# Properties

 Label 150.2.e.b.107.1 Level $150$ Weight $2$ Character 150.107 Analytic conductor $1.198$ Analytic rank $0$ Dimension $8$ CM no Inner twists $8$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 150.e (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.19775603032$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 107.1 Root $$0.965926 + 0.258819i$$ of defining polynomial Character $$\chi$$ $$=$$ 150.107 Dual form 150.2.e.b.143.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 + 0.707107i) q^{2} +(-1.67303 - 0.448288i) q^{3} -1.00000i q^{4} +(1.50000 - 0.866025i) q^{6} +(2.44949 + 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})$$ $$q+(-0.707107 + 0.707107i) q^{2} +(-1.67303 - 0.448288i) q^{3} -1.00000i q^{4} +(1.50000 - 0.866025i) q^{6} +(2.44949 + 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.59808 + 1.50000i) q^{9} +5.19615i q^{11} +(-0.448288 + 1.67303i) q^{12} -3.46410 q^{14} -1.00000 q^{16} +(2.12132 - 2.12132i) q^{17} +(-2.89778 + 0.776457i) q^{18} -1.00000i q^{19} +(-3.00000 - 5.19615i) q^{21} +(-3.67423 - 3.67423i) q^{22} +(4.24264 + 4.24264i) q^{23} +(-0.866025 - 1.50000i) q^{24} +(-3.67423 - 3.67423i) q^{27} +(2.44949 - 2.44949i) q^{28} -2.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.32937 - 8.69333i) q^{33} +3.00000i q^{34} +(1.50000 - 2.59808i) q^{36} +(-2.44949 - 2.44949i) q^{37} +(0.707107 + 0.707107i) q^{38} -5.19615i q^{41} +(5.79555 + 1.55291i) q^{42} +(-2.44949 + 2.44949i) q^{43} +5.19615 q^{44} -6.00000 q^{46} +(1.67303 + 0.448288i) q^{48} +5.00000i q^{49} +(-4.50000 + 2.59808i) q^{51} +(-4.24264 - 4.24264i) q^{53} +5.19615 q^{54} +3.46410i q^{56} +(-0.448288 + 1.67303i) q^{57} -10.3923 q^{59} +14.0000 q^{61} +(1.41421 - 1.41421i) q^{62} +(2.68973 + 10.0382i) q^{63} +1.00000i q^{64} +(4.50000 + 7.79423i) q^{66} +(3.67423 + 3.67423i) q^{67} +(-2.12132 - 2.12132i) q^{68} +(-5.19615 - 9.00000i) q^{69} +(0.776457 + 2.89778i) q^{72} +(-6.12372 + 6.12372i) q^{73} +3.46410 q^{74} -1.00000 q^{76} +(-12.7279 + 12.7279i) q^{77} -14.0000i q^{79} +(4.50000 + 7.79423i) q^{81} +(3.67423 + 3.67423i) q^{82} +(-2.12132 - 2.12132i) q^{83} +(-5.19615 + 3.00000i) q^{84} -3.46410i q^{86} +(-3.67423 + 3.67423i) q^{88} +15.5885 q^{89} +(4.24264 - 4.24264i) q^{92} +(3.34607 + 0.896575i) q^{93} +(-1.50000 + 0.866025i) q^{96} +(4.89898 + 4.89898i) q^{97} +(-3.53553 - 3.53553i) q^{98} +(-7.79423 + 13.5000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 12q^{6} + O(q^{10})$$ $$8q + 12q^{6} - 8q^{16} - 24q^{21} - 16q^{31} + 12q^{36} - 48q^{46} - 36q^{51} + 112q^{61} + 36q^{66} - 8q^{76} + 36q^{81} - 12q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 + 0.707107i −0.500000 + 0.500000i
$$3$$ −1.67303 0.448288i −0.965926 0.258819i
$$4$$ 1.00000i 0.500000i
$$5$$ 0 0
$$6$$ 1.50000 0.866025i 0.612372 0.353553i
$$7$$ 2.44949 + 2.44949i 0.925820 + 0.925820i 0.997433 0.0716124i $$-0.0228145\pi$$
−0.0716124 + 0.997433i $$0.522814\pi$$
$$8$$ 0.707107 + 0.707107i 0.250000 + 0.250000i
