Properties

Label 441.2.bn.a.101.45
Level $441$
Weight $2$
Character 441.101
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(5,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([35, 29]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bn (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 101.45
Character \(\chi\) \(=\) 441.101
Dual form 441.2.bn.a.131.45

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.54352 - 1.23092i) q^{2} +(1.45809 - 0.934863i) q^{3} +(0.422260 - 1.85004i) q^{4} +(0.158635 - 2.11684i) q^{5} +(1.09986 - 3.23777i) q^{6} +(-1.92384 + 1.81628i) q^{7} +(0.0876991 + 0.182109i) q^{8} +(1.25206 - 2.72623i) q^{9} +O(q^{10})\) \(q+(1.54352 - 1.23092i) q^{2} +(1.45809 - 0.934863i) q^{3} +(0.422260 - 1.85004i) q^{4} +(0.158635 - 2.11684i) q^{5} +(1.09986 - 3.23777i) q^{6} +(-1.92384 + 1.81628i) q^{7} +(0.0876991 + 0.182109i) q^{8} +(1.25206 - 2.72623i) q^{9} +(-2.36080 - 3.46265i) q^{10} +(-1.38819 - 0.544826i) q^{11} +(-1.11384 - 3.09228i) q^{12} +(3.55990 + 1.39716i) q^{13} +(-0.733796 + 5.17154i) q^{14} +(-1.74765 - 3.23485i) q^{15} +(3.77892 + 1.81983i) q^{16} +(-6.30801 - 1.94576i) q^{17} +(-1.42318 - 5.74918i) q^{18} +(4.25341 - 2.45571i) q^{19} +(-3.84925 - 1.18734i) q^{20} +(-1.10716 + 4.44682i) q^{21} +(-2.81335 + 0.867802i) q^{22} +(-5.05282 + 5.44564i) q^{23} +(0.298120 + 0.183545i) q^{24} +(0.488312 + 0.0736012i) q^{25} +(7.21456 - 2.22540i) q^{26} +(-0.723034 - 5.14560i) q^{27} +(2.54783 + 4.32611i) q^{28} +(-0.894419 + 2.89963i) q^{29} +(-6.67937 - 2.84184i) q^{30} +9.07582i q^{31} +(7.67879 - 1.75263i) q^{32} +(-2.53345 + 0.503366i) q^{33} +(-12.1316 + 4.76132i) q^{34} +(3.53958 + 4.36057i) q^{35} +(-4.51495 - 3.46754i) q^{36} +(1.72032 - 1.59623i) q^{37} +(3.54246 - 9.02603i) q^{38} +(6.49680 - 1.29083i) q^{39} +(0.399408 - 0.156756i) q^{40} +(5.62403 + 3.83440i) q^{41} +(3.76475 + 8.22658i) q^{42} +(-3.93716 + 2.68431i) q^{43} +(-1.59413 + 2.33816i) q^{44} +(-5.57237 - 3.08289i) q^{45} +(-1.09600 + 14.6251i) q^{46} +(-6.40352 - 8.02976i) q^{47} +(7.21130 - 0.879291i) q^{48} +(0.402283 - 6.98843i) q^{49} +(0.844318 - 0.487467i) q^{50} +(-11.0167 + 3.06003i) q^{51} +(4.08800 - 5.99599i) q^{52} +(-0.805100 + 0.867691i) q^{53} +(-7.44983 - 7.05235i) q^{54} +(-1.37353 + 2.85216i) q^{55} +(-0.499479 - 0.191062i) q^{56} +(3.90611 - 7.55700i) q^{57} +(2.18866 + 5.57661i) q^{58} +(10.4630 + 5.03874i) q^{59} +(-6.72256 + 1.86728i) q^{60} +(13.5152 - 3.08476i) q^{61} +(11.1716 + 14.0087i) q^{62} +(2.54283 + 7.51891i) q^{63} +(4.46485 - 5.59874i) q^{64} +(3.52228 - 7.31409i) q^{65} +(-3.29084 + 3.89543i) q^{66} -6.78473 q^{67} +(-6.26336 + 10.8485i) q^{68} +(-2.27654 + 12.6639i) q^{69} +(10.8309 + 2.37372i) q^{70} +(-10.3163 - 2.35462i) q^{71} +(0.606276 - 0.0110764i) q^{72} +(-3.47567 + 1.36410i) q^{73} +(0.690533 - 4.58138i) q^{74} +(0.780811 - 0.349188i) q^{75} +(-2.74711 - 8.90593i) q^{76} +(3.66021 - 1.47319i) q^{77} +(8.43905 - 9.98946i) q^{78} -7.07945 q^{79} +(4.45176 - 7.71067i) q^{80} +(-5.86468 - 6.82682i) q^{81} +(13.4006 - 1.00424i) q^{82} +(-4.48679 - 11.4322i) q^{83} +(7.75929 + 3.92600i) q^{84} +(-5.11954 + 13.0444i) q^{85} +(-2.77293 + 8.98961i) q^{86} +(1.40662 + 5.06409i) q^{87} +(-0.0225256 - 0.300583i) q^{88} +(-6.51950 - 0.982657i) q^{89} +(-12.3959 + 2.10063i) q^{90} +(-9.38627 + 3.77786i) q^{91} +(7.94106 + 11.6474i) q^{92} +(8.48465 + 13.2334i) q^{93} +(-19.7680 - 4.51191i) q^{94} +(-4.52360 - 9.39334i) q^{95} +(9.55790 - 9.73411i) q^{96} +(-6.36809 - 3.67662i) q^{97} +(-7.98125 - 11.2820i) q^{98} +(-3.22343 + 3.10238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 21 q^{2} - 11 q^{3} + 99 q^{4} - 18 q^{5} - 34 q^{6} - 5 q^{7} - 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 21 q^{2} - 11 q^{3} + 99 q^{4} - 18 q^{5} - 34 q^{6} - 5 q^{7} - 23 q^{9} - 22 q^{10} - 18 q^{11} - 72 q^{12} - 4 q^{13} + 66 q^{14} - 10 q^{15} - 105 q^{16} - 9 q^{17} - 27 q^{18} - 36 q^{19} - 27 q^{20} - 11 q^{21} - 9 q^{22} - 27 q^{23} - 8 q^{24} + 38 q^{25} + 6 q^{26} - 29 q^{27} - 26 q^{28} + 3 q^{29} - 16 q^{30} - 21 q^{32} - 11 q^{33} - 13 q^{34} + 28 q^{36} - 13 q^{37} - 90 q^{38} - 15 q^{39} - 31 q^{40} - 27 q^{41} - 4 q^{42} - 9 q^{43} + 51 q^{44} - 11 q^{45} - 108 q^{46} + 75 q^{47} - 15 q^{48} - 13 q^{49} - 45 q^{50} - 38 q^{51} + 64 q^{52} - 12 q^{53} - 41 q^{54} + 14 q^{55} + 3 q^{56} - 7 q^{57} - 90 q^{58} + 15 q^{59} - 69 q^{60} - 56 q^{61} + 66 q^{62} + 13 q^{63} + 64 q^{64} - 21 q^{65} - 204 q^{66} - 26 q^{67} + 3 q^{68} + 58 q^{69} - 22 q^{70} - 63 q^{71} - 18 q^{72} - 22 q^{73} - 12 q^{74} + 118 q^{75} - 63 q^{76} - 69 q^{77} - 147 q^{78} - 2 q^{79} - 45 q^{80} + 29 q^{81} - 28 q^{82} - 51 q^{83} - 31 q^{84} - 10 q^{85} - 72 q^{86} - 67 q^{87} + 4 q^{88} + 132 q^{89} + 58 q^{90} - 13 q^{91} - 15 q^{92} + 217 q^{93} - 7 q^{94} - 21 q^{95} - 44 q^{96} + 3 q^{97} + 21 q^{98} - 148 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.54352 1.23092i 1.09143 0.870390i 0.0992370 0.995064i \(-0.468360\pi\)
0.992198 + 0.124674i \(0.0397884\pi\)
\(3\) 1.45809 0.934863i 0.841829 0.539744i
\(4\) 0.422260 1.85004i 0.211130 0.925021i
\(5\) 0.158635 2.11684i 0.0709438 0.946679i −0.842233 0.539114i \(-0.818759\pi\)
0.913176 0.407565i \(-0.133622\pi\)
\(6\) 1.09986 3.23777i 0.449015 1.32182i
\(7\) −1.92384 + 1.81628i −0.727141 + 0.686488i
\(8\) 0.0876991 + 0.182109i 0.0310063 + 0.0643853i
\(9\) 1.25206 2.72623i 0.417354 0.908744i
\(10\) −2.36080 3.46265i −0.746550 1.09499i
\(11\) −1.38819 0.544826i −0.418556 0.164271i 0.146710 0.989180i \(-0.453132\pi\)
−0.565267 + 0.824908i \(0.691227\pi\)
\(12\) −1.11384 3.09228i −0.321538 0.892666i
\(13\) 3.55990 + 1.39716i 0.987337 + 0.387501i 0.803402 0.595437i \(-0.203021\pi\)
0.183935 + 0.982938i \(0.441116\pi\)
\(14\) −0.733796 + 5.17154i −0.196115 + 1.38215i
\(15\) −1.74765 3.23485i −0.451241 0.835234i
\(16\) 3.77892 + 1.81983i 0.944729 + 0.454958i
\(17\) −6.30801 1.94576i −1.52992 0.471917i −0.588312 0.808634i \(-0.700207\pi\)
−0.941606 + 0.336717i \(0.890684\pi\)
\(18\) −1.42318 5.74918i −0.335447 1.35510i
\(19\) 4.25341 2.45571i 0.975799 0.563378i 0.0747997 0.997199i \(-0.476168\pi\)
0.900999 + 0.433821i \(0.142835\pi\)
\(20\) −3.84925 1.18734i −0.860719 0.265497i
\(21\) −1.10716 + 4.44682i −0.241602 + 0.970376i
\(22\) −2.81335 + 0.867802i −0.599807 + 0.185016i
\(23\) −5.05282 + 5.44564i −1.05359 + 1.13550i −0.0630821 + 0.998008i \(0.520093\pi\)
−0.990504 + 0.137487i \(0.956097\pi\)
\(24\) 0.298120 + 0.183545i 0.0608535 + 0.0374660i
\(25\) 0.488312 + 0.0736012i 0.0976624 + 0.0147202i
\(26\) 7.21456 2.22540i 1.41489 0.436436i
\(27\) −0.723034 5.14560i −0.139148 0.990272i
\(28\) 2.54783 + 4.32611i 0.481494 + 0.817559i
\(29\) −0.894419 + 2.89963i −0.166089 + 0.538449i −0.999908 0.0135905i \(-0.995674\pi\)
0.833818 + 0.552039i \(0.186150\pi\)
\(30\) −6.67937 2.84184i −1.21948 0.518847i
\(31\) 9.07582i 1.63006i 0.579416 + 0.815032i \(0.303281\pi\)
−0.579416 + 0.815032i \(0.696719\pi\)
\(32\) 7.67879 1.75263i 1.35743 0.309825i
\(33\) −2.53345 + 0.503366i −0.441018 + 0.0876247i
\(34\) −12.1316 + 4.76132i −2.08056 + 0.816559i
\(35\) 3.53958 + 4.36057i 0.598298 + 0.737072i
\(36\) −4.51495 3.46754i −0.752491 0.577924i
\(37\) 1.72032 1.59623i 0.282819 0.262418i −0.525988 0.850492i \(-0.676304\pi\)
0.808807 + 0.588074i \(0.200114\pi\)
\(38\) 3.54246 9.02603i 0.574662 1.46422i
\(39\) 6.49680 1.29083i 1.04032 0.206699i
\(40\) 0.399408 0.156756i 0.0631519 0.0247853i
\(41\) 5.62403 + 3.83440i 0.878325 + 0.598832i 0.916320 0.400446i \(-0.131145\pi\)
−0.0379951 + 0.999278i \(0.512097\pi\)
\(42\) 3.76475 + 8.22658i 0.580913 + 1.26939i
\(43\) −3.93716 + 2.68431i −0.600411 + 0.409354i −0.825027 0.565094i \(-0.808840\pi\)
0.224615 + 0.974448i \(0.427888\pi\)
\(44\) −1.59413 + 2.33816i −0.240324 + 0.352491i
\(45\) −5.57237 3.08289i −0.830680 0.459570i
\(46\) −1.09600 + 14.6251i −0.161596 + 2.15635i
\(47\) −6.40352 8.02976i −0.934050 1.17126i −0.984999 0.172560i \(-0.944796\pi\)
0.0509492 0.998701i \(-0.483775\pi\)
\(48\) 7.21130 0.879291i 1.04086 0.126915i
\(49\) 0.402283 6.98843i 0.0574690 0.998347i
