# Properties

 Label 384.2.j.a.289.2 Level $384$ Weight $2$ Character 384.289 Analytic conductor $3.066$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 384.j (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.06625543762$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.18939904.2 Defining polynomial: $$x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 289.2 Root $$0.500000 + 0.0297061i$$ of defining polynomial Character $$\chi$$ $$=$$ 384.289 Dual form 384.2.j.a.97.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 - 0.707107i) q^{3} +(0.334904 - 0.334904i) q^{5} +4.55765i q^{7} +1.00000i q^{9} +O(q^{10})$$ $$q+(-0.707107 - 0.707107i) q^{3} +(0.334904 - 0.334904i) q^{5} +4.55765i q^{7} +1.00000i q^{9} +(-2.47363 + 2.47363i) q^{11} +(0.0594122 + 0.0594122i) q^{13} -0.473626 q^{15} +3.61706 q^{17} +(2.55765 + 2.55765i) q^{19} +(3.22274 - 3.22274i) q^{21} -2.82843i q^{23} +4.77568i q^{25} +(0.707107 - 0.707107i) q^{27} +(5.16333 + 5.16333i) q^{29} +0.557647 q^{31} +3.49824 q^{33} +(1.52637 + 1.52637i) q^{35} +(-4.38607 + 4.38607i) q^{37} -0.0840215i q^{39} -9.27391i q^{41} +(-1.61040 + 1.61040i) q^{43} +(0.334904 + 0.334904i) q^{45} -2.82843 q^{47} -13.7721 q^{49} +(-2.55765 - 2.55765i) q^{51} +(0.493523 - 0.493523i) q^{53} +1.65685i q^{55} -3.61706i q^{57} +(4.00000 - 4.00000i) q^{59} +(-2.72922 - 2.72922i) q^{61} -4.55765 q^{63} +0.0397948 q^{65} +(3.77568 + 3.77568i) q^{67} +(-2.00000 + 2.00000i) q^{69} -9.11529i q^{71} -0.541560i q^{73} +(3.37691 - 3.37691i) q^{75} +(-11.2739 - 11.2739i) q^{77} +10.9937 q^{79} -1.00000 q^{81} +(-10.6417 - 10.6417i) q^{83} +(1.21137 - 1.21137i) q^{85} -7.30205i q^{87} +14.6533i q^{89} +(-0.270780 + 0.270780i) q^{91} +(-0.394316 - 0.394316i) q^{93} +1.71313 q^{95} +4.31724 q^{97} +(-2.47363 - 2.47363i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + O(q^{10})$$ $$8q - 8q^{11} + 8q^{15} - 8q^{19} + 16q^{29} - 24q^{31} + 24q^{35} + 16q^{37} - 8q^{43} - 8q^{49} + 8q^{51} - 16q^{53} + 32q^{59} - 16q^{61} - 8q^{63} - 16q^{65} - 16q^{67} - 16q^{69} + 16q^{75} - 16q^{77} + 24q^{79} - 8q^{81} - 40q^{83} + 16q^{85} - 8q^{91} + 48q^{95} - 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$133$$ $$257$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{3}{4}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −0.707107 0.707107i −0.408248 0.408248i
$$4$$ 0 0
$$5$$ 0.334904 0.334904i 0.149774 0.149774i −0.628243 0.778017i $$-0.716226\pi$$
0.778017 + 0.628243i $$0.216226\pi$$
$$6$$ 0 0
$$7$$ 4.55765i 1.72263i 0.508072 + 0.861314i $$0.330358\pi$$
−0.508072 + 0.861314i $$0.669642\pi$$
$$8$$ 0 0
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ −2.47363 + 2.47363i −0.745826 + 0.745826i −0.973692 0.227866i $$-0.926825\pi$$
0.227866 + 0.973692i $$0.426825\pi$$
$$12$$ 0 0
$$13$$ 0.0594122 + 0.0594122i 0.0164780 + 0.0164780i 0.715298 0.698820i $$-0.246291\pi$$
−0.698820 + 0.715298i $$0.746291\pi$$
$$14$$ 0 0
$$15$$ −0.473626 −0.122290
$$16$$ 0 0
$$17$$ 3.61706 0.877266 0.438633 0.898666i $$-0.355463\pi$$
0.438633 + 0.898666i $$0.355463\pi$$
$$18$$ 0 0
$$19$$ 2.55765 + 2.55765i 0.586765 + 0.586765i 0.936754 0.349989i $$-0.113815\pi$$
−0.349989 + 0.936754i $$0.613815\pi$$
$$20$$ 0 0
$$21$$ 3.22274 3.22274i 0.703260 0.703260i
$$22$$ 0 0
$$23$$ 2.82843i 0.589768i −0.955533 0.294884i $$-0.904719\pi$$
0.955533 0.294884i $$-0.0952810\pi$$
$$24$$ 0 0
$$25$$ 4.77568i 0.955136i
$$26$$ 0 0
$$27$$ 0.707107 0.707107i 0.136083 0.136083i
$$28$$ 0 0
$$29$$ 5.16333 + 5.16333i 0.958807 + 0.958807i 0.999184 0.0403780i $$-0.0128562\pi$$
−0.0403780 + 0.999184i $$0.512856\pi$$
$$30$$ 0 0
$$31$$ 0.557647 0.100156 0.0500782 0.998745i $$-0.484053\pi$$
0.0500782 + 0.998745i $$0.484053\pi$$
$$32$$ 0 0
$$33$$ 3.49824 0.608965
$$34$$ 0 0
$$35$$ 1.52637 + 1.52637i 0.258004 + 0.258004i
$$36$$ 0 0
$$37$$ −4.38607 + 4.38607i −0.721066 + 0.721066i −0.968822 0.247756i $$-0.920307\pi$$
0.247756 + 0.968822i $$0.420307\pi$$
$$38$$ 0 0
$$39$$ 0.0840215i 0.0134542i
$$40$$ 0 0
$$41$$ 9.27391i 1.44834i −0.689620 0.724171i $$-0.742223\pi$$
