Properties

Label 201.3.n.a.13.2
Level $201$
Weight $3$
Character 201.13
Analytic conductor $5.477$
Analytic rank $0$
Dimension $220$
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] = [201,3,Mod(7,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([0, 23]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.n (of order \(66\), degree \(20\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(220\)
Relative dimension: \(11\) over \(\Q(\zeta_{66})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 201.13
Dual form 201.3.n.a.31.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.93043 - 2.45475i) q^{2} +(1.30900 + 1.13425i) q^{3} +(-1.35617 + 5.59021i) q^{4} +(2.11556 + 3.29187i) q^{5} +(0.257370 - 5.40286i) q^{6} +(0.841588 - 2.10218i) q^{7} +(4.97788 - 2.27332i) q^{8} +(0.426945 + 2.96946i) q^{9} +O(q^{10})\) \(q+(-1.93043 - 2.45475i) q^{2} +(1.30900 + 1.13425i) q^{3} +(-1.35617 + 5.59021i) q^{4} +(2.11556 + 3.29187i) q^{5} +(0.257370 - 5.40286i) q^{6} +(0.841588 - 2.10218i) q^{7} +(4.97788 - 2.27332i) q^{8} +(0.426945 + 2.96946i) q^{9} +(3.99677 - 11.5479i) q^{10} +(-19.8557 + 0.945845i) q^{11} +(-8.11593 + 5.77933i) q^{12} +(1.94996 + 20.4209i) q^{13} +(-6.78496 + 1.99224i) q^{14} +(-0.964555 + 6.70862i) q^{15} +(5.26171 + 2.71260i) q^{16} +(5.41288 + 22.3122i) q^{17} +(6.46510 - 6.78040i) q^{18} +(-1.58924 + 0.636235i) q^{19} +(-21.2713 + 7.36207i) q^{20} +(3.48604 - 1.79718i) q^{21} +(40.6520 + 46.9149i) q^{22} +(-22.2628 - 4.29081i) q^{23} +(9.09455 + 2.67040i) q^{24} +(4.02454 - 8.81251i) q^{25} +(46.3638 - 44.2078i) q^{26} +(-2.80925 + 4.37128i) q^{27} +(10.6103 + 7.55558i) q^{28} +(10.2295 - 17.7180i) q^{29} +(18.3300 - 10.5828i) q^{30} +(-1.92621 + 20.1722i) q^{31} +(-7.64128 - 39.6467i) q^{32} +(-27.0639 - 21.2833i) q^{33} +(44.3216 - 56.3595i) q^{34} +(8.70055 - 1.67689i) q^{35} +(-17.1789 - 1.64039i) q^{36} +(34.6113 + 59.9485i) q^{37} +(4.62972 + 2.67297i) q^{38} +(-20.6099 + 28.9426i) q^{39} +(18.0145 + 11.5772i) q^{40} +(26.9108 + 28.2232i) q^{41} +(-11.1412 - 5.08802i) q^{42} +(5.99845 - 20.4288i) q^{43} +(21.6403 - 112.280i) q^{44} +(-8.87187 + 7.68752i) q^{45} +(32.4441 + 62.9328i) q^{46} +(-0.810498 - 2.34178i) q^{47} +(3.81079 + 9.51890i) q^{48} +(31.7521 + 30.2755i) q^{49} +(-29.4016 + 7.13275i) q^{50} +(-18.2222 + 35.3461i) q^{51} +(-116.801 - 16.7935i) q^{52} +(-16.7759 - 57.1336i) q^{53} +(16.1535 - 1.54247i) q^{54} +(-45.1195 - 63.3615i) q^{55} +(-0.589619 - 12.3776i) q^{56} +(-2.80196 - 0.969767i) q^{57} +(-63.2404 + 9.09260i) q^{58} +(16.8046 + 36.7969i) q^{59} +(-36.1945 - 14.4901i) q^{60} +(-83.0996 - 3.95852i) q^{61} +(53.2360 - 34.2127i) q^{62} +(6.60167 + 1.60155i) q^{63} +(-67.0652 + 77.3974i) q^{64} +(-63.0976 + 49.6205i) q^{65} +107.521i q^{66} +(-6.50800 - 66.6832i) q^{67} -132.071 q^{68} +(-24.2751 - 30.8683i) q^{69} +(-20.9122 - 18.1205i) q^{70} +(-30.1381 + 124.231i) q^{71} +(8.87582 + 13.8111i) q^{72} +(4.05487 - 85.1221i) q^{73} +(80.3437 - 200.689i) q^{74} +(15.2637 - 6.97071i) q^{75} +(-1.40141 - 9.74702i) q^{76} +(-14.7220 + 42.5364i) q^{77} +(110.833 - 5.27962i) q^{78} +(55.9213 - 39.8213i) q^{79} +(2.20192 + 23.0595i) q^{80} +(-8.63544 + 2.53559i) q^{81} +(17.3313 - 120.542i) q^{82} +(-46.0140 - 23.7219i) q^{83} +(5.31895 + 21.9250i) q^{84} +(-61.9976 + 65.0212i) q^{85} +(-61.7272 + 24.7119i) q^{86} +(33.4870 - 11.5900i) q^{87} +(-96.6892 + 49.8467i) q^{88} +(-24.0454 - 27.7499i) q^{89} +(35.9975 + 6.93795i) q^{90} +(44.5695 + 13.0868i) q^{91} +(54.1788 - 118.635i) q^{92} +(-25.4017 + 24.2205i) q^{93} +(-4.18387 + 6.51022i) q^{94} +(-5.45653 - 3.88558i) q^{95} +(34.9670 - 60.5646i) q^{96} +(-14.6804 + 8.47576i) q^{97} +(13.0235 - 136.388i) q^{98} +(-11.2859 - 58.5571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 220 q - 26 q^{4} + 33 q^{6} + 15 q^{7} - 33 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 220 q - 26 q^{4} + 33 q^{6} + 15 q^{7} - 33 q^{8} + 66 q^{9} + 93 q^{10} + 69 q^{11} - 21 q^{12} + 27 q^{13} - 6 q^{14} - 27 q^{15} + 58 q^{16} + 8 q^{17} + 54 q^{19} + 12 q^{20} + 15 q^{21} - 69 q^{22} - 164 q^{23} + 56 q^{25} - 71 q^{26} + 152 q^{28} - 119 q^{29} - 18 q^{30} - 76 q^{31} - 676 q^{32} - 30 q^{33} + 24 q^{34} + 327 q^{35} - 21 q^{36} + 86 q^{37} - 108 q^{38} - 27 q^{39} - 115 q^{40} - 6 q^{41} + 132 q^{42} - 385 q^{43} - 189 q^{44} + 541 q^{46} + 794 q^{47} + 174 q^{48} + 40 q^{49} - 714 q^{50} - 240 q^{51} + 924 q^{52} - 748 q^{53} + 355 q^{55} - 899 q^{56} + 195 q^{57} - 1672 q^{58} - 466 q^{59} - 516 q^{60} - 217 q^{61} - 818 q^{62} + 219 q^{63} + 691 q^{64} - 68 q^{65} - 72 q^{67} - 198 q^{68} + 69 q^{69} - 44 q^{70} + 481 q^{71} + 264 q^{72} - 1458 q^{73} + 703 q^{74} + 396 q^{75} + 1270 q^{76} + 1096 q^{77} + 741 q^{78} - 89 q^{79} + 3363 q^{80} - 198 q^{81} - 28 q^{82} + 1023 q^{83} + 321 q^{84} - 237 q^{85} + 329 q^{86} + 126 q^{87} + 1768 q^{88} - 1409 q^{89} - 279 q^{90} + 916 q^{91} - 1340 q^{92} + 177 q^{93} - 1144 q^{94} - 357 q^{95} + 105 q^{96} + 441 q^{97} + 397 q^{98} + 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{19}{66}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.93043 2.45475i −0.965217 1.22737i −0.973799 0.227410i \(-0.926974\pi\)
0.00858173 0.999963i \(-0.497268\pi\)
\(3\) 1.30900 + 1.13425i 0.436332 + 0.378084i
\(4\) −1.35617 + 5.59021i −0.339043 + 1.39755i
\(5\) 2.11556 + 3.29187i 0.423111 + 0.658374i 0.985728 0.168343i \(-0.0538418\pi\)
−0.562617 + 0.826718i \(0.690205\pi\)
\(6\) 0.257370 5.40286i 0.0428950 0.900476i
\(7\) 0.841588 2.10218i 0.120227 0.300312i −0.856031 0.516925i \(-0.827077\pi\)
0.976258 + 0.216613i \(0.0695009\pi\)
\(8\) 4.97788 2.27332i 0.622235 0.284165i
\(9\) 0.426945 + 2.96946i 0.0474383 + 0.329940i
\(10\) 3.99677 11.5479i 0.399677 1.15479i
\(11\) −19.8557 + 0.945845i −1.80507 + 0.0859859i −0.922920 0.384991i \(-0.874205\pi\)
−0.882146 + 0.470977i \(0.843902\pi\)
\(12\) −8.11593 + 5.77933i −0.676328 + 0.481611i
\(13\) 1.94996 + 20.4209i 0.149997 + 1.57084i 0.686622 + 0.727015i \(0.259093\pi\)
−0.536625 + 0.843821i \(0.680301\pi\)
\(14\) −6.78496 + 1.99224i −0.484640 + 0.142303i
\(15\) −0.964555 + 6.70862i −0.0643036 + 0.447242i
\(16\) 5.26171 + 2.71260i 0.328857 + 0.169538i
\(17\) 5.41288 + 22.3122i 0.318405 + 1.31248i 0.875977 + 0.482353i \(0.160218\pi\)
−0.557572 + 0.830128i \(0.688267\pi\)
\(18\) 6.46510 6.78040i 0.359172 0.376689i
\(19\) −1.58924 + 0.636235i −0.0836441 + 0.0334860i −0.413107 0.910682i \(-0.635557\pi\)
0.329463 + 0.944168i \(0.393132\pi\)
\(20\) −21.2713 + 7.36207i −1.06357 + 0.368104i
\(21\) 3.48604 1.79718i 0.166002 0.0855800i
\(22\) 40.6520 + 46.9149i 1.84782 + 2.13250i
\(23\) −22.2628 4.29081i −0.967950 0.186557i −0.319308 0.947651i \(-0.603451\pi\)
−0.648642 + 0.761094i \(0.724663\pi\)
\(24\) 9.09455 + 2.67040i 0.378939 + 0.111267i
\(25\) 4.02454 8.81251i 0.160982 0.352501i
\(26\) 46.3638 44.2078i 1.78322 1.70030i
\(27\) −2.80925 + 4.37128i −0.104046 + 0.161899i
\(28\) 10.6103 + 7.55558i 0.378940 + 0.269842i
\(29\) 10.2295 17.7180i 0.352740 0.610964i −0.633988 0.773343i \(-0.718583\pi\)
0.986729 + 0.162378i \(0.0519165\pi\)
\(30\) 18.3300 10.5828i 0.611000 0.352761i
\(31\) −1.92621 + 20.1722i −0.0621357 + 0.650715i 0.909733 + 0.415193i \(0.136286\pi\)
−0.971869 + 0.235522i \(0.924320\pi\)
\(32\) −7.64128 39.6467i −0.238790 1.23896i
\(33\) −27.0639 21.2833i −0.820118 0.644948i
\(34\) 44.3216 56.3595i 1.30358 1.65763i
\(35\) 8.70055 1.67689i 0.248587 0.0479112i
\(36\) −17.1789 1.64039i −0.477193 0.0455664i
\(37\) 34.6113 + 59.9485i 0.935441 + 1.62023i 0.773846 + 0.633374i \(0.218330\pi\)
0.161595 + 0.986857i \(0.448336\pi\)
\(38\) 4.62972 + 2.67297i 0.121835 + 0.0703412i
\(39\) −20.6099 + 28.9426i −0.528459 + 0.742117i
\(40\) 18.0145 + 11.5772i 0.450362 + 0.289430i
\(41\) 26.9108 + 28.2232i 0.656360 + 0.688371i 0.964833 0.262862i \(-0.0846665\pi\)
−0.308473 + 0.951233i \(0.599818\pi\)
\(42\) −11.1412 5.08802i −0.265267 0.121143i
\(43\) 5.99845 20.4288i 0.139499 0.475089i −0.859874 0.510507i \(-0.829458\pi\)
0.999373 + 0.0354175i \(0.0112761\pi\)
\(44\) 21.6403 112.280i 0.491825 2.55183i
