 0.938086 0.346404i \(-0.112597\pi\)
−0.346404 + 0.938086i \(0.612597\pi\)
\(398\) −15.0478 4.16100i −0.754278 0.208572i
\(399\) −44.1703 −2.21128
\(400\) 3.52615 1.88845i 0.176308 0.0944227i
\(401\) 24.9259 1.24474 0.622371 0.782722i \(-0.286170\pi\)
0.622371 + 0.782722i \(0.286170\pi\)
\(402\) −26.0448 7.20187i −1.29900 0.359196i
\(403\) −10.9403 10.9403i −0.544977 0.544977i
\(404\) 13.2809 3.33244i 0.660751 0.165795i
\(405\) −4.59336 + 4.59336i −0.228246 + 0.228246i
\(406\) 4.11346 + 7.25784i 0.204148 + 0.360200i
\(407\) 17.1012i 0.847675i
\(408\) 10.6422 + 0.254759i 0.526865 + 0.0126125i
\(409\) 21.5355i 1.06486i 0.846474 + 0.532430i \(0.178721\pi\)
−0.846474 + 0.532430i \(0.821279\pi\)
\(410\) 7.88857 4.47094i 0.389589 0.220804i
\(411\) 41.5898 41.5898i 2.05148 2.05148i
\(412\) 9.37643 15.6581i 0.461943 0.771417i
\(413\) 23.9824 + 23.9824i 1.18010 + 1.18010i
\(414\) −3.29347 + 11.9105i −0.161865 + 0.585368i
\(415\) 3.46445 0.170063
\(416\) −10.2704 6.48903i −0.503546 0.318151i
\(417\) 22.9580 1.12426
\(418\) −3.31439 + 11.9861i −0.162112 + 0.586261i
\(419\) −17.2979 17.2979i −0.845060 0.845060i 0.144452 0.989512i \(-0.453858\pi\)
−0.989512 + 0.144452i \(0.953858\pi\)
\(420\) 11.9763 19.9997i 0.584386 0.975888i
\(421\) −19.4330 + 19.4330i −0.947105 + 0.947105i −0.998670 0.0515648i \(-0.983579\pi\)
0.0515648 + 0.998670i \(0.483579\pi\)
\(422\) 14.9592 8.47830i 0.728203 0.412717i
\(423\) 9.23874i 0.449203i
\(424\) 0.143890 6.01077i 0.00698791 0.291909i
\(425\) 1.45616i 0.0706341i
\(426\) −3.46218 6.10871i −0.167743 0.295968i
\(427\) −4.60744 + 4.60744i −0.222970 + 0.222970i
\(428\) 27.8468 6.98729i 1.34603 0.337744i
\(429\) −9.10767 9.10767i −0.439723 0.439723i
\(430\) −14.7620 4.08198i −0.711888 0.196850i
\(431\) 28.3769 1.36687 0.683433 0.730013i \(-0.260486\pi\)
0.683433 + 0.730013i \(0.260486\pi\)
\(432\) −6.73280 2.03640i −0.323932 0.0979763i
\(433\) 9.04007 0.434438 0.217219 0.976123i \(-0.430301\pi\)
0.217219 + 0.976123i \(0.430301\pi\)
\(434\) −44.2842 12.2454i −2.12571 0.587799i
\(435\) −2.39071 2.39071i −0.114626 0.114626i
\(436\) −0.932664 3.71699i −0.0446665 0.178012i
\(437\) −6.36208 + 6.36208i −0.304340 + 0.304340i
\(438\) −2.51263 4.43331i −0.120058 0.211832i
\(439\) 28.2949i 1.35044i 0.737615 + 0.675221i \(0.235952\pi\)
−0.737615 + 0.675221i \(0.764048\pi\)
\(440\) −4.52850 4.75063i −0.215888 0.226477i
\(441\) 49.0834i 2.33731i
\(442\) −3.84757 + 2.18066i −0.183010 + 0.103723i