0.689620 0.724171i $$-0.257777\pi$$
$$42$$ 0 0
$$43$$ −1.61040 + 1.61040i −0.245583 + 0.245583i −0.819155 0.573572i $$-0.805557\pi$$
0.573572 + 0.819155i $$0.305557\pi$$
$$44$$ 0 0
$$45$$ 0.334904 + 0.334904i 0.0499245 + 0.0499245i
$$46$$ 0 0
$$47$$ −2.82843 −0.412568 −0.206284 0.978492i $$-0.566137\pi$$
−0.206284 + 0.978492i $$0.566137\pi$$
$$48$$ 0 0
$$49$$ −13.7721 −1.96745
$$50$$ 0 0
$$51$$ −2.55765 2.55765i −0.358142 0.358142i
$$52$$ 0 0
$$53$$ 0.493523 0.493523i 0.0677906 0.0677906i −0.672399 0.740189i $$-0.734736\pi$$
0.740189 + 0.672399i $$0.234736\pi$$
$$54$$ 0 0
$$55$$ 1.65685i 0.223410i
$$56$$ 0 0
$$57$$ 3.61706i 0.479091i
$$58$$ 0 0
$$59$$ 4.00000 4.00000i 0.520756 0.520756i −0.397044 0.917800i $$-0.629964\pi$$
0.917800 + 0.397044i $$0.129964\pi$$
$$60$$ 0 0
$$61$$ −2.72922 2.72922i −0.349441 0.349441i 0.510460 0.859901i $$-0.329475\pi$$
−0.859901 + 0.510460i $$0.829475\pi$$
$$62$$ 0 0
$$63$$ −4.55765 −0.574210
$$64$$ 0 0
$$65$$ 0.0397948 0.00493593
$$66$$ 0 0
$$67$$ 3.77568 + 3.77568i 0.461273 + 0.461273i 0.899072 0.437800i $$-0.144242\pi$$
−0.437800 + 0.899072i $$0.644242\pi$$
$$68$$ 0 0
$$69$$ −2.00000 + 2.00000i −0.240772 + 0.240772i
$$70$$ 0 0
$$71$$ 9.11529i 1.08179i −0.841091 0.540893i $$-0.818086\pi$$
0.841091 0.540893i $$-0.181914\pi$$
$$72$$ 0 0
$$73$$ 0.541560i 0.0633848i −0.999498 0.0316924i $$-0.989910\pi$$
0.999498 0.0316924i $$-0.0100897\pi$$
$$74$$ 0 0
$$75$$ 3.37691 3.37691i 0.389933 0.389933i
$$76$$ 0 0
$$77$$ −11.2739 11.2739i −1.28478 1.28478i
$$78$$ 0 0
$$79$$ 10.9937 1.23689 0.618445 0.785828i $$-0.287763\pi$$
0.618445 + 0.785828i $$0.287763\pi$$
$$80$$ 0 0
$$81$$ −1.00000 −0.111111
$$82$$ 0 0
$$83$$ −10.6417 10.6417i −1.16807 1.16807i −0.982660 0.185415i $$-0.940637\pi$$
−0.185415 0.982660i $$-0.559363\pi$$
$$84$$ 0 0
$$85$$ 1.21137 1.21137i 0.131391 0.131391i
$$86$$ 0 0
$$87$$ 7.30205i 0.782862i
$$88$$ 0 0
$$89$$ 14.6533i 1.55325i 0.629964 + 0.776625i $$0.283070\pi$$
−0.629964 + 0.776625i $$0.716930\pi$$
$$90$$ 0 0
$$91$$ −0.270780 + 0.270780i −0.0283854 + 0.0283854i
$$92$$ 0 0
$$93$$ −0.394316 0.394316i −0.0408887 0.0408887i
$$94$$ 0 0
$$95$$ 1.71313 0.175764
$$96$$ 0 0
$$97$$ 4.31724 0.438349 0.219175 0.975686i $$-0.429664\pi$$
0.219175 + 0.975686i $$0.429664\pi$$
$$98$$ 0 0
$$99$$ −2.47363 2.47363i −0.248609 0.248609i
$$100$$ 0 0
$$101$$ 0.453728 0.453728i 0.0451477 0.0451477i −0.684173 0.729320i $$-0.739836\pi$$
0.729320 + 0.684173i $$0.239836\pi$$
$$102$$ 0 0
$$103$$ 1.33686i 0.131724i −0.997829 0.0658622i $$-0.979020\pi$$
0.997829 0.0658622i $$-0.0209798\pi$$
$$104$$ 0 0
$$105$$ 2.15862i 0.210660i
$$106$$ 0 0
$$107$$ 6.06255 6.06255i 0.586088 0.586088i −0.350481 0.936570i $$-0.613982\pi$$
0.936570 + 0.350481i $$0.113982\pi$$
$$108$$ 0 0
$$109$$ −5.71627 5.71627i −0.547519 0.547519i 0.378203 0.925722i $$-0.376542\pi$$
−0.925722 + 0.378203i $$0.876542\pi$$
$$110$$ 0 0
$$111$$ 6.20285 0.588748
$$112$$ 0 0
$$113$$ −9.55136 −0.898516 −0.449258 0.893402i $$-0.648312\pi$$
−0.449258 + 0.893402i $$0.648312\pi$$
$$114$$ 0 0
$$115$$ −0.947252 0.947252i −0.0883317 0.0883317i
$$116$$ 0 0
$$117$$ −0.0594122 + 0.0594122i −0.00549266 + 0.00549266i
$$118$$ 0 0
$$119$$ 16.4853i 1.51120i
$$120$$ 0 0
$$121$$ 1.23765i 0.112514i
$$122$$ 0 0
$$123$$ −6.55765 + 6.55765i −0.591283 + 0.591283i
$$124$$ 0 0
$$125$$ 3.27391 + 3.27391i 0.292828 + 0.292828i
$$126$$ 0 0
$$127$$ −5.09921 −0.452481 −0.226241 0.974071i $$-0.572644\pi$$
−0.226241 + 0.974071i $$0.572644\pi$$
$$128$$ 0 0
$$129$$ 2.27744 0.200518
$$130$$ 0 0
$$131$$ 2.11882 + 2.11882i 0.185123 + 0.185123i 0.793584 0.608461i $$-0.208213\pi$$
−0.608461 + 0.793584i $$0.708213\pi$$
$$132$$ 0 0
$$133$$ −11.6569 + 11.6569i −1.01078 + 1.01078i
$$134$$ 0 0
$$135$$ 0.473626i 0.0407632i
$$136$$ 0 0
$$137$$ 3.37941i 0.288723i −0.989525 0.144361i $$-0.953887\pi$$
0.989525 0.144361i $$-0.0461127\pi$$
$$138$$ 0 0
$$139$$ 5.88118 5.88118i 0.498835 0.498835i −0.412240 0.911075i $$-0.635254\pi$$
0.911075 + 0.412240i $$0.135254\pi$$
$$140$$ 0 0