\(45\) −8.87187 + 7.68752i −0.197153 + 0.170834i
\(46\) 32.4441 + 62.9328i 0.705307 + 1.36810i
\(47\) −0.810498 2.34178i −0.0172446 0.0498251i 0.936050 0.351867i \(-0.114453\pi\)
−0.953295 + 0.302042i \(0.902332\pi\)
\(48\) 3.81079 + 9.51890i 0.0793915 + 0.198310i
\(49\) 31.7521 + 30.2755i 0.648001 + 0.617868i
\(50\) −29.4016 + 7.13275i −0.588032 + 0.142655i
\(51\) −18.2222 + 35.3461i −0.357298 + 0.693062i
\(52\) −116.801 16.7935i −2.24618 0.322952i
\(53\) −16.7759 57.1336i −0.316527 1.07799i −0.952058 0.305917i \(-0.901037\pi\)
0.635531 0.772075i \(-0.280781\pi\)
\(54\) 16.1535 1.54247i 0.299138 0.0285642i
\(55\) −45.1195 63.3615i −0.820355 1.15203i
\(56\) −0.589619 12.3776i −0.0105289 0.221029i
\(57\) −2.80196 0.969767i −0.0491572 0.0170135i
\(58\) −63.2404 + 9.09260i −1.09035 + 0.156769i
\(59\) 16.8046 + 36.7969i 0.284823 + 0.623676i 0.996922 0.0784039i \(-0.0249824\pi\)
−0.712099 + 0.702080i \(0.752255\pi\)
\(60\) −36.1945 14.4901i −0.603242 0.241502i
\(61\) −83.0996 3.95852i −1.36229 0.0648938i −0.646342 0.763048i \(-0.723702\pi\)
−0.715947 + 0.698154i \(0.754005\pi\)
\(62\) 53.2360 34.2127i 0.858645 0.551817i
\(63\) 6.60167 + 1.60155i 0.104788 + 0.0254214i
\(64\) −67.0652 + 77.3974i −1.04789 + 1.20933i
\(65\) −63.0976 + 49.6205i −0.970732 + 0.763392i
\(66\) 107.521i 1.62911i
\(67\) −6.50800 66.6832i −0.0971343 0.995271i
\(68\) −132.071 −1.94221
\(69\) −24.2751 30.8683i −0.351813 0.447367i
\(70\) −20.9122 18.1205i −0.298746 0.258865i
\(71\) −30.1381 + 124.231i −0.424480 + 1.74973i 0.210880 + 0.977512i \(0.432367\pi\)
−0.635359 + 0.772217i \(0.719148\pi\)
\(72\) 8.87582 + 13.8111i 0.123275 + 0.191820i
\(73\) 4.05487 85.1221i 0.0555461 1.16606i −0.783284 0.621664i \(-0.786457\pi\)
0.838830 0.544393i \(-0.183240\pi\)
\(74\) 80.3437 200.689i 1.08573 2.71201i
\(75\) 15.2637 6.97071i 0.203516 0.0929428i
\(76\) −1.40141 9.74702i −0.0184396 0.128250i
\(77\) −14.7220 + 42.5364i −0.191195 + 0.552421i
\(78\) 110.833 5.27962i 1.42093 0.0676874i
\(79\) 55.9213 39.8213i 0.707864 0.504068i −0.168509 0.985700i \(-0.553895\pi\)
0.876373 + 0.481632i \(0.159956\pi\)
\(80\) 2.20192 + 23.0595i 0.0275240 + 0.288244i
\(81\) −8.63544 + 2.53559i −0.106610 + 0.0313036i
\(82\) 17.3313 120.542i 0.211358 1.47003i
\(83\) −46.0140 23.7219i −0.554386 0.285806i 0.158181 0.987410i \(-0.449437\pi\)
−0.712567 + 0.701604i \(0.752467\pi\)
\(84\) 5.31895 + 21.9250i 0.0633208 + 0.261012i
\(85\) −61.9976 + 65.0212i −0.729383 + 0.764955i
\(86\) −61.7272 + 24.7119i −0.717758 + 0.287347i
\(87\) 33.4870 11.5900i 0.384908 0.133218i
\(88\) −96.6892 + 49.8467i −1.09874 + 0.566440i
\(89\) −24.0454 27.7499i −0.270173 0.311797i 0.604408 0.796675i \(-0.293410\pi\)
−0.874582 + 0.484878i \(0.838864\pi\)
\(90\) 35.9975 + 6.93795i 0.399972 + 0.0770883i
\(91\) 44.5695 + 13.0868i 0.489774 + 0.143811i
\(92\) 54.1788 118.635i 0.588900 1.28951i
\(93\) −25.4017 + 24.2205i −0.273137 + 0.260435i
\(94\) −4.18387 + 6.51022i −0.0445092 + 0.0692577i
\(95\) −5.45653 3.88558i −0.0574371 0.0409008i
\(96\) 34.9670 60.5646i 0.364239 0.630881i
\(97\) −14.6804 + 8.47576i −0.151345 + 0.0873790i −0.573760 0.819024i \(-0.694516\pi\)
0.422415 + 0.906402i \(0.361182\pi\)
\(98\) 13.0235 136.388i 0.132893 1.39172i
\(99\) −11.2859 58.5571i −0.113999 0.591485i
\(100\) 43.8059 + 34.4493i 0.438059 + 0.344493i
\(101\) 34.4137 43.7606i 0.340730 0.433273i −0.585246 0.810856i \(-0.699002\pi\)
0.925976 + 0.377583i \(0.123245\pi\)
\(102\) 121.943 23.5025i 1.19552 0.230417i
\(103\) 106.098 + 10.1311i 1.03008 + 0.0983605i 0.596383 0.802700i \(-0.296604\pi\)
0.433694 + 0.901060i \(0.357210\pi\)
\(104\) 56.1298 + 97.2197i 0.539710 + 0.934805i
\(105\) 13.2910 + 7.67357i 0.126581 + 0.0730816i
\(106\) −107.864 + 151.473i −1.01758 + 1.42899i
\(107\) −4.17878 2.68554i −0.0390540 0.0250985i 0.520968 0.853576i \(-0.325571\pi\)
−0.560022 + 0.828478i \(0.689207\pi\)
\(108\) −20.6266 21.6325i −0.190987 0.200301i
\(109\) −126.299 57.6790i −1.15871 0.529165i −0.259096 0.965852i \(-0.583425\pi\)
−0.899614 + 0.436687i \(0.856152\pi\)
\(110\) −68.4362 + 233.072i −0.622147 + 2.11884i
\(111\) −22.6907 + 117.730i −0.204420 + 1.06063i
\(112\) 10.1306 8.77820i 0.0904517 0.0783768i
\(113\) 26.9065 + 52.1913i 0.238110 + 0.461870i 0.977366 0.211555i \(-0.0678528\pi\)
−0.739256 + 0.673425i \(0.764822\pi\)
\(114\) 3.02846 + 8.75017i 0.0265655 + 0.0767559i
\(115\) −32.9735 82.3639i −0.286726 0.716208i
\(116\) 85.1743 + 81.2135i 0.734261 + 0.700116i
\(117\) −59.8065 + 14.5089i −0.511166 + 0.124008i
\(118\) 57.8869 112.285i 0.490567 0.951567i
\(119\) 51.4597 + 7.39880i 0.432435 + 0.0621747i
\(120\) 10.4494 + 35.5875i 0.0870785 + 0.296562i
\(121\) 272.903 26.0591i 2.25540 0.215364i
\(122\) 150.701 + 211.630i 1.23526 + 1.73467i
\(123\) 3.21388 + 67.4677i 0.0261291 + 0.548518i
\(124\) −110.154 38.1248i −0.888342 0.307458i
\(125\) 134.354 19.3173i 1.07484 0.154538i
\(126\) −8.81270 19.2971i −0.0699421 0.153152i
\(127\) −155.489 62.2485i −1.22432 0.490145i −0.332748 0.943016i \(-0.607976\pi\)
−0.891576 + 0.452870i \(0.850400\pi\)
\(128\) 158.133 + 7.53282i 1.23542 + 0.0588501i
\(129\) 31.0234 19.9375i 0.240491 0.154554i
\(130\) 243.612 + 59.0995i 1.87393 + 0.454612i
\(131\) 73.5103 84.8354i 0.561147 0.647599i −0.402296 0.915510i \(-0.631788\pi\)
0.963444 + 0.267911i \(0.0863333\pi\)
\(132\) 155.681 122.429i 1.17940 0.927494i
\(133\) 3.87632i 0.0291453i
\(134\) −151.127 + 144.703i −1.12781 + 1.07987i
\(135\) −20.3328 −0.150614
\(136\) 77.6674 + 98.7621i 0.571084 + 0.726192i
\(137\) 78.5865 + 68.0956i 0.573624 + 0.497048i 0.892682 0.450687i \(-0.148821\pi\)
−0.319058 + 0.947735i \(0.603366\pi\)
\(138\) −28.9124 + 119.179i −0.209510 + 0.863613i
\(139\) −16.8493 26.2180i −0.121218 0.188619i 0.775342 0.631542i \(-0.217578\pi\)
−0.896559 + 0.442923i \(0.853941\pi\)
\(140\) −2.42524 + 50.9121i −0.0173231 + 0.363658i
\(141\) 1.59523 3.98469i 0.0113137 0.0282602i
\(142\) 363.135 165.838i 2.55729 1.16787i
\(143\) −58.0327 403.627i −0.405823 2.82256i
\(144\) −5.80851 + 16.7826i −0.0403369 + 0.116546i
\(145\) 79.9663 3.80926i 0.551492 0.0262708i
\(146\) −216.781 + 154.369i −1.48480 + 1.05732i
\(147\) 7.22326 + 75.6454i 0.0491378 + 0.514595i
\(148\) −382.064 + 112.184i −2.58151 + 0.758000i
\(149\) −9.82748 + 68.3516i −0.0659562 + 0.458736i 0.929901 + 0.367809i \(0.119892\pi\)
−0.995858 + 0.0909267i \(0.971017\pi\)
\(150\) −46.5769 24.0121i −0.310513 0.160081i
\(151\) 47.5717 + 196.093i 0.315045 + 1.29863i 0.880576 + 0.473905i \(0.157156\pi\)
−0.565531 + 0.824727i \(0.691329\pi\)
\(152\) −6.46467 + 6.77995i −0.0425307 + 0.0446049i
\(153\) −63.9442 + 25.5994i −0.417936 + 0.167316i
\(154\) 132.836 45.9750i 0.862572 0.298539i
\(155\) −70.4792 + 36.3345i −0.454704 + 0.234416i
\(156\) −133.845 154.465i −0.857978 0.990159i
\(157\) −108.153 20.8447i −0.688871 0.132769i −0.167209 0.985921i \(-0.553476\pi\)
−0.521662 + 0.853152i \(0.674688\pi\)
\(158\) −205.704 60.4001i −1.30192 0.382279i
\(159\) 42.8442 93.8158i 0.269461 0.590036i
\(160\) 114.346 109.029i 0.714665 0.681432i
\(161\) −27.7562 + 43.1895i −0.172399 + 0.268258i
\(162\) 22.8944 + 16.3030i 0.141323 + 0.100636i
\(163\) −9.43909 + 16.3490i −0.0579085 + 0.100300i −0.893526 0.449011i \(-0.851777\pi\)
0.835618 + 0.549311i \(0.185110\pi\)
\(164\) −194.269 + 112.161i −1.18457 + 0.683911i
\(165\) 12.8066 134.117i 0.0776158 0.812830i
\(166\) 30.5958 + 158.746i 0.184312 + 0.956303i
\(167\) 186.015 + 146.284i 1.11386 + 0.875953i 0.993163 0.116736i \(-0.0372431\pi\)
0.120702 + 0.992689i \(0.461486\pi\)
\(168\) 13.2675 16.8710i 0.0789734 0.100423i
\(169\) −247.263 + 47.6561i −1.46310 + 0.281988i
\(170\) 279.293 + 26.6692i 1.64290 + 0.156878i
\(171\) −2.56779 4.44755i −0.0150163 0.0260091i
\(172\) 106.067 + 61.2376i 0.616666 + 0.356032i
\(173\) 166.073 233.217i 0.959959 1.34807i 0.0225864 0.999745i \(-0.492810\pi\)
0.937372 0.348329i \(-0.113251\pi\)
\(174\) −93.0948 59.8284i −0.535028 0.343842i
\(175\) −15.1385 15.8768i −0.0865059 0.0907248i
\(176\) −107.041 48.8839i −0.608187 0.277750i
\(177\) −19.7398 + 67.2276i −0.111524 + 0.379817i