\(443\) −13.1232 + 13.1232i −0.623504 + 0.623504i −0.946426 0.322922i \(-0.895335\pi\)
0.322922 + 0.946426i \(0.395335\pi\)
\(444\) 32.6844 + 19.5722i 1.55113 + 0.928857i
\(445\) 6.61857 + 6.61857i 0.313750 + 0.313750i
\(446\) 8.07489 29.2020i 0.382357 1.38275i
\(447\) −47.3624 −2.24016
\(448\) −36.0355 1.72628i −1.70252 0.0815588i
\(449\) −14.3902 −0.679116 −0.339558 0.940585i \(-0.610277\pi\)
−0.339558 + 0.940585i \(0.610277\pi\)
\(450\) −1.38717 + 5.01657i −0.0653920 + 0.236483i
\(451\) −10.5203 10.5203i −0.495380 0.495380i
\(452\) 4.39331 + 2.63082i 0.206644 + 0.123743i
\(453\) 26.2111 26.2111i 1.23151 1.23151i
\(454\) 14.0299 7.95163i 0.658458 0.373189i
\(455\) 9.68477i 0.454029i
\(456\) −19.1150 20.0526i −0.895143 0.939051i
\(457\) 4.54538i 0.212624i −0.994333 0.106312i \(-0.966096\pi\)
0.994333 0.106312i \(-0.0339042\pi\)
\(458\) 4.56754 + 8.05902i 0.213427 + 0.376573i
\(459\) −1.81066 + 1.81066i −0.0845146 + 0.0845146i
\(460\) −1.15565 4.60568i −0.0538826 0.214741i
\(461\) 19.8046 + 19.8046i 0.922393 + 0.922393i 0.997198 0.0748050i \(-0.0238334\pi\)
−0.0748050 + 0.997198i \(0.523833\pi\)
\(462\) −36.8660 10.1941i −1.71516 0.474274i
\(463\) −14.5997 −0.678506 −0.339253 0.940695i \(-0.610174\pi\)
−0.339253 + 0.940695i \(0.610174\pi\)
\(464\) −1.51481 + 5.00833i −0.0703235 + 0.232506i
\(465\) 18.6207 0.863513
\(466\) 35.5312 + 9.82505i 1.64595 + 0.455137i
\(467\) 19.8105 + 19.8105i 0.916722 + 0.916722i 0.996789 0.0800671i \(-0.0255135\pi\)
−0.0800671 + 0.996789i \(0.525513\pi\)
\(468\) 15.3325 3.84722i 0.708746 0.177838i
\(469\) 23.5738 23.5738i 1.08853 1.08853i
\(470\) 1.75045 + 3.08851i 0.0807421 + 0.142462i
\(471\) 7.69661i 0.354641i
\(472\) −0.509084 + 21.2662i −0.0234325 + 0.978855i
\(473\) 25.1306i 1.15550i
\(474\) −16.1009 + 9.12537i −0.739539 + 0.419142i
\(475\) −2.67964 + 2.67964i −0.122950 + 0.122950i
\(476\) −6.74734 + 11.2676i −0.309264 + 0.516451i
\(477\) 5.53204 + 5.53204i 0.253295 + 0.253295i
\(478\) −1.93058 + 6.98172i −0.0883025 + 0.319337i
\(479\) 21.0378 0.961243 0.480621 0.876928i \(-0.340411\pi\)
0.480621 + 0.876928i \(0.340411\pi\)
\(480\) 14.2624 3.21796i 0.650987 0.146879i
\(481\) −15.8273 −0.721661
\(482\) −4.33399 + 15.6734i −0.197408 + 0.713904i
\(483\) −19.5680 19.5680i −0.890375 0.890375i
\(484\) 5.77000 9.63555i 0.262273 0.437980i
\(485\) −13.1743 + 13.1743i −0.598214 + 0.598214i
\(486\) −27.1480 + 15.3865i −1.23146 + 0.697944i
\(487\) 10.2724i 0.465485i 0.972538 + 0.232743i \(0.0747699\pi\)
−0.972538 + 0.232743i \(0.925230\pi\)