$$141$$ 2.00000 + 2.00000i 0.168430 + 0.168430i
$$142$$ 0 0
$$143$$ −0.293927 −0.0245794
$$144$$ 0 0
$$145$$ 3.45844 0.287208
$$146$$ 0 0
$$147$$ 9.73838 + 9.73838i 0.803208 + 0.803208i
$$148$$ 0 0
$$149$$ 9.99176 9.99176i 0.818557 0.818557i −0.167342 0.985899i $$-0.553518\pi$$
0.985899 + 0.167342i $$0.0535185\pi$$
$$150$$ 0 0
$$151$$ 9.97685i 0.811905i −0.913894 0.405952i $$-0.866940\pi$$
0.913894 0.405952i $$-0.133060\pi$$
$$152$$ 0 0
$$153$$ 3.61706i 0.292422i
$$154$$ 0 0
$$155$$ 0.186758 0.186758i 0.0150008 0.0150008i
$$156$$ 0 0
$$157$$ 16.1618 + 16.1618i 1.28985 + 1.28985i 0.934877 + 0.354971i $$0.115509\pi$$
0.354971 + 0.934877i $$0.384491\pi$$
$$158$$ 0 0
$$159$$ −0.697947 −0.0553508
$$160$$ 0 0
$$161$$ 12.8910 1.01595
$$162$$ 0 0
$$163$$ −7.50490 7.50490i −0.587829 0.587829i 0.349214 0.937043i $$-0.386449\pi$$
−0.937043 + 0.349214i $$0.886449\pi$$
$$164$$ 0 0
$$165$$ 1.17157 1.17157i 0.0912068 0.0912068i
$$166$$ 0 0
$$167$$ 5.83822i 0.451775i 0.974153 + 0.225888i $$0.0725282\pi$$
−0.974153 + 0.225888i $$0.927472\pi$$
$$168$$ 0 0
$$169$$ 12.9929i 0.999457i
$$170$$ 0 0
$$171$$ −2.55765 + 2.55765i −0.195588 + 0.195588i
$$172$$ 0 0
$$173$$ 3.62530 + 3.62530i 0.275627 + 0.275627i 0.831360 0.555734i $$-0.187563\pi$$
−0.555734 + 0.831360i $$0.687563\pi$$
$$174$$ 0 0
$$175$$ −21.7659 −1.64534
$$176$$ 0 0
$$177$$ −5.65685 −0.425195
$$178$$ 0 0
$$179$$ 9.28334 + 9.28334i 0.693869 + 0.693869i 0.963081 0.269212i $$-0.0867632\pi$$
−0.269212 + 0.963081i $$0.586763\pi$$
$$180$$ 0 0
$$181$$ 10.8316 10.8316i 0.805104 0.805104i −0.178785 0.983888i $$-0.557217\pi$$
0.983888 + 0.178785i $$0.0572165\pi$$
$$182$$ 0 0
$$183$$ 3.85970i 0.285317i
$$184$$ 0 0
$$185$$ 2.93783i 0.215993i
$$186$$ 0 0
$$187$$ −8.94725 + 8.94725i −0.654288 + 0.654288i
$$188$$ 0 0
$$189$$ 3.22274 + 3.22274i 0.234420 + 0.234420i
$$190$$ 0 0
$$191$$ 8.63001 0.624446 0.312223 0.950009i $$-0.398926\pi$$
0.312223 + 0.950009i $$0.398926\pi$$
$$192$$ 0 0
$$193$$ 11.4514 0.824288 0.412144 0.911119i $$-0.364780\pi$$
0.412144 + 0.911119i $$0.364780\pi$$
$$194$$ 0 0
$$195$$ −0.0281391 0.0281391i −0.00201509 0.00201509i
$$196$$ 0 0
$$197$$ −7.48999 + 7.48999i −0.533640 + 0.533640i −0.921654 0.388014i $$-0.873161\pi$$
0.388014 + 0.921654i $$0.373161\pi$$
$$198$$ 0 0
$$199$$ 3.68000i 0.260868i 0.991457 + 0.130434i $$0.0416371\pi$$
−0.991457 + 0.130434i $$0.958363\pi$$
$$200$$ 0 0
$$201$$ 5.33962i 0.376627i
$$202$$ 0 0
$$203$$ −23.5326 + 23.5326i −1.65167 + 1.65167i
$$204$$ 0 0
$$205$$ −3.10587 3.10587i −0.216923 0.216923i
$$206$$ 0 0
$$207$$ 2.82843 0.196589
$$208$$ 0 0
$$209$$ −12.6533 −0.875249
$$210$$ 0 0
$$211$$ 10.1188 + 10.1188i 0.696609 + 0.696609i 0.963677 0.267069i $$-0.0860551\pi$$
−0.267069 + 0.963677i $$0.586055\pi$$
$$212$$ 0 0
$$213$$ −6.44549 + 6.44549i −0.441637 + 0.441637i
$$214$$ 0 0
$$215$$ 1.07866i 0.0735637i
$$216$$ 0 0
$$217$$ 2.54156i 0.172532i
$$218$$ 0 0
$$219$$ −0.382941 + 0.382941i −0.0258767 + 0.0258767i
$$220$$ 0 0
$$221$$ 0.214897 + 0.214897i 0.0144556 + 0.0144556i
$$222$$ 0 0
$$223$$ 4.86156 0.325554 0.162777 0.986663i $$-0.447955\pi$$
0.162777 + 0.986663i $$0.447955\pi$$
$$224$$ 0 0
$$225$$ −4.77568 −0.318379
$$226$$ 0 0
$$227$$ 10.6417 + 10.6417i 0.706312 + 0.706312i 0.965758 0.259445i $$-0.0835398\pi$$
−0.259445 + 0.965758i $$0.583540\pi$$
$$228$$ 0 0
$$229$$ 20.1712 20.1712i 1.33295 1.33295i 0.430229 0.902720i $$-0.358433\pi$$
0.902720 0.430229i $$-0.141567\pi$$
$$230$$ 0 0
$$231$$ 15.9437i 1.04902i
$$232$$ 0 0
$$233$$ 13.5702i 0.889014i 0.895775 + 0.444507i $$0.146621\pi$$
−0.895775 + 0.444507i $$0.853379\pi$$
$$234$$ 0 0
$$235$$ −0.947252 + 0.947252i −0.0617919 + 0.0617919i
$$236$$ 0 0
$$237$$ −7.77373 7.77373i −0.504958 0.504958i
$$238$$ 0 0
$$239$$ −29.3629 −1.89933 −0.949665 0.313267i $$-0.898576\pi$$
−0.949665 + 0.313267i $$0.898576\pi$$
$$240$$ 0 0
$$241$$ 24.0063 1.54638 0.773190 0.634175i $$-0.218660\pi$$
0.773190 + 0.634175i $$0.218660\pi$$
$$242$$ 0 0
$$243$$ 0.707107 + 0.707107i 0.0453609 + 0.0453609i
$$244$$ 0 0
$$245$$ −4.61235 + 4.61235i −0.294672 + 0.294672i