\(178\) −21.7009 + 112.595i −0.121915 + 0.632555i
\(179\) −65.9410 + 57.1382i −0.368386 + 0.319208i −0.819306 0.573356i \(-0.805641\pi\)
0.450921 + 0.892564i \(0.351096\pi\)
\(180\) −30.9431 60.0212i −0.171906 0.333451i
\(181\) −2.76285 7.98273i −0.0152644 0.0441035i 0.937111 0.349031i \(-0.113489\pi\)
−0.952376 + 0.304927i \(0.901368\pi\)
\(182\) −53.9137 134.670i −0.296229 0.739945i
\(183\) −104.287 99.4376i −0.569875 0.543375i
\(184\) −120.576 + 29.2515i −0.655305 + 0.158975i
\(185\) −124.121 + 240.761i −0.670923 + 1.30141i
\(186\) 108.492 + 15.5987i 0.583288 + 0.0838641i
\(187\) −128.580 437.905i −0.687596 2.34174i
\(188\) 14.1902 1.35500i 0.0754799 0.00720746i
\(189\) 6.82501 + 9.58439i 0.0361112 + 0.0507110i
\(190\) 0.995363 + 20.8952i 0.00523875 + 0.109975i
\(191\) 71.7870 + 24.8457i 0.375848 + 0.130082i 0.508460 0.861086i \(-0.330215\pi\)
−0.132612 + 0.991168i \(0.542336\pi\)
\(192\) −175.576 + 25.2441i −0.914460 + 0.131479i
\(193\) 3.53845 + 7.74812i 0.0183339 + 0.0401457i 0.918577 0.395241i \(-0.129339\pi\)
−0.900244 + 0.435387i \(0.856612\pi\)
\(194\) 49.1455 + 19.6749i 0.253327 + 0.101417i
\(195\) −138.877 6.61551i −0.712188 0.0339257i
\(196\) −212.308 + 136.442i −1.08320 + 0.696132i
\(197\) 78.9982 + 19.1648i 0.401006 + 0.0972830i 0.431190 0.902261i \(-0.358094\pi\)
−0.0301835 + 0.999544i \(0.509609\pi\)
\(198\) −121.956 + 140.745i −0.615939 + 0.710832i
\(199\) 62.5118 49.1598i 0.314130 0.247034i −0.448628 0.893718i \(-0.648087\pi\)
0.762758 + 0.646684i \(0.223845\pi\)
\(200\) 53.0167i 0.265084i
\(201\) 67.1166 94.6698i 0.333913 0.470994i
\(202\) −173.855 −0.860666
\(203\) −28.6374 36.4155i −0.141071 0.179387i
\(204\) −172.880 149.801i −0.847451 0.734320i
\(205\) −35.9759 + 148.295i −0.175492 + 0.723388i
\(206\) −179.946 280.001i −0.873524 1.35923i
\(207\) 3.23641 67.9407i 0.0156348 0.328216i
\(208\) −45.1335 + 112.738i −0.216988 + 0.542010i
\(209\) 30.9537 14.1361i 0.148104 0.0676367i
\(210\) −6.82076 47.4394i −0.0324798 0.225902i
\(211\) −43.8330 + 126.647i −0.207740 + 0.600224i −0.999950 0.0100244i \(-0.996809\pi\)
0.792210 + 0.610248i \(0.208930\pi\)
\(212\) 342.140 16.2981i 1.61387 0.0768780i
\(213\) −180.360 + 128.433i −0.846759 + 0.602974i
\(214\) 1.47454 + 15.4421i 0.00689038 + 0.0721593i
\(215\) 79.9391 23.4722i 0.371810 0.109173i
\(216\) −4.04679 + 28.1460i −0.0187351 + 0.130306i
\(217\) 40.7845 + 21.0259i 0.187947 + 0.0968935i
\(218\) 102.225 + 421.379i 0.468924 + 1.93293i
\(219\) 101.858 106.825i 0.465104 0.487787i
\(220\) 415.394 166.299i 1.88815 0.755903i
\(221\) −445.079 + 154.043i −2.01393 + 0.697029i
\(222\) 332.801 171.571i 1.49910 0.772842i
\(223\) 47.2569 + 54.5373i 0.211914 + 0.244562i 0.851748 0.523951i \(-0.175542\pi\)
−0.639834 + 0.768513i \(0.720997\pi\)
\(224\) −89.7756 17.3028i −0.400784 0.0772448i
\(225\) 27.8867 + 8.18827i 0.123941 + 0.0363923i
\(226\) 76.1752 166.800i 0.337058 0.738055i
\(227\) 277.251 264.358i 1.22137 1.16457i 0.240346 0.970687i \(-0.422739\pi\)
0.981024 0.193887i \(-0.0621095\pi\)
\(228\) 9.22114 14.3484i 0.0404436 0.0629314i
\(229\) 270.223 + 192.425i 1.18001 + 0.840284i 0.989940 0.141485i \(-0.0451879\pi\)
0.190074 + 0.981770i \(0.439127\pi\)
\(230\) −138.529 + 239.940i −0.602301 + 1.04322i
\(231\) −67.5181 + 38.9816i −0.292286 + 0.168751i
\(232\) 10.6424 111.453i 0.0458726 0.480400i
\(233\) 20.6562 + 107.175i 0.0886532 + 0.459977i 0.998941 + 0.0460014i \(0.0146479\pi\)
−0.910288 + 0.413975i \(0.864140\pi\)
\(234\) 151.068 + 118.801i 0.645590 + 0.507698i
\(235\) 5.99419 7.62223i 0.0255072 0.0324350i
\(236\) −228.492 + 44.0382i −0.968187 + 0.186603i
\(237\) 118.368 + 11.3028i 0.499444 + 0.0476911i
\(238\) −81.1775 140.604i −0.341082 0.590771i
\(239\) −41.8832 24.1813i −0.175244 0.101177i 0.409812 0.912170i \(-0.365594\pi\)
−0.585056 + 0.810993i \(0.698927\pi\)
\(240\) −23.2730 + 32.6824i −0.0969710 + 0.136177i
\(241\) 224.528 + 144.296i 0.931653 + 0.598737i 0.916016 0.401141i \(-0.131386\pi\)
0.0156366 + 0.999878i \(0.495023\pi\)
\(242\) −590.790 619.603i −2.44128 2.56034i
\(243\) −14.1798 6.47568i −0.0583529 0.0266489i
\(244\) 134.826 459.176i 0.552567 1.88187i
\(245\) −32.4898 + 168.573i −0.132612 + 0.688054i
\(246\) 159.412 138.131i 0.648016 0.561509i
\(247\) −16.0914 31.2130i −0.0651474 0.126368i
\(248\) 36.2694 + 104.793i 0.146247 + 0.422554i
\(249\) −33.3256 83.2434i −0.133838 0.334311i
\(250\) −306.781 292.516i −1.22713 1.17006i
\(251\) 356.297 86.4367i 1.41951 0.344369i 0.548712 0.836011i \(-0.315118\pi\)
0.870797 + 0.491642i \(0.163603\pi\)
\(252\) −17.9060 + 34.7328i −0.0710555 + 0.137829i
\(253\) 446.104 + 64.1400i 1.76325 + 0.253518i
\(254\) 147.357 + 501.853i 0.580147 + 1.97580i
\(255\) −154.905 + 14.7916i −0.607471 + 0.0580064i
\(256\) −49.1571 69.0314i −0.192020 0.269654i
\(257\) 2.87564 + 60.3671i 0.0111893 + 0.234892i 0.997533 + 0.0701939i \(0.0223618\pi\)
−0.986344 + 0.164698i \(0.947335\pi\)
\(258\) −108.830 37.6665i −0.421822 0.145994i
\(259\) 155.151 22.3074i 0.599040 0.0861290i
\(260\) −191.818 420.023i −0.737761 1.61547i
\(261\) 56.9803 + 22.8115i 0.218315 + 0.0874002i
\(262\) −350.156 16.6800i −1.33647 0.0636641i
\(263\) −124.021 + 79.7037i −0.471564 + 0.303056i −0.754754 0.656008i \(-0.772244\pi\)
0.283190 + 0.959064i \(0.408607\pi\)
\(264\) −183.105 44.4207i −0.693578 0.168260i
\(265\) 152.586 176.094i 0.575796 0.664504i
\(266\) 9.51538 7.48298i 0.0357721 0.0281315i
\(267\) 63.5981i 0.238195i
\(268\) 381.599 + 54.0527i 1.42388 + 0.201689i
\(269\) 303.573 1.12852 0.564262 0.825596i \(-0.309161\pi\)
0.564262 + 0.825596i \(0.309161\pi\)
\(270\) 39.2512 + 49.9120i 0.145375 + 0.184859i
\(271\) 31.7406 + 27.5034i 0.117124 + 0.101488i 0.711454 0.702733i \(-0.248037\pi\)
−0.594330 + 0.804221i \(0.702583\pi\)
\(272\) −32.0431 + 132.083i −0.117805 + 0.485600i
\(273\) 43.4976 + 67.6836i 0.159332 + 0.247925i
\(274\) 15.4514 324.364i 0.0563918 1.18381i
\(275\) −71.5749 + 178.785i −0.260272 + 0.650129i
\(276\) 205.482 93.8404i 0.744499 0.340001i
\(277\) −55.4252 385.491i −0.200091 1.39166i −0.804009 0.594617i \(-0.797304\pi\)
0.603918 0.797046i \(-0.293605\pi\)
\(278\) −31.8321 + 91.9729i −0.114504 + 0.330838i
\(279\) −60.7229 + 2.89259i −0.217645 + 0.0103677i
\(280\) 39.4982 28.1265i 0.141065 0.100452i
\(281\) 37.9428 + 397.355i 0.135028 + 1.41408i 0.768272 + 0.640124i \(0.221117\pi\)
−0.633244 + 0.773952i \(0.718277\pi\)
\(282\) −12.8609 + 3.77630i −0.0456060 + 0.0133911i
\(283\) 43.3319 301.380i 0.153116 1.06495i −0.757839 0.652441i \(-0.773745\pi\)
0.910955 0.412505i \(-0.135346\pi\)
\(284\) −653.604 336.956i −2.30142 1.18647i
\(285\) −2.73535 11.2753i −0.00959773 0.0395624i
\(286\) −878.773 + 921.630i −3.07263 + 3.22248i
\(287\) 81.9782 32.8191i 0.285638 0.114352i
\(288\) 114.467 39.6175i 0.397455 0.137561i
\(289\) −211.661 + 109.119i −0.732391 + 0.377574i
\(290\) −163.720 188.944i −0.564553 0.651529i
\(291\) −28.8303 5.55659i −0.0990732 0.0190948i
\(292\) 470.352 + 138.108i 1.61079 + 0.472972i
\(293\) 30.7317 67.2931i 0.104886 0.229669i −0.849911 0.526926i \(-0.823344\pi\)
0.954798 + 0.297257i \(0.0960717\pi\)
\(294\) 171.746 163.760i 0.584171 0.557006i
\(295\) −85.5795 + 133.164i −0.290100 + 0.451405i
\(296\) 308.573 + 219.734i 1.04248 + 0.742344i
\(297\) 51.6452 89.4521i 0.173890 0.301186i
\(298\) 186.757 107.824i 0.626702 0.361827i
\(299\) 44.2105 462.993i 0.147861 1.54847i
\(300\) 18.2675 + 94.7809i 0.0608917 + 0.315936i
\(301\) −37.8970 29.8025i −0.125904 0.0990116i
\(302\) 389.526 495.322i 1.28982 1.64014i
\(303\) 94.6829 18.2486i 0.312485 0.0602265i
\(304\) −10.0880 0.963284i −0.0331841 0.00316870i
\(305\) −162.771 281.928i −0.533676 0.924353i
\(306\) 186.280 + 107.549i 0.608759 + 0.351467i
\(307\) −201.698 + 283.245i −0.656995 + 0.922621i −0.999859 0.0167642i \(-0.994664\pi\)
0.342864 + 0.939385i \(0.388603\pi\)
\(308\) −217.822 139.986i −0.707215 0.454499i
\(309\) 127.391 + 133.603i 0.412267 + 0.432374i
\(310\) 225.247 + 102.867i 0.726605 + 0.331829i
\(311\) −138.121 + 470.397i −0.444119 + 1.51253i 0.368441 + 0.929651i \(0.379892\pi\)
−0.812559 + 0.582878i \(0.801926\pi\)