\(488\) −4.08561 0.0978041i −0.184947 0.00442738i
\(489\) 19.5191i 0.882685i
\(490\) 9.29976 + 16.4086i 0.420120 + 0.741265i
\(491\) −5.95681 + 5.95681i −0.268827 + 0.268827i −0.828627 0.559801i \(-0.810878\pi\)
0.559801 + 0.828627i \(0.310878\pi\)
\(492\) 32.1471 8.06632i 1.44930 0.363658i
\(493\) 1.34690 + 1.34690i 0.0606612 + 0.0606612i
\(494\) 11.0932 + 3.06748i 0.499108 + 0.138013i
\(495\) 8.54009 0.383849
\(496\) −13.6051 25.4036i −0.610886 1.14066i
\(497\) 8.66284 0.388581
\(498\) 12.2054 + 3.37501i 0.546935 + 0.151238i
\(499\) −2.81466 2.81466i −0.126002 0.126002i 0.641294 0.767295i \(-0.278398\pi\)
−0.767295 + 0.641294i \(0.778398\pi\)
\(500\) −0.486749 1.93986i −0.0217681 0.0867534i
\(501\) −29.3673 + 29.3673i −1.31203 + 1.31203i
\(502\) −19.5524 34.4985i −0.872666 1.53974i
\(503\) 5.49759i 0.245125i −0.992461 0.122563i \(-0.960889\pi\)
0.992461 0.122563i \(-0.0391113\pi\)
\(504\) 33.9789 32.3901i 1.51354 1.44277i
\(505\) 6.84632i 0.304657i
\(506\) −6.77831 + 3.84169i −0.301333 + 0.170784i
\(507\) 15.3298 15.3298i 0.680821 0.680821i
\(508\) −23.5682 14.1132i −1.04567 0.626173i
\(509\) −4.37578 4.37578i −0.193953 0.193953i 0.603449 0.797402i \(-0.293793\pi\)
−0.797402 + 0.603449i \(0.793793\pi\)
\(510\) 1.41856 5.13008i 0.0628150 0.227164i
\(511\) 6.28693 0.278118
\(512\) −14.8109 17.1066i −0.654556 0.756013i
\(513\) 6.66402 0.294224
\(514\) 9.13990 33.0535i 0.403144 1.45793i
\(515\) −6.45263 6.45263i −0.284337 0.284337i
\(516\) −48.0304 28.7618i −2.11442 1.26617i
\(517\) 4.11887 4.11887i 0.181148 0.181148i
\(518\) −40.8904 + 23.1751i −1.79662 + 1.01826i
\(519\) 62.5532i 2.74578i
\(520\) −4.39673 + 4.19115i −0.192810 + 0.183794i
\(521\) 33.8729i 1.48400i 0.670401 + 0.741999i \(0.266122\pi\)
−0.670401 + 0.741999i \(0.733878\pi\)
\(522\) −3.35707 5.92325i −0.146935 0.259253i
\(523\) 27.8060 27.8060i 1.21587 1.21587i 0.246804 0.969065i \(-0.420620\pi\)
0.969065 0.246804i \(-0.0793803\pi\)
\(524\) −3.58450 14.2855i −0.156590 0.624065i
\(525\) −8.24183 8.24183i −0.359703 0.359703i
\(526\) 30.7616 + 8.50615i 1.34127 + 0.370886i
\(527\) −10.4907 −0.456981
\(528\) −11.3260 21.1482i −0.492902 0.920356i
\(529\) 17.3630 0.754915
\(530\) −2.89751 0.801215i −0.125860 0.0348025i
\(531\) −19.5724 19.5724i −0.849372 0.849372i
\(532\) 33.1514 8.31832i 1.43730 0.360645i
\(533\) −9.73658 + 9.73658i −0.421738 + 0.421738i
\(534\) 16.8697 + 29.7651i 0.730023 + 1.28806i
\(535\) 14.3550i 0.620622i
\(536\) 20.9038 + 0.500410i 0.902907 + 0.0216144i
\(537\) 3.81905i 0.164804i