$$246$$ 0 0
$$247$$ 0.303911i 0.0193374i
$$248$$ 0 0
$$249$$ 15.0496i 0.953729i
$$250$$ 0 0
$$251$$ 15.7570 15.7570i 0.994571 0.994571i −0.00541463 0.999985i $$-0.501724\pi$$
0.999985 + 0.00541463i $$0.00172354\pi$$
$$252$$ 0 0
$$253$$ 6.99647 + 6.99647i 0.439864 + 0.439864i
$$254$$ 0 0
$$255$$ −1.71313 −0.107281
$$256$$ 0 0
$$257$$ 8.66038 0.540220 0.270110 0.962829i $$-0.412940\pi$$
0.270110 + 0.962829i $$0.412940\pi$$
$$258$$ 0 0
$$259$$ −19.9902 19.9902i −1.24213 1.24213i
$$260$$ 0 0
$$261$$ −5.16333 + 5.16333i −0.319602 + 0.319602i
$$262$$ 0 0
$$263$$ 13.3208i 0.821394i −0.911772 0.410697i $$-0.865285\pi$$
0.911772 0.410697i $$-0.134715\pi$$
$$264$$ 0 0
$$265$$ 0.330566i 0.0203065i
$$266$$ 0 0
$$267$$ 10.3615 10.3615i 0.634111 0.634111i
$$268$$ 0 0
$$269$$ 11.6714 + 11.6714i 0.711616 + 0.711616i 0.966873 0.255257i $$-0.0821602\pi$$
−0.255257 + 0.966873i $$0.582160\pi$$
$$270$$ 0 0
$$271$$ 21.9769 1.33500 0.667499 0.744610i $$-0.267365\pi$$
0.667499 + 0.744610i $$0.267365\pi$$
$$272$$ 0 0
$$273$$ 0.382941 0.0231766
$$274$$ 0 0
$$275$$ −11.8132 11.8132i −0.712365 0.712365i
$$276$$ 0 0
$$277$$ 10.9504 10.9504i 0.657945 0.657945i −0.296949 0.954893i $$-0.595969\pi$$
0.954893 + 0.296949i $$0.0959690\pi$$
$$278$$ 0 0
$$279$$ 0.557647i 0.0333855i
$$280$$ 0 0
$$281$$ 22.8910i 1.36556i −0.730624 0.682780i $$-0.760771\pi$$
0.730624 0.682780i $$-0.239229\pi$$
$$282$$ 0 0
$$283$$ 4.48528 4.48528i 0.266622 0.266622i −0.561115 0.827738i $$-0.689628\pi$$
0.827738 + 0.561115i $$0.189628\pi$$
$$284$$ 0 0
$$285$$ −1.21137 1.21137i −0.0717552 0.0717552i
$$286$$ 0 0
$$287$$ 42.2672 2.49496
$$288$$ 0 0
$$289$$ −3.91688 −0.230405
$$290$$ 0 0
$$291$$ −3.05275 3.05275i −0.178955 0.178955i
$$292$$ 0 0
$$293$$ −21.6221 + 21.6221i −1.26318 + 1.26318i −0.313636 + 0.949543i $$0.601547\pi$$
−0.949543 + 0.313636i $$0.898453\pi$$
$$294$$ 0 0
$$295$$ 2.67923i 0.155991i
$$296$$ 0 0
$$297$$ 3.49824i 0.202988i
$$298$$ 0 0
$$299$$ 0.168043 0.168043i 0.00971818 0.00971818i
$$300$$ 0 0
$$301$$ −7.33962 7.33962i −0.423048 0.423048i
$$302$$ 0 0
$$303$$ −0.641669 −0.0368629
$$304$$ 0 0
$$305$$ −1.82805 −0.104674
$$306$$ 0 0
$$307$$ −12.1118 12.1118i −0.691255 0.691255i 0.271253 0.962508i $$-0.412562\pi$$
−0.962508 + 0.271253i $$0.912562\pi$$
$$308$$ 0 0
$$309$$ −0.945300 + 0.945300i −0.0537762 + 0.0537762i
$$310$$ 0 0
$$311$$ 26.8651i 1.52338i 0.647943 + 0.761689i $$0.275630\pi$$
−0.647943 + 0.761689i $$0.724370\pi$$
$$312$$ 0 0
$$313$$ 19.6890i 1.11289i 0.830885 + 0.556445i $$0.187835\pi$$
−0.830885 + 0.556445i $$0.812165\pi$$
$$314$$ 0 0
$$315$$ −1.52637 + 1.52637i −0.0860014 + 0.0860014i
$$316$$ 0 0
$$317$$ −21.3447 21.3447i −1.19884 1.19884i −0.974515 0.224323i $$-0.927983\pi$$
−0.224323 0.974515i $$-0.572017\pi$$
$$318$$ 0 0
$$319$$ −25.5443 −1.43021
$$320$$ 0 0
$$321$$ −8.57373 −0.478539
$$322$$ 0 0
$$323$$ 9.25116 + 9.25116i 0.514748 + 0.514748i
$$324$$ 0 0
$$325$$ −0.283734 + 0.283734i −0.0157387 + 0.0157387i
$$326$$ 0 0
$$327$$ 8.08402i 0.447047i
$$328$$ 0 0
$$329$$ 12.8910i 0.710702i
$$330$$ 0 0
$$331$$ 14.6926 14.6926i 0.807576 0.807576i −0.176690 0.984266i $$-0.556539\pi$$
0.984266 + 0.176690i $$0.0565391\pi$$
$$332$$ 0 0
$$333$$ −4.38607 4.38607i −0.240355 0.240355i
$$334$$ 0 0
$$335$$ 2.52898 0.138173
$$336$$ 0 0
$$337$$ −23.0098 −1.25342 −0.626712 0.779251i $$-0.715600\pi$$
−0.626712 + 0.779251i $$0.715600\pi$$
$$338$$ 0 0
$$339$$ 6.75383 + 6.75383i 0.366818 + 0.366818i
$$340$$ 0 0
$$341$$ −1.37941 + 1.37941i −0.0746993 + 0.0746993i
$$342$$ 0 0
$$343$$ 30.8651i 1.66656i
$$344$$ 0 0
$$345$$ 1.33962i 0.0721225i
$$346$$ 0 0
$$347$$ −10.9026 + 10.9026i −0.585284 + 0.585284i −0.936350 0.351067i $$-0.885819\pi$$
0.351067 + 0.936350i $$0.385819\pi$$
$$348$$ 0 0
$$349$$ −20.0563 20.0563i −1.07359 1.07359i −0.997068 0.0765186i $$-0.975620\pi$$
−0.0765186 0.997068i $$-0.524380\pi$$
$$350$$ 0 0
$$351$$ 0.0840215 0.00448474
$$352$$ 0 0
$$353$$ −12.2117 −0.649965 −0.324983 0.945720i $$-0.605358\pi$$
−0.324983 + 0.945720i $$0.605358\pi$$
$$354$$ 0 0