\(50\) 0.844318 0.487467i 0.119405 0.0689382i
\(51\) −11.0167 + 3.06003i −1.54264 + 0.428490i
\(52\) 4.08800 5.99599i 0.566903 0.831494i
\(53\) −0.805100 + 0.867691i −0.110589 + 0.119187i −0.785920 0.618328i \(-0.787810\pi\)
0.675331 + 0.737515i \(0.264001\pi\)
\(54\) −7.44983 7.05235i −1.01379 0.959704i
\(55\) −1.37353 + 2.85216i −0.185206 + 0.384585i
\(56\) −0.499479 0.191062i −0.0667457 0.0255317i
\(57\) 3.90611 7.55700i 0.517377 1.00095i
\(58\) 2.18866 + 5.57661i 0.287385 + 0.732244i
\(59\) 10.4630 + 5.03874i 1.36217 + 0.655988i 0.965120 0.261808i \(-0.0843186\pi\)
0.397053 + 0.917796i \(0.370033\pi\)
\(60\) −6.72256 + 1.86728i −0.867879 + 0.241065i
\(61\) 13.5152 3.08476i 1.73044 0.394963i 0.762671 0.646786i \(-0.223887\pi\)
0.967773 + 0.251824i \(0.0810303\pi\)
\(62\) 11.1716 + 14.0087i 1.41879 + 1.77911i
\(63\) 2.54283 + 7.51891i 0.320367 + 0.947294i
\(64\) 4.46485 5.59874i 0.558106 0.699842i
\(65\) 3.52228 7.31409i 0.436885 0.907201i
\(66\) −3.29084 + 3.89543i −0.405074 + 0.479494i
\(67\) −6.78473 −0.828887 −0.414444 0.910075i \(-0.636024\pi\)
−0.414444 + 0.910075i \(0.636024\pi\)
\(68\) −6.26336 + 10.8485i −0.759545 + 1.31557i
\(69\) −2.27654 + 12.6639i −0.274063 + 1.52456i
\(70\) 10.8309 + 2.37372i 1.29454 + 0.283713i
\(71\) −10.3163 2.35462i −1.22432 0.279442i −0.438971 0.898501i \(-0.644657\pi\)
−0.785344 + 0.619059i \(0.787514\pi\)
\(72\) 0.606276 0.0110764i 0.0714503 0.00130536i
\(73\) −3.47567 + 1.36410i −0.406796 + 0.159656i −0.559911 0.828553i \(-0.689165\pi\)
0.153115 + 0.988208i \(0.451069\pi\)
\(74\) 0.690533 4.58138i 0.0802728 0.532575i
\(75\) 0.780811 0.349188i 0.0901603 0.0403207i
\(76\) −2.74711 8.90593i −0.315116 1.02158i
\(77\) 3.66021 1.47319i 0.417120 0.167885i
\(78\) 8.43905 9.98946i 0.955534 1.13108i
\(79\) −7.07945 −0.796500 −0.398250 0.917277i \(-0.630382\pi\)
−0.398250 + 0.917277i \(0.630382\pi\)
\(80\) 4.45176 7.71067i 0.497722 0.862079i
\(81\) −5.86468 6.82682i −0.651632 0.758536i
\(82\) 13.4006 1.00424i 1.47985 0.110900i
\(83\) −4.48679 11.4322i −0.492489 1.25484i −0.933899 0.357537i \(-0.883617\pi\)
0.441410 0.897306i \(-0.354478\pi\)
\(84\) 7.75929 + 3.92600i 0.846608 + 0.428362i
\(85\) −5.11954 + 13.0444i −0.555292 + 1.41486i
\(86\) −2.77293 + 8.98961i −0.299013 + 0.969375i
\(87\) 1.40662 + 5.06409i 0.150805 + 0.542928i
\(88\) −0.0225256 0.300583i −0.00240124 0.0320423i
\(89\) −6.51950 0.982657i −0.691066 0.104161i −0.205886 0.978576i \(-0.566008\pi\)
−0.485180 + 0.874414i \(0.661246\pi\)
\(90\) −12.3959 + 2.10063i −1.30664 + 0.221426i
\(91\) −9.38627 + 3.77786i −0.983949 + 0.396027i
\(92\) 7.94106 + 11.6474i 0.827913 + 1.21433i
\(93\) 8.48465 + 13.2334i 0.879817 + 1.37224i
\(94\) −19.7680 4.51191i −2.03891 0.465368i
\(95\) −4.52360 9.39334i −0.464111 0.963737i
\(96\) 9.55790 9.73411i 0.975499 0.993484i
\(97\) −6.36809 3.67662i −0.646582 0.373304i 0.140564 0.990072i \(-0.455109\pi\)
−0.787145 + 0.616768i \(0.788442\pi\)
\(98\) −7.98125 11.2820i −0.806228 1.13965i
\(99\) −3.22343 + 3.10238i −0.323967 + 0.311801i
\(100\) 0.342360 0.872319i 0.0342360 0.0872319i
\(101\) 2.36121 + 1.60985i 0.234949 + 0.160186i 0.675072 0.737752i \(-0.264113\pi\)
−0.440123 + 0.897938i \(0.645065\pi\)
\(102\) −13.2379 + 18.2839i −1.31074 + 1.81037i
\(103\) 10.8133 + 0.810346i 1.06547 + 0.0798457i 0.595906 0.803054i \(-0.296793\pi\)
0.469561 + 0.882900i \(0.344412\pi\)
\(104\) 0.0577649 + 0.770818i 0.00566431 + 0.0755850i
\(105\) 9.23757 + 3.04910i 0.901494 + 0.297561i
\(106\) −0.174633 + 2.33031i −0.0169618 + 0.226340i
\(107\) −0.427802 + 2.83828i −0.0413571 + 0.274387i −0.999946 0.0104075i \(-0.996687\pi\)
0.958589 + 0.284794i \(0.0919252\pi\)
\(108\) −9.82488 0.835138i −0.945400 0.0803612i
\(109\) 0.513679 0.0774247i 0.0492015 0.00741594i −0.124395 0.992233i \(-0.539699\pi\)
0.173597 + 0.984817i \(0.444461\pi\)
\(110\) 1.39070 + 6.09306i 0.132598 + 0.580951i
\(111\) 1.01613 3.93571i 0.0964472 0.373561i
\(112\) −10.5753 + 3.36250i −0.999274 + 0.317727i
\(113\) −0.223709 + 1.48421i −0.0210447 + 0.139623i −0.996886 0.0788590i \(-0.974872\pi\)
0.975841 + 0.218482i \(0.0701104\pi\)
\(114\) −3.27288 16.4725i −0.306533 1.54279i
\(115\) 10.7260 + 11.5599i 1.00020 + 1.07796i
\(116\) 4.98677 + 2.87911i 0.463010 + 0.267319i
\(117\) 8.26618 7.95578i 0.764209 0.735512i
\(118\) 22.3522 5.10175i 2.05769 0.469654i
\(119\) 15.6696 7.71376i 1.43643 0.707120i
\(120\) 0.435827 0.601956i 0.0397854 0.0549508i
\(121\) −6.43332 5.96925i −0.584847 0.542659i
\(122\) 17.0639 21.3975i 1.54490 1.93724i
\(123\) 11.7850 + 0.333205i 1.06262 + 0.0300441i
\(124\) 16.7906 + 3.83235i 1.50784 + 0.344155i
\(125\) 2.59507 11.3698i 0.232111 1.01694i
\(126\) 13.1801 + 8.47559i 1.17417 + 0.755065i
\(127\) 1.25946 + 5.51806i 0.111759 + 0.489649i 0.999567 + 0.0294341i \(0.00937051\pi\)
−0.887808 + 0.460215i \(0.847772\pi\)
\(128\) 1.61489i 0.142737i
\(129\) −3.23128 + 7.59468i −0.284498 + 0.668674i
\(130\) −3.56633 15.6251i −0.312787 1.37041i
\(131\) 12.4754 8.50557i 1.08998 0.743135i 0.121590 0.992580i \(-0.461201\pi\)
0.968389 + 0.249446i \(0.0802484\pi\)
\(132\) −0.138528 + 4.89954i −0.0120573 + 0.426450i
\(133\) −3.72262 + 12.4497i −0.322792 + 1.07953i
\(134\) −10.4724 + 8.35145i −0.904676 + 0.721455i
\(135\) −11.0071 + 0.714274i −0.947341 + 0.0614749i
\(136\) −0.198866 1.31939i −0.0170526 0.113137i
\(137\) −8.03925 + 0.602459i −0.686840 + 0.0514715i −0.413579 0.910468i \(-0.635721\pi\)
−0.273261 + 0.961940i \(0.588102\pi\)
\(138\) 12.0744 + 22.3493i 1.02784 + 1.90250i
\(139\) −7.20191 + 10.5633i −0.610858 + 0.895964i −0.999679 0.0253495i \(-0.991930\pi\)
0.388821 + 0.921313i \(0.372883\pi\)
\(140\) 9.56186 4.70707i 0.808125 0.397820i
\(141\) −16.8437 5.72171i −1.41849 0.481855i
\(142\) −18.8217 + 9.06407i −1.57948 + 0.760640i
\(143\) −4.18062 3.87905i −0.349601 0.324382i
\(144\) 9.69272 8.02367i 0.807726 0.668639i
\(145\) 5.99617 + 2.35332i 0.497955 + 0.195433i
\(146\) −3.68567 + 6.38377i −0.305029 + 0.528325i
\(147\) −5.94666 10.5659i −0.490472 0.871457i
\(148\) −2.22666 3.85669i −0.183030 0.317018i
\(149\) 2.02957 + 13.4653i 0.166269 + 1.10312i 0.903846 + 0.427858i \(0.140732\pi\)
−0.737577 + 0.675263i \(0.764030\pi\)
\(150\) 0.775377 1.50009i 0.0633093 0.122482i
\(151\) −9.81897 + 3.02875i −0.799057 + 0.246476i −0.667284 0.744804i \(-0.732543\pi\)
−0.131773 + 0.991280i \(0.542067\pi\)
\(152\) 0.820226 + 0.559221i 0.0665291 + 0.0453588i
\(153\) −13.2026 + 14.7609i −1.06737 + 1.19335i
\(154\) 3.83624 6.77932i 0.309133 0.546293i
\(155\) 19.2120 + 1.43974i 1.54315 + 0.115643i
\(156\) 0.355243 12.5644i 0.0284422 1.00596i
\(157\) 3.81641 7.92485i 0.304582 0.632472i −0.691356 0.722515i \(-0.742986\pi\)
0.995938 + 0.0900430i \(0.0287005\pi\)
\(158\) −10.9273 + 8.71422i −0.869328 + 0.693266i
\(159\) −0.362736 + 2.01783i −0.0287669 + 0.160024i
\(160\) −2.49192 16.5328i −0.197003 1.30703i
\(161\) −0.170001 19.6538i −0.0133980 1.54894i
\(162\) −17.4555 3.31840i −1.37144 0.260718i
\(163\) −0.102862 1.37259i −0.00805674 0.107510i 0.991726 0.128376i \(-0.0409765\pi\)
−0.999782 + 0.0208666i \(0.993357\pi\)
\(164\) 9.46859 8.78557i 0.739373 0.686038i
\(165\) 0.663649 + 5.44276i 0.0516650 + 0.423719i
\(166\) −20.9975 12.1229i −1.62972 0.940921i
\(167\) −6.25791 + 5.80649i −0.484252 + 0.449320i −0.884125 0.467251i \(-0.845245\pi\)
0.399873 + 0.916570i \(0.369054\pi\)
\(168\) −0.906903 + 0.188359i −0.0699690 + 0.0145322i
\(169\) 1.19114 + 1.10522i 0.0916260 + 0.0850165i
\(170\) 8.15443 + 26.4360i 0.625417 + 2.02755i
\(171\) −1.36930 14.6705i −0.104713 1.12188i
\(172\) 3.30358 + 8.41739i 0.251896 + 0.641820i
\(173\) −0.904816 + 3.96426i −0.0687919 + 0.301397i −0.997606 0.0691480i \(-0.977972\pi\)
0.928814 + 0.370545i \(0.120829\pi\)
\(174\) 8.40462 + 6.08511i 0.637153 + 0.461311i
\(175\) −1.07311 + 0.745313i −0.0811197 + 0.0563404i
\(176\) −4.25438 4.58513i −0.320686 0.345617i
\(177\) 19.9666 2.43458i 1.50078 0.182994i
\(178\) −11.2726 + 6.50822i −0.844915 + 0.487812i
\(179\) 0.0278243 0.0902041i 0.00207968 0.00674217i −0.954527 0.298124i \(-0.903639\pi\)
0.956607 + 0.291382i \(0.0941152\pi\)