\(312\) −36.7979 + 190.926i −0.117942 + 0.611941i
\(313\) −248.263 + 215.121i −0.793173 + 0.687288i −0.954037 0.299688i \(-0.903117\pi\)
0.160864 + 0.986977i \(0.448572\pi\)
\(314\) 157.613 + 305.727i 0.501953 + 0.973653i
\(315\) 8.69413 + 25.1200i 0.0276004 + 0.0797461i
\(316\) 146.771 + 366.616i 0.464465 + 1.16018i
\(317\) 270.212 + 257.646i 0.852403 + 0.812765i 0.983931 0.178548i \(-0.0571398\pi\)
−0.131528 + 0.991312i \(0.541988\pi\)
\(318\) −313.002 + 75.9335i −0.984283 + 0.238785i
\(319\) −186.355 + 361.479i −0.584185 + 1.13316i
\(320\) −396.662 57.0314i −1.23957 0.178223i
\(321\) −2.42393 8.25515i −0.00755118 0.0257170i
\(322\) 159.601 15.2400i 0.495655 0.0473293i
\(323\) −22.7981 32.0155i −0.0705825 0.0991192i
\(324\) −2.46338 51.7126i −0.00760301 0.159607i
\(325\) 187.807 + 65.0006i 0.577867 + 0.200002i
\(326\) 58.3542 8.39006i 0.179000 0.0257364i
\(327\) −99.9029 218.757i −0.305514 0.668981i
\(328\) 198.119 + 79.3149i 0.604021 + 0.241814i
\(329\) −5.60496 0.266997i −0.0170364 0.000811542i
\(330\) −353.946 + 227.467i −1.07256 + 0.689294i
\(331\) −602.780 146.233i −1.82109 0.441791i −0.828158 0.560494i \(-0.810611\pi\)
−0.992930 + 0.118703i \(0.962126\pi\)
\(332\) 195.013 225.057i 0.587389 0.677883i
\(333\) −163.238 + 128.372i −0.490204 + 0.385501i
\(334\) 739.013i 2.21261i
\(335\) 205.744 162.496i 0.614162 0.485061i
\(336\) 23.2176 0.0691000
\(337\) −201.536 256.273i −0.598029 0.760455i 0.388958 0.921255i \(-0.372835\pi\)
−0.986987 + 0.160800i \(0.948593\pi\)
\(338\) 594.309 + 514.971i 1.75831 + 1.52358i
\(339\) −23.9776 + 98.8369i −0.0707303 + 0.291554i
\(340\) −279.403 434.759i −0.821773 1.27870i
\(341\) 19.1665 402.355i 0.0562068 1.17993i
\(342\) −5.96065 + 14.8890i −0.0174288 + 0.0435350i
\(343\) 191.295 87.3616i 0.557712 0.254698i
\(344\) −16.5818 115.329i −0.0482028 0.335258i
\(345\) 50.2592 145.214i 0.145679 0.420911i
\(346\) −893.081 + 42.5427i −2.58116 + 0.122956i
\(347\) 243.730 173.559i 0.702391 0.500170i −0.172182 0.985065i \(-0.555082\pi\)
0.874572 + 0.484895i \(0.161142\pi\)
\(348\) 19.3762 + 202.917i 0.0556789 + 0.583096i
\(349\) −188.026 + 55.2094i −0.538756 + 0.158193i −0.539780 0.841806i \(-0.681492\pi\)
0.00102345 + 0.999999i \(0.499674\pi\)
\(350\) −9.74967 + 67.8105i −0.0278562 + 0.193744i
\(351\) −94.7432 48.8435i −0.269924 0.139155i
\(352\) 189.223 + 779.987i 0.537565 + 2.21587i
\(353\) −472.496 + 495.539i −1.33852 + 1.40379i −0.492817 + 0.870133i \(0.664033\pi\)
−0.845698 + 0.533661i \(0.820816\pi\)
\(354\) 203.133 81.3222i 0.573822 0.229724i
\(355\) −472.710 + 163.607i −1.33158 + 0.460864i
\(356\) 187.738 96.7855i 0.527353 0.271869i
\(357\) 58.9685 + 68.0533i 0.165178 + 0.190626i
\(358\) 267.555 + 51.5669i 0.747360 + 0.144042i
\(359\) 565.590 + 166.072i 1.57546 + 0.462597i 0.948585 0.316523i \(-0.102516\pi\)
0.626875 + 0.779120i \(0.284334\pi\)
\(360\) −26.6869 + 58.4361i −0.0741303 + 0.162323i
\(361\) −259.147 + 247.096i −0.717859 + 0.684477i
\(362\) −14.2621 + 22.1922i −0.0393980 + 0.0613045i
\(363\) 386.787 + 275.430i 1.06553 + 0.758760i
\(364\) −133.602 + 231.405i −0.367038 + 0.635728i
\(365\) 288.789 166.733i 0.791204 0.456802i
\(366\) −42.7747 + 447.956i −0.116871 + 1.22392i
\(367\) −69.6564 361.412i −0.189799 0.984773i −0.944452 0.328649i \(-0.893407\pi\)
0.754653 0.656124i \(-0.227805\pi\)
\(368\) −105.501 82.9673i −0.286689 0.225455i
\(369\) −72.3184 + 91.9603i −0.195985 + 0.249215i
\(370\) 830.613 160.088i 2.24490 0.432669i
\(371\) −134.224 12.8168i −0.361789 0.0345467i
\(372\) −100.949 174.848i −0.271367 0.470022i
\(373\) 362.264 + 209.153i 0.971217 + 0.560732i 0.899607 0.436700i \(-0.143853\pi\)
0.0716100 + 0.997433i \(0.477186\pi\)
\(374\) −826.730 + 1160.98i −2.21051 + 3.10422i
\(375\) 197.780 + 127.106i 0.527414 + 0.338948i
\(376\) −9.35818 9.81458i −0.0248888 0.0261026i
\(377\) 381.763 + 174.345i 1.01263 + 0.462454i
\(378\) 10.3520 35.2557i 0.0273863 0.0932691i
\(379\) −74.1146 + 384.543i −0.195553 + 1.01463i 0.742948 + 0.669349i \(0.233427\pi\)
−0.938501 + 0.345276i \(0.887785\pi\)
\(380\) 29.1212 25.2336i 0.0766347 0.0664043i
\(381\) −132.929 257.847i −0.348896 0.676764i
\(382\) −77.5901 224.182i −0.203116 0.586864i
\(383\) −157.568 393.586i −0.411405 1.02764i −0.978914 0.204273i \(-0.934517\pi\)
0.567509 0.823367i \(-0.307907\pi\)
\(384\) 198.452 + 189.223i 0.516802 + 0.492769i
\(385\) −171.170 + 41.5253i −0.444597 + 0.107858i
\(386\) 12.1889 23.6432i 0.0315775 0.0612519i
\(387\) 63.2237 + 9.09019i 0.163369 + 0.0234889i
\(388\) −27.4721 93.5614i −0.0708044 0.241138i
\(389\) 36.3333 3.46941i 0.0934017 0.00891879i −0.0482505 0.998835i \(-0.515365\pi\)
0.141652 + 0.989916i \(0.454759\pi\)
\(390\) 251.853 + 353.678i 0.645777 + 0.906867i
\(391\) −24.7687 519.958i −0.0633470 1.32982i
\(392\) 226.884 + 78.5253i 0.578785 + 0.200320i
\(393\) 192.449 27.6701i 0.489693 0.0704073i
\(394\) −105.456 230.917i −0.267655 0.586084i
\(395\) 249.391 + 99.8413i 0.631371 + 0.252763i
\(396\) 342.652 + 16.3225i 0.865283 + 0.0412185i
\(397\) 208.726 134.140i 0.525759 0.337885i −0.250687 0.968068i \(-0.580657\pi\)
0.776447 + 0.630183i \(0.217020\pi\)
\(398\) −241.350 58.5508i −0.606407 0.147113i
\(399\) −4.39672 + 5.07409i −0.0110194 + 0.0127170i
\(400\) 45.0808 35.4520i 0.112702 0.0886299i
\(401\) 559.163i 1.39442i −0.716867 0.697210i \(-0.754424\pi\)
0.716867 0.697210i \(-0.245576\pi\)
\(402\) −361.955 + 17.9995i −0.900384 + 0.0447750i
\(403\) −415.689 −1.03149
\(404\) 197.960 + 251.727i 0.490000 + 0.623086i
\(405\) −26.6156 23.0626i −0.0657175 0.0569446i
\(406\) −34.1081 + 140.595i −0.0840100 + 0.346294i
\(407\) −743.935 1157.59i −1.82785 2.84419i
\(408\) −10.3548 + 217.374i −0.0253794 + 0.532779i
\(409\) 59.8576 149.517i 0.146351 0.365567i −0.837021 0.547171i \(-0.815705\pi\)
0.983372 + 0.181604i \(0.0581289\pi\)
\(410\) 433.475 197.961i 1.05726 0.482832i
\(411\) 25.6319 + 178.274i 0.0623647 + 0.433756i
\(412\) −200.522 + 579.371i −0.486704 + 1.40624i
\(413\) 91.4963 4.35851i 0.221541 0.0105533i
\(414\) −173.025 + 123.210i −0.417934 + 0.297610i
\(415\) −19.2559 201.657i −0.0463998 0.485921i
\(416\) 794.720 233.351i 1.91039 0.560940i
\(417\) 7.68216 53.4306i 0.0184225 0.128131i
\(418\) −94.4546 48.6947i −0.225968 0.116495i
\(419\) 13.7093 + 56.5104i 0.0327190 + 0.134870i 0.985829 0.167756i \(-0.0536520\pi\)
−0.953110 + 0.302625i \(0.902137\pi\)
\(420\) −60.9218 + 63.8929i −0.145052 + 0.152126i
\(421\) 412.398 165.099i 0.979569 0.392160i 0.174054 0.984736i \(-0.444313\pi\)
0.805515 + 0.592576i \(0.201889\pi\)
\(422\) 395.504 136.885i 0.937213 0.324372i
\(423\) 6.60780 3.40656i 0.0156213 0.00805332i
\(424\) −213.392 246.267i −0.503282 0.580818i
\(425\) 218.411 + 42.0952i 0.513908 + 0.0990476i
\(426\) 663.444 + 194.805i 1.55738 + 0.457288i
\(427\) −78.2572 + 171.359i −0.183272 + 0.401310i
\(428\) 20.6799 19.7182i 0.0483174 0.0460706i
\(429\) 381.850 594.170i 0.890092 1.38501i
\(430\) −211.936 150.919i −0.492874 0.350974i
\(431\) 317.894 550.608i 0.737572 1.27751i −0.216013 0.976390i \(-0.569305\pi\)
0.953586 0.301122i \(-0.0973613\pi\)
\(432\) −26.6390 + 15.3800i −0.0616644 + 0.0356020i
\(433\) 37.8604 396.492i 0.0874375 0.915686i −0.840218 0.542249i \(-0.817573\pi\)
0.927655 0.373438i \(-0.121821\pi\)
\(434\) −27.1186 140.705i −0.0624853 0.324205i
\(435\) 108.996 + 85.7156i 0.250566 + 0.197047i
\(436\) 493.721 627.818i 1.13239 1.43995i
\(437\) 38.1109 7.34528i 0.0872104 0.0168084i
\(438\) −458.859 43.8157i −1.04762 0.100036i
\(439\) 427.257 + 740.032i 0.973252 + 1.68572i 0.685588 + 0.727990i \(0.259545\pi\)
0.287664 + 0.957732i \(0.407122\pi\)
\(440\) −368.641 212.835i −0.837820 0.483715i
\(441\) −76.3457 + 107.213i −0.173120 + 0.243112i
\(442\) 1237.33 + 795.186i 2.79940 + 1.79906i
\(443\) −147.637 154.837i −0.333267 0.349520i 0.535684 0.844419i \(-0.320054\pi\)
−0.868951 + 0.494898i \(0.835205\pi\)
\(444\) −627.365 286.508i −1.41298 0.645289i
\(445\) 40.4796 137.861i 0.0909655 0.309800i
\(446\) 42.6491 221.284i 0.0956257 0.496153i
\(447\) −90.3921 + 78.3252i −0.202220 + 0.175224i
\(448\) 106.262 + 206.120i 0.237193 + 0.460090i