$$355$$ −3.05275 3.05275i −0.162023 0.162023i
$$356$$ 0 0
$$357$$ 11.6569 11.6569i 0.616946 0.616946i
$$358$$ 0 0
$$359$$ 33.4780i 1.76690i −0.468522 0.883452i $$-0.655214\pi$$
0.468522 0.883452i $$-0.344786\pi$$
$$360$$ 0 0
$$361$$ 5.91688i 0.311415i
$$362$$ 0 0
$$363$$ −0.875150 + 0.875150i −0.0459335 + 0.0459335i
$$364$$ 0 0
$$365$$ −0.181370 0.181370i −0.00949337 0.00949337i
$$366$$ 0 0
$$367$$ 0.702379 0.0366639 0.0183319 0.999832i $$-0.494164\pi$$
0.0183319 + 0.999832i $$0.494164\pi$$
$$368$$ 0 0
$$369$$ 9.27391 0.482781
$$370$$ 0 0
$$371$$ 2.24930 + 2.24930i 0.116778 + 0.116778i
$$372$$ 0 0
$$373$$ −18.9598 + 18.9598i −0.981702 + 0.981702i −0.999836 0.0181339i $$-0.994227\pi$$
0.0181339 + 0.999836i $$0.494227\pi$$
$$374$$ 0 0
$$375$$ 4.63001i 0.239093i
$$376$$ 0 0
$$377$$ 0.613530i 0.0315984i
$$378$$ 0 0
$$379$$ −1.77844 + 1.77844i −0.0913523 + 0.0913523i −0.751306 0.659954i $$-0.770576\pi$$
0.659954 + 0.751306i $$0.270576\pi$$
$$380$$ 0 0
$$381$$ 3.60568 + 3.60568i 0.184725 + 0.184725i
$$382$$ 0 0
$$383$$ −25.4880 −1.30238 −0.651188 0.758916i $$-0.725729\pi$$
−0.651188 + 0.758916i $$0.725729\pi$$
$$384$$ 0 0
$$385$$ −7.55136 −0.384853
$$386$$ 0 0
$$387$$ −1.61040 1.61040i −0.0818610 0.0818610i
$$388$$ 0 0
$$389$$ 11.7049 11.7049i 0.593462 0.593462i −0.345103 0.938565i $$-0.612156\pi$$
0.938565 + 0.345103i $$0.112156\pi$$
$$390$$ 0 0
$$391$$ 10.2306i 0.517383i
$$392$$ 0 0
$$393$$ 2.99647i 0.151152i
$$394$$ 0 0
$$395$$ 3.68184 3.68184i 0.185253 0.185253i
$$396$$ 0 0
$$397$$ 9.04646 + 9.04646i 0.454029 + 0.454029i 0.896689 0.442661i $$-0.145965\pi$$
−0.442661 + 0.896689i $$0.645965\pi$$
$$398$$ 0 0
$$399$$ 16.4853 0.825296
$$400$$ 0 0
$$401$$ −18.0853 −0.903137 −0.451568 0.892237i $$-0.649135\pi$$
−0.451568 + 0.892237i $$0.649135\pi$$
$$402$$ 0 0
$$403$$ 0.0331311 + 0.0331311i 0.00165038 + 0.00165038i
$$404$$ 0 0
$$405$$ −0.334904 + 0.334904i −0.0166415 + 0.0166415i
$$406$$ 0 0
$$407$$ 21.6990i 1.07558i
$$408$$ 0 0
$$409$$ 25.2271i 1.24740i −0.781665 0.623699i $$-0.785629\pi$$
0.781665 0.623699i $$-0.214371\pi$$
$$410$$ 0 0
$$411$$ −2.38960 + 2.38960i −0.117870 + 0.117870i
$$412$$ 0 0
$$413$$ 18.2306 + 18.2306i 0.897069 + 0.897069i
$$414$$ 0 0
$$415$$ −7.12787 −0.349894
$$416$$ 0 0
$$417$$ −8.31724 −0.407297
$$418$$ 0 0
$$419$$ 7.25283 + 7.25283i 0.354324 + 0.354324i 0.861716 0.507392i $$-0.169390\pi$$
−0.507392 + 0.861716i $$0.669390\pi$$
$$420$$ 0 0
$$421$$ −2.39550 + 2.39550i −0.116749 + 0.116749i −0.763068 0.646318i $$-0.776308\pi$$
0.646318 + 0.763068i $$0.276308\pi$$
$$422$$ 0 0
$$423$$ 2.82843i 0.137523i
$$424$$ 0 0
$$425$$ 17.2739i 0.837908i
$$426$$ 0 0
$$427$$ 12.4388 12.4388i 0.601957 0.601957i
$$428$$ 0 0
$$429$$ 0.207838 + 0.207838i 0.0100345 + 0.0100345i
$$430$$ 0 0
$$431$$ 4.42454 0.213123 0.106561 0.994306i $$-0.466016\pi$$
0.106561 + 0.994306i $$0.466016\pi$$
$$432$$ 0 0
$$433$$ 7.31371 0.351474 0.175737 0.984437i $$-0.443769\pi$$
0.175737 + 0.984437i $$0.443769\pi$$
$$434$$ 0 0
$$435$$ −2.44549 2.44549i −0.117252 0.117252i
$$436$$ 0 0
$$437$$ 7.23412 7.23412i 0.346055 0.346055i
$$438$$ 0 0
$$439$$ 29.6533i 1.41527i 0.706576 + 0.707637i $$0.250239\pi$$
−0.706576 + 0.707637i $$0.749761\pi$$
$$440$$ 0 0
$$441$$ 13.7721i 0.655817i
$$442$$ 0 0
$$443$$ 10.3056 10.3056i 0.489633 0.489633i −0.418557 0.908190i $$-0.637464\pi$$
0.908190 + 0.418557i $$0.137464\pi$$
$$444$$ 0 0
$$445$$ 4.90746 + 4.90746i 0.232636 + 0.232636i
$$446$$ 0 0
$$447$$ −14.1305 −0.668349
$$448$$ 0 0
$$449$$ −6.48844 −0.306208 −0.153104 0.988210i $$-0.548927\pi$$
−0.153104 + 0.988210i $$0.548927\pi$$
$$450$$ 0 0
$$451$$ 22.9402 + 22.9402i 1.08021 + 1.08021i
$$452$$ 0 0
$$453$$ −7.05470 + 7.05470i −0.331459 + 0.331459i
$$454$$ 0 0
$$455$$ 0.181370i 0.00850278i
$$456$$ 0 0
$$457$$ 9.00353i 0.421167i −0.977576 0.210584i $$-0.932464\pi$$
0.977576 0.210584i $$-0.0675364\pi$$
$$458$$ 0 0
$$459$$ 2.55765 2.55765i 0.119381 0.119381i
$$460$$ 0 0
$$461$$ −14.6218 14.6218i −0.681004 0.681004i 0.279223 0.960226i $$-0.409923\pi$$
−0.960226 + 0.279223i $$0.909923\pi$$