\(538\) 8.88358 5.03487i 0.382998 0.217069i
\(539\) 21.8827 21.8827i 0.942553 0.942553i
\(540\) −1.80688 + 3.01738i −0.0777558 + 0.129847i
\(541\) 3.03066 + 3.03066i 0.130298 + 0.130298i 0.769248 0.638950i \(-0.220631\pi\)
−0.638950 + 0.769248i \(0.720631\pi\)
\(542\) −2.51747 + 9.10416i −0.108135 + 0.391057i
\(543\) 43.8211 1.88054
\(544\) −8.03529 + 1.81296i −0.344510 + 0.0777301i
\(545\) −1.91611 −0.0820771
\(546\) −9.43473 + 34.1197i −0.403769 + 1.46019i
\(547\) −18.4783 18.4783i −0.790074 0.790074i 0.191432 0.981506i \(-0.438687\pi\)
−0.981506 + 0.191432i \(0.938687\pi\)
\(548\) −23.3823 + 39.0470i −0.998843 + 1.66801i
\(549\) 3.76021 3.76021i 0.160482 0.160482i
\(550\) −2.85495 + 1.61808i −0.121736 + 0.0689951i
\(551\) 4.95716i 0.211182i
\(552\) 0.415378 17.3517i 0.0176797 0.738539i
\(553\) 22.8329i 0.970953i
\(554\) −11.6882 20.6228i −0.496585 0.876181i
\(555\) 13.4691 13.4691i 0.571734 0.571734i
\(556\) −17.2308 + 4.32353i −0.730747 + 0.183358i
\(557\) −30.2060 30.2060i −1.27987 1.27987i −0.940741 0.339127i \(-0.889868\pi\)
−0.339127 0.940741i \(-0.610132\pi\)
\(558\) 36.1411 + 9.99370i 1.52998 + 0.423067i
\(559\) 23.2585 0.983729
\(560\) −5.22225 + 17.2659i −0.220680 + 0.729620i
\(561\) −8.73334 −0.368722
\(562\) 0.650807 + 0.179960i 0.0274526 + 0.00759117i
\(563\) 2.86747 + 2.86747i 0.120850 + 0.120850i 0.764945 0.644095i \(-0.222766\pi\)
−0.644095 + 0.764945i \(0.722766\pi\)
\(564\) 3.15810 + 12.5862i 0.132980 + 0.529973i
\(565\) 1.81047 1.81047i 0.0761670 0.0761670i
\(566\) −0.476226 0.840258i −0.0200173 0.0353187i
\(567\) 29.2944i 1.23025i
\(568\) 3.74890 + 3.93279i 0.157300 + 0.165016i
\(569\) 35.8628i 1.50345i 0.659479 + 0.751723i \(0.270777\pi\)
−0.659479 + 0.751723i \(0.729223\pi\)
\(570\) −12.0509 + 6.82999i −0.504757 + 0.286077i
\(571\) −17.6509 + 17.6509i −0.738667 + 0.738667i −0.972320 0.233653i \(-0.924932\pi\)
0.233653 + 0.972320i \(0.424932\pi\)
\(572\) 8.55082 + 5.12044i 0.357528 + 0.214096i
\(573\) 0.121988 + 0.121988i 0.00509613 + 0.00509613i
\(574\) −10.8981 + 39.4117i −0.454876 + 1.64501i
\(575\) −2.37423 −0.0990122
\(576\) 29.4092 + 1.40884i 1.22538 + 0.0587018i
\(577\) 36.1387 1.50448 0.752238 0.658892i \(-0.228975\pi\)
0.752238 + 0.658892i \(0.228975\pi\)
\(578\) 5.60830 20.2818i 0.233274 0.843612i
\(579\) −2.00845 2.00845i −0.0834685 0.0834685i
\(580\) 2.24454 + 1.34408i 0.0931993 + 0.0558100i
\(581\) −11.0474 + 11.0474i −0.458322 + 0.458322i
\(582\) −59.2475 + 33.5792i −2.45589 + 1.39190i