$$9$$ 2.59808 + 1.50000i 0.866025 + 0.500000i
$$10$$ 0 0
$$11$$ 5.19615i 1.56670i 0.621582 + 0.783349i $$0.286490\pi$$
−0.621582 + 0.783349i $$0.713510\pi$$
$$12$$ −0.448288 + 1.67303i −0.129410 + 0.482963i
$$13$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$14$$ −3.46410 −0.925820
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 2.12132 2.12132i 0.514496 0.514496i −0.401405 0.915901i $$-0.631478\pi$$
0.915901 + 0.401405i $$0.131478\pi$$
$$18$$ −2.89778 + 0.776457i −0.683013 + 0.183013i
$$19$$ 1.00000i 0.229416i −0.993399 0.114708i $$-0.963407\pi$$
0.993399 0.114708i $$-0.0365932\pi$$
$$20$$ 0 0
$$21$$ −3.00000 5.19615i −0.654654 1.13389i
$$22$$ −3.67423 3.67423i −0.783349 0.783349i
$$23$$ 4.24264 + 4.24264i 0.884652 + 0.884652i 0.994003 0.109351i $$-0.0348774\pi$$
−0.109351 + 0.994003i $$0.534877\pi$$
$$24$$ −0.866025 1.50000i −0.176777 0.306186i
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −3.67423 3.67423i −0.707107 0.707107i
$$28$$ 2.44949 2.44949i 0.462910 0.462910i
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ 0.707107 0.707107i 0.125000 0.125000i
$$33$$ 2.32937 8.69333i 0.405492 1.51331i
$$34$$ 3.00000i 0.514496i
$$35$$ 0 0
$$36$$ 1.50000 2.59808i 0.250000 0.433013i
$$37$$ −2.44949 2.44949i −0.402694 0.402694i 0.476488 0.879181i $$-0.341910\pi$$
−0.879181 + 0.476488i $$0.841910\pi$$
$$38$$ 0.707107 + 0.707107i 0.114708 + 0.114708i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 5.19615i 0.811503i −0.913984 0.405751i $$-0.867010\pi$$
0.913984 0.405751i $$-0.132990\pi$$
$$42$$ 5.79555 + 1.55291i 0.894274 + 0.239620i
$$43$$ −2.44949 + 2.44949i −0.373544 + 0.373544i −0.868766 0.495222i $$-0.835087\pi$$
0.495222 + 0.868766i $$0.335087\pi$$
$$44$$ 5.19615 0.783349
$$45$$ 0 0
$$46$$ −6.00000 −0.884652
$$47$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$48$$ 1.67303 + 0.448288i 0.241481 + 0.0647048i
$$49$$ 5.00000i 0.714286i
$$50$$ 0 0
$$51$$ −4.50000 + 2.59808i −0.630126 + 0.363803i
$$52$$ 0 0
$$53$$ −4.24264 4.24264i −0.582772 0.582772i 0.352892 0.935664i $$-0.385198\pi$$
−0.935664 + 0.352892i $$0.885198\pi$$
$$54$$ 5.19615 0.707107
$$55$$ 0 0
$$56$$ 3.46410i 0.462910i
$$57$$ −0.448288 + 1.67303i −0.0593772 + 0.221599i
$$58$$ 0 0
$$59$$ −10.3923 −1.35296 −0.676481 0.736460i $$-0.736496\pi$$
−0.676481 + 0.736460i $$0.736496\pi$$
$$60$$ 0 0
$$61$$ 14.0000 1.79252 0.896258 0.443533i $$-0.146275\pi$$
0.896258 + 0.443533i $$0.146275\pi$$
$$62$$ 1.41421 1.41421i 0.179605 0.179605i
$$63$$ 2.68973 + 10.0382i 0.338874 + 1.26469i
$$64$$ 1.00000i 0.125000i
$$65$$ 0 0
$$66$$ 4.50000 + 7.79423i 0.553912 + 0.959403i
$$67$$ 3.67423 + 3.67423i 0.448879 + 0.448879i 0.894982 0.446103i $$-0.147188\pi$$
−0.446103 + 0.894982i $$0.647188\pi$$
$$68$$ −2.12132 2.12132i −0.257248 0.257248i
$$69$$ −5.19615 9.00000i −0.625543 1.08347i
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0.776457 + 2.89778i 0.0915064 + 0.341506i
$$73$$ −6.12372 + 6.12372i −0.716728 + 0.716728i −0.967934 0.251206i $$-0.919173\pi$$