$$462$$ 0 0
$$463$$ 18.6435 0.866437 0.433219 0.901289i $$-0.357378\pi$$
0.433219 + 0.901289i $$0.357378\pi$$
$$464$$ 0 0
$$465$$ −0.264116 −0.0122481
$$466$$ 0 0
$$467$$ −23.5138 23.5138i −1.08809 1.08809i −0.995725 0.0923633i $$-0.970558\pi$$
−0.0923633 0.995725i $$-0.529442\pi$$
$$468$$ 0 0
$$469$$ −17.2082 + 17.2082i −0.794601 + 0.794601i
$$470$$ 0 0
$$471$$ 22.8562i 1.05316i
$$472$$ 0 0
$$473$$ 7.96703i 0.366325i
$$474$$ 0 0
$$475$$ −12.2145 + 12.2145i −0.560440 + 0.560440i
$$476$$ 0 0
$$477$$ 0.493523 + 0.493523i 0.0225969 + 0.0225969i
$$478$$ 0 0
$$479$$ 1.08864 0.0497412 0.0248706 0.999691i $$-0.492083\pi$$
0.0248706 + 0.999691i $$0.492083\pi$$
$$480$$ 0 0
$$481$$ −0.521173 −0.0237634
$$482$$ 0 0
$$483$$ −9.11529 9.11529i −0.414760 0.414760i
$$484$$ 0 0
$$485$$ 1.44586 1.44586i 0.0656531 0.0656531i
$$486$$ 0 0
$$487$$ 35.3298i 1.60095i 0.599369 + 0.800473i $$0.295418\pi$$
−0.599369 + 0.800473i $$0.704582\pi$$
$$488$$ 0 0
$$489$$ 10.6135i 0.479960i
$$490$$ 0 0
$$491$$ −12.8910 + 12.8910i −0.581761 + 0.581761i −0.935387 0.353626i $$-0.884949\pi$$
0.353626 + 0.935387i $$0.384949\pi$$
$$492$$ 0 0
$$493$$ 18.6761 + 18.6761i 0.841128 + 0.841128i
$$494$$ 0 0
$$495$$ −1.65685 −0.0744701
$$496$$ 0 0
$$497$$ 41.5443 1.86352
$$498$$ 0 0
$$499$$ 14.3798 + 14.3798i 0.643728 + 0.643728i 0.951470 0.307742i $$-0.0995734\pi$$
−0.307742 + 0.951470i $$0.599573\pi$$
$$500$$ 0 0
$$501$$ 4.12825 4.12825i 0.184437 0.184437i
$$502$$ 0 0
$$503$$ 30.2969i 1.35087i 0.737420 + 0.675435i $$0.236044\pi$$
−0.737420 + 0.675435i $$0.763956\pi$$
$$504$$ 0 0
$$505$$ 0.303911i 0.0135239i
$$506$$ 0 0
$$507$$ −9.18740 + 9.18740i −0.408027 + 0.408027i
$$508$$ 0 0
$$509$$ −10.5825 10.5825i −0.469063 0.469063i 0.432548 0.901611i $$-0.357615\pi$$
−0.901611 + 0.432548i $$0.857615\pi$$
$$510$$ 0 0
$$511$$ 2.46824 0.109188
$$512$$ 0 0
$$513$$ 3.61706 0.159697
$$514$$ 0 0
$$515$$ −0.447718 0.447718i −0.0197288 0.0197288i
$$516$$ 0 0
$$517$$ 6.99647 6.99647i 0.307704 0.307704i
$$518$$ 0 0
$$519$$ 5.12695i 0.225048i
$$520$$ 0 0
$$521$$ 24.9049i 1.09110i 0.838078 + 0.545551i $$0.183680\pi$$
−0.838078 + 0.545551i $$0.816320\pi$$
$$522$$ 0 0
$$523$$ −12.9008 + 12.9008i −0.564112 + 0.564112i −0.930473 0.366361i $$-0.880604\pi$$
0.366361 + 0.930473i $$0.380604\pi$$
$$524$$ 0 0
$$525$$ 15.3908 + 15.3908i 0.671709 + 0.671709i
$$526$$ 0 0
$$527$$ 2.01704 0.0878638
$$528$$ 0 0
$$529$$ 15.0000 0.652174
$$530$$ 0 0
$$531$$ 4.00000 + 4.00000i 0.173585 + 0.173585i
$$532$$ 0 0
$$533$$ 0.550984 0.550984i 0.0238657 0.0238657i
$$534$$ 0 0
$$535$$ 4.06074i 0.175561i
$$536$$ 0 0
$$537$$ 13.1286i 0.566542i
$$538$$ 0 0
$$539$$ 34.0671 34.0671i 1.46738 1.46738i
$$540$$ 0 0
$$541$$ −18.2767 18.2767i −0.785776 0.785776i 0.195023 0.980799i $$-0.437522\pi$$
−0.980799 + 0.195023i $$0.937522\pi$$
$$542$$ 0 0
$$543$$ −15.3181 −0.657364
$$544$$ 0 0
$$545$$ −3.82880 −0.164008
$$546$$ 0 0
$$547$$ 13.7355 + 13.7355i 0.587287 + 0.587287i 0.936896 0.349609i $$-0.113685\pi$$
−0.349609 + 0.936896i $$0.613685\pi$$
$$548$$ 0 0
$$549$$ 2.72922 2.72922i 0.116480 0.116480i
$$550$$ 0 0
$$551$$ 26.4120i 1.12519i
$$552$$ 0 0
$$553$$ 50.1055i 2.13070i
$$554$$ 0 0
$$555$$ 2.07736 2.07736i 0.0881789 0.0881789i
$$556$$ 0 0
$$557$$ 27.5525 + 27.5525i 1.16744 + 1.16744i 0.982808 + 0.184631i $$0.0591089\pi$$
0.184631 + 0.982808i $$0.440891\pi$$
$$558$$ 0 0
$$559$$ −0.191354 −0.00809342
$$560$$ 0 0
$$561$$ 12.6533 0.534224
$$562$$ 0 0
$$563$$ −19.8928 19.8928i −0.838383 0.838383i 0.150263 0.988646i $$-0.451988\pi$$
−0.988646 + 0.150263i $$0.951988\pi$$
$$564$$ 0 0
$$565$$ −3.19879 + 3.19879i −0.134574 + 0.134574i
$$566$$ 0 0
$$567$$ 4.55765i 0.191403i
$$568$$ 0 0
$$569$$ 13.4849i 0.565317i 0.959221 + 0.282658i $$0.0912163\pi$$
−0.959221 + 0.282658i $$0.908784\pi$$
$$570$$ 0 0
$$571$$ −14.8284 + 14.8284i −0.620550 + 0.620550i −0.945672 0.325122i $$-0.894595\pi$$
0.325122 + 0.945672i $$0.394595\pi$$
$$572$$ 0 0
$$573$$ −6.10234 6.10234i −0.254929 0.254929i
$$574$$ 0 0
$$575$$ 13.5077 0.563308
$$576$$ 0 0