\(583\) 4.93265i 0.204290i
\(584\) 2.72071 + 2.85417i 0.112584 + 0.118106i
\(585\) 7.90391i 0.326786i
\(586\) 7.36297 + 12.9913i 0.304161 + 0.536666i
\(587\) −11.4005 + 11.4005i −0.470550 + 0.470550i −0.902093 0.431542i \(-0.857970\pi\)
0.431542 + 0.902093i \(0.357970\pi\)
\(588\) 16.7783 + 66.8675i 0.691927 + 2.75757i
\(589\) 19.3051 + 19.3051i 0.795453 + 0.795453i
\(590\) 10.2514 + 2.83471i 0.422045 + 0.116703i
\(591\) 43.6029 1.79358
\(592\) −28.2167 8.53441i −1.15970 0.350762i
\(593\) −35.0454 −1.43914 −0.719572 0.694418i \(-0.755662\pi\)
−0.719572 + 0.694418i \(0.755662\pi\)
\(594\) 5.56200 + 1.53800i 0.228212 + 0.0631048i
\(595\) 4.64336 + 4.64336i 0.190359 + 0.190359i
\(596\) 35.5472 8.91945i 1.45607 0.365355i
\(597\) −20.1764 + 20.1764i −0.825764 + 0.825764i
\(598\) 3.55550 + 6.27337i 0.145395 + 0.256537i
\(599\) 18.2753i 0.746707i 0.927689 + 0.373354i \(0.121792\pi\)
−0.927689 + 0.373354i \(0.878208\pi\)
\(600\) 0.174953 7.30837i 0.00714242 0.298363i
\(601\) 0.480142i 0.0195854i −0.999952 0.00979269i \(-0.996883\pi\)
0.999952 0.00979269i \(-0.00311716\pi\)
\(602\) 60.0893 34.0563i 2.44906 1.38803i
\(603\) −19.2389 + 19.2389i −0.783470 + 0.783470i
\(604\) −14.7362 + 24.6086i −0.599608 + 1.00131i
\(605\) −3.97078 3.97078i −0.161435 0.161435i
\(606\) 6.66956 24.1197i 0.270932 0.979798i
\(607\) −38.6107 −1.56716 −0.783581 0.621290i \(-0.786609\pi\)
−0.783581 + 0.621290i \(0.786609\pi\)
\(608\) 18.1229 + 11.4504i 0.734980 + 0.464376i
\(609\) 15.2468 0.617833
\(610\) −0.544598 + 1.96948i −0.0220501 + 0.0797419i
\(611\) −3.81204 3.81204i −0.154218 0.154218i
\(612\) 5.50662 9.19572i 0.222592 0.371715i
\(613\) −5.53592 + 5.53592i −0.223594 + 0.223594i −0.810010 0.586416i \(-0.800538\pi\)
0.586416 + 0.810010i \(0.300538\pi\)
\(614\) −4.16461 + 2.36034i −0.168070 + 0.0952557i
\(615\) 16.5718i 0.668241i
\(616\) 29.5890 + 0.708322i 1.19218 + 0.0285391i
\(617\) 31.8836i 1.28358i −0.766879 0.641792i \(-0.778191\pi\)
0.766879 0.641792i \(-0.221809\pi\)
\(618\) −16.4468 29.0188i −0.661586 1.16731i
\(619\) −29.4054 + 29.4054i −1.18190 + 1.18190i −0.202650 + 0.979251i \(0.564955\pi\)
−0.979251 + 0.202650i \(0.935045\pi\)
\(620\) −13.9755 + 3.50671i −0.561269 + 0.140833i
\(621\) 2.95224 + 2.95224i 0.118469 + 0.118469i
\(622\) 27.8615 + 7.70422i 1.11714 + 0.308911i
\(623\) −42.2102 −1.69112
\(624\) −19.5728 + 10.4823i −0.783537 + 0.419628i
\(625\) −1.00000 −0.0400000
\(626\) −3.36642 0.930878i −0.134549 0.0372054i
\(627\) 16.0712 + 16.0712i 0.641822 + 0.641822i