0.251206 + 0.967934i $$0.419173\pi$$
$$74$$ 3.46410 0.402694
$$75$$ 0 0
$$76$$ −1.00000 −0.114708
$$77$$ −12.7279 + 12.7279i −1.45048 + 1.45048i
$$78$$ 0 0
$$79$$ 14.0000i 1.57512i −0.616236 0.787562i $$-0.711343\pi$$
0.616236 0.787562i $$-0.288657\pi$$
$$80$$ 0 0
$$81$$ 4.50000 + 7.79423i 0.500000 + 0.866025i
$$82$$ 3.67423 + 3.67423i 0.405751 + 0.405751i
$$83$$ −2.12132 2.12132i −0.232845 0.232845i 0.581034 0.813879i $$-0.302648\pi$$
−0.813879 + 0.581034i $$0.802648\pi$$
$$84$$ −5.19615 + 3.00000i −0.566947 + 0.327327i
$$85$$ 0 0
$$86$$ 3.46410i 0.373544i
$$87$$ 0 0
$$88$$ −3.67423 + 3.67423i −0.391675 + 0.391675i
$$89$$ 15.5885 1.65237 0.826187 0.563397i $$-0.190506\pi$$
0.826187 + 0.563397i $$0.190506\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 4.24264 4.24264i 0.442326 0.442326i
$$93$$ 3.34607 + 0.896575i 0.346971 + 0.0929705i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.50000 + 0.866025i −0.153093 + 0.0883883i
$$97$$ 4.89898 + 4.89898i 0.497416 + 0.497416i 0.910633 0.413217i $$-0.135595\pi$$
−0.413217 + 0.910633i $$0.635595\pi$$
$$98$$ −3.53553 3.53553i −0.357143 0.357143i
$$99$$ −7.79423 + 13.5000i −0.783349 + 1.35680i
$$100$$ 0 0
$$101$$ 10.3923i 1.03407i −0.855963 0.517036i $$-0.827035\pi$$
0.855963 0.517036i $$-0.172965\pi$$
$$102$$ 1.34486 5.01910i 0.133161 0.496965i
$$103$$ 9.79796 9.79796i 0.965422 0.965422i −0.0340002 0.999422i $$-0.510825\pi$$
0.999422 + 0.0340002i $$0.0108247\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ 6.36396 6.36396i 0.615227 0.615227i −0.329076 0.944303i $$-0.606737\pi$$
0.944303 + 0.329076i $$0.106737\pi$$
$$108$$ −3.67423 + 3.67423i −0.353553 + 0.353553i
$$109$$ 10.0000i 0.957826i 0.877862 + 0.478913i $$0.158969\pi$$
−0.877862 + 0.478913i $$0.841031\pi$$
$$110$$ 0 0
$$111$$ 3.00000 + 5.19615i 0.284747 + 0.493197i
$$112$$ −2.44949 2.44949i −0.231455 0.231455i
$$113$$ −6.36396 6.36396i −0.598671 0.598671i 0.341288 0.939959i $$-0.389137\pi$$
−0.939959 + 0.341288i $$0.889137\pi$$
$$114$$ −0.866025 1.50000i −0.0811107 0.140488i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 7.34847 7.34847i 0.676481 0.676481i
$$119$$ 10.3923 0.952661
$$120$$ 0 0
$$121$$ −16.0000 −1.45455
$$122$$ −9.89949 + 9.89949i −0.896258 + 0.896258i
$$123$$ −2.32937 + 8.69333i −0.210032 + 0.783851i
$$124$$ 2.00000i 0.179605i
$$125$$ 0 0
$$126$$ −9.00000 5.19615i −0.801784 0.462910i
$$127$$ −7.34847 7.34847i −0.652071 0.652071i 0.301420 0.953491i $$-0.402539\pi$$
−0.953491 + 0.301420i $$0.902539\pi$$
$$128$$ −0.707107 0.707107i −0.0625000 0.0625000i
$$129$$ 5.19615 3.00000i 0.457496 0.264135i
$$130$$ 0 0
$$131$$ 10.3923i 0.907980i −0.891007 0.453990i $$-0.850000\pi$$
0.891007 0.453990i $$-0.150000\pi$$
$$132$$ −8.69333 2.32937i −0.756657 0.202746i
$$133$$ 2.44949 2.44949i 0.212398 0.212398i
$$134$$ −5.19615 −0.448879
$$135$$ 0 0
$$136$$ 3.00000 0.257248
$$137$$ 14.8492 14.8492i 1.26866 1.26866i 0.321874 0.946783i $$-0.395687\pi$$
0.946783 0.321874i $$-0.104313\pi$$