\(180\) −8.05646 + 9.00734i −0.600493 + 0.671368i
\(181\) −15.3644 12.2527i −1.14203 0.910738i −0.145129 0.989413i \(-0.546360\pi\)
−0.996900 + 0.0786743i \(0.974931\pi\)
\(182\) −9.83769 + 17.3849i −0.729218 + 1.28866i
\(183\) 16.8226 17.1327i 1.24356 1.26649i
\(184\) −1.43483 0.442586i −0.105777 0.0326279i
\(185\) −3.10605 3.89486i −0.228361 0.286356i
\(186\) 29.3854 + 9.98209i 2.15464 + 0.731923i
\(187\) 7.69665 + 6.13787i 0.562835 + 0.448846i
\(188\) −17.5593 + 8.45613i −1.28065 + 0.616727i
\(189\) 10.7368 + 8.58606i 0.780990 + 0.624544i
\(190\) −18.5447 8.93066i −1.34537 0.647898i
\(191\) 4.47472 + 9.29185i 0.323779 + 0.672335i 0.997794 0.0663830i \(-0.0211459\pi\)
−0.674015 + 0.738718i \(0.735432\pi\)
\(192\) 1.27610 12.3375i 0.0920944 0.890382i
\(193\) 2.14581 1.03337i 0.154459 0.0743834i −0.355057 0.934844i \(-0.615539\pi\)
0.509516 + 0.860461i \(0.329824\pi\)
\(194\) −14.3549 + 2.16365i −1.03062 + 0.155341i
\(195\) −1.70187 13.9575i −0.121873 0.999514i
\(196\) −12.7590 3.69517i −0.911358 0.263941i
\(197\) 12.3703i 0.881351i −0.897667 0.440675i \(-0.854739\pi\)
0.897667 0.440675i \(-0.145261\pi\)
\(198\) −1.15665 + 8.75637i −0.0821996 + 0.622288i
\(199\) −22.4565 1.68288i −1.59190 0.119296i −0.750931 0.660381i \(-0.770395\pi\)
−0.840968 + 0.541084i \(0.818014\pi\)
\(200\) 0.0294211 + 0.0953808i 0.00208038 + 0.00674444i
\(201\) −9.89276 + 6.34280i −0.697782 + 0.447386i
\(202\) 5.62617 0.421623i 0.395856 0.0296653i
\(203\) −3.54582 7.20293i −0.248868 0.505547i
\(204\) 1.00927 + 21.6734i 0.0706633 + 1.51744i
\(205\) 9.00897 11.2969i 0.629214 0.789009i
\(206\) 17.6881 12.0595i 1.23238 0.840226i
\(207\) 8.51965 + 20.5934i 0.592157 + 1.43134i
\(208\) 10.9100 + 11.7581i 0.756470 + 0.815281i
\(209\) −7.24249 + 1.09163i −0.500974 + 0.0755096i
\(210\) 18.0116 6.66434i 1.24292 0.459883i
\(211\) 8.94621 + 1.34842i 0.615882 + 0.0928293i 0.449572 0.893244i \(-0.351577\pi\)
0.166310 + 0.986073i \(0.446815\pi\)
\(212\) 1.26530 + 1.85586i 0.0869014 + 0.127461i
\(213\) −17.2433 + 6.21105i −1.18149 + 0.425574i
\(214\) 2.83336 + 4.90753i 0.193685 + 0.335472i
\(215\) 5.05768 + 8.76016i 0.344931 + 0.597438i
\(216\) 0.873651 0.582936i 0.0594444 0.0396637i
\(217\) −16.4842 17.4604i −1.11902 1.18529i
\(218\) 0.697572 0.751804i 0.0472455 0.0509186i
\(219\) −3.79259 + 5.23825i −0.256280 + 0.353968i
\(220\) 4.69662 + 3.74543i 0.316646 + 0.252517i
\(221\) −19.7373 15.7400i −1.32768 1.05879i
\(222\) −3.27611 7.32563i −0.219878 0.491664i
\(223\) 9.08182 9.78788i 0.608164 0.655445i −0.351634 0.936138i \(-0.614374\pi\)
0.959798 + 0.280693i \(0.0905642\pi\)
\(224\) −11.5895 + 17.3186i −0.774353 + 1.15715i
\(225\) 0.812051 1.23910i 0.0541367 0.0826066i
\(226\) 1.48164 + 2.56628i 0.0985573 + 0.170706i
\(227\) −1.87507 3.24772i −0.124453 0.215559i 0.797066 0.603892i \(-0.206384\pi\)
−0.921519 + 0.388333i \(0.873051\pi\)
\(228\) −12.3314 10.4175i −0.816665 0.689914i
\(229\) 9.79856 + 14.3718i 0.647507 + 0.949718i 0.999904 + 0.0138674i \(0.00441427\pi\)
−0.352397 + 0.935851i \(0.614633\pi\)
\(230\) 30.7851 + 4.64010i 2.02991 + 0.305959i
\(231\) 3.95969 5.56984i 0.260529 0.366469i
\(232\) −0.606489 + 0.0914135i −0.0398180 + 0.00600159i
\(233\) −8.30325 8.94877i −0.543964 0.586254i 0.399912 0.916553i \(-0.369041\pi\)
−0.943876 + 0.330300i \(0.892850\pi\)
\(234\) 2.96612 22.4549i 0.193902 1.46792i
\(235\) −18.0135 + 12.2814i −1.17507 + 0.801152i
\(236\) 13.7400 17.2294i 0.894398 1.12154i
\(237\) −10.3225 + 6.61832i −0.670518 + 0.429906i
\(238\) 14.6914 31.1944i 0.952302 2.02203i
\(239\) −3.37282 + 0.252758i −0.218170 + 0.0163496i −0.183367 0.983045i \(-0.558700\pi\)
−0.0348033 + 0.999394i \(0.511080\pi\)
\(240\) −0.717352 15.4046i −0.0463049 0.994366i
\(241\) 1.51316 + 4.90554i 0.0974712 + 0.315994i 0.991156 0.132701i \(-0.0423651\pi\)
−0.893685 + 0.448695i \(0.851889\pi\)
\(242\) −17.2776 1.29478i −1.11065 0.0832316i
\(243\) −14.9334 4.47145i −0.957977 0.286844i
\(244\) 26.3063i 1.68409i
\(245\) −14.7296 1.96018i −0.941037 0.125231i
\(246\) 18.6005 13.9920i 1.18593 0.892099i
\(247\) 18.5727 2.79938i 1.18175 0.178121i
\(248\) −1.65279 + 0.795941i −0.104952 + 0.0505423i
\(249\) −17.2297 12.4746i −1.09188 0.790545i
\(250\) −9.98969 20.7438i −0.631803 1.31195i
\(251\) 5.28394 + 2.54461i 0.333519 + 0.160614i 0.593147 0.805094i \(-0.297885\pi\)
−0.259627 + 0.965709i \(0.583600\pi\)
\(252\) 14.9840 1.52941i 0.943905 0.0963436i
\(253\) 9.98123 4.80671i 0.627514 0.302195i
\(254\) 8.73629 + 6.96696i 0.548164 + 0.437146i
\(255\) 4.72995 + 23.8060i 0.296201 + 1.49079i
\(256\) 10.9175 + 13.6901i 0.682343 + 0.855631i
\(257\) −17.2461 5.31971i −1.07578 0.331835i −0.294268 0.955723i \(-0.595076\pi\)
−0.781513 + 0.623889i \(0.785552\pi\)
\(258\) 4.36088 + 15.7000i 0.271496 + 0.977438i
\(259\) −0.410430 + 6.19546i −0.0255029 + 0.384967i
\(260\) −12.0440 9.60481i −0.746940 0.595665i
\(261\) 6.78521 + 6.06891i 0.419994 + 0.375656i
\(262\) 8.78636 28.4847i 0.542823 1.75979i
\(263\) 21.2153 12.2487i 1.30819 0.755286i 0.326399 0.945232i \(-0.394165\pi\)
0.981794 + 0.189946i \(0.0608314\pi\)
\(264\) −0.313849 0.417220i −0.0193161 0.0256781i
\(265\) 1.70904 + 1.84191i 0.104986 + 0.113148i
\(266\) 9.57866 + 23.7987i 0.587306 + 1.45919i
\(267\) −10.4247 + 4.66204i −0.637980 + 0.285312i
\(268\) −2.86492 + 12.5520i −0.175003 + 0.766738i
\(269\) 3.16894 + 8.07433i 0.193214 + 0.492301i 0.994346 0.106186i \(-0.0338640\pi\)
−0.801132 + 0.598487i \(0.795769\pi\)
\(270\) −16.1105 + 14.6513i −0.980454 + 0.891652i
\(271\) −6.43922 20.8754i −0.391155 1.26809i −0.910493 0.413524i \(-0.864298\pi\)
0.519338 0.854569i \(-0.326178\pi\)
\(272\) −20.2965 18.8324i −1.23066 1.14188i
\(273\) −10.1543 + 14.2833i −0.614564 + 0.864467i
\(274\) −11.6672 + 10.8256i −0.704840 + 0.653996i
\(275\) −0.637772 0.368218i −0.0384591 0.0222044i
\(276\) 22.4675 + 9.55917i 1.35239 + 0.575394i
\(277\) 8.33172 7.73071i 0.500605 0.464493i −0.388991 0.921241i \(-0.627176\pi\)
0.889596 + 0.456748i \(0.150986\pi\)
\(278\) 1.88620 + 25.1696i 0.113127 + 1.50957i
\(279\) 24.7428 + 11.3635i 1.48131 + 0.680314i
\(280\) −0.483682 + 1.02701i −0.0289055 + 0.0613754i
\(281\) −2.62081 17.3879i −0.156344 1.03728i −0.920075 0.391742i \(-0.871873\pi\)
0.763731 0.645535i \(-0.223366\pi\)
\(282\) −33.0415 + 11.9016i −1.96759 + 0.708728i
\(283\) 3.72568 2.97113i 0.221468 0.176615i −0.506470 0.862257i \(-0.669050\pi\)
0.727939 + 0.685642i \(0.240479\pi\)
\(284\) −8.71229 + 18.0913i −0.516979 + 1.07352i
\(285\) −15.3773 9.46741i −0.910873 0.560801i
\(286\) −11.2277 0.841398i −0.663906 0.0497529i
\(287\) −17.7840 + 2.83804i −1.04976 + 0.167524i
\(288\) 4.83623 23.1286i 0.284977 1.36286i
\(289\) 21.9590 + 14.9714i 1.29170 + 0.880669i
\(290\) 12.1520 3.74839i 0.713588 0.220113i
\(291\) −12.7224 + 0.592447i −0.745800 + 0.0347299i
\(292\) 1.05600 + 7.00613i 0.0617980 + 0.410003i
\(293\) −6.59391 11.4210i −0.385221 0.667222i 0.606579 0.795023i \(-0.292541\pi\)
−0.991800 + 0.127801i \(0.959208\pi\)
\(294\) −22.1845 8.98877i −1.29383 0.524236i
\(295\) 12.3260 21.3493i 0.717648 1.24300i
\(296\) 0.441558 + 0.173299i 0.0256650 + 0.0100728i
\(297\) −1.79975 + 7.53703i −0.104432 + 0.437343i
\(298\) 19.7074 + 18.2858i 1.14162 + 1.05927i
\(299\) −25.5959 + 12.3263i −1.48025 + 0.712851i
\(300\) −0.316307 1.59198i −0.0182620 0.0919130i
\(301\) 2.69900 12.3151i 0.155568 0.709833i
\(302\) −11.4277 + 16.7613i −0.657588 + 0.964504i
\(303\) 4.94784 + 0.139894i 0.284246 + 0.00803669i
\(304\) 20.5422 1.53943i 1.17818 0.0882923i
\(305\) −4.38595 29.0989i −0.251139 1.66620i
\(306\) −2.20910 + 39.0351i −0.126286 + 2.23149i
\(307\) 9.45142 7.53725i 0.539421 0.430174i −0.315505 0.948924i \(-0.602174\pi\)
0.854926 + 0.518750i \(0.173603\pi\)
\(308\) −1.17990 7.39361i −0.0672310 0.421290i
\(309\) 16.5244 8.92741i 0.940038 0.507863i
\(310\) 31.4264 21.4262i 1.78490 1.21692i
\(311\) 1.67153 + 7.32344i 0.0947836 + 0.415274i 0.999952 0.00977856i \(-0.00311266\pi\)
−0.905169 + 0.425053i \(0.860256\pi\)
\(312\) 0.804836 + 1.06992i 0.0455649 + 0.0605724i
\(313\) 5.29246i 0.299147i −0.988751 0.149574i \(-0.952210\pi\)