$$577$$ −11.6176 −0.483648 −0.241824 0.970320i $$-0.577746\pi$$
−0.241824 + 0.970320i $$0.577746\pi$$
$$578$$ 0 0
$$579$$ −8.09735 8.09735i −0.336514 0.336514i
$$580$$ 0 0
$$581$$ 48.5010 48.5010i 2.01216 2.01216i
$$582$$ 0 0
$$583$$ 2.44158i 0.101120i
$$584$$ 0 0
$$585$$ 0.0397948i 0.00164531i
$$586$$ 0 0
$$587$$ −17.0268 + 17.0268i −0.702773 + 0.702773i −0.965005 0.262232i $$-0.915541\pi$$
0.262232 + 0.965005i $$0.415541\pi$$
$$588$$ 0 0
$$589$$ 1.42627 + 1.42627i 0.0587682 + 0.0587682i
$$590$$ 0 0
$$591$$ 10.5925 0.435715
$$592$$ 0 0
$$593$$ 41.5372 1.70573 0.852865 0.522132i $$-0.174863\pi$$
0.852865 + 0.522132i $$0.174863\pi$$
$$594$$ 0 0
$$595$$ 5.52099 + 5.52099i 0.226338 + 0.226338i
$$596$$ 0 0
$$597$$ 2.60215 2.60215i 0.106499 0.106499i
$$598$$ 0 0
$$599$$ 6.43160i 0.262788i 0.991330 + 0.131394i $$0.0419453\pi$$
−0.991330 + 0.131394i $$0.958055\pi$$
$$600$$ 0 0
$$601$$ 3.45844i 0.141073i 0.997509 + 0.0705364i $$0.0224711\pi$$
−0.997509 + 0.0705364i $$0.977529\pi$$
$$602$$ 0 0
$$603$$ −3.77568 + 3.77568i −0.153758 + 0.153758i
$$604$$ 0 0
$$605$$ −0.414494 0.414494i −0.0168516 0.0168516i
$$606$$ 0 0
$$607$$ 30.1019 1.22180 0.610900 0.791708i $$-0.290808\pi$$
0.610900 + 0.791708i $$0.290808\pi$$
$$608$$ 0 0
$$609$$ 33.2802 1.34858
$$610$$ 0 0
$$611$$ −0.168043 0.168043i −0.00679829 0.00679829i
$$612$$ 0 0
$$613$$ −2.50490 + 2.50490i −0.101172 + 0.101172i −0.755881 0.654709i $$-0.772791\pi$$
0.654709 + 0.755881i $$0.272791\pi$$
$$614$$ 0 0
$$615$$ 4.39236i 0.177117i
$$616$$ 0 0
$$617$$ 22.9098i 0.922315i −0.887318 0.461157i $$-0.847434\pi$$
0.887318 0.461157i $$-0.152566\pi$$
$$618$$ 0 0
$$619$$ −28.6104 + 28.6104i −1.14995 + 1.14995i −0.163386 + 0.986562i $$0.552242\pi$$
−0.986562 + 0.163386i $$0.947758\pi$$
$$620$$ 0 0
$$621$$ −2.00000 2.00000i −0.0802572 0.0802572i
$$622$$ 0 0
$$623$$ −66.7847 −2.67567
$$624$$ 0 0
$$625$$ −21.6855 −0.867420
$$626$$ 0 0
$$627$$ 8.94725 + 8.94725i 0.357319 + 0.357319i
$$628$$ 0 0
$$629$$ −15.8647 + 15.8647i −0.632567 + 0.632567i
$$630$$ 0 0
$$631$$ 11.1851i 0.445270i 0.974902 + 0.222635i $$0.0714659\pi$$
−0.974902 + 0.222635i $$0.928534\pi$$
$$632$$ 0 0
$$633$$ 14.3102i 0.568779i
$$634$$ 0 0
$$635$$ −1.70774 + 1.70774i −0.0677698 + 0.0677698i
$$636$$ 0 0
$$637$$ −0.818234 0.818234i −0.0324196 0.0324196i
$$638$$ 0 0
$$639$$ 9.11529 0.360595
$$640$$ 0 0
$$641$$ −6.69312 −0.264362 −0.132181 0.991226i $$-0.542198\pi$$
−0.132181 + 0.991226i $$0.542198\pi$$
$$642$$ 0 0
$$643$$ −17.9410 17.9410i −0.707522 0.707522i 0.258491 0.966014i $$-0.416775\pi$$
−0.966014 + 0.258491i $$0.916775\pi$$
$$644$$ 0 0
$$645$$ 0.762725 0.762725i 0.0300323 0.0300323i
$$646$$ 0 0
$$647$$ 6.72999i 0.264583i 0.991211 + 0.132292i $$0.0422335\pi$$
−0.991211 + 0.132292i $$0.957766\pi$$
$$648$$ 0 0
$$649$$ 19.7890i 0.776786i
$$650$$ 0 0
$$651$$ 1.79715 1.79715i 0.0704360 0.0704360i
$$652$$ 0 0
$$653$$ −26.1731 26.1731i −1.02423 1.02423i −0.999699 0.0245347i $$-0.992190\pi$$
−0.0245347 0.999699i $$-0.507810\pi$$
$$654$$ 0 0
$$655$$ 1.41921 0.0554529
$$656$$ 0 0
$$657$$ 0.541560 0.0211283
$$658$$ 0 0
$$659$$ 13.9741 + 13.9741i 0.544353 + 0.544353i 0.924802 0.380449i $$-0.124230\pi$$
−0.380449 + 0.924802i $$0.624230\pi$$
$$660$$ 0 0
$$661$$ −11.9241 + 11.9241i −0.463794 + 0.463794i −0.899897 0.436103i $$-0.856358\pi$$
0.436103 + 0.899897i $$0.356358\pi$$
$$662$$ 0 0
$$663$$ 0.303911i 0.0118029i
$$664$$ 0 0
$$665$$ 7.80785i 0.302776i
$$666$$ 0 0
$$667$$ 14.6041 14.6041i 0.565473 0.565473i
$$668$$ 0 0
$$669$$ −3.43764 3.43764i −0.132907 0.132907i
$$670$$ 0 0
$$671$$ 13.5021 0.521244
$$672$$ 0 0
$$673$$ −37.3066 −1.43807 −0.719033 0.694976i $$-0.755415\pi$$
−0.719033 + 0.694976i $$0.755415\pi$$
$$674$$ 0 0
$$675$$ 3.37691 + 3.37691i 0.129978 + 0.129978i
$$676$$ 0 0
$$677$$ −0.447461 + 0.447461i −0.0171973 + 0.0171973i −0.715653 0.698456i $$-0.753871\pi$$
0.698456 + 0.715653i $$0.253871\pi$$
$$678$$ 0 0
$$679$$ 19.6764i 0.755113i
$$680$$ 0 0
$$681$$ 15.0496i 0.576702i
$$682$$ 0 0
$$683$$ −4.27521 + 4.27521i −0.163586 + 0.163586i −0.784153 0.620567i $$-0.786902\pi$$