\(449\) 282.058 + 814.952i 0.628191 + 1.81504i 0.577603 + 0.816318i \(0.303988\pi\)
0.0505873 + 0.998720i \(0.483891\pi\)
\(450\) −33.7333 84.2617i −0.0749629 0.187248i
\(451\) −561.028 534.939i −1.24396 1.18612i
\(452\) −328.250 + 79.6326i −0.726217 + 0.176178i
\(453\) −160.148 + 310.644i −0.353528 + 0.685748i
\(454\) −1184.15 170.255i −2.60826 0.375010i
\(455\) 51.2093 + 174.403i 0.112548 + 0.383303i
\(456\) −16.1524 + 1.54237i −0.0354219 + 0.00338238i
\(457\) 461.719 + 648.393i 1.01033 + 1.41880i 0.905516 + 0.424311i \(0.139484\pi\)
0.104809 + 0.994492i \(0.466577\pi\)
\(458\) −49.2933 1034.79i −0.107627 2.25938i
\(459\) −112.739 39.0193i −0.245619 0.0850095i
\(460\) 505.149 72.6295i 1.09815 0.157890i
\(461\) 245.726 + 538.066i 0.533029 + 1.16717i 0.964267 + 0.264933i \(0.0853497\pi\)
−0.431238 + 0.902238i \(0.641923\pi\)
\(462\) 226.029 + 90.4884i 0.489241 + 0.195862i
\(463\) 342.263 + 16.3040i 0.739229 + 0.0352138i 0.413819 0.910359i \(-0.364195\pi\)
0.325410 + 0.945573i \(0.394498\pi\)
\(464\) 101.886 65.4784i 0.219583 0.141117i
\(465\) −133.470 32.3794i −0.287031 0.0696330i
\(466\) 223.211 257.599i 0.478994 0.552788i
\(467\) −449.204 + 353.258i −0.961894 + 0.756442i −0.969894 0.243526i \(-0.921696\pi\)
0.00800057 + 0.999968i \(0.497453\pi\)
\(468\) 354.007i 0.756426i
\(469\) −145.657 42.4387i −0.310570 0.0904877i
\(470\) −30.2820 −0.0644298
\(471\) −117.928 149.958i −0.250379 0.318383i
\(472\) 167.302 + 144.968i 0.354454 + 0.307136i
\(473\) −99.7810 + 411.303i −0.210954 + 0.869562i
\(474\) −200.757 312.383i −0.423537 0.659036i
\(475\) −0.789123 + 16.5657i −0.00166131 + 0.0348752i
\(476\) −111.149 + 277.637i −0.233506 + 0.583271i
\(477\) 162.494 74.2084i 0.340658 0.155573i
\(478\) 21.4939 + 149.493i 0.0449662 + 0.312747i
\(479\) 25.3244 73.1699i 0.0528692 0.152756i −0.915475 0.402376i \(-0.868185\pi\)
0.968344 + 0.249620i \(0.0803057\pi\)
\(480\) 273.346 13.0211i 0.569470 0.0271272i
\(481\) −1156.71 + 823.689i −2.40480 + 1.71245i
\(482\) −79.2281 829.714i −0.164374 1.72140i
\(483\) −85.3206 + 25.0524i −0.176647 + 0.0518683i
\(484\) −224.427 + 1560.93i −0.463693 + 3.22506i
\(485\) −58.9584 30.3952i −0.121564 0.0626705i
\(486\) 11.4769 + 47.3086i 0.0236151 + 0.0973428i
\(487\) −131.789 + 138.216i −0.270614 + 0.283812i −0.844993 0.534778i \(-0.820395\pi\)
0.574379 + 0.818590i \(0.305244\pi\)
\(488\) −422.659 + 169.207i −0.866104 + 0.346736i
\(489\) −30.8996 + 10.6945i −0.0631894 + 0.0218701i
\(490\) 476.524 245.665i 0.972499 0.501358i
\(491\) −504.499 582.223i −1.02749 1.18579i −0.982397 0.186807i \(-0.940186\pi\)
−0.0450961 0.998983i \(-0.514359\pi\)
\(492\) −381.517 73.5314i −0.775441 0.149454i
\(493\) 450.697 + 132.337i 0.914193 + 0.268431i
\(494\) −45.5565 + 99.7549i −0.0922197 + 0.201933i
\(495\) 168.886 161.033i 0.341184 0.325319i
\(496\) −64.8542 + 100.915i −0.130754 + 0.203458i
\(497\) 235.792 + 167.907i 0.474431 + 0.337841i
\(498\) −140.008 + 242.502i −0.281142 + 0.486951i
\(499\) −95.7201 + 55.2640i −0.191824 + 0.110750i −0.592836 0.805323i \(-0.701992\pi\)
0.401012 + 0.916073i \(0.368658\pi\)
\(500\) −74.2200 + 777.267i −0.148440 + 1.55453i
\(501\) 77.5705 + 402.474i 0.154831 + 0.803341i
\(502\) −899.988 707.758i −1.79280 1.40988i
\(503\) 130.552 166.010i 0.259546 0.330040i −0.638763 0.769404i \(-0.720554\pi\)
0.898309 + 0.439364i \(0.144796\pi\)
\(504\) 36.5032 7.03541i 0.0724269 0.0139591i
\(505\) 216.858 + 20.7075i 0.429422 + 0.0410049i
\(506\) −703.726 1218.89i −1.39076 2.40887i
\(507\) −377.721 218.077i −0.745011 0.430132i
\(508\) 558.852 784.798i 1.10010 1.54488i
\(509\) −767.230 493.068i −1.50733 0.968700i −0.993866 0.110587i \(-0.964727\pi\)
−0.513461 0.858113i \(-0.671637\pi\)
\(510\) 335.344 + 351.698i 0.657537 + 0.689605i
\(511\) −175.530 80.1619i −0.343503 0.156873i
\(512\) 103.847 353.670i 0.202826 0.690763i
\(513\) 1.68341 8.73435i 0.00328150 0.0170260i
\(514\) 142.635 123.594i 0.277500 0.240455i
\(515\) 191.106 + 370.694i 0.371080 + 0.719794i
\(516\) 69.3819 + 200.466i 0.134461 + 0.388500i
\(517\) 18.3080 + 45.7312i 0.0354120 + 0.0884549i
\(518\) −354.269 337.794i −0.683916 0.652113i
\(519\) 481.915 116.911i 0.928546 0.225263i
\(520\) −201.289 + 390.446i −0.387094 + 0.750857i
\(521\) −350.462 50.3889i −0.672672 0.0967157i −0.202489 0.979284i \(-0.564903\pi\)
−0.470183 + 0.882569i \(0.655812\pi\)
\(522\) −54.0003 183.908i −0.103449 0.352315i
\(523\) 49.0381 4.68257i 0.0937630 0.00895328i −0.0480691 0.998844i \(-0.515307\pi\)
0.141832 + 0.989891i \(0.454701\pi\)
\(524\) 374.555 + 525.989i 0.714800 + 1.00380i
\(525\) −1.80795 37.9536i −0.00344372 0.0722926i
\(526\) 435.068 + 150.578i 0.827125 + 0.286271i
\(527\) −460.511 + 66.2115i −0.873835 + 0.125639i
\(528\) −84.6694 185.400i −0.160359 0.351137i
\(529\) −13.8833 5.55805i −0.0262445 0.0105067i
\(530\) −726.822 34.6228i −1.37136 0.0653261i
\(531\) −102.092 + 65.6108i −0.192264 + 0.123561i
\(532\) −21.6694 5.25695i −0.0407320 0.00988149i
\(533\) −523.867 + 604.575i −0.982865 + 1.13429i
\(534\) −156.117 + 122.772i −0.292355 + 0.229910i
\(535\) 19.4374i 0.0363316i
\(536\) −183.988 317.146i −0.343262 0.591690i
\(537\) −151.126 −0.281426
\(538\) −586.028 745.195i −1.08927 1.38512i
\(539\) −659.096 571.110i −1.22281 1.05957i
\(540\) 27.5748 113.665i 0.0510644 0.210490i
\(541\) −126.815 197.328i −0.234408 0.364746i 0.704044 0.710157i \(-0.251376\pi\)
−0.938452 + 0.345411i \(0.887740\pi\)
\(542\) 6.24070 131.009i 0.0115142 0.241713i
\(543\) 5.43787 13.5831i 0.0100145 0.0250150i
\(544\) 843.244 385.097i 1.55008 0.707898i
\(545\) −77.3217 537.784i −0.141875 0.986761i
\(546\) 82.1768 237.434i 0.150507 0.434861i
\(547\) 518.373 24.6931i 0.947665 0.0451428i 0.431945 0.901900i \(-0.357827\pi\)
0.515720 + 0.856757i \(0.327524\pi\)
\(548\) −487.245 + 346.966i −0.889134 + 0.633149i
\(549\) −23.7242 248.451i −0.0432135 0.452553i
\(550\) 577.044 169.435i 1.04917 0.308064i
\(551\) −4.98428 + 34.6664i −0.00904587 + 0.0629154i
\(552\) −191.012 98.4737i −0.346037 0.178394i
\(553\) −36.6492 151.070i −0.0662734 0.273183i
\(554\) −839.288 + 880.220i −1.51496 + 1.58884i
\(555\) −435.557 + 174.371i −0.784787 + 0.314181i
\(556\) 169.415 58.6350i 0.304703 0.105459i
\(557\) 235.945 121.638i 0.423600 0.218381i −0.233227 0.972422i \(-0.574928\pi\)
0.656827 + 0.754041i \(0.271898\pi\)
\(558\) 124.322 + 143.475i 0.222800 + 0.257124i
\(559\) 428.871 + 82.6581i 0.767211 + 0.147868i
\(560\) 50.3285 + 14.7778i 0.0898724 + 0.0263889i
\(561\) 328.383 719.059i 0.585353 1.28174i
\(562\) 902.161 860.209i 1.60527 1.53062i
\(563\) 323.364 503.165i 0.574359 0.893720i −0.425578 0.904922i \(-0.639929\pi\)
0.999937 + 0.0112014i \(0.00356558\pi\)
\(564\) 20.1119 + 14.3216i 0.0356593 + 0.0253929i
\(565\) −114.885 + 198.986i −0.203336 + 0.352188i
\(566\) −823.461 + 475.425i −1.45488 + 0.839974i
\(567\) −1.93719 + 20.2872i −0.00341657 + 0.0357799i
\(568\) 132.393 + 686.919i 0.233086 + 1.20936i
\(569\) 89.2324 + 70.1731i 0.156823 + 0.123327i 0.693487 0.720469i \(-0.256073\pi\)
−0.536664 + 0.843796i \(0.680316\pi\)
\(570\) −22.3975 + 28.4808i −0.0392939 + 0.0499663i
\(571\) −36.4515 + 7.02545i −0.0638380 + 0.0123038i −0.221070 0.975258i \(-0.570955\pi\)
0.157232 + 0.987562i \(0.449743\pi\)
\(572\) 2335.06 + 222.971i 4.08227 + 0.389810i
\(573\) 65.7876 + 113.948i 0.114813 + 0.198861i
\(574\) −238.816 137.881i −0.416056 0.240210i
\(575\) −127.411 + 178.923i −0.221584 + 0.311171i
\(576\) −258.462 166.103i −0.448718 0.288374i
\(577\) −667.033 699.564i −1.15604 1.21242i −0.973370 0.229241i \(-0.926376\pi\)
−0.182667 0.983175i \(-0.558473\pi\)
\(578\) 676.456 + 308.927i 1.17034 + 0.534476i
\(579\) −4.15650 + 14.1557i −0.00717876 + 0.0244486i
\(580\) −87.1533 + 452.194i −0.150264 + 0.779646i
\(581\) −88.5926 + 76.7659i −0.152483 + 0.132127i
\(582\) 42.0150 + 81.4977i 0.0721907 + 0.140030i
\(583\) 387.138 + 1118.56i 0.664044 + 1.91863i
\(584\) −173.325 432.946i −0.296790 0.741345i
\(585\) −174.285 166.181i −0.297924 0.284070i
\(586\) −224.513 + 54.4663i −0.383128 + 0.0929459i
\(587\) −110.699 + 214.727i −0.188585 + 0.365804i −0.964106 0.265518i \(-0.914457\pi\)