0.988751 0.149574i \(-0.0477901\pi\)
\(314\) −3.86413 16.9299i −0.218065 0.955407i
\(315\) 16.3197 4.19000i 0.919511 0.236080i
\(316\) −2.98937 + 13.0973i −0.168165 + 0.736779i
\(317\) 29.8491 + 6.81286i 1.67649 + 0.382648i 0.951871 0.306500i \(-0.0991580\pi\)
0.724620 + 0.689148i \(0.242015\pi\)
\(318\) 1.92389 + 3.56106i 0.107887 + 0.199695i
\(319\) 2.82142 3.53795i 0.157969 0.198087i
\(320\) −11.1433 10.3395i −0.622932 0.577997i
\(321\) 2.02963 + 4.53840i 0.113283 + 0.253309i
\(322\) −24.4547 30.1269i −1.36280 1.67890i
\(323\) −31.6088 + 7.21450i −1.75876 + 0.401425i
\(324\) −15.1063 + 7.96722i −0.839240 + 0.442623i
\(325\) 1.63551 + 0.944261i 0.0907217 + 0.0523782i
\(326\) −1.84832 1.99201i −0.102369 0.110327i
\(327\) 0.676610 0.593112i 0.0374166 0.0327992i
\(328\) −0.205056 + 1.36046i −0.0113223 + 0.0751188i
\(329\) 26.9036 + 3.81738i 1.48324 + 0.210459i
\(330\) 7.72395 + 7.58413i 0.425189 + 0.417492i
\(331\) 4.85471 + 21.2699i 0.266839 + 1.16910i 0.913667 + 0.406463i \(0.133238\pi\)
−0.646828 + 0.762636i \(0.723905\pi\)
\(332\) −23.0445 + 3.47341i −1.26473 + 0.190628i
\(333\) −2.19773 6.68857i −0.120435 0.366531i
\(334\) −2.51191 + 16.6654i −0.137445 + 0.911891i
\(335\) −1.07630 + 14.3622i −0.0588044 + 0.784690i
\(336\) −12.2763 + 14.7893i −0.669728 + 0.806824i
\(337\) 0.956012 + 12.7571i 0.0520773 + 0.694923i 0.960750 + 0.277415i \(0.0894775\pi\)
−0.908673 + 0.417508i \(0.862903\pi\)
\(338\) 3.19898 + 0.239730i 0.174001 + 0.0130396i
\(339\) 1.06135 + 2.37325i 0.0576444 + 0.128897i
\(340\) 21.9709 + 14.9795i 1.19154 + 0.812377i
\(341\) 4.94474 12.5990i 0.267773 0.682274i
\(342\) −20.1717 20.9587i −1.09076 1.13332i
\(343\) 11.9190 + 14.1752i 0.643565 + 0.765391i
\(344\) −0.834122 0.481581i −0.0449729 0.0259651i
\(345\) 26.4464 + 6.82802i 1.42383 + 0.367608i
\(346\) 3.48307 + 7.23268i 0.187251 + 0.388831i
\(347\) −6.31673 1.44175i −0.339100 0.0773973i 0.0495802 0.998770i \(-0.484212\pi\)
−0.388680 + 0.921373i \(0.627069\pi\)
\(348\) 9.96274 0.463937i 0.534059 0.0248697i
\(349\) −10.8880 15.9698i −0.582822 0.854843i 0.415683 0.909510i \(-0.363543\pi\)
−0.998505 + 0.0546669i \(0.982590\pi\)
\(350\) −0.738953 + 2.47132i −0.0394987 + 0.132098i
\(351\) 4.61528 19.3280i 0.246346 1.03165i
\(352\) −11.6145 1.75061i −0.619057 0.0933078i
\(353\) −0.202156 2.69759i −0.0107597 0.143578i 0.989237 0.146325i \(-0.0467446\pi\)
−0.999996 + 0.00274719i \(0.999126\pi\)
\(354\) 27.8221 28.3351i 1.47873 1.50599i
\(355\) −6.62087 + 21.4643i −0.351400 + 1.13921i
\(356\) −4.57088 + 11.6464i −0.242256 + 0.617259i
\(357\) 15.6364 25.8963i 0.827568 1.37058i
\(358\) −0.0680864 0.173481i −0.00359848 0.00916878i
\(359\) 34.2770 2.56871i 1.80907 0.135571i 0.873077 0.487582i \(-0.162121\pi\)
0.935996 + 0.352011i \(0.114502\pi\)
\(360\) 0.0727298 1.28515i 0.00383320 0.0677331i
\(361\) 2.56099 4.43576i 0.134789 0.233461i
\(362\) −38.7975 −2.03915
\(363\) −14.9608 2.68944i −0.785239 0.141159i
\(364\) 3.02574 + 18.9602i 0.158592 + 0.993786i
\(365\) 2.33621 + 7.57382i 0.122283 + 0.396432i
\(366\) 4.87704 47.1519i 0.254927 2.46467i
\(367\) −4.08896 + 27.1284i −0.213442 + 1.41609i 0.583537 + 0.812086i \(0.301668\pi\)
−0.796979 + 0.604007i \(0.793570\pi\)
\(368\) −29.0043 + 11.3834i −1.51196 + 0.593399i
\(369\) 17.4951 10.5315i 0.910757 0.548248i
\(370\) −9.58851 2.18852i −0.498483 0.113775i
\(371\) −0.0270875 3.13158i −0.00140631 0.162583i
\(372\) 28.0650 10.1090i 1.45510 0.524129i
\(373\) 11.5687 20.0376i 0.599004 1.03751i −0.393964 0.919126i \(-0.628896\pi\)
0.992968 0.118380i \(-0.0377702\pi\)
\(374\) 19.4352 1.00497
\(375\) −6.84532 19.0042i −0.353491 0.981372i
\(376\) 0.900709 1.87034i 0.0464505 0.0964555i
\(377\) −7.23528 + 9.07275i −0.372636 + 0.467271i
\(378\) 27.1413 + 0.0366161i 1.39600 + 0.00188333i
\(379\) −5.62350 7.05164i −0.288860 0.362218i 0.616136 0.787640i \(-0.288697\pi\)
−0.904995 + 0.425422i \(0.860126\pi\)
\(380\) −19.2882 + 4.40241i −0.989464 + 0.225839i
\(381\) 6.99505 + 6.86842i 0.358367 + 0.351880i
\(382\) 18.3443 + 8.83416i 0.938578 + 0.451995i
\(383\) 2.81018 + 7.16023i 0.143594 + 0.365871i 0.984518 0.175282i \(-0.0560836\pi\)
−0.840925 + 0.541152i \(0.817988\pi\)
\(384\) 1.50970 + 2.35465i 0.0770415 + 0.120160i
\(385\) −2.53786 7.98178i −0.129342 0.406789i
\(386\) 2.04011 4.23634i 0.103839 0.215624i
\(387\) 2.38849 + 14.0945i 0.121414 + 0.716466i
\(388\) −9.49088 + 10.2287i −0.481827 + 0.519286i
\(389\) 0.746429 1.09481i 0.0378455 0.0555091i −0.806850 0.590757i \(-0.798829\pi\)
0.844695 + 0.535248i \(0.179782\pi\)
\(390\) −19.8074 19.4488i −1.00298 0.984828i
\(391\) 42.4692 24.5196i 2.14776 1.24001i
\(392\) 1.30794 0.539620i 0.0660607 0.0272549i
\(393\) 10.2387 24.0647i 0.516474 1.21390i
\(394\) −15.2269 19.0939i −0.767119 0.961937i
\(395\) −1.12305 + 14.9861i −0.0565068 + 0.754030i
\(396\) 4.37842 + 7.27349i 0.220024 + 0.365506i
\(397\) 11.5284 16.9091i 0.578596 0.848644i −0.419660 0.907681i \(-0.637851\pi\)
0.998256 + 0.0590370i \(0.0188030\pi\)
\(398\) −36.7336 + 25.0445i −1.84129 + 1.25537i
\(399\) 6.21089 + 21.6330i 0.310933 + 1.08300i
\(400\) 1.71135 + 1.16678i 0.0855675 + 0.0583389i
\(401\) 21.9595 8.61845i 1.09660 0.430385i 0.253062 0.967450i \(-0.418562\pi\)
0.843541 + 0.537065i \(0.180467\pi\)
\(402\) −7.46223 + 21.9674i −0.372182 + 1.09564i
\(403\) −12.6803 + 32.3090i −0.631652 + 1.60942i
\(404\) 3.97532 3.68856i 0.197780 0.183513i
\(405\) −15.3816 + 11.3316i −0.764319 + 0.563073i
\(406\) −14.3393 6.75327i −0.711646 0.335159i
\(407\) −3.25781 + 1.27860i −0.161484 + 0.0633776i
\(408\) −1.52341 1.73788i −0.0754201 0.0860377i
\(409\) 14.1744 3.23521i 0.700877 0.159971i 0.142790 0.989753i \(-0.454393\pi\)
0.558087 + 0.829782i \(0.311536\pi\)
\(410\) 28.5263i 1.40881i
\(411\) −11.1587 + 8.39404i −0.550421 + 0.414048i
\(412\) 6.06520 19.6629i 0.298811 0.968721i
\(413\) −29.2809 + 9.31008i −1.44082 + 0.458119i
\(414\) 38.4991 + 21.2994i 1.89213 + 1.04681i
\(415\) −24.9118 + 7.68427i −1.22287 + 0.377206i
\(416\) 29.7844 + 4.48927i 1.46030 + 0.220105i
\(417\) −0.625838 + 22.1350i −0.0306474 + 1.08396i
\(418\) −9.83524 + 10.5999i −0.481057 + 0.518456i
\(419\) −11.6928 + 3.60674i −0.571229 + 0.176201i −0.566895 0.823790i \(-0.691856\pi\)
−0.00433377 + 0.999991i \(0.501379\pi\)
\(420\) 9.54161 15.8024i 0.465583 0.771077i
\(421\) 22.4530 + 6.92585i 1.09429 + 0.337545i 0.788801 0.614649i \(-0.210702\pi\)
0.305494 + 0.952194i \(0.401178\pi\)
\(422\) 15.4685 8.93072i 0.752993 0.434741i
\(423\) −29.9086 + 7.40373i −1.45421 + 0.359982i
\(424\) −0.228621 0.0705202i −0.0111028 0.00342476i
\(425\) −2.93707 1.41442i −0.142469 0.0686093i
\(426\) −18.9701 + 30.8120i −0.919106 + 1.49285i
\(427\) −20.3983 + 30.4819i −0.987141 + 1.47512i
\(428\) 5.07029 + 1.98994i 0.245082 + 0.0961874i
\(429\) −9.72211 1.74770i −0.469388 0.0843797i
\(430\) 18.5897 + 7.29591i 0.896474 + 0.351840i
\(431\) 15.0526 + 22.0780i 0.725056 + 1.06346i 0.994930 + 0.100566i \(0.0320655\pi\)
−0.269874 + 0.962896i \(0.586982\pi\)
\(432\) 6.63184 20.7606i 0.319074 0.998845i
\(433\) 5.26920 + 10.9416i 0.253221 + 0.525820i 0.988367 0.152090i \(-0.0486003\pi\)
−0.735145 + 0.677910i \(0.762886\pi\)
\(434\) −46.9360 6.65979i −2.25300 0.319680i
\(435\) 10.9430 2.17424i 0.524677 0.104247i
\(436\) 0.0736672 0.983021i 0.00352802 0.0470782i
\(437\) −8.11880 + 35.5708i −0.388375 + 1.70158i
\(438\) 0.593906 + 12.7537i 0.0283779 + 0.609397i
\(439\) 17.0614 13.6060i 0.814296 0.649379i −0.125127 0.992141i \(-0.539934\pi\)
0.939422 + 0.342761i \(0.111362\pi\)
\(440\) −0.639860 −0.0305041
\(441\) −18.5484 9.84666i −0.883257 0.468889i
\(442\) −49.8397 −2.37063
\(443\) 2.08187 1.66024i 0.0989128 0.0788803i −0.572785 0.819706i \(-0.694137\pi\)
0.671698 + 0.740826i \(0.265565\pi\)
\(444\) −6.85215 3.54178i −0.325189 0.168086i
\(445\) −3.11435 + 13.6449i −0.147634 + 0.646828i
\(446\) 1.96992 26.2868i 0.0932785 1.24472i
\(447\) 15.5475 + 17.7363i 0.735372 + 0.838897i
\(448\) 1.57923 + 18.8804i 0.0746116 + 0.892017i
\(449\) 9.11866 + 18.9351i 0.430336 + 0.893602i 0.997545 + 0.0700282i \(0.0223089\pi\)
−0.567209 + 0.823574i \(0.691977\pi\)