0.620567 + 0.784153i $$0.286902\pi$$
$$684$$ 0 0
$$685$$ −1.13178 1.13178i −0.0432430 0.0432430i
$$686$$ 0 0
$$687$$ −28.5264 −1.08835
$$688$$ 0 0
$$689$$ 0.0586426 0.00223410
$$690$$ 0 0
$$691$$ 20.0786 + 20.0786i 0.763827 + 0.763827i 0.977012 0.213185i $$-0.0683836\pi$$
−0.213185 + 0.977012i $$0.568384\pi$$
$$692$$ 0 0
$$693$$ 11.2739 11.2739i 0.428261 0.428261i
$$694$$ 0 0
$$695$$ 3.93926i 0.149425i
$$696$$ 0 0
$$697$$ 33.5443i 1.27058i
$$698$$ 0 0
$$699$$ 9.59558 9.59558i 0.362938 0.362938i
$$700$$ 0 0
$$701$$ 10.4467 + 10.4467i 0.394565 + 0.394565i 0.876311 0.481746i $$-0.159997\pi$$
−0.481746 + 0.876311i $$0.659997\pi$$
$$702$$ 0 0
$$703$$ −22.4361 −0.846192
$$704$$ 0 0
$$705$$ 1.33962 0.0504529
$$706$$ 0 0
$$707$$ 2.06793 + 2.06793i 0.0777727 + 0.0777727i
$$708$$ 0 0
$$709$$ −16.0916 + 16.0916i −0.604332 + 0.604332i −0.941459 0.337127i $$-0.890545\pi$$
0.337127 + 0.941459i $$0.390545\pi$$
$$710$$ 0 0
$$711$$ 10.9937i 0.412296i
$$712$$ 0 0
$$713$$ 1.57726i 0.0590690i
$$714$$ 0 0
$$715$$ −0.0984373 + 0.0984373i −0.00368135 + 0.00368135i
$$716$$ 0 0
$$717$$ 20.7627 + 20.7627i 0.775398 + 0.775398i
$$718$$ 0 0
$$719$$ 30.9957 1.15594 0.577972 0.816057i $$-0.303844\pi$$
0.577972 + 0.816057i $$0.303844\pi$$
$$720$$ 0 0
$$721$$ 6.09292 0.226912
$$722$$ 0 0
$$723$$ −16.9750 16.9750i −0.631307 0.631307i
$$724$$ 0 0
$$725$$ −24.6584 + 24.6584i −0.915790 + 0.915790i
$$726$$ 0 0
$$727$$ 41.1117i 1.52475i −0.647135 0.762375i $$-0.724033\pi$$
0.647135 0.762375i $$-0.275967\pi$$
$$728$$ 0 0
$$729$$ 1.00000i 0.0370370i
$$730$$ 0 0
$$731$$ −5.82490 + 5.82490i −0.215442 + 0.215442i
$$732$$ 0 0
$$733$$ −0.146061 0.146061i −0.00539490 0.00539490i 0.704404 0.709799i $$-0.251214\pi$$
−0.709799 + 0.704404i $$0.751214\pi$$
$$734$$ 0 0
$$735$$ 6.52284 0.240599
$$736$$ 0 0
$$737$$ −18.6792 −0.688058
$$738$$ 0 0
$$739$$ −1.50766 1.50766i −0.0554601 0.0554601i 0.678833 0.734293i $$-0.262486\pi$$
−0.734293 + 0.678833i $$0.762486\pi$$
$$740$$ 0 0
$$741$$ 0.214897 0.214897i 0.00789445 0.00789445i
$$742$$ 0 0
$$743$$ 40.5175i 1.48644i −0.669046 0.743221i $$-0.733297\pi$$
0.669046 0.743221i $$-0.266703\pi$$
$$744$$ 0 0
$$745$$ 6.69256i 0.245196i
$$746$$ 0 0
$$747$$ 10.6417 10.6417i 0.389358 0.389358i
$$748$$ 0 0
$$749$$ 27.6309 + 27.6309i 1.00961 + 1.00961i
$$750$$ 0 0
$$751$$ 12.5843 0.459208 0.229604 0.973284i $$-0.426257\pi$$
0.229604 + 0.973284i $$0.426257\pi$$
$$752$$ 0 0
$$753$$ −22.2837 −0.812064
$$754$$ 0 0
$$755$$ −3.34129 3.34129i −0.121602 0.121602i
$$756$$ 0 0
$$757$$ 7.49900 7.49900i 0.272556 0.272556i −0.557572 0.830128i $$-0.688267\pi$$
0.830128 + 0.557572i $$0.188267\pi$$
$$758$$ 0 0
$$759$$ 9.89450i 0.359148i
$$760$$ 0 0
$$761$$ 42.8182i 1.55216i −0.630635 0.776079i $$-0.717206\pi$$
0.630635 0.776079i $$-0.282794\pi$$
$$762$$ 0 0
$$763$$ 26.0527 26.0527i 0.943172 0.943172i
$$764$$ 0 0
$$765$$ 1.21137 + 1.21137i 0.0437971 + 0.0437971i
$$766$$ 0 0
$$767$$ 0.475298 0.0171620
$$768$$ 0 0
$$769$$ 12.7455 0.459614 0.229807 0.973236i $$-0.426190\pi$$
0.229807 + 0.973236i $$0.426190\pi$$
$$770$$ 0 0
$$771$$ −6.12382 6.12382i −0.220544 0.220544i
$$772$$ 0 0
$$773$$ 22.8765 22.8765i 0.822809 0.822809i −0.163701 0.986510i $$-0.552343\pi$$
0.986510 + 0.163701i $$0.0523432\pi$$
$$774$$ 0 0
$$775$$ 2.66314i 0.0956630i
$$776$$ 0 0
$$777$$ 28.2704i 1.01419i
$$778$$ 0 0
$$779$$ 23.7194 23.7194i 0.849836 0.849836i
$$780$$ 0 0
$$781$$ 22.5478 + 22.5478i 0.806825 + 0.806825i
$$782$$ 0 0
$$783$$ 7.30205 0.260954
$$784$$ 0 0
$$785$$ 10.8253 0.386370
$$786$$ 0 0
$$787$$ 5.20470 + 5.20470i 0.185528 + 0.185528i 0.793759 0.608232i $$-0.208121\pi$$
−0.608232 + 0.793759i $$0.708121\pi$$
$$788$$ 0 0
$$789$$ −9.41921 + 9.41921i −0.335333 + 0.335333i
$$790$$ 0 0
$$791$$ 43.5317i 1.54781i
$$792$$ 0 0
$$793$$ 0.324298i 0.0115162i
$$794$$ 0 0
$$795$$ −0.233745 + 0.233745i −0.00829009 + 0.00829009i
$$796$$ 0 0
$$797$$ −17.0149 17.0149i −0.602698 0.602698i 0.338330 0.941028i $$-0.390138\pi$$
−0.941028 + 0.338330i $$0.890138\pi$$
$$798$$ 0 0
$$799$$ −10.2306