\(628\) 1.44945 + 5.77658i 0.0578395 + 0.230511i
\(629\) −7.58837 + 7.58837i −0.302568 + 0.302568i
\(630\) −11.5733 20.4201i −0.461092 0.813556i
\(631\) 30.7381i 1.22367i 0.790987 + 0.611833i \(0.209568\pi\)
−0.790987 + 0.611833i \(0.790432\pi\)
\(632\) 10.3658 9.88109i 0.412328 0.393049i
\(633\) 31.4254i 1.24905i
\(634\) 28.2294 15.9994i 1.12113 0.635416i
\(635\) −9.71239 + 9.71239i −0.385424 + 0.385424i
\(636\) −9.42747 5.64540i −0.373823 0.223855i
\(637\) −20.2525 20.2525i −0.802435 0.802435i
\(638\) 1.14407 4.13740i 0.0452941 0.163801i
\(639\) −7.06989 −0.279681
\(640\) −10.0984 + 5.10114i −0.399176 + 0.201640i
\(641\) 13.6348 0.538540 0.269270 0.963065i \(-0.413218\pi\)
0.269270 + 0.963065i \(0.413218\pi\)
\(642\) 13.9844 50.5731i 0.551921 1.99596i
\(643\) 14.9224 + 14.9224i 0.588480 + 0.588480i 0.937220 0.348740i \(-0.113390\pi\)
−0.348740 + 0.937220i \(0.613390\pi\)
\(644\) 18.3716 + 11.0014i 0.723942 + 0.433514i
\(645\) −19.7932 + 19.7932i −0.779356 + 0.779356i
\(646\) 6.78935 3.84794i 0.267123 0.151395i
\(647\) 4.87972i 0.191841i 0.995389 + 0.0959207i \(0.0305795\pi\)
−0.995389 + 0.0959207i \(0.969420\pi\)
\(648\) 13.2992 12.6773i 0.522442 0.498013i
\(649\) 17.4518i 0.685043i
\(650\) 1.49754 + 2.64228i 0.0587384 + 0.103639i
\(651\) −59.3771 + 59.3771i −2.32717 + 2.32717i
\(652\) 3.67591 + 14.6498i 0.143960 + 0.573730i
\(653\) −10.2913 10.2913i −0.402731 0.402731i 0.476463 0.879194i \(-0.341919\pi\)
−0.879194 + 0.476463i \(0.841919\pi\)
\(654\) −6.75050 1.86664i −0.263966 0.0729914i
\(655\) −7.36417 −0.287742
\(656\) −22.6085 + 12.1081i −0.882713 + 0.472743i
\(657\) −5.13088 −0.200174
\(658\) −15.4303 4.26677i −0.601537 0.166336i
\(659\) −21.9025 21.9025i −0.853201 0.853201i 0.137325 0.990526i \(-0.456149\pi\)
−0.990526 + 0.137325i \(0.956149\pi\)
\(660\) −11.6344 + 2.91928i −0.452867 + 0.113633i
\(661\) 5.40595 5.40595i 0.210267 0.210267i −0.594114 0.804381i \(-0.702497\pi\)
0.804381 + 0.594114i \(0.202497\pi\)
\(662\) 3.37599 + 5.95663i 0.131212 + 0.231511i
\(663\) 8.08276i 0.313908i
\(664\) −9.79615 0.234507i −0.380164 0.00910063i
\(665\) 17.0895i 0.662704i
\(666\) 33.3714 18.9136i 1.29311 0.732887i
\(667\) 2.19608 2.19608i 0.0850326 0.0850326i
\(668\) 16.5106 27.5717i 0.638816 1.06678i
\(669\) −39.1546 39.1546i −1.51380 1.51380i
\(670\) 2.78641 10.0768i 0.107648 0.389299i
\(671\) 3.35280 0.129433
\(672\) −35.2183 + 55.7410i −1.35857 + 2.15025i
\(673\) 35.3820 1.36388 0.681938 0.731410i \(-0.261138\pi\)
0.681938 + 0.731410i \(0.261138\pi\)