\(450\) −0.271811 2.91214i −0.0128133 0.137280i
\(451\) −5.71816 8.38700i −0.269258 0.394929i
\(452\) 2.65139 + 1.04059i 0.124711 + 0.0489454i
\(453\) −11.4855 + 13.5956i −0.539636 + 0.638777i
\(454\) −6.89189 2.70487i −0.323452 0.126946i
\(455\) 6.50812 + 20.4685i 0.305105 + 0.959580i
\(456\) 1.71876 + 0.0485957i 0.0804883 + 0.00227570i
\(457\) −29.1739 14.0494i −1.36470 0.657203i −0.399017 0.916943i \(-0.630649\pi\)
−0.965678 + 0.259740i \(0.916363\pi\)
\(458\) 32.8148 + 10.1220i 1.53334 + 0.472972i
\(459\) −5.45122 + 33.8654i −0.254441 + 1.58070i
\(460\) 25.9154 14.9623i 1.20831 0.697619i
\(461\) 38.2583 + 11.8011i 1.78186 + 0.549632i 0.997500 0.0706676i \(-0.0225130\pi\)
0.784365 + 0.620300i \(0.212989\pi\)
\(462\) −0.744142 13.4712i −0.0346206 0.626738i
\(463\) −8.09882 + 2.49815i −0.376384 + 0.116099i −0.477174 0.878809i \(-0.658339\pi\)
0.100791 + 0.994908i \(0.467863\pi\)
\(464\) −8.65678 + 9.32979i −0.401881 + 0.433124i
\(465\) 29.3589 15.8614i 1.36149 0.735553i
\(466\) −23.8315 3.59201i −1.10397 0.166397i
\(467\) −0.532162 + 0.164150i −0.0246255 + 0.00759596i −0.307043 0.951695i \(-0.599340\pi\)
0.282418 + 0.959291i \(0.408864\pi\)
\(468\) −11.2280 18.6522i −0.519016 0.862197i
\(469\) 13.0527 12.3229i 0.602718 0.569021i
\(470\) −12.6869 + 41.1298i −0.585202 + 1.89718i
\(471\) −1.84398 15.1230i −0.0849661 0.696830i
\(472\) 2.34731i 0.108044i
\(473\) 6.92803 1.58128i 0.318551 0.0727072i
\(474\) −7.78638 + 22.9217i −0.357640 + 1.05283i
\(475\) 2.25773 0.886095i 0.103592 0.0406568i
\(476\) −7.65413 32.2467i −0.350826 1.47802i
\(477\) 1.35749 + 3.28129i 0.0621553 + 0.150240i
\(478\) −4.89490 + 4.54181i −0.223888 + 0.207737i
\(479\) −6.00193 + 15.2927i −0.274235 + 0.698739i 0.725707 + 0.688004i \(0.241513\pi\)
−0.999942 + 0.0107359i \(0.996583\pi\)
\(480\) −19.0893 21.7767i −0.871305 0.993966i
\(481\) 8.35435 3.27884i 0.380925 0.149502i
\(482\) 8.37392 + 5.70924i 0.381422 + 0.260049i
\(483\) −18.6215 28.4982i −0.847309 1.29671i
\(484\) −13.7599 + 9.38134i −0.625450 + 0.426424i
\(485\) −8.79301 + 12.8970i −0.399270 + 0.585622i
\(486\) −28.5540 + 11.4800i −1.29524 + 0.520743i
\(487\) −3.01818 + 40.2749i −0.136767 + 1.82503i 0.333777 + 0.942652i \(0.391677\pi\)
−0.470544 + 0.882377i \(0.655942\pi\)
\(488\) 1.74703 + 2.19071i 0.0790845 + 0.0991688i
\(489\) −1.43317 1.90520i −0.0648101 0.0861563i
\(490\) −25.1482 + 15.1053i −1.13608 + 0.682388i
\(491\) 0.916988 0.529423i 0.0413831 0.0238925i −0.479166 0.877724i \(-0.659061\pi\)
0.520549 + 0.853832i \(0.325727\pi\)
\(492\) 5.59277 21.6620i 0.252141 0.976598i
\(493\) 11.2840 16.5506i 0.508206 0.745402i
\(494\) 25.2216 27.1824i 1.13477 1.22299i
\(495\) 6.05590 + 7.31562i 0.272192 + 0.328813i
\(496\) −16.5164 + 34.2968i −0.741610 + 1.53997i
\(497\) 24.1234 14.2073i 1.08208 0.637284i
\(498\) −41.9495 + 1.95348i −1.87980 + 0.0875374i
\(499\) 11.0801 + 28.2317i 0.496015 + 1.26382i 0.931537 + 0.363647i \(0.118469\pi\)
−0.435522 + 0.900178i \(0.643436\pi\)
\(500\) −19.9387 9.60199i −0.891687 0.429414i
\(501\) −3.69633 + 14.3167i −0.165140 + 0.639622i
\(502\) 11.2881 2.57643i 0.503812 0.114992i
\(503\) 11.6298 + 14.5834i 0.518549 + 0.650240i 0.970300 0.241904i \(-0.0777719\pi\)
−0.451751 + 0.892144i \(0.649200\pi\)
\(504\) −1.14626 + 1.12247i −0.0510584 + 0.0499990i
\(505\) 3.78235 4.74292i 0.168313 0.211057i
\(506\) 9.48958 19.7053i 0.421863 0.876008i
\(507\) 2.77001 + 0.497953i 0.123021 + 0.0221149i
\(508\) 10.7405 0.476531
\(509\) −4.07396 + 7.05630i −0.180575 + 0.312765i −0.942076 0.335398i \(-0.891129\pi\)
0.761502 + 0.648163i \(0.224463\pi\)
\(510\) 36.6040 + 30.9229i 1.62085 + 1.36929i
\(511\) 4.20903 8.93707i 0.186196 0.395353i
\(512\) 30.5540 + 6.97374i 1.35031 + 0.308199i
\(513\) −15.7114 20.1108i −0.693677 0.887913i
\(514\) −33.1678 + 13.0174i −1.46297 + 0.574174i
\(515\) 3.43074 22.7615i 0.151177 1.00299i
\(516\) 12.6860 + 9.18492i 0.558471 + 0.404344i
\(517\) 4.51451 + 14.6357i 0.198548 + 0.643677i
\(518\) 6.99259 + 10.0680i 0.307237 + 0.442364i
\(519\) 2.38674 + 6.62613i 0.104766 + 0.290855i
\(520\) 1.64086 0.0719566
\(521\) 4.15742 7.20086i 0.182140 0.315476i −0.760469 0.649374i \(-0.775031\pi\)
0.942609 + 0.333899i \(0.108364\pi\)
\(522\) 17.9435 + 1.01547i 0.785364 + 0.0444458i
\(523\) 8.68565 0.650900i 0.379797 0.0284619i 0.116536 0.993186i \(-0.462821\pi\)
0.263261 + 0.964725i \(0.415202\pi\)
\(524\) −10.4678 26.6715i −0.457288 1.16515i
\(525\) −0.867930 + 2.08995i −0.0378796 + 0.0912128i
\(526\) 17.6692 45.0204i 0.770414 1.96298i
\(527\) 17.6594 57.2504i 0.769256 2.49387i
\(528\) −10.4897 2.70828i −0.456508 0.117863i
\(529\) −2.40526 32.0960i −0.104577 1.39548i
\(530\) 4.90519 + 0.739339i 0.213068 + 0.0321148i
\(531\) 26.8372 22.2159i 1.16463 0.964088i
\(532\) 21.4606 + 12.1440i 0.930436 + 0.526510i
\(533\) 14.6637 + 21.5077i 0.635155 + 0.931602i
\(534\) −10.3521 + 20.0279i −0.447981 + 0.866692i
\(535\) 5.94031 + 1.35584i 0.256822 + 0.0586180i
\(536\) −0.595015 1.23556i −0.0257007 0.0533681i
\(537\) −0.0437581 0.157538i −0.00188830 0.00679825i
\(538\) 14.8302 + 8.56220i 0.639374 + 0.369143i
\(539\) −4.36593 + 9.48213i −0.188054 + 0.408424i
\(540\) −3.32642 + 20.6652i −0.143147 + 0.889289i
\(541\) −2.20611 + 5.62107i −0.0948479 + 0.241669i −0.970422 0.241416i \(-0.922388\pi\)
0.875574 + 0.483084i \(0.160484\pi\)
\(542\) −35.6350 24.2955i −1.53066 1.04358i
\(543\) −33.8574 3.50195i −1.45296 0.150283i
\(544\) −51.8481 3.88548i −2.22297 0.166588i
\(545\) −0.0824080 1.09966i −0.00352997 0.0471042i
\(546\) 1.90828 + 34.5457i 0.0816669 + 1.47842i
\(547\) 2.16251 28.8566i 0.0924621 1.23382i −0.737246 0.675624i \(-0.763874\pi\)
0.829709 0.558197i \(-0.188507\pi\)
\(548\) −2.28008 + 15.1273i −0.0974002 + 0.646208i
\(549\) 8.51210 40.7079i 0.363288 1.73737i
\(550\) −1.43766 + 0.216693i −0.0613021 + 0.00923981i
\(551\) 3.31632 + 14.5298i 0.141280 + 0.618989i
\(552\) −2.50587 + 0.696038i −0.106657 + 0.0296253i
\(553\) 13.6197 12.8582i 0.579168 0.546788i
\(554\) 3.34433 22.1882i 0.142087 0.942686i
\(555\) −8.17007 2.77533i −0.346800 0.117806i
\(556\) 16.5014 + 17.7843i 0.699815 + 0.754221i
\(557\) −4.14645 2.39395i −0.175691 0.101435i 0.409576 0.912276i \(-0.365677\pi\)
−0.585266 + 0.810841i \(0.699010\pi\)
\(558\) 52.1785 12.9165i 2.20889 0.546801i
\(559\) −17.7663 + 4.05504i −0.751434 + 0.171510i
\(560\) 5.44026 + 22.9197i 0.229893 + 0.968533i
\(561\) 16.9605 + 1.75427i 0.716072 + 0.0740651i
\(562\) −25.4484 23.6127i −1.07348 0.996040i
\(563\) −18.1785 + 22.7951i −0.766132 + 0.960699i −0.999933 0.0115858i \(-0.996312\pi\)
0.233801 + 0.972284i \(0.424883\pi\)
\(564\) −17.6978 + 28.7454i −0.745212 + 1.21040i
\(565\) 3.10635 + 0.709003i 0.130685 + 0.0298280i
\(566\) 2.09345 9.17200i 0.0879943 0.385528i
\(567\) 23.6821 + 2.48179i 0.994554 + 0.104225i
\(568\) −0.475929 2.08518i −0.0199696 0.0874923i
\(569\) 24.6840i 1.03481i 0.855741 + 0.517404i \(0.173102\pi\)
−0.855741 + 0.517404i \(0.826898\pi\)
\(570\) −35.3888 + 4.31504i −1.48227 + 0.180737i
\(571\) −3.38604 14.8352i −0.141701 0.620833i −0.995040 0.0994765i \(-0.968283\pi\)
0.853339 0.521357i \(-0.174574\pi\)
\(572\) −8.94171 + 6.09635i −0.373872 + 0.254901i
\(573\) 15.2112 + 9.36512i 0.635455 + 0.391233i
\(574\) −23.9566 + 26.2712i −0.999931 + 1.09654i
\(575\) −2.86816 + 2.28728i −0.119610 + 0.0953862i
\(576\) −9.67320 19.1822i −0.403050 0.799257i
\(577\) 1.98385 + 13.1620i 0.0825887 + 0.547940i 0.991414 + 0.130763i \(0.0417426\pi\)
−0.908825 + 0.417178i \(0.863019\pi\)
\(578\) 52.3227 3.92104i 2.17634 0.163094i
\(579\) 2.16273 3.51278i 0.0898799 0.145986i
\(580\) 6.88569 10.0995i 0.285913 0.419357i
\(581\) 29.3958 + 13.8443i 1.21954 + 0.574360i
\(582\) −18.9080 + 16.5747i −0.783763 + 0.687042i
\(583\) 1.59038 0.765885i 0.0658666 0.0317197i
\(584\) −0.553227 0.513320i −0.0228927 0.0212413i
\(585\) −15.5298 18.7602i −0.642078 0.775640i
\(586\) −24.2362 9.51199i −1.00119 0.392937i
\(587\) 9.22951 15.9860i 0.380943 0.659812i −0.610255 0.792205i \(-0.708933\pi\)
0.991197 + 0.132393i \(0.0422662\pi\)
\(588\) −22.0583 + 6.54003i −0.909669 + 0.269706i
\(589\) 22.2875 + 38.6031i 0.918342 + 1.59062i