$$138$$ 10.0382 + 2.68973i 0.854508 + 0.228965i
$$139$$ 7.00000i 0.593732i −0.954919 0.296866i $$-0.904058\pi$$
0.954919 0.296866i $$-0.0959415\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −2.59808 1.50000i −0.216506 0.125000i
$$145$$ 0 0
$$146$$ 8.66025i 0.716728i
$$147$$ 2.24144 8.36516i 0.184871 0.689947i
$$148$$ −2.44949 + 2.44949i −0.201347 + 0.201347i
$$149$$ −20.7846 −1.70274 −0.851371 0.524564i $$-0.824228\pi$$
−0.851371 + 0.524564i $$0.824228\pi$$
$$150$$ 0 0
$$151$$ −14.0000 −1.13930 −0.569652 0.821886i $$-0.692922\pi$$
−0.569652 + 0.821886i $$0.692922\pi$$
$$152$$ 0.707107 0.707107i 0.0573539 0.0573539i
$$153$$ 8.69333 2.32937i 0.702814 0.188319i
$$154$$ 18.0000i 1.45048i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −12.2474 12.2474i −0.977453 0.977453i 0.0222985 0.999751i $$-0.492902\pi$$
−0.999751 + 0.0222985i $$0.992902\pi$$
$$158$$ 9.89949 + 9.89949i 0.787562 + 0.787562i
$$159$$ 5.19615 + 9.00000i 0.412082 + 0.713746i
$$160$$ 0 0
$$161$$ 20.7846i 1.63806i
$$162$$ −8.69333 2.32937i −0.683013 0.183013i
$$163$$ 3.67423 3.67423i 0.287788 0.287788i −0.548417 0.836205i $$-0.684769\pi$$
0.836205 + 0.548417i $$0.184769\pi$$
$$164$$ −5.19615 −0.405751
$$165$$ 0 0
$$166$$ 3.00000 0.232845
$$167$$ −8.48528 + 8.48528i −0.656611 + 0.656611i −0.954577 0.297966i $$-0.903692\pi$$
0.297966 + 0.954577i $$0.403692\pi$$
$$168$$ 1.55291 5.79555i 0.119810 0.447137i
$$169$$ 13.0000i 1.00000i
$$170$$ 0 0
$$171$$ 1.50000 2.59808i 0.114708 0.198680i
$$172$$ 2.44949 + 2.44949i 0.186772 + 0.186772i
$$173$$ 8.48528 + 8.48528i 0.645124 + 0.645124i 0.951811 0.306687i $$-0.0992203\pi$$
−0.306687 + 0.951811i $$0.599220\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 5.19615i 0.391675i
$$177$$ 17.3867 + 4.65874i 1.30686 + 0.350173i
$$178$$ −11.0227 + 11.0227i −0.826187 + 0.826187i
$$179$$ 15.5885 1.16514 0.582568 0.812782i $$-0.302048\pi$$
0.582568 + 0.812782i $$0.302048\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ −23.4225 6.27603i −1.73144 0.463937i
$$184$$ 6.00000i 0.442326i
$$185$$ 0 0
$$186$$ −3.00000 + 1.73205i −0.219971 + 0.127000i
$$187$$ 11.0227 + 11.0227i 0.806060 + 0.806060i
$$188$$ 0 0
$$189$$ 18.0000i 1.30931i
$$190$$ 0 0
$$191$$ 10.3923i 0.751961i 0.926628 + 0.375980i $$0.122694\pi$$
−0.926628 + 0.375980i $$0.877306\pi$$
$$192$$ 0.448288 1.67303i 0.0323524 0.120741i
$$193$$ −6.12372 + 6.12372i −0.440795 + 0.440795i −0.892279 0.451484i $$-0.850895\pi$$
0.451484 + 0.892279i $$0.350895\pi$$
$$194$$ −6.92820 −0.497416
$$195$$ 0 0
$$196$$ 5.00000 0.357143
$$197$$ 4.24264 4.24264i 0.302276 0.302276i −0.539628 0.841904i $$-0.681435\pi$$
0.841904 + 0.539628i $$0.181435\pi$$
$$198$$ −4.03459 15.0573i −0.286726 1.07008i
$$199$$ 16.0000i 1.13421i 0.823646 + 0.567105i $$0.191937\pi$$
−0.823646 + 0.567105i $$0.808063\pi$$
$$200$$ 0 0
$$201$$ −4.50000 7.79423i −0.317406 0.549762i
$$202$$ 7.34847 + 7.34847i 0.517036 + 0.517036i
$$203$$ 0 0
$$204$$ 2.59808 + 4.50000i 0.181902 + 0.315063i
$$205$$ 0 0