0.775521 + 0.631322i \(0.217487\pi\)
\(588\) −432.670 62.2085i −0.735833 0.105797i
\(589\) −9.77303 33.2839i −0.0165926 0.0565091i
\(590\) 492.090 46.9889i 0.834052 0.0796423i
\(591\) 81.6707 + 114.690i 0.138191 + 0.194062i
\(592\) 19.4983 + 409.319i 0.0329362 + 0.691417i
\(593\) −538.123 186.246i −0.907458 0.314074i −0.166827 0.985986i \(-0.553352\pi\)
−0.740631 + 0.671912i \(0.765473\pi\)
\(594\) −319.280 + 45.9055i −0.537508 + 0.0772820i
\(595\) 84.5102 + 185.051i 0.142034 + 0.311011i
\(596\) −368.772 147.634i −0.618746 0.247708i
\(597\) 137.587 + 6.55409i 0.230465 + 0.0109784i
\(598\) −1221.88 + 785.253i −2.04327 + 1.31313i
\(599\) −579.661 140.624i −0.967715 0.234765i −0.279398 0.960175i \(-0.590135\pi\)
−0.688317 + 0.725410i \(0.741650\pi\)
\(600\) 60.1343 69.3987i 0.100224 0.115664i
\(601\) 232.401 182.762i 0.386690 0.304097i −0.405823 0.913952i \(-0.633015\pi\)
0.792513 + 0.609855i \(0.208772\pi\)
\(602\) 150.559i 0.250098i
\(603\) 195.235 47.7953i 0.323772 0.0792625i
\(604\) −1160.72 −1.92172
\(605\) 663.126 + 843.233i 1.09608 + 1.39377i
\(606\) −227.575 197.195i −0.375536 0.325404i
\(607\) 191.818 790.687i 0.316011 1.30261i −0.563255 0.826283i \(-0.690451\pi\)
0.879266 0.476331i \(-0.158034\pi\)
\(608\) 37.3685 + 58.1464i 0.0614613 + 0.0956356i
\(609\) 3.81801 80.1498i 0.00626930 0.131609i
\(610\) −377.843 + 943.805i −0.619414 + 1.54722i
\(611\) 46.2407 21.1174i 0.0756804 0.0345621i
\(612\) −56.3868 392.179i −0.0921353 0.640815i
\(613\) 96.7154 279.441i 0.157774 0.455858i −0.838215 0.545341i \(-0.816400\pi\)
0.995988 + 0.0894831i \(0.0285215\pi\)
\(614\) 1084.66 51.6686i 1.76654 0.0841508i
\(615\) −215.296 + 153.311i −0.350074 + 0.249287i
\(616\) 23.4146 + 245.209i 0.0380107 + 0.398067i
\(617\) 268.868 78.9466i 0.435766 0.127952i −0.0564896 0.998403i \(-0.517991\pi\)
0.492255 + 0.870451i \(0.336173\pi\)
\(618\) 82.0434 570.625i 0.132756 0.923341i
\(619\) −231.906 119.556i −0.374646 0.193143i 0.260612 0.965444i \(-0.416076\pi\)
−0.635258 + 0.772300i \(0.719106\pi\)
\(620\) −107.536 443.269i −0.173445 0.714950i
\(621\) 81.2983 85.2632i 0.130915 0.137300i
\(622\) 1421.34 569.018i 2.28511 0.914820i
\(623\) −78.5718 + 27.1940i −0.126118 + 0.0436500i
\(624\) −186.953 + 96.3810i −0.299604 + 0.154457i
\(625\) 189.217 + 218.368i 0.302748 + 0.349389i
\(626\) 1007.32 + 194.146i 1.60914 + 0.310137i
\(627\) 56.5522 + 16.6052i 0.0901948 + 0.0264836i
\(628\) 263.200 576.328i 0.419109 0.917720i
\(629\) −1150.24 + 1096.75i −1.82867 + 1.74364i
\(630\) 44.8799 69.8345i 0.0712379 0.110848i
\(631\) 888.646 + 632.802i 1.40831 + 1.00286i 0.995766 + 0.0919204i \(0.0293005\pi\)
0.412548 + 0.910936i \(0.364639\pi\)
\(632\) 187.843 325.353i 0.297219 0.514799i
\(633\) −201.027 + 116.063i −0.317578 + 0.183354i
\(634\) 110.831 1160.67i 0.174812 1.83071i
\(635\) −124.032 643.541i −0.195326 1.01345i
\(636\) 466.346 + 366.739i 0.733248 + 0.576633i
\(637\) −556.337 + 707.440i −0.873371 + 1.11058i
\(638\) 1247.08 240.356i 1.95468 0.376733i
\(639\) −381.766 36.4542i −0.597443 0.0570489i
\(640\) 309.743 + 536.491i 0.483973 + 0.838266i
\(641\) −87.8381 50.7134i −0.137033 0.0791160i 0.429916 0.902869i \(-0.358543\pi\)
−0.566949 + 0.823753i \(0.691876\pi\)
\(642\) −15.5851 + 21.8862i −0.0242758 + 0.0340906i
\(643\) 368.663 + 236.926i 0.573349 + 0.368469i 0.794956 0.606667i \(-0.207494\pi\)
−0.221607 + 0.975136i \(0.571130\pi\)
\(644\) −203.796 213.736i −0.316454 0.331887i
\(645\) 131.264 + 59.9460i 0.203509 + 0.0929396i
\(646\) −34.5797 + 117.768i −0.0535289 + 0.182303i
\(647\) −40.6760 + 211.047i −0.0628687 + 0.326194i −0.999723 0.0235255i \(-0.992511\pi\)
0.936855 + 0.349719i \(0.113723\pi\)
\(648\) −37.2219 + 32.2530i −0.0574413 + 0.0497731i
\(649\) −368.471 714.734i −0.567752 1.10129i
\(650\) −202.989 586.497i −0.312290 0.902304i
\(651\) 29.5382 + 73.7828i 0.0453735 + 0.113338i
\(652\) −78.5932 74.9385i −0.120542 0.114936i
\(653\) −361.960 + 87.8105i −0.554303 + 0.134472i −0.503119 0.864217i \(-0.667814\pi\)
−0.0511833 + 0.998689i \(0.516299\pi\)
\(654\) −344.137 + 667.532i −0.526203 + 1.02069i
\(655\) 434.783 + 62.5123i 0.663790 + 0.0954386i
\(656\) 65.0384 + 221.501i 0.0991440 + 0.337653i
\(657\) 254.498 24.3016i 0.387364 0.0369888i
\(658\) 10.1646 + 14.2742i 0.0154477 + 0.0216933i
\(659\) 8.10267 + 170.096i 0.0122954 + 0.258112i 0.996643 + 0.0818731i \(0.0260902\pi\)
−0.984347 + 0.176239i \(0.943607\pi\)
\(660\) 732.374 + 253.477i 1.10966 + 0.384056i
\(661\) −449.329 + 64.6037i −0.679771 + 0.0977363i −0.473547 0.880769i \(-0.657027\pi\)
−0.206224 + 0.978505i \(0.566118\pi\)
\(662\) 804.663 + 1761.97i 1.21550 + 2.66158i
\(663\) −757.331 303.190i −1.14228 0.457300i
\(664\) −282.980 13.4800i −0.426174 0.0203012i
\(665\) −12.7603 + 8.20058i −0.0191885 + 0.0123317i
\(666\) 630.240 + 152.895i 0.946307 + 0.229572i
\(667\) −303.762 + 350.560i −0.455415 + 0.525577i
\(668\) −1070.03 + 841.479i −1.60184 + 1.25970i
\(669\) 124.990i 0.186832i
\(670\) −796.062 191.363i −1.18815 0.285617i
\(671\) 1653.75 2.46460
\(672\) −97.8902 124.477i −0.145670 0.185234i
\(673\) −76.5591 66.3388i −0.113758 0.0985718i 0.596124 0.802892i \(-0.296706\pi\)
−0.709882 + 0.704320i \(0.751252\pi\)
\(674\) −240.035 + 989.438i −0.356135 + 1.46801i
\(675\) 27.2160 + 42.3490i 0.0403200 + 0.0627392i
\(676\) 68.9235 1446.88i 0.101958 2.14036i
\(677\) 2.23571 5.58453i 0.00330238 0.00824894i −0.926708 0.375783i \(-0.877374\pi\)
0.930010 + 0.367534i \(0.119798\pi\)
\(678\) 288.907 131.939i 0.426116 0.194601i
\(679\) 5.46273 + 37.9941i 0.00804525 + 0.0559560i
\(680\) −160.802 + 464.608i −0.236474 + 0.683247i
\(681\) 662.770 31.5716i 0.973230 0.0463607i
\(682\) −1024.68 + 729.671i −1.50246 + 1.06990i
\(683\) 69.2186 + 724.890i 0.101345 + 1.06133i 0.892906 + 0.450242i \(0.148662\pi\)
−0.791561 + 0.611090i \(0.790731\pi\)
\(684\) 28.3451 8.32287i 0.0414402 0.0121679i
\(685\) −57.9077 + 402.757i −0.0845368 + 0.587966i
\(686\) −583.733 300.935i −0.850923 0.438681i
\(687\) 135.463 + 558.385i 0.197180 + 0.812788i
\(688\) 86.9774 91.2193i 0.126421 0.132586i
\(689\) 1134.00 453.987i 1.64587 0.658907i
\(690\) −453.487 + 156.953i −0.657227 + 0.227468i
\(691\) −768.639 + 396.261i −1.11236 + 0.573460i −0.913610 0.406591i \(-0.866718\pi\)
−0.198747 + 0.980051i \(0.563687\pi\)
\(692\) 1078.51 + 1244.66i 1.55854 + 1.79865i
\(693\) −132.596 25.5558i −0.191336 0.0368770i
\(694\) −896.548 263.250i −1.29186 0.379323i
\(695\) 50.6607 110.931i 0.0728930 0.159613i
\(696\) 140.346 133.820i 0.201647 0.192270i
\(697\) −484.057 + 753.207i −0.694486 + 1.08064i
\(698\) 498.497 + 354.978i 0.714179 + 0.508564i
\(699\) −94.5241 + 163.721i −0.135228 + 0.234221i
\(700\) 109.285 63.0959i 0.156122 0.0901370i
\(701\) 61.8951 648.195i 0.0882955 0.924672i −0.837447 0.546518i \(-0.815953\pi\)
0.925743 0.378154i \(-0.123441\pi\)
\(702\) 62.9971 + 326.860i 0.0897394 + 0.465612i
\(703\) −93.1469 73.2516i −0.132499 0.104199i
\(704\) 1258.42 1600.21i 1.78753 2.27303i
\(705\) 16.4919 3.17855i 0.0233928 0.00450859i
\(706\) 2128.55 + 203.252i 3.01494 + 0.287892i
\(707\) −63.0307 109.172i −0.0891523 0.154416i
\(708\) −349.046 201.522i −0.493003 0.284635i
\(709\) 656.673 922.168i 0.926196 1.30066i −0.0274170 0.999624i \(-0.508728\pi\)
0.953613 0.301036i \(-0.0973324\pi\)
\(710\) 1314.15 + 844.553i 1.85091 + 1.18951i
\(711\) 142.123 + 149.055i 0.199892 + 0.209641i
\(712\) −182.780 83.4727i −0.256713 0.117237i
\(713\) 129.438 440.825i 0.181540 0.618268i
\(714\) 53.2188 276.125i 0.0745361 0.386730i
\(715\) 1205.92 1044.93i 1.68659 1.46144i
\(716\) −229.987 446.113i −0.321212 0.623063i
\(717\) −27.3973 79.1594i −0.0382110 0.110404i
\(718\) −684.169 1708.97i −0.952882 2.38018i
\(719\) 1011.59 + 964.550i 1.40694 + 1.34152i 0.865621 + 0.500700i \(0.166924\pi\)
0.541321 + 0.840816i \(0.317924\pi\)
\(720\) −67.5344 + 16.3837i −0.0937978 + 0.0227551i
\(721\) 110.588 214.511i 0.153382 0.297519i
\(722\) 1106.83 + 159.137i 1.53300 + 0.220412i
\(723\) 130.239 + 443.554i 0.180137 + 0.613491i
\(724\) 48.3721 4.61897i 0.0668122 0.00637980i
\(725\) −114.971 161.454i −0.158581 0.222695i