\(590\) −7.25373 48.1254i −0.298631 1.98129i
\(591\) −11.5646 18.0371i −0.475703 0.741947i
\(592\) 9.40582 2.90131i 0.386577 0.119243i
\(593\) 9.60241 + 6.54681i 0.394324 + 0.268845i 0.744208 0.667947i \(-0.232827\pi\)
−0.349885 + 0.936793i \(0.613779\pi\)
\(594\) 6.49951 + 13.8489i 0.266678 + 0.568227i
\(595\) −13.8430 34.3937i −0.567509 1.41001i
\(596\) 25.7684 + 1.93107i 1.05551 + 0.0790998i
\(597\) −34.3169 + 18.5400i −1.40450 + 0.758790i
\(598\) −24.3352 + 50.5325i −0.995138 + 2.06643i
\(599\) −5.10362 + 4.07000i −0.208528 + 0.166296i −0.722185 0.691700i \(-0.756862\pi\)
0.513657 + 0.857996i \(0.328291\pi\)
\(600\) 0.132067 + 0.111569i 0.00539160 + 0.00455479i
\(601\) −5.32773 35.3471i −0.217322 1.44184i −0.785463 0.618909i \(-0.787575\pi\)
0.568141 0.822932i \(-0.307663\pi\)
\(602\) −10.9930 22.3309i −0.448040 0.910141i
\(603\) −8.49490 + 18.4968i −0.345939 + 0.753246i
\(604\) 1.45716 + 19.4444i 0.0592909 + 0.791183i
\(605\) −13.6565 + 12.6714i −0.555215 + 0.515165i
\(606\) 7.80930 5.87446i 0.317231 0.238634i
\(607\) −35.0267 20.2227i −1.42169 0.820813i −0.425247 0.905077i \(-0.639813\pi\)
−0.996443 + 0.0842640i \(0.973146\pi\)
\(608\) 28.3571 26.3115i 1.15003 1.06707i
\(609\) −11.9039 7.18767i −0.482370 0.291259i
\(610\) −42.5881 39.5160i −1.72434 1.59996i
\(611\) −11.5770 37.5318i −0.468357 1.51838i
\(612\) 21.7333 + 30.6583i 0.878517 + 1.23929i
\(613\) 17.4786 + 44.5348i 0.705954 + 1.79874i 0.593097 + 0.805131i \(0.297905\pi\)
0.112858 + 0.993611i \(0.464000\pi\)
\(614\) 5.31073 23.2678i 0.214324 0.939013i
\(615\) 2.57485 24.8940i 0.103828 1.00382i
\(616\) 0.589278 + 0.537360i 0.0237427 + 0.0216509i
\(617\) −9.31819 10.0426i −0.375136 0.404301i 0.517060 0.855949i \(-0.327027\pi\)
−0.892196 + 0.451649i \(0.850836\pi\)
\(618\) 14.5168 34.1198i 0.583951 1.37250i
\(619\) −2.86077 + 1.65167i −0.114984 + 0.0663860i −0.556389 0.830922i \(-0.687814\pi\)
0.441405 + 0.897308i \(0.354480\pi\)
\(620\) 10.7761 34.9351i 0.432777 1.40303i
\(621\) 31.6745 + 22.0624i 1.27105 + 0.885334i
\(622\) 11.5946 + 9.24638i 0.464901 + 0.370746i
\(623\) 14.3272 9.95075i 0.574008 0.398668i
\(624\) 26.9000 + 6.94513i 1.07686 + 0.278028i
\(625\) −21.2968 6.56921i −0.851874 0.262768i
\(626\) −6.51458 8.16902i −0.260375 0.326500i
\(627\) −9.53969 + 8.36244i −0.380979 + 0.333964i
\(628\) −13.0498 10.4069i −0.520743 0.415279i
\(629\) −13.9577 + 6.72167i −0.556530 + 0.268011i
\(630\) 20.0323 26.5556i 0.798105 1.05800i
\(631\) 13.9143 + 6.70077i 0.553920 + 0.266754i 0.689835 0.723967i \(-0.257683\pi\)
−0.135915 + 0.990720i \(0.543397\pi\)
\(632\) −0.620861 1.28923i −0.0246965 0.0512829i
\(633\) 14.3050 6.39736i 0.568572 0.254272i
\(634\) 54.4588 26.2260i 2.16283 1.04157i
\(635\) 11.8806 1.79072i 0.471469 0.0710625i
\(636\) 3.57990 + 1.52313i 0.141952 + 0.0603959i
\(637\) 11.1960 24.3160i 0.443602 0.963436i
\(638\) 8.93385i 0.353695i
\(639\) −19.3358 + 25.1764i −0.764914 + 0.995963i
\(640\) 3.41846 + 0.256178i 0.135126 + 0.0101263i
\(641\) −8.45861 27.4222i −0.334095 1.08311i −0.954345 0.298706i \(-0.903445\pi\)
0.620250 0.784404i \(-0.287031\pi\)
\(642\) 8.71918 + 4.50682i 0.344118 + 0.177870i
\(643\) 1.64279 0.123110i 0.0647855 0.00485500i −0.0422979 0.999105i \(-0.513468\pi\)
0.107083 + 0.994250i \(0.465849\pi\)
\(644\) −36.4322 7.98452i −1.43563 0.314634i
\(645\) 15.5641 + 8.04488i 0.612836 + 0.316767i
\(646\) −39.9084 + 50.0435i −1.57017 + 1.96894i
\(647\) 10.9803 7.48622i 0.431679 0.294314i −0.327920 0.944705i \(-0.606348\pi\)
0.759599 + 0.650392i \(0.225395\pi\)
\(648\) 0.728898 1.66672i 0.0286338 0.0654749i
\(649\) −11.7795 12.6953i −0.462386 0.498334i
\(650\) 3.68675 0.555688i 0.144606 0.0217959i
\(651\) −40.3585 10.0484i −1.58177 0.393826i
\(652\) −2.58279 0.389292i −0.101150 0.0152459i
\(653\) −17.1923 25.2165i −0.672787 0.986798i −0.999136 0.0415484i \(-0.986771\pi\)
0.326349 0.945249i \(-0.394181\pi\)
\(654\) 0.314290 1.74833i 0.0122897 0.0683652i
\(655\) −16.0259 27.7576i −0.626183 1.08458i
\(656\) 14.2748 + 24.7246i 0.557336 + 0.965335i
\(657\) −0.632898 + 11.1834i −0.0246917 + 0.436306i
\(658\) 46.2252 27.2239i 1.80204 1.06130i
\(659\) 6.99671 7.54066i 0.272553 0.293743i −0.581911 0.813252i \(-0.697695\pi\)
0.854465 + 0.519510i \(0.173885\pi\)
\(660\) 10.3496 + 1.07048i 0.402856 + 0.0416684i
\(661\) −31.4218 25.0581i −1.22217 0.974645i −0.222167 0.975009i \(-0.571313\pi\)
−1.00000 0.000363494i \(0.999884\pi\)
\(662\) 33.6748 + 26.8548i 1.30881 + 1.04374i
\(663\) −43.4936 4.49865i −1.68915 0.174713i
\(664\) 1.68841 1.81967i 0.0655231 0.0706171i
\(665\) 25.7636 + 9.85514i 0.999068 + 0.382166i
\(666\) −11.6253 7.61873i −0.450472 0.295220i
\(667\) −11.2710 19.5220i −0.436416 0.755895i
\(668\) 8.09979 + 14.0292i 0.313390 + 0.542808i
\(669\) 4.09180 22.7619i 0.158198 0.880025i
\(670\) 16.0174 + 23.4932i 0.618805 + 0.907621i
\(671\) −20.4424 3.08119i −0.789170 0.118948i
\(672\) −0.707987 + 36.0866i −0.0273112 + 1.39207i
\(673\) 6.93239 1.04489i 0.267224 0.0402775i −0.0140635 0.999901i \(-0.504477\pi\)
0.281287 + 0.959624i \(0.409239\pi\)
\(674\) 17.1786 + 18.5141i 0.661693 + 0.713136i
\(675\) 0.0256562 2.56588i 0.000987506 0.0987606i
\(676\) 2.54766 1.73697i 0.0979870 0.0668064i
\(677\) 4.21965 5.29127i 0.162174 0.203360i −0.694104 0.719874i \(-0.744199\pi\)
0.856278 + 0.516515i \(0.172771\pi\)
\(678\) 4.55949 + 2.35674i 0.175106 + 0.0905099i
\(679\) 18.9289 4.49300i 0.726425 0.172426i
\(680\) −2.82448 + 0.211665i −0.108314 + 0.00811700i
\(681\) −5.77020 2.98254i −0.221114 0.114291i
\(682\) −7.87601 25.5334i −0.301588 0.977724i
\(683\) 24.3651 + 1.82591i 0.932303 + 0.0698665i 0.532214 0.846610i \(-0.321360\pi\)
0.400089 + 0.916476i \(0.368979\pi\)
\(684\) −27.7192 3.66150i −1.05987 0.140001i
\(685\) 17.1134i 0.653868i
\(686\) 35.8458 + 7.20850i 1.36860 + 0.275222i
\(687\) 27.7229 + 11.7951i 1.05769 + 0.450013i
\(688\) −19.7632 + 2.97882i −0.753465 + 0.113567i
\(689\) −4.07837 + 1.96404i −0.155374 + 0.0748239i
\(690\) 49.2253 22.0141i 1.87398 0.838064i
\(691\) 16.5585 + 34.3840i 0.629914 + 1.30803i 0.934642 + 0.355591i \(0.115720\pi\)
−0.304727 + 0.952440i \(0.598565\pi\)
\(692\) 6.95198 + 3.34790i 0.264274 + 0.127268i
\(693\) 0.566556 11.8231i 0.0215217 0.449123i
\(694\) −11.5247 + 5.55000i −0.437471 + 0.210675i
\(695\) 21.2182 + 16.9210i 0.804854 + 0.641849i
\(696\) −0.798858 + 0.700274i −0.0302806 + 0.0265438i
\(697\) −28.0156 35.1305i −1.06117 1.33066i
\(698\) −36.4634 11.2475i −1.38016 0.425723i
\(699\) −20.4728 5.28573i −0.774351 0.199925i
\(700\) 0.925728 + 2.30002i 0.0349892 + 0.0869325i
\(701\) 11.9879 + 9.56001i 0.452776 + 0.361077i 0.823167 0.567799i \(-0.192205\pi\)
−0.370391 + 0.928876i \(0.620776\pi\)
\(702\) −16.6674 35.5142i −0.629070 1.34040i
\(703\) 3.39737 11.0140i 0.128134 0.415401i
\(704\) −9.24841 + 5.33957i −0.348563 + 0.201243i
\(705\) −14.7839 + 34.7476i −0.556795 + 1.30867i
\(706\) −3.63254 3.91495i −0.136712 0.147341i
\(707\) −7.46650 + 1.19153i −0.280807 + 0.0448121i
\(708\) 3.92703 37.9671i 0.147587 1.42689i
\(709\) −1.64221 + 7.19498i −0.0616744 + 0.270213i −0.996358 0.0852672i \(-0.972826\pi\)
0.934684 + 0.355481i \(0.115683\pi\)
\(710\) 16.2014 + 41.2804i 0.608027 + 1.54923i
\(711\) −8.86391 + 19.3002i −0.332422 + 0.723815i
\(712\) −0.392804 1.27344i −0.0147209 0.0477241i
\(713\) −49.4237 45.8585i −1.85093 1.71741i
\(714\) −7.74107 59.2187i −0.289702 2.21620i
\(715\) −8.87452 + 8.23435i −0.331888 + 0.307947i
\(716\) −0.155132 0.0895656i −0.00579756 0.00334722i
\(717\) −4.68159 + 3.52167i −0.174837 + 0.131519i
\(718\) 49.7455 46.1571i 1.85649 1.72257i
\(719\) −2.49098 33.2398i −0.0928978 1.23963i −0.827629 0.561276i \(-0.810311\pi\)
0.734731 0.678359i \(-0.237308\pi\)
\(720\) −15.4472 21.7908i −0.575683 0.812093i
\(721\) −22.2748 + 18.0810i −0.829558 + 0.673371i
\(722\) −1.50712 9.99906i −0.0560891 0.372127i
\(723\) 6.79234 + 5.73814i 0.252610 + 0.213404i
\(724\) −29.1558 + 23.2510i −1.08357 + 0.864117i
\(725\) −0.650172 + 1.35010i −0.0241468 + 0.0501413i
\(726\) −26.4028 + 14.2643i −0.979900 + 0.529398i
\(727\) 28.5325 + 2.13821i 1.05821 + 0.0793020i 0.592449 0.805608i \(-0.298161\pi\)