$$206$$ 13.8564i 0.965422i
$$207$$ 4.65874 + 17.3867i 0.323805 + 1.20846i
$$208$$ 0 0
$$209$$ 5.19615 0.359425
$$210$$ 0 0
$$211$$ 23.0000 1.58339 0.791693 0.610920i $$-0.209200\pi$$
0.791693 + 0.610920i $$0.209200\pi$$
$$212$$ −4.24264 + 4.24264i −0.291386 + 0.291386i
$$213$$ 0 0
$$214$$ 9.00000i 0.615227i
$$215$$ 0 0
$$216$$ 5.19615i 0.353553i
$$217$$ −4.89898 4.89898i −0.332564 0.332564i
$$218$$ −7.07107 7.07107i −0.478913 0.478913i
$$219$$ 12.9904 7.50000i 0.877809 0.506803i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ −5.79555 1.55291i −0.388972 0.104225i
$$223$$ 9.79796 9.79796i 0.656120 0.656120i −0.298340 0.954460i $$-0.596433\pi$$
0.954460 + 0.298340i $$0.0964329\pi$$
$$224$$ 3.46410 0.231455
$$225$$ 0 0
$$226$$ 9.00000 0.598671
$$227$$ −8.48528 + 8.48528i −0.563188 + 0.563188i −0.930212 0.367024i $$-0.880377\pi$$
0.367024 + 0.930212i $$0.380377\pi$$
$$228$$ 1.67303 + 0.448288i 0.110799 + 0.0296886i
$$229$$ 16.0000i 1.05731i −0.848837 0.528655i $$-0.822697\pi$$
0.848837 0.528655i $$-0.177303\pi$$
$$230$$ 0 0
$$231$$ 27.0000 15.5885i 1.77647 1.02565i
$$232$$ 0 0
$$233$$ 12.7279 + 12.7279i 0.833834 + 0.833834i 0.988039 0.154205i $$-0.0492816\pi$$
−0.154205 + 0.988039i $$0.549282\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 10.3923i 0.676481i
$$237$$ −6.27603 + 23.4225i −0.407672 + 1.52145i
$$238$$ −7.34847 + 7.34847i −0.476331 + 0.476331i
$$239$$ −20.7846 −1.34444 −0.672222 0.740349i $$-0.734660\pi$$
−0.672222 + 0.740349i $$0.734660\pi$$
$$240$$ 0 0
$$241$$ −1.00000 −0.0644157 −0.0322078 0.999481i $$-0.510254\pi$$
−0.0322078 + 0.999481i $$0.510254\pi$$
$$242$$ 11.3137 11.3137i 0.727273 0.727273i
$$243$$ −4.03459 15.0573i −0.258819 0.965926i
$$244$$ 14.0000i 0.896258i
$$245$$ 0 0
$$246$$ −4.50000 7.79423i −0.286910 0.496942i
$$247$$ 0 0
$$248$$ −1.41421 1.41421i −0.0898027 0.0898027i
$$249$$ 2.59808 + 4.50000i 0.164646 + 0.285176i
$$250$$ 0 0
$$251$$ 5.19615i 0.327978i 0.986462 + 0.163989i $$0.0524362\pi$$
−0.986462 + 0.163989i $$0.947564\pi$$
$$252$$ 10.0382 2.68973i 0.632347 0.169437i
$$253$$ −22.0454 + 22.0454i −1.38598 + 1.38598i
$$254$$ 10.3923 0.652071
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −4.24264 + 4.24264i −0.264649 + 0.264649i −0.826940 0.562291i $$-0.809920\pi$$
0.562291 + 0.826940i $$0.309920\pi$$
$$258$$ −1.55291 + 5.79555i −0.0966802 + 0.360815i
$$259$$ 12.0000i 0.745644i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 7.34847 + 7.34847i 0.453990 + 0.453990i
$$263$$ −12.7279 12.7279i −0.784837 0.784837i 0.195805 0.980643i $$-0.437268\pi$$
−0.980643 + 0.195805i $$0.937268\pi$$
$$264$$ 7.79423 4.50000i 0.479702 0.276956i
$$265$$ 0 0
$$266$$ 3.46410i 0.212398i
$$267$$ −26.0800 6.98811i −1.59607 0.427666i
$$268$$ 3.67423 3.67423i 0.224440 0.224440i
$$269$$ −20.7846 −1.26726 −0.633630 0.773636i $$-0.718436\pi$$
−0.633630 + 0.773636i $$0.718436\pi$$
$$270$$ 0 0
$$271$$ −10.0000 −0.607457 −0.303728 0.952759i $$-0.598232\pi$$
−0.303728 + 0.952759i $$0.598232\pi$$