\(674\) 2.03539 7.36076i 0.0784002 0.283526i
\(675\) 1.24345 + 1.24345i 0.0478605 + 0.0478605i
\(676\) −8.61861 + 14.3925i −0.331485 + 0.553559i
\(677\) 5.17061 5.17061i 0.198723 0.198723i −0.600730 0.799452i \(-0.705123\pi\)
0.799452 + 0.600730i \(0.205123\pi\)
\(678\) 8.14205 4.61460i 0.312694 0.177223i
\(679\) 84.0196i 3.22438i
\(680\) −0.0985665 + 4.11746i −0.00377985 + 0.157897i
\(681\) 29.4733i 1.12942i
\(682\) 11.6572 + 20.5681i 0.446377 + 0.787593i
\(683\) 26.5989 26.5989i 1.01778 1.01778i 0.0179409 0.999839i \(-0.494289\pi\)
0.999839 0.0179409i \(-0.00571108\pi\)
\(684\) −27.0554 + 6.78872i −1.03449 + 0.259573i
\(685\) 16.0912 + 16.0912i 0.614811 + 0.614811i
\(686\) −38.9500 10.7704i −1.48712 0.411216i
\(687\) 16.9299 0.645916
\(688\) 41.4651 + 12.5415i 1.58084 + 0.478140i
\(689\) 4.56520 0.173920
\(690\) −8.36447 2.31293i −0.318430 0.0880517i
\(691\) −21.7989 21.7989i −0.829270 0.829270i 0.158146 0.987416i \(-0.449448\pi\)
−0.987416 + 0.158146i \(0.949448\pi\)
\(692\) −11.7802 46.9484i −0.447818 1.78471i
\(693\) −27.2324 + 27.2324i −1.03447 + 1.03447i
\(694\) −4.01887 7.09093i −0.152554 0.269168i
\(695\) 8.88246i 0.336931i
\(696\) 6.59817 + 6.92182i 0.250103 + 0.262371i
\(697\) 9.33640i 0.353641i
\(698\) −2.70880 + 1.53524i −0.102530 + 0.0581099i
\(699\) 47.6409 47.6409i 1.80194 1.80194i
\(700\) 7.73792 + 4.63366i 0.292466 + 0.175136i
\(701\) −15.2175 15.2175i −0.574756 0.574756i 0.358698 0.933454i \(-0.383221\pi\)
−0.933454 + 0.358698i \(0.883221\pi\)
\(702\) 1.42343 5.14767i 0.0537237 0.194286i
\(703\) 27.9285 1.05334
\(704\) 12.4833 + 13.7395i 0.470482 + 0.517826i
\(705\) 6.48816 0.244358
\(706\) −0.508527 + 1.83903i −0.0191387 + 0.0692130i
\(707\) 21.8313 + 21.8313i 0.821052 + 0.821052i
\(708\) 33.3545 + 19.9735i 1.25354 + 0.750650i
\(709\) 4.87350 4.87350i 0.183028 0.183028i −0.609646 0.792674i \(-0.708688\pi\)
0.792674 + 0.609646i \(0.208688\pi\)
\(710\) 2.36346 1.33952i 0.0886992 0.0502713i
\(711\) 18.6343i 0.698842i
\(712\) −18.2668 19.1628i −0.684576 0.718156i
\(713\) 17.1048i 0.640579i
\(714\) 11.8352 + 20.8822i 0.442921 + 0.781495i
\(715\) 3.52377 3.52377i 0.131781 0.131781i
\(716\) −0.719218 2.86633i −0.0268784 0.107120i
\(717\) 9.36121 + 9.36121i 0.349601 + 0.349601i
\(718\) 31.6492 + 8.75160i 1.18114 + 0.326607i
\(719\) 9.27351 0.345843 0.172922 0.984936i \(-0.444679\pi\)
0.172922 + 0.984936i \(0.444679\pi\)
\(720\) 4.26197 14.0910i 0.158834 0.525142i
\(721\) 41.1520 1.53258