0.465762 + 0.884910i \(0.345780\pi\)
\(728\) −1.51115 1.37801i −0.0560069 0.0510725i
\(729\) −25.9544 + 7.44089i −0.961276 + 0.275589i
\(730\) 12.9287 + 8.81467i 0.478514 + 0.326246i
\(731\) 30.0587 9.27188i 1.11176 0.342933i
\(732\) −24.5927 38.3569i −0.908974 1.41771i
\(733\) −5.25718 34.8791i −0.194178 1.28829i −0.847332 0.531063i \(-0.821793\pi\)
0.653154 0.757225i \(-0.273446\pi\)
\(734\) 27.0815 + 46.9065i 0.999596 + 1.73135i
\(735\) −23.3096 + 10.9120i −0.859786 + 0.402496i
\(736\) −29.2553 + 50.6717i −1.07836 + 1.86778i
\(737\) 9.41853 + 3.69650i 0.346936 + 0.136162i
\(738\) 14.0406 37.7906i 0.516843 1.39109i
\(739\) 2.90642 + 2.69676i 0.106914 + 0.0992020i 0.731819 0.681499i \(-0.238672\pi\)
−0.624905 + 0.780701i \(0.714862\pi\)
\(740\) −8.51722 + 4.10168i −0.313099 + 0.150781i
\(741\) 24.4636 21.4447i 0.898695 0.787790i
\(742\) −3.89652 4.80032i −0.143046 0.176225i
\(743\) 5.97782 8.76785i 0.219305 0.321661i −0.700782 0.713375i \(-0.747165\pi\)
0.920087 + 0.391714i \(0.128118\pi\)
\(744\) −1.66582 + 2.70568i −0.0610719 + 0.0991952i
\(745\) 28.8258 2.16020i 1.05610 0.0791436i
\(746\) −6.80806 45.1685i −0.249261 1.65374i
\(747\) −36.7844 2.08173i −1.34587 0.0761665i
\(748\) 14.6053 11.6473i 0.534023 0.425869i
\(749\) −4.33208 6.23738i −0.158291 0.227909i
\(750\) −33.9585 20.9074i −1.23999 0.763429i
\(751\) −33.8833 + 23.1012i −1.23642 + 0.842976i −0.991944 0.126680i \(-0.959568\pi\)
−0.244475 + 0.969656i \(0.578615\pi\)
\(752\) −9.58557 41.9971i −0.349550 1.53148i
\(753\) 10.0833 1.22948i 0.367457 0.0448049i
\(754\) 22.9100i 0.834334i
\(755\) 4.85375 + 21.2657i 0.176646 + 0.773936i
\(756\) 20.4183 16.2380i 0.742606 0.590572i
\(757\) 3.92007 17.1750i 0.142478 0.624235i −0.852378 0.522927i \(-0.824840\pi\)
0.994855 0.101308i \(-0.0323028\pi\)
\(758\) −17.3600 3.96230i −0.630543 0.143917i
\(759\) 10.0599 16.3397i 0.365152 0.593093i
\(760\) 1.31390 1.64757i 0.0476601 0.0597638i
\(761\) −6.40804 5.94579i −0.232291 0.215535i 0.555435 0.831560i \(-0.312552\pi\)
−0.787727 + 0.616025i \(0.788742\pi\)
\(762\) 19.2515 + 1.99123i 0.697407 + 0.0721345i
\(763\) −0.847610 + 1.08194i −0.0306855 + 0.0391687i
\(764\) 19.0798 4.35484i 0.690283 0.157553i
\(765\) 29.1520 + 30.2894i 1.05399 + 1.09512i
\(766\) 13.1512 + 7.59287i 0.475173 + 0.274341i
\(767\) 30.2075 + 32.5559i 1.09073 + 1.17553i
\(768\) 28.7171 + 9.75505i 1.03624 + 0.352005i
\(769\) −5.48326 + 36.3790i −0.197731 + 1.31186i 0.641095 + 0.767462i \(0.278481\pi\)
−0.838826 + 0.544400i \(0.816758\pi\)
\(770\) −13.7422 9.19615i −0.495233 0.331406i
\(771\) −30.1196 + 8.36610i −1.08473 + 0.301298i
\(772\) −1.00568 4.40618i −0.0361953 0.158582i
\(773\) −31.9143 + 4.81031i −1.14788 + 0.173015i −0.695307 0.718713i \(-0.744732\pi\)
−0.452572 + 0.891728i \(0.649493\pi\)
\(774\) 21.0359 + 18.8152i 0.756120 + 0.676298i
\(775\) −0.667991 + 4.43183i −0.0239949 + 0.159196i
\(776\) 0.111070 1.48212i 0.00398717 0.0532051i
\(777\) 5.19346 + 9.41724i 0.186314 + 0.337841i
\(778\) −0.195492 2.60866i −0.00700872 0.0935249i
\(779\) 33.3374 + 2.49830i 1.19444 + 0.0895107i
\(780\) −26.5405 2.74515i −0.950302 0.0982921i
\(781\) 13.0381 + 8.88924i 0.466541 + 0.318082i
\(782\) 35.3705 90.1226i 1.26485 3.22278i
\(783\) 15.5671 + 2.50579i 0.556321 + 0.0895496i
\(784\) 14.2380 25.6766i 0.508498 0.917022i
\(785\) −16.1702 9.33587i −0.577139 0.333212i
\(786\) −13.8180 49.7473i −0.492871 1.77443i
\(787\) −0.384426 0.798269i −0.0137033 0.0284552i 0.894005 0.448057i \(-0.147884\pi\)
−0.907708 + 0.419602i \(0.862170\pi\)
\(788\) −22.8856 5.22350i −0.815267 0.186079i
\(789\) 19.4831 37.6931i 0.693615 1.34191i
\(790\) 16.7132 + 24.5137i 0.594627 + 0.872158i
\(791\) −2.26536 3.26169i −0.0805468 0.115972i
\(792\) −0.847664 0.314939i −0.0301204 0.0111909i
\(793\) 52.4226 + 7.90144i 1.86158 + 0.280588i
\(794\) −3.01933 40.2902i −0.107152 1.42984i
\(795\) 4.21388 + 1.08795i 0.149451 + 0.0385857i
\(796\) −12.5959 + 40.8348i −0.446449 + 1.44735i
\(797\) 14.9486 38.0884i 0.529506 1.34916i −0.376705 0.926333i \(-0.622943\pi\)
0.906211 0.422826i \(-0.138962\pi\)
\(798\) 36.2151 + 25.7459i 1.28200 + 0.911395i
\(799\) 24.7695 + 63.1116i 0.876281 + 2.23273i
\(800\) 3.87864 0.290664i 0.137131 0.0102765i
\(801\) −10.8418 + 16.5433i −0.383075 + 0.584530i
\(802\) 23.2863 40.3330i 0.822268 1.42421i
\(803\) 5.56810 0.196494
\(804\) 7.55712 + 20.9803i 0.266519 + 0.739919i
\(805\) −41.6310 2.75792i −1.46730 0.0972040i
\(806\) 20.1973 + 65.4780i 0.711419 + 2.30637i
\(807\) 12.1690 + 8.81059i 0.428369 + 0.310147i
\(808\) −0.0860914 + 0.571179i −0.00302869 + 0.0200940i
\(809\) 18.8361 7.39264i 0.662243 0.259911i −0.0103248 0.999947i \(-0.503287\pi\)
0.672568 + 0.740035i \(0.265191\pi\)
\(810\) −9.79359 + 36.4241i −0.344112 + 1.27981i
\(811\) −22.0746 5.03839i −0.775145 0.176922i −0.183391 0.983040i \(-0.558707\pi\)
−0.591754 + 0.806118i \(0.701564\pi\)
\(812\) −14.8230 + 3.51841i −0.520184 + 0.123472i
\(813\) −28.9047 24.4185i −1.01373 0.856395i
\(814\) −3.45465 + 5.98363i −0.121086 + 0.209726i
\(815\) −2.92187 −0.102349
\(816\) −47.1999 8.48491i −1.65233 0.297031i
\(817\) −10.1545 + 21.0860i −0.355260 + 0.737705i
\(818\) 17.8962 22.4411i 0.625725 0.784634i
\(819\) −1.45288 + 30.3193i −0.0507678 + 1.05944i
\(820\) −17.0956 21.4372i −0.597004 0.748619i
\(821\) −43.3380 + 9.89162i −1.51251 + 0.345220i −0.896687 0.442666i \(-0.854033\pi\)
−0.615821 + 0.787886i \(0.711176\pi\)
\(822\) −6.89140 + 26.6919i −0.240365 + 0.930987i
\(823\) 10.7861 + 5.19430i 0.375979 + 0.181062i 0.612323 0.790607i \(-0.290235\pi\)
−0.236344 + 0.971669i \(0.575949\pi\)
\(824\) 0.800746 + 2.04027i 0.0278953 + 0.0710761i
\(825\) −1.27416 + 0.0593344i −0.0443607 + 0.00206576i
\(826\) −33.7358 + 50.4127i −1.17382 + 1.75408i
\(827\) 20.0292 41.5910i 0.696482 1.44626i −0.189186 0.981941i \(-0.560585\pi\)
0.885668 0.464319i \(-0.153701\pi\)
\(828\) 41.6962 7.06592i 1.44904 0.245558i
\(829\) −30.6817 + 33.0670i −1.06562 + 1.14846i −0.0771536 + 0.997019i \(0.524583\pi\)
−0.988466 + 0.151445i \(0.951607\pi\)
\(830\) −28.9932 + 42.5252i −1.00637 + 1.47607i
\(831\) 4.92126 19.0611i 0.170717 0.661222i
\(832\) 23.7167 13.6928i 0.822229 0.474714i
\(833\) −16.1354 + 43.3004i −0.559060 + 1.50027i
\(834\) 26.2804 + 34.9362i 0.910015 + 1.20974i
\(835\) 11.2987 + 14.1681i 0.391007 + 0.490307i
\(836\) −1.03865 + 13.8599i −0.0359226 + 0.479353i
\(837\) 46.7005 6.56213i 1.61421 0.226820i
\(838\) −13.6084 + 19.9599i −0.470096 + 0.689504i
\(839\) −33.8422 + 23.0732i −1.16836 + 0.796575i −0.982548 0.186010i \(-0.940444\pi\)
−0.185813 + 0.982585i \(0.559492\pi\)
\(840\) 0.254858 + 1.94965i 0.00879344 + 0.0672692i
\(841\) 16.3530 + 11.1493i 0.563898 + 0.384459i
\(842\) 43.1819 16.9477i 1.48815 0.584055i
\(843\) −20.0767 22.9031i −0.691479 0.788825i
\(844\) 6.27226 15.9815i 0.215900 0.550105i
\(845\) 2.52852 2.34612i 0.0869837 0.0807091i
\(846\) −37.0512 + 48.2429i −1.27385 + 1.65862i
\(847\) 23.2185 0.200835i 0.797796 0.00690076i
\(848\) −4.62145 + 1.81379i −0.158701 + 0.0622857i
\(849\) 2.65478 7.81517i 0.0911118 0.268216i
\(850\) −6.27446 + 1.43211i −0.215212 + 0.0491208i
\(851\) 17.4337i 0.597620i
\(852\) 4.20953 + 34.5235i 0.144216 + 1.18276i
\(853\) 3.68829 11.9571i 0.126285 0.409405i −0.870247 0.492615i \(-0.836041\pi\)
0.996532 + 0.0832102i \(0.0265173\pi\)
\(854\) 6.03556 + 72.1581i 0.206533 + 2.46920i
\(855\) −31.2723 + 0.571330i −1.06949 + 0.0195391i
\(856\) −0.554394 + 0.171008i −0.0189488 + 0.00584493i
\(857\) −8.69815 1.31104i −0.297123 0.0447841i −0.00121107 0.999999i \(-0.500385\pi\)
−0.295912 + 0.955215i \(0.595624\pi\)
\(858\) −17.1576 + 9.26950i −0.585750 + 0.316456i
\(859\) 19.7812 21.3190i 0.674925 0.727396i −0.299003 0.954252i \(-0.596654\pi\)
0.973928 + 0.226856i \(0.0728446\pi\)
\(860\) 18.3423 5.65785i 0.625468 0.192931i
\(861\) −23.2776 + 20.7637i −0.793297 + 0.707627i
\(862\) 50.4102 + 15.5495i 1.71698 + 0.529618i
\(863\) −47.5644 + 27.4613i −1.61911 + 0.934795i −0.631961 + 0.775000i \(0.717750\pi\)
−0.987150 + 0.159795i \(0.948917\pi\)
\(864\) −14.5704 38.2448i −0.495694 1.30111i