$$272$$ −2.12132 + 2.12132i −0.128624 + 0.128624i
$$273$$ 0 0
$$274$$ 21.0000i 1.26866i
$$275$$ 0 0
$$276$$ −9.00000 + 5.19615i −0.541736 + 0.312772i
$$277$$ −9.79796 9.79796i −0.588702 0.588702i 0.348578 0.937280i $$-0.386665\pi$$
−0.937280 + 0.348578i $$0.886665\pi$$
$$278$$ 4.94975 + 4.94975i 0.296866 + 0.296866i
$$279$$ −5.19615 3.00000i −0.311086 0.179605i
$$280$$ 0 0
$$281$$ 20.7846i 1.23991i 0.784639 + 0.619953i $$0.212848\pi$$
−0.784639 + 0.619953i $$0.787152\pi$$
$$282$$ 0 0
$$283$$ 6.12372 6.12372i 0.364018 0.364018i −0.501272 0.865290i $$-0.667134\pi$$
0.865290 + 0.501272i $$0.167134\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 12.7279 12.7279i 0.751305 0.751305i
$$288$$ 2.89778 0.776457i 0.170753 0.0457532i
$$289$$ 8.00000i 0.470588i
$$290$$ 0 0
$$291$$ −6.00000 10.3923i −0.351726 0.609208i
$$292$$ 6.12372 + 6.12372i 0.358364 + 0.358364i
$$293$$ 21.2132 + 21.2132i 1.23929 + 1.23929i 0.960292 + 0.278996i $$0.0900018\pi$$
0.278996 + 0.960292i $$0.409998\pi$$
$$294$$ 4.33013 + 7.50000i 0.252538 + 0.437409i
$$295$$ 0 0
$$296$$ 3.46410i 0.201347i
$$297$$ 19.0919 19.0919i 1.10782 1.10782i
$$298$$ 14.6969 14.6969i 0.851371 0.851371i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −12.0000 −0.691669
$$302$$ 9.89949 9.89949i 0.569652 0.569652i
$$303$$ −4.65874 + 17.3867i −0.267638 + 0.998838i
$$304$$ 1.00000i 0.0573539i
$$305$$ 0 0
$$306$$ −4.50000 + 7.79423i −0.257248 + 0.445566i
$$307$$ −1.22474 1.22474i −0.0698999 0.0698999i 0.671293 0.741192i $$-0.265739\pi$$
−0.741192 + 0.671293i $$0.765739\pi$$
$$308$$ 12.7279 + 12.7279i 0.725241 + 0.725241i
$$309$$ −20.7846 + 12.0000i −1.18240 + 0.682656i
$$310$$ 0 0
$$311$$ 31.1769i 1.76788i −0.467600 0.883940i $$-0.654881\pi$$
0.467600 0.883940i $$-0.345119\pi$$
$$312$$ 0 0
$$313$$ 14.6969 14.6969i 0.830720 0.830720i −0.156895 0.987615i $$-0.550148\pi$$
0.987615 + 0.156895i $$0.0501485\pi$$
$$314$$ 17.3205 0.977453
$$315$$ 0 0
$$316$$ −14.0000 −0.787562
$$317$$ −8.48528 + 8.48528i −0.476581 + 0.476581i −0.904036 0.427456i $$-0.859410\pi$$
0.427456 + 0.904036i $$0.359410\pi$$
$$318$$ −10.0382 2.68973i −0.562914 0.150832i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −13.5000 + 7.79423i −0.753497 + 0.435031i
$$322$$ −14.6969 14.6969i −0.819028 0.819028i
$$323$$ −2.12132 2.12132i −0.118033 0.118033i
$$324$$ 7.79423 4.50000i 0.433013 0.250000i
$$325$$ 0 0
$$326$$ 5.19615i 0.287788i
$$327$$ 4.48288 16.7303i 0.247904 0.925189i
$$328$$ 3.67423 3.67423i 0.202876 0.202876i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −13.0000 −0.714545 −0.357272 0.934000i $$-0.616293\pi$$
−0.357272 + 0.934000i $$0.616293\pi$$
$$332$$ −2.12132 + 2.12132i −0.116423 + 0.116423i
$$333$$ −2.68973 10.0382i −0.147396 0.550090i
$$334$$ 12.0000i 0.656611i
$$335$$ 0 0
$$336$$ 3.00000 + 5.19615i 0.163663 + 0.283473i
$$337$$ 3.67423 + 3.67423i 0.200148 + 0.200148i 0.800064 0.599915i $$-0.204799\pi$$
−0.599915 + 0.800064i $$0.704799\pi$$
$$338$$ −9.19239 9.19239i −0.500000 0.500000i