\(726\) −70.5565 1481.16i −0.0971853 2.04017i
\(727\) 343.513 + 118.891i 0.472507 + 0.163536i 0.552935 0.833224i \(-0.313508\pi\)
−0.0804284 + 0.996760i \(0.525629\pi\)
\(728\) 251.612 36.1763i 0.345621 0.0496928i
\(729\) −11.2162 24.5601i −0.0153857 0.0336901i
\(730\) −966.776 387.039i −1.32435 0.530190i
\(731\) 488.281 + 23.2597i 0.667963 + 0.0318190i
\(732\) 697.309 448.133i 0.952607 0.612204i
\(733\) −635.914 154.271i −0.867549 0.210465i −0.222805 0.974863i \(-0.571521\pi\)
−0.644745 + 0.764398i \(0.723036\pi\)
\(734\) −752.707 + 868.671i −1.02549 + 1.18348i
\(735\) −233.734 + 183.810i −0.318005 + 0.250082i
\(736\) 915.437i 1.24380i
\(737\) 192.293 + 1317.89i 0.260913 + 1.78818i
\(738\) 365.345 0.495048
\(739\) −52.5984 66.8843i −0.0711751 0.0905065i 0.749162 0.662387i \(-0.230457\pi\)
−0.820337 + 0.571880i \(0.806214\pi\)
\(740\) −1177.57 1020.37i −1.59132 1.37888i
\(741\) 14.3398 59.1094i 0.0193519 0.0797697i
\(742\) 227.648 + 354.227i 0.306803 + 0.477395i
\(743\) 11.1168 233.371i 0.0149621 0.314093i −0.978963 0.204037i \(-0.934594\pi\)
0.993925 0.110056i \(-0.0351032\pi\)
\(744\) −71.3857 + 178.313i −0.0959485 + 0.239668i
\(745\) −245.795 + 112.251i −0.329927 + 0.150672i
\(746\) −185.909 1293.02i −0.249207 1.73327i
\(747\) 50.7958 146.765i 0.0679998 0.196472i
\(748\) 2622.36 124.918i 3.50583 0.167003i
\(749\) −9.16230 + 6.52445i −0.0122327 + 0.00871088i
\(750\) −69.7896 730.869i −0.0930528 0.974492i
\(751\) −1219.38 + 358.043i −1.62368 + 0.476756i −0.962004 0.273034i \(-0.911973\pi\)
−0.661676 + 0.749790i \(0.730155\pi\)
\(752\) 2.08771 14.5203i 0.00277621 0.0193090i
\(753\) 564.432 + 290.985i 0.749578 + 0.386434i
\(754\) −308.995 1273.69i −0.409807 1.68925i
\(755\) −544.873 + 571.447i −0.721687 + 0.756883i
\(756\) −62.8346 + 25.1552i −0.0831146 + 0.0332741i
\(757\) 718.854 248.798i 0.949610 0.328663i 0.192018 0.981391i \(-0.438497\pi\)
0.757592 + 0.652728i \(0.226376\pi\)
\(758\) 1087.03 560.403i 1.43408 0.739317i
\(759\) 511.197 + 589.953i 0.673514 + 0.777277i
\(760\) −35.9951 6.93748i −0.0473620 0.00912827i
\(761\) −1169.05 343.265i −1.53621 0.451071i −0.599264 0.800551i \(-0.704540\pi\)
−0.936944 + 0.349480i \(0.886358\pi\)
\(762\) −376.338 + 824.065i −0.493881 + 1.08145i
\(763\) −227.544 + 216.963i −0.298223 + 0.284355i
\(764\) −236.248 + 367.609i −0.309225 + 0.481164i
\(765\) −219.548 156.339i −0.286990 0.204365i
\(766\) −661.980 + 1146.58i −0.864203 + 1.49684i
\(767\) −718.655 + 414.916i −0.936969 + 0.540959i
\(768\) 13.9526 146.118i 0.0181675 0.190258i
\(769\) 122.031 + 633.159i 0.158689 + 0.823354i 0.970807 + 0.239862i \(0.0771021\pi\)
−0.812119 + 0.583493i \(0.801686\pi\)
\(770\) 432.366 + 340.016i 0.561514 + 0.441580i
\(771\) −64.7073 + 82.2821i −0.0839265 + 0.106721i
\(772\) −48.1123 + 9.27289i −0.0623217 + 0.0120115i
\(773\) −939.434 89.7051i −1.21531 0.116048i −0.532363 0.846516i \(-0.678696\pi\)
−0.682947 + 0.730468i \(0.739302\pi\)
\(774\) −99.7351 172.746i −0.128857 0.223186i
\(775\) 170.015 + 98.1584i 0.219375 + 0.126656i
\(776\) −53.8094 + 75.5647i −0.0693420 + 0.0973771i
\(777\) 228.395 + 146.780i 0.293944 + 0.188907i
\(778\) −78.6555 82.4916i −0.101100 0.106030i
\(779\) −60.7242 27.7318i −0.0779515 0.0355992i
\(780\) 225.323 767.378i 0.288875 0.983818i
\(781\) 480.910 2495.20i 0.615762 3.19488i
\(782\) −1228.55 + 1064.55i −1.57104 + 1.36131i
\(783\) 48.7130 + 94.4901i 0.0622133 + 0.120677i
\(784\) 84.9448 + 245.432i 0.108348 + 0.313051i
\(785\) −160.185 400.123i −0.204058 0.509711i
\(786\) −439.434 419.000i −0.559076 0.533078i
\(787\) −181.704 + 44.0808i −0.230881 + 0.0560112i −0.349530 0.936925i \(-0.613659\pi\)
0.118649 + 0.992936i \(0.462144\pi\)
\(788\) −214.270 + 415.626i −0.271916 + 0.527444i
\(789\) −252.748 36.3396i −0.320339 0.0460578i
\(790\) −236.349 804.930i −0.299176 1.01890i
\(791\) 132.360 12.6388i 0.167332 0.0159783i
\(792\) −189.299 265.833i −0.239014 0.335648i
\(793\) −81.2041 1704.68i −0.102401 2.14967i
\(794\) −732.213 253.422i −0.922183 0.319171i
\(795\) 399.469 57.4350i 0.502477 0.0722452i
\(796\) 190.037 + 416.123i 0.238740 + 0.522768i
\(797\) −510.687 204.448i −0.640762 0.256522i 0.0284484 0.999595i \(-0.490943\pi\)
−0.669211 + 0.743073i \(0.733368\pi\)
\(798\) 20.9432 + 0.997647i 0.0262446 + 0.00125018i
\(799\) 47.8631 30.7598i 0.0599038 0.0384978i
\(800\) −380.140 92.2210i −0.475175 0.115276i
\(801\) 72.1363 83.2497i 0.0900578 0.103932i
\(802\) −1372.60 + 1079.43i −1.71147 + 1.34592i
\(803\) 1694.00i 2.10959i
\(804\) 438.202 + 503.584i 0.545028 + 0.626349i
\(805\) −200.894 −0.249558
\(806\) 802.460 + 1020.41i 0.995608 + 1.26602i
\(807\) 397.376 + 344.328i 0.492411 + 0.426677i
\(808\) 71.8254 296.068i 0.0888928 0.366421i
\(809\) −411.676 640.580i −0.508870 0.791817i 0.487834 0.872936i \(-0.337787\pi\)
−0.996704 + 0.0811189i \(0.974151\pi\)
\(810\) −5.23305 + 109.855i −0.00646056 + 0.135624i
\(811\) 252.472 630.644i 0.311309 0.777613i −0.687374 0.726304i \(-0.741236\pi\)
0.998683 0.0513088i \(-0.0163393\pi\)
\(812\) 242.407 110.704i 0.298531 0.136335i
\(813\) 10.3526 + 72.0036i 0.0127338 + 0.0885653i
\(814\) −1405.46 + 4060.81i −1.72661 + 4.98871i
\(815\) −73.7877 + 3.51494i −0.0905370 + 0.00431281i
\(816\) −191.760 + 136.552i −0.235000 + 0.167343i
\(817\) 3.46458 + 36.2827i 0.00424061 + 0.0444097i
\(818\) −482.578 + 141.698i −0.589948 + 0.173224i
\(819\) −19.8320 + 137.935i −0.0242149 + 0.168419i
\(820\) −780.209 402.226i −0.951474 0.490519i
\(821\) 140.138 + 577.656i 0.170692 + 0.703601i 0.991246 + 0.132032i \(0.0421500\pi\)
−0.820554 + 0.571569i \(0.806335\pi\)
\(822\) 388.136 407.066i 0.472185 0.495214i
\(823\) 995.892 398.695i 1.21007 0.484441i 0.323147 0.946349i \(-0.395259\pi\)
0.886928 + 0.461908i \(0.152835\pi\)
\(824\) 551.174 190.763i 0.668901 0.231509i
\(825\) −296.479 + 152.846i −0.359369 + 0.185267i
\(826\) −187.327 216.187i −0.226788 0.261727i
\(827\) −568.347 109.540i −0.687239 0.132455i −0.166335 0.986069i \(-0.553193\pi\)
−0.520905 + 0.853615i \(0.674405\pi\)
\(828\) 375.414 + 110.231i 0.453398 + 0.133130i
\(829\) −230.365 + 504.429i −0.277883 + 0.608479i −0.996186 0.0872510i \(-0.972192\pi\)
0.718303 + 0.695730i \(0.244919\pi\)
\(830\) −457.845 + 436.555i −0.551621 + 0.525969i
\(831\) 364.692 567.472i 0.438860 0.682879i
\(832\) −1711.29 1218.61i −2.05684 1.46467i
\(833\) −503.643 + 872.335i −0.604614 + 1.04722i
\(834\) −145.989 + 84.2865i −0.175046 + 0.101063i
\(835\) −88.0223 + 921.811i −0.105416 + 1.10397i
\(836\) 37.0452 + 192.209i 0.0443124 + 0.229915i
\(837\) −82.7670 65.0887i −0.0988853 0.0777643i
\(838\) 112.254 142.742i 0.133954 0.170337i
\(839\) 614.636 118.461i 0.732581 0.141193i 0.190700 0.981648i \(-0.438924\pi\)
0.541881 + 0.840455i \(0.317712\pi\)
\(840\) 83.6055 + 7.98336i 0.0995304 + 0.00950400i
\(841\) 211.216 + 365.837i 0.251148 + 0.435002i
\(842\) −1201.39 693.620i −1.42682 0.823777i
\(843\) −401.034 + 563.174i −0.475723 + 0.668059i
\(844\) −648.540 416.791i −0.768412 0.493828i
\(845\) −679.977 713.139i −0.804706 0.843952i
\(846\) −21.1182 9.64434i −0.0249624 0.0113999i
\(847\) 174.891 595.624i 0.206483 0.703216i
\(848\) 66.7105 346.127i 0.0786680 0.408169i
\(849\) 398.562 345.356i 0.469449 0.406780i
\(850\) −318.295 617.405i −0.374464 0.726359i
\(851\) −513.318 1483.14i −0.603194 1.74282i
\(852\) −473.372 1182.43i −0.555601 1.38782i
\(853\) −924.828 881.822i −1.08421 1.03379i −0.999300 0.0373996i \(-0.988093\pi\)
−0.0849059 0.996389i \(-0.527059\pi\)
\(854\) 571.714 138.696i 0.669455 0.162408i
\(855\) 9.20844 17.8619i 0.0107701 0.0208911i
\(856\) −26.9065 3.86858i −0.0314329 0.00451936i
\(857\) 78.4922 + 267.320i 0.0915895 + 0.311925i 0.992527 0.122023i \(-0.0389382\pi\)
−0.900938 + 0.433948i \(0.857120\pi\)
\(858\) −2195.67 + 209.661i −2.55906 + 0.244360i
\(859\) 911.512 + 1280.04i 1.06113 + 1.49015i 0.859803 + 0.510627i \(0.170587\pi\)
0.201329 + 0.979524i \(0.435474\pi\)
\(860\) 22.8037 + 478.709i 0.0265160 + 0.556638i
\(861\) 144.534 + 50.0238i 0.167868 + 0.0580997i
\(862\) −1965.28 + 282.564i −2.27990 + 0.327801i