\(865\) 8.24816 + 2.54422i 0.280446 + 0.0865061i
\(866\) 21.6013 + 10.4027i 0.734043 + 0.353496i
\(867\) 46.0144 + 1.30100i 1.56273 + 0.0441842i
\(868\) −39.2630 + 23.1236i −1.33267 + 0.784866i
\(869\) 9.82766 + 3.85707i 0.333380 + 0.130842i
\(870\) 14.2145 16.8259i 0.481915 0.570452i
\(871\) −24.1529 9.47933i −0.818391 0.321195i
\(872\) 0.0591489 + 0.0867555i 0.00200304 + 0.00293791i
\(873\) −17.9966 + 12.7575i −0.609091 + 0.431777i
\(874\) 31.2532 + 64.8979i 1.05715 + 2.19520i
\(875\) 15.6581 + 26.5869i 0.529342 + 0.898802i
\(876\) 8.08952 + 9.22836i 0.273320 + 0.311797i
\(877\) 2.22830 29.7347i 0.0752445 1.00407i −0.823991 0.566603i \(-0.808257\pi\)
0.899235 0.437465i \(-0.144124\pi\)
\(878\) 9.58676 42.0023i 0.323537 1.41751i
\(879\) −20.2916 10.4884i −0.684419 0.353766i
\(880\) −10.3809 + 8.27848i −0.349939 + 0.279067i
\(881\) −44.2706 −1.49151 −0.745757 0.666219i \(-0.767912\pi\)
−0.745757 + 0.666219i \(0.767912\pi\)
\(882\) −40.7503 + 7.63302i −1.37213 + 0.257017i
\(883\) −32.6168 −1.09764 −0.548821 0.835940i \(-0.684923\pi\)
−0.548821 + 0.835940i \(0.684923\pi\)
\(884\) −37.4539 + 29.8685i −1.25971 + 1.00459i
\(885\) −1.98620 42.6523i −0.0667655 1.43374i
\(886\) 1.16980 5.12523i 0.0393002 0.172185i
\(887\) −2.54645 + 33.9800i −0.0855013 + 1.14094i 0.775162 + 0.631762i \(0.217668\pi\)
−0.860664 + 0.509174i \(0.829951\pi\)
\(888\) 0.805842 0.160111i 0.0270423 0.00537297i
\(889\) −12.4453 8.32831i −0.417403 0.279323i
\(890\) 11.9886 + 24.8946i 0.401860 + 0.834470i
\(891\) 4.42189 + 12.6722i 0.148139 + 0.424534i
\(892\) −14.2731 20.9348i −0.477898 0.700948i
\(893\) −46.9555 18.4287i −1.57131 0.616693i
\(894\) 45.8298 + 8.23862i 1.53278 + 0.275541i
\(895\) −0.186534 0.0732090i −0.00623513 0.00244711i
\(896\) −2.93308 3.10678i −0.0979874 0.103790i
\(897\) −25.7978 + 41.9016i −0.861362 + 1.39905i
\(898\) 37.3824 + 18.0024i 1.24747 + 0.600748i
\(899\) −26.3165 8.11758i −0.877706 0.270736i
\(900\) −1.94949 2.02555i −0.0649829 0.0675183i
\(901\) 6.76690 3.90687i 0.225438 0.130157i
\(902\) −19.1498 5.90694i −0.637619 0.196680i
\(903\) −7.57759 20.4798i −0.252166 0.681525i
\(904\) −0.289907 + 0.0894245i −0.00964217 + 0.00297421i
\(905\) −28.3744 + 30.5803i −0.943197 + 1.01652i
\(906\) −0.993051 + 35.1228i −0.0329919 + 1.16688i
\(907\) −49.2059 7.41660i −1.63386 0.246264i −0.732951 0.680281i \(-0.761858\pi\)
−0.900905 + 0.434017i \(0.857096\pi\)
\(908\) −6.80018 + 2.09758i −0.225672 + 0.0696106i
\(909\) 7.34519 4.42158i 0.243625 0.146655i
\(910\) 35.2405 + 23.5827i 1.16821 + 0.781758i
\(911\) −2.51710 + 8.16024i −0.0833953 + 0.270361i −0.987660 0.156610i \(-0.949943\pi\)
0.904265 + 0.426971i \(0.140419\pi\)
\(912\) 28.5133 21.4488i 0.944170 0.710241i
\(913\) 18.3146i 0.606124i
\(914\) −62.3241 + 14.2251i −2.06150 + 0.470524i
\(915\) −33.5986 38.3285i −1.11073 1.26710i
\(916\) 30.7260 12.0591i 1.01522 0.398443i
\(917\) −8.55211 + 39.0220i −0.282415 + 1.28862i
\(918\) 33.2714 + 58.9820i 1.09812 + 1.94669i
\(919\) −0.415072 + 0.385131i −0.0136920 + 0.0127043i −0.686989 0.726668i \(-0.741068\pi\)
0.673297 + 0.739372i \(0.264878\pi\)
\(920\) −1.16450 + 2.96709i −0.0383923 + 0.0978221i
\(921\) 6.73473 19.8258i 0.221917 0.653282i
\(922\) 73.5786 28.8775i 2.42318 0.951030i
\(923\) −33.4351 22.7956i −1.10053 0.750328i
\(924\) −8.63242 9.67752i −0.283986 0.318367i
\(925\) 0.957538 0.652839i 0.0314837 0.0214652i
\(926\) −9.42568 + 13.8249i −0.309747 + 0.454315i
\(927\) 15.7481 28.4650i 0.517236 0.934913i
\(928\) −1.78606 + 23.8333i −0.0586302 + 0.782365i
\(929\) −0.124139 0.155665i −0.00407287 0.00510721i 0.779791 0.626040i \(-0.215325\pi\)
−0.783864 + 0.620933i \(0.786754\pi\)
\(930\) 25.7920 60.6207i 0.845755 1.98783i
\(931\) −15.4505 30.7125i −0.506368 1.00656i
\(932\) −20.0617 + 11.5826i −0.657144 + 0.379402i
\(933\) 9.28366 + 9.11560i 0.303933 + 0.298431i
\(934\) −0.619348 + 0.908416i −0.0202657 + 0.0297243i
\(935\) 14.2138 15.3189i 0.464842 0.500981i
\(936\) 2.17375 + 0.807632i 0.0710514 + 0.0263983i
\(937\) 12.3877 25.7234i 0.404689 0.840346i −0.594650 0.803985i \(-0.702709\pi\)
0.999339 0.0363606i \(-0.0115765\pi\)
\(938\) 4.97861 35.0875i 0.162557 1.14565i
\(939\) −4.94772 7.71688i −0.161463 0.251831i
\(940\) 15.1147 + 38.5117i 0.492989 + 1.25611i
\(941\) 1.75654 + 0.845904i 0.0572615 + 0.0275757i 0.462295 0.886726i \(-0.347026\pi\)
−0.405034 + 0.914302i \(0.632740\pi\)
\(942\) −21.4614 21.0728i −0.699249 0.686590i
\(943\) −49.2979 + 11.2519i −1.60536 + 0.366413i
\(944\) 30.3693 + 38.0820i 0.988438 + 1.23946i
\(945\) 19.8785 21.3661i 0.646649 0.695039i
\(946\) 8.74714 10.9686i 0.284394 0.356619i
\(947\) −9.78533 + 20.3194i −0.317980 + 0.660293i −0.997291 0.0735579i \(-0.976565\pi\)
0.679311 + 0.733851i \(0.262279\pi\)
\(948\) 7.88539 + 21.8917i 0.256106 + 0.711009i
\(949\) −14.2789 −0.463512
\(950\) 2.39415 4.14679i 0.0776765 0.134540i
\(951\) 49.8918 17.9710i 1.61785 0.582751i
\(952\) 2.77896 + 2.17709i 0.0900665 + 0.0705599i
\(953\) 49.1481 + 11.2177i 1.59206 + 0.363378i 0.924502 0.381178i \(-0.124481\pi\)
0.667560 + 0.744556i \(0.267339\pi\)
\(954\) 6.13432 + 3.39378i 0.198606 + 0.109878i
\(955\) 20.3792 7.99825i 0.659455 0.258817i
\(956\) −0.956595 + 6.34659i −0.0309385 + 0.205263i
\(957\) 0.806391 7.79631i 0.0260669 0.252019i
\(958\) 9.55990 + 30.9924i 0.308866 + 1.00132i
\(959\) 14.3720 15.7605i 0.464095 0.508934i
\(960\) −25.9141 4.65845i −0.836372 0.150351i
\(961\) −51.3704 −1.65711
\(962\) 8.85913 15.3445i 0.285630 0.494726i
\(963\) 7.20217 + 4.71998i 0.232087 + 0.152099i
\(964\) 9.71441 0.727994i 0.312880 0.0234471i
\(965\) −1.84707 4.70626i −0.0594593 0.151500i
\(966\) −63.8216 21.0660i −2.05343 0.677787i
\(967\) −22.0263 + 56.1220i −0.708317 + 1.80476i −0.125612 + 0.992079i \(0.540089\pi\)
−0.582706 + 0.812683i \(0.698006\pi\)
\(968\) 0.522858 1.69506i 0.0168053 0.0544814i
\(969\) −39.3439 + 40.0693i −1.26391 + 1.28721i
\(970\) 2.30291 + 30.7302i 0.0739421 + 0.986689i
\(971\) 3.80351 + 0.573286i 0.122060 + 0.0183976i 0.209788 0.977747i \(-0.432723\pi\)
−0.0877280 + 0.996144i \(0.527961\pi\)
\(972\) −14.5781 + 25.7393i −0.467594 + 0.825588i
\(973\) −5.33051 33.4026i −0.170888 1.07084i
\(974\) 44.9164 + 65.8803i 1.43921 + 2.11094i
\(975\) 3.26748 0.152157i 0.104643 0.00487294i
\(976\) 56.6866 + 12.9383i 1.81449 + 0.414146i
\(977\) 10.6456 + 22.1059i 0.340584 + 0.707231i 0.998966 0.0454532i \(-0.0144732\pi\)
−0.658382 + 0.752684i \(0.728759\pi\)
\(978\) −4.55727 1.17661i −0.145726 0.0376239i
\(979\) 8.51496 + 4.91612i 0.272139 + 0.157120i
\(980\) −9.84612 + 26.4226i −0.314523 + 0.844039i
\(981\) 0.432080 1.49735i 0.0137953 0.0478067i
\(982\) 0.763715 1.94591i 0.0243711 0.0620966i
\(983\) 22.2399 + 15.1629i 0.709342 + 0.483621i 0.863451 0.504432i \(-0.168298\pi\)
−0.154109 + 0.988054i \(0.549251\pi\)
\(984\) 0.972852 + 2.17537i 0.0310134 + 0.0693483i
\(985\) −26.1860 1.96237i −0.834356 0.0625264i
\(986\) −2.95531 39.4359i −0.0941163 1.25590i
\(987\) 42.7966 19.5851i 1.36223 0.623400i
\(988\) 2.66353 35.5423i 0.0847381 1.13075i
\(989\) 5.27596 35.0037i 0.167766 1.11305i
\(990\) 18.3523 + 3.83751i 0.583276 + 0.121964i
\(991\) 14.0228 2.11360i 0.445449 0.0671406i 0.0775122 0.996991i \(-0.475302\pi\)
0.367937 + 0.929851i \(0.380064\pi\)
\(992\) 15.9066 + 69.6912i 0.505034 + 2.21270i
\(993\) 26.9630 + 26.4749i 0.855646 + 0.840157i
\(994\) 19.7471 51.6232i 0.626339 1.63739i
\(995\) −7.12478 + 47.2698i −0.225871 + 1.49855i
\(996\) −30.3539 + 26.6080i −0.961800 + 0.843108i
\(997\) 2.55477 + 2.75339i 0.0809105 + 0.0872008i 0.772209 0.635368i \(-0.219152\pi\)
−0.691299 + 0.722569i \(0.742961\pi\)
\(998\) 51.8533 + 29.9375i 1.64139 + 0.947656i
\(999\) −9.45740 7.69797i −0.299219 0.243553i
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 441.2.bn.a.101.45 yes 648
9.5 odd 6 441.2.bd.a.248.10 648
49.33 odd 42 441.2.bd.a.425.10 yes 648
441.131 even 42 inner 441.2.bn.a.131.45 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.bd.a.248.10 648 9.5 odd 6
441.2.bd.a.425.10 yes 648 49.33 odd 42
441.2.bn.a.101.45 yes 648 1.1 even 1 trivial
441.2.bn.a.131.45 yes 648 441.131 even 42 inner