$$339$$ 7.79423 + 13.5000i 0.423324 + 0.733219i
$$340$$ 0 0
$$341$$ 10.3923i 0.562775i
$$342$$ 0.776457 + 2.89778i 0.0419860 + 0.156694i
$$343$$ 4.89898 4.89898i 0.264520 0.264520i
$$344$$ −3.46410 −0.186772
$$345$$ 0 0
$$346$$ −12.0000 −0.645124
$$347$$ −6.36396 + 6.36396i −0.341635 + 0.341635i −0.856982 0.515347i $$-0.827663\pi$$
0.515347 + 0.856982i $$0.327663\pi$$
$$348$$ 0 0
$$349$$ 22.0000i 1.17763i −0.808267 0.588817i $$-0.799594\pi$$
0.808267 0.588817i $$-0.200406\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 3.67423 + 3.67423i 0.195837 + 0.195837i
$$353$$ −12.7279 12.7279i −0.677439 0.677439i 0.281981 0.959420i $$-0.409008\pi$$
−0.959420 + 0.281981i $$0.909008\pi$$
$$354$$ −15.5885 + 9.00000i −0.828517 + 0.478345i
$$355$$ 0 0
$$356$$ 15.5885i 0.826187i
$$357$$ −17.3867 4.65874i −0.920200 0.246567i
$$358$$ −11.0227 + 11.0227i −0.582568 + 0.582568i
$$359$$ 10.3923 0.548485 0.274242 0.961661i $$-0.411573\pi$$
0.274242 + 0.961661i $$0.411573\pi$$
$$360$$ 0 0
$$361$$ 18.0000 0.947368
$$362$$ 1.41421 1.41421i 0.0743294 0.0743294i
$$363$$ 26.7685 + 7.17260i 1.40498 + 0.376464i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 21.0000 12.1244i 1.09769 0.633750i
$$367$$ −14.6969 14.6969i −0.767174 0.767174i 0.210434 0.977608i $$-0.432512\pi$$
−0.977608 + 0.210434i $$0.932512\pi$$
$$368$$ −4.24264 4.24264i −0.221163 0.221163i
$$369$$ 7.79423 13.5000i 0.405751 0.702782i
$$370$$ 0 0
$$371$$ 20.7846i 1.07908i
$$372$$ 0.896575 3.34607i 0.0464853 0.173485i
$$373$$ 2.44949 2.44949i 0.126830 0.126830i −0.640843 0.767672i $$-0.721415\pi$$
0.767672 + 0.640843i $$0.221415\pi$$
$$374$$ −15.5885 −0.806060
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 12.7279 + 12.7279i 0.654654 + 0.654654i
$$379$$ 11.0000i 0.565032i 0.959263 + 0.282516i $$0.0911690\pi$$
−0.959263 + 0.282516i $$0.908831\pi$$
$$380$$ 0 0
$$381$$ 9.00000 + 15.5885i 0.461084 + 0.798621i
$$382$$ −7.34847 7.34847i −0.375980 0.375980i
$$383$$ −4.24264 4.24264i −0.216789 0.216789i 0.590355 0.807144i $$-0.298988\pi$$
−0.807144 + 0.590355i $$0.798988\pi$$
$$384$$ 0.866025 + 1.50000i 0.0441942 + 0.0765466i
$$385$$ 0 0
$$386$$ 8.66025i 0.440795i
$$387$$ −10.0382 + 2.68973i −0.510270 + 0.136726i
$$388$$ 4.89898 4.89898i 0.248708 0.248708i
$$389$$ 10.3923 0.526911 0.263455 0.964672i $$-0.415138\pi$$
0.263455 + 0.964672i $$0.415138\pi$$
$$390$$ 0 0
$$391$$ 18.0000 0.910299
$$392$$ −3.53553 + 3.53553i −0.178571 + 0.178571i
$$393$$ −4.65874 + 17.3867i −0.235002 + 0.877041i
$$394$$ 6.00000i 0.302276i
$$395$$ 0 0
$$396$$ 13.5000 + 7.79423i 0.678401 + 0.391675i
$$397$$ 19.5959 + 19.5959i 0.983491 + 0.983491i 0.999866 0.0163750i $$-0.00521255\pi$$
−0.0163750 + 0.999866i $$0.505213\pi$$
$$398$$ −11.3137 11.3137i −0.567105 0.567105i
$$399$$ −5.19615 + 3.00000i −0.260133 + 0.150188i
$$400$$ 0 0
$$401$$ 5.19615i 0.259483i 0.991548 + 0.129742i $$0.0414148\pi$$
−0.991548 + 0.129742i $$0.958585\pi$$
$$402$$ 8.69333 + 2.32937i 0.433584 + 0.116178i
$$403$$ 0 0
$$404$$ −10.3923 −0.517036