\(863\) 62.8434 + 137.608i 0.0728197 + 0.159453i 0.942541 0.334090i \(-0.108429\pi\)
−0.869722 + 0.493543i \(0.835702\pi\)
\(864\) 194.773 + 77.9755i 0.225432 + 0.0902494i
\(865\) 1119.06 + 53.3072i 1.29371 + 0.0616268i
\(866\) −1046.38 + 672.465i −1.20829 + 0.776518i
\(867\) −400.832 97.2407i −0.462320 0.112158i
\(868\) −172.850 + 199.479i −0.199136 + 0.229815i
\(869\) −1072.69 + 843.575i −1.23440 + 0.970742i
\(870\) 433.027i 0.497732i
\(871\) 1349.04 262.928i 1.54884 0.301869i
\(872\) −759.826 −0.871360
\(873\) −31.4362 39.9744i −0.0360094 0.0457897i
\(874\) −91.6014 79.3731i −0.104807 0.0908159i
\(875\) 72.4626 298.695i 0.0828145 0.341366i
\(876\) 459.040 + 714.280i 0.524018 + 0.815388i
\(877\) 3.93247 82.5527i 0.00448400 0.0941308i −0.995516 0.0945945i \(-0.969845\pi\)
1.00000 0.000463675i \(0.000147592\pi\)
\(878\) 991.798 2477.39i 1.12961 2.82163i
\(879\) 116.555 53.2289i 0.132600 0.0605562i
\(880\) −65.5315 455.781i −0.0744676 0.517934i
\(881\) −317.950 + 918.656i −0.360897 + 1.04274i 0.607713 + 0.794157i \(0.292087\pi\)
−0.968610 + 0.248586i \(0.920034\pi\)
\(882\) 410.560 19.5574i 0.465488 0.0221739i
\(883\) −415.766 + 296.065i −0.470856 + 0.335295i −0.790730 0.612165i \(-0.790299\pi\)
0.319874 + 0.947460i \(0.396359\pi\)
\(884\) −257.532 2696.99i −0.291326 3.05090i
\(885\) −263.065 + 77.2429i −0.297249 + 0.0872801i
\(886\) −95.0829 + 661.316i −0.107317 + 0.746406i
\(887\) 211.257 + 108.910i 0.238170 + 0.122785i 0.573180 0.819429i \(-0.305709\pi\)
−0.335010 + 0.942214i \(0.608740\pi\)
\(888\) 154.688 + 637.631i 0.174198 + 0.718053i
\(889\) −261.716 + 274.479i −0.294393 + 0.308751i
\(890\) −416.557 + 166.764i −0.468042 + 0.187376i
\(891\) 169.065 58.5138i 0.189747 0.0656721i
\(892\) −368.963 + 190.214i −0.413636 + 0.213244i
\(893\) 2.77800 + 3.20598i 0.00311086 + 0.00359012i
\(894\) 366.765 + 70.6881i 0.410251 + 0.0790695i
\(895\) −327.594 96.1902i −0.366026 0.107475i
\(896\) 148.918 326.086i 0.166204 0.363935i
\(897\) 583.022 555.911i 0.649969 0.619745i
\(898\) 1456.01 2265.59i 1.62139 2.52293i
\(899\) 337.706 + 240.479i 0.375646 + 0.267496i
\(900\) −83.5933 + 144.788i −0.0928815 + 0.160875i
\(901\) 1183.97 683.565i 1.31406 0.758673i
\(902\) −230.112 + 2409.85i −0.255113 + 2.67167i
\(903\) −15.8034 81.9961i −0.0175011 0.0908041i
\(904\) 252.585 + 198.635i 0.279408 + 0.219729i
\(905\) 20.4332 25.9829i 0.0225781 0.0287104i
\(906\) 1071.71 206.555i 1.18290 0.227985i
\(907\) −627.152 59.8858i −0.691458 0.0660262i −0.256590 0.966520i \(-0.582599\pi\)
−0.434868 + 0.900494i \(0.643205\pi\)
\(908\) 1101.82 + 1908.41i 1.21346 + 2.10177i
\(909\) 144.638 + 83.5069i 0.159118 + 0.0918668i
\(910\) 329.259 462.379i 0.361823 0.508109i
\(911\) 387.215 + 248.848i 0.425044 + 0.273159i 0.735627 0.677387i \(-0.236888\pi\)
−0.310583 + 0.950546i \(0.600524\pi\)
\(912\) −12.1125 12.7032i −0.0132813 0.0139290i
\(913\) 936.079 + 427.493i 1.02528 + 0.468229i
\(914\) 700.324 2385.08i 0.766218 2.60950i
\(915\) 106.710 553.666i 0.116623 0.605099i
\(916\) −1442.17 + 1249.64i −1.57442 + 1.36424i
\(917\) −116.474 225.929i −0.127017 0.246378i
\(918\) 121.853 + 352.070i 0.132737 + 0.383518i
\(919\) 310.361 + 775.245i 0.337716 + 0.843574i 0.995878 + 0.0906980i \(0.0289098\pi\)
−0.658162 + 0.752876i \(0.728666\pi\)
\(920\) −351.378 335.038i −0.381932 0.364172i
\(921\) −585.292 + 141.990i −0.635496 + 0.154170i
\(922\) 846.457 1641.90i 0.918066 1.78080i
\(923\) −2595.67 373.200i −2.81221 0.404334i
\(924\) −126.349 430.306i −0.136742 0.465699i
\(925\) 667.592 63.7473i 0.721721 0.0689160i
\(926\) −620.694 871.642i −0.670296 0.941299i
\(927\) 15.2139 + 319.380i 0.0164120 + 0.344530i
\(928\) −780.626 270.177i −0.841192 0.291139i
\(929\) 1738.62 249.976i 1.87150 0.269081i 0.889355 0.457217i \(-0.151154\pi\)
0.982143 + 0.188137i \(0.0602448\pi\)
\(930\) 178.171 + 390.140i 0.191582 + 0.419505i
\(931\) −69.7239 27.9132i −0.0748914 0.0299820i
\(932\) −627.142 29.8744i −0.672899 0.0320541i
\(933\) −714.348 + 459.084i −0.765647 + 0.492051i
\(934\) 1734.32 + 420.741i 1.85687 + 0.450472i
\(935\) 1169.51 1349.68i 1.25081 1.44351i
\(936\) −264.726 + 208.183i −0.282827 + 0.222418i
\(937\) 1324.46i 1.41351i −0.707457 0.706756i \(-0.750158\pi\)
0.707457 0.706756i \(-0.249842\pi\)
\(938\) 177.006 + 439.477i 0.188705 + 0.468526i
\(939\) −568.977 −0.605940
\(940\) 34.4807 + 43.8458i 0.0366816 + 0.0466445i
\(941\) −306.140 265.272i −0.325335 0.281904i 0.476844 0.878988i \(-0.341781\pi\)
−0.802179 + 0.597084i \(0.796326\pi\)
\(942\) −140.456 + 578.969i −0.149104 + 0.614617i
\(943\) −478.010 743.798i −0.506903 0.788757i
\(944\) −11.3944 + 239.199i −0.0120704 + 0.253388i
\(945\) −17.1119 + 42.7434i −0.0181078 + 0.0452311i
\(946\) 1202.27 549.056i 1.27089 0.580398i
\(947\) −67.3485 468.419i −0.0711178 0.494635i −0.993985 0.109517i \(-0.965070\pi\)
0.922867 0.385118i \(-0.125839\pi\)
\(948\) −223.712 + 646.375i −0.235984 + 0.681830i
\(949\) 1746.17 83.1805i 1.84001 0.0876507i
\(950\) 42.1880 30.0420i 0.0444085 0.0316231i
\(951\) 61.4704 + 643.747i 0.0646376 + 0.676916i
\(952\) 272.980 80.1542i 0.286744 0.0841956i
\(953\) 22.8666 159.041i 0.0239943 0.166884i −0.974301 0.225250i \(-0.927680\pi\)
0.998295 + 0.0583661i \(0.0185891\pi\)
\(954\) −495.846 255.627i −0.519755 0.267952i
\(955\) 70.0806 + 288.876i 0.0733828 + 0.302488i
\(956\) 191.979 201.342i 0.200815 0.210609i
\(957\) −653.946 + 261.801i −0.683329 + 0.273564i
\(958\) −228.501 + 79.0849i −0.238519 + 0.0825521i
\(959\) 209.287 107.895i 0.218235 0.112508i
\(960\) −454.542 524.569i −0.473481 0.546426i
\(961\) 540.428 + 104.159i 0.562360 + 0.108386i
\(962\) 4254.90 + 1249.35i 4.42298 + 1.29870i
\(963\) 6.19050 13.5553i 0.00642835 0.0140761i
\(964\) −1111.14 + 1059.47i −1.15264 + 1.09904i
\(965\) −18.0200 + 28.0397i −0.0186736 + 0.0290567i
\(966\) 226.203 + 161.079i 0.234165 + 0.166748i
\(967\) −322.905 + 559.288i −0.333925 + 0.578375i −0.983278 0.182112i \(-0.941706\pi\)
0.649353 + 0.760487i \(0.275040\pi\)
\(968\) 1299.24 750.116i 1.34219 0.774913i
\(969\) 6.47097 67.7670i 0.00667798 0.0699350i
\(970\) 39.2029 + 203.404i 0.0404154 + 0.209695i
\(971\) −324.504 255.192i −0.334195 0.262814i 0.436933 0.899494i \(-0.356065\pi\)
−0.771128 + 0.636680i \(0.780307\pi\)
\(972\) 55.4306 70.4857i 0.0570274 0.0725162i
\(973\) −69.2952 + 13.3556i −0.0712181 + 0.0137262i
\(974\) 593.696 + 56.6911i 0.609544 + 0.0582044i
\(975\) 172.111 + 298.106i 0.176525 + 0.305749i
\(976\) −426.509 246.245i −0.436996 0.252300i
\(977\) 994.352 1396.37i 1.01776 1.42924i 0.117920 0.993023i \(-0.462377\pi\)
0.899840 0.436221i \(-0.143683\pi\)
\(978\) 85.9018 + 55.2058i 0.0878342 + 0.0564476i
\(979\) 503.687 + 528.252i 0.514491 + 0.539583i
\(980\) −898.299 410.239i −0.916631 0.418611i
\(981\) 117.353 399.667i 0.119626 0.407408i
\(982\) −455.308 + 2362.36i −0.463653 + 2.40566i
\(983\) 904.482 783.738i 0.920124 0.797292i −0.0594804 0.998229i \(-0.518944\pi\)
0.979604 + 0.200938i \(0.0643989\pi\)
\(984\) 169.374 + 328.540i 0.172128 + 0.333882i
\(985\) 104.037 + 300.596i 0.105622 + 0.305174i
\(986\) −545.189 1361.82i −0.552930 1.38115i
\(987\) −7.03403 6.70694i −0.00712668 0.00679528i
\(988\) 196.310 47.6242i 0.198694 0.0482027i
\(989\) −221.199 + 429.066i −0.223659 + 0.433838i
\(990\) −721.318 103.710i −0.728604 0.104757i
\(991\) −151.171 514.841i −0.152544 0.519516i 0.847391 0.530970i \(-0.178172\pi\)
−0.999934 + 0.0114537i \(0.996354\pi\)
\(992\) 814.479 77.7733i 0.821047 0.0784005i
\(993\) −623.172 875.123i −0.627565 0.881292i
\(994\) −43.0125 902.943i −0.0432721 0.908394i
\(995\) 294.075 + 101.780i 0.295553 + 0.102292i
\(996\) 510.543 73.4050i 0.512594 0.0736998i
\(997\) 12.8839 + 28.2118i 0.0129226 + 0.0282966i 0.915983 0.401216i \(-0.131412\pi\)
−0.903061 + 0.429513i \(0.858685\pi\)
\(998\) 320.441 + 128.285i 0.321083 + 0.128542i
\(999\) −359.284 17.1148i −0.359643 0.0171319i
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 201.3.n.a.13.2 220
67.31 odd 66 inner 201.3.n.a.31.2 yes 220
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.n.a.13.2 220 1.1 even 1 trivial
201.3.n.a.31.2 yes 220 67.31 odd 66 inner