\(722\) 6.32328 + 1.74850i 0.235328 + 0.0650726i
\(723\) 21.0152 + 21.0152i 0.781563 + 0.781563i
\(724\) −32.8893 + 8.25254i −1.22232 + 0.306703i
\(725\) 0.924966 0.924966i 0.0343524 0.0343524i
\(726\) −10.1209 17.8574i −0.375622 0.662751i
\(727\) 10.6056i 0.393341i 0.980470 + 0.196670i \(0.0630129\pi\)
−0.980470 + 0.196670i \(0.936987\pi\)
\(728\) 0.655557 27.3848i 0.0242965 1.01495i
\(729\) 37.5430i 1.39048i
\(730\) 1.71525 0.972138i 0.0634843 0.0359805i
\(731\) 11.1513 11.1513i 0.412445 0.412445i
\(732\) −3.83726 + 6.40799i −0.141829 + 0.236846i
\(733\) −29.6530 29.6530i −1.09526 1.09526i −0.994957 0.100301i \(-0.968019\pi\)
−0.100301 0.994957i \(-0.531981\pi\)
\(734\) 1.94657 7.03956i 0.0718492 0.259835i
\(735\) 34.4702 1.27145
\(736\) 2.95599 + 13.1013i 0.108959 + 0.482921i
\(737\) −17.1544 −0.631892
\(738\) 8.89409 32.1645i 0.327396 1.18399i
\(739\) 30.8751 + 30.8751i 1.13576 + 1.13576i 0.989202 + 0.146559i \(0.0468197\pi\)
0.146559 + 0.989202i \(0.453180\pi\)
\(740\) −7.57252 + 12.6456i −0.278371 + 0.464863i
\(741\) 14.8740 14.8740i 0.546410 0.546410i
\(742\) 11.7944 6.68461i 0.432986 0.245400i
\(743\) 22.3956i 0.821617i 0.911722 + 0.410808i \(0.134753\pi\)
−0.911722 + 0.410808i \(0.865247\pi\)
\(744\) −52.6521 1.26042i −1.93032 0.0462093i
\(745\) 18.3245i 0.671360i
\(746\) 18.2493 + 32.1993i 0.668155 + 1.17890i
\(747\) 9.01594 9.01594i 0.329876 0.329876i
\(748\) 6.55468 1.64469i 0.239663 0.0601359i
\(749\) 45.7749 + 45.7749i 1.67258 + 1.67258i
\(750\) −3.52303 0.974182i −0.128643 0.0355721i
\(751\) 20.6448 0.753341 0.376670 0.926347i \(-0.377069\pi\)
0.376670 + 0.926347i \(0.377069\pi\)
\(752\) −4.74054 8.85161i −0.172870 0.322785i
\(753\) −72.4724 −2.64104
\(754\) −3.82919 1.05884i −0.139451 0.0385608i
\(755\) 10.1411 + 10.1411i 0.369073 + 0.369073i
\(756\) −3.86000 15.3835i −0.140387 0.559491i
\(757\) 24.1323 24.1323i 0.877104 0.877104i −0.116130 0.993234i \(-0.537049\pi\)
0.993234 + 0.116130i \(0.0370490\pi\)
\(758\) −13.3381 23.5339i −0.484461 0.854788i
\(759\) 14.2395i 0.516860i
\(760\) 7.75839 7.39562i 0.281426 0.268267i
\(761\) 50.1874i 1.81929i −0.415383 0.909647i \(-0.636352\pi\)
0.415383 0.909647i \(-0.363648\pi\)
\(762\) −43.6786 + 24.7554i −1.58231 + 0.896792i
\(763\) 6.11004 6.11004i 0.221198 0.221198i
\(764\) −0.114530 0.0685832i −0.00414354 0.00248125i
\(765\) −3.78953 3.78953i −0.137011 0.137011i
\(766\) −8.25631 + 29.8581i −0.298312 + 1.07882i
\(767\) −16.1517 −0.583206
\(768\) −40.5465 + 8.13374i −1.46309 + 0.293501i
\(769\) −28.6887