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 12.7279 12.7279i 0.630900 0.630900i
$$408$$ −5.01910 1.34486i −0.248482 0.0665807i
$$409$$ 5.00000i 0.247234i 0.992330 + 0.123617i $$0.0394494\pi$$
−0.992330 + 0.123617i $$0.960551\pi$$
$$410$$ 0 0
$$411$$ −31.5000 + 18.1865i −1.55378 + 0.897076i
$$412$$ −9.79796 9.79796i −0.482711 0.482711i
$$413$$ −25.4558 25.4558i −1.25260 1.25260i
$$414$$ −15.5885 9.00000i −0.766131 0.442326i
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −3.13801 + 11.7112i −0.153669 + 0.573501i
$$418$$ −3.67423 + 3.67423i −0.179713 + 0.179713i
$$419$$ 25.9808 1.26924 0.634622 0.772823i $$-0.281156\pi$$
0.634622 + 0.772823i $$0.281156\pi$$
$$420$$ 0 0
$$421$$ 4.00000 0.194948 0.0974740 0.995238i $$-0.468924\pi$$
0.0974740 + 0.995238i $$0.468924\pi$$
$$422$$ −16.2635 + 16.2635i −0.791693 + 0.791693i
$$423$$ 0 0
$$424$$ 6.00000i 0.291386i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 34.2929 + 34.2929i 1.65955 + 1.65955i
$$428$$ −6.36396 6.36396i −0.307614 0.307614i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 10.3923i 0.500580i 0.968171 + 0.250290i $$0.0805259\pi$$
−0.968171 + 0.250290i $$0.919474\pi$$
$$432$$ 3.67423 + 3.67423i 0.176777 + 0.176777i
$$433$$ −15.9217 + 15.9217i −0.765147 + 0.765147i −0.977248 0.212101i $$-0.931970\pi$$
0.212101 + 0.977248i $$0.431970\pi$$
$$434$$ 6.92820 0.332564
$$435$$ 0 0
$$436$$ 10.0000 0.478913
$$437$$ 4.24264 4.24264i 0.202953 0.202953i
$$438$$ −3.88229 + 14.4889i −0.185503 + 0.692306i
$$439$$ 4.00000i 0.190910i 0.995434 + 0.0954548i $$0.0304305\pi$$
−0.995434 + 0.0954548i $$0.969569\pi$$
$$440$$ 0 0
$$441$$ −7.50000 + 12.9904i −0.357143 + 0.618590i
$$442$$ 0 0
$$443$$ 14.8492 + 14.8492i 0.705509 + 0.705509i 0.965587 0.260079i $$-0.0837485\pi$$
−0.260079 + 0.965587i $$0.583748\pi$$
$$444$$ 5.19615 3.00000i 0.246598 0.142374i
$$445$$ 0 0
$$446$$ 13.8564i 0.656120i
$$447$$ 34.7733 + 9.31749i 1.64472 + 0.440702i
$$448$$ −2.44949 + 2.44949i −0.115728 + 0.115728i
$$449$$ 25.9808 1.22611 0.613054 0.790041i $$-0.289941\pi$$
0.613054 + 0.790041i $$0.289941\pi$$
$$450$$ 0 0
$$451$$ 27.0000 1.27138
$$452$$ −6.36396 + 6.36396i −0.299336 + 0.299336i
$$453$$ 23.4225 + 6.27603i 1.10048 + 0.294874i
$$454$$ 12.0000i 0.563188i
$$455$$ 0 0
$$456$$ −1.50000 + 0.866025i −0.0702439 + 0.0405554i
$$457$$ 18.3712 + 18.3712i 0.859367 + 0.859367i 0.991264 0.131896i $$-0.0421066\pi$$
−0.131896 + 0.991264i $$0.542107\pi$$
$$458$$ 11.3137 + 11.3137i 0.528655 + 0.528655i
$$459$$ −15.5885 −0.727607
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ −8.06918 + 30.1146i −0.375412 + 1.40106i
$$463$$ −24.4949 + 24.4949i −1.13837 + 1.13837i −0.149633 + 0.988742i $$0.547809\pi$$
−0.988742 + 0.149633i $$0.952191\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −18.0000 −0.833834
$$467$$ −8.48528 + 8.48528i −0.392652 + 0.392652i −0.875632 0.482980i $$-0.839555\pi$$
0.482980 + 0.875632i $$0.339555\pi$$
$$468$$ 0 0
$$469$$ 18.0000i 0.831163i
$$470$$ 0 0
$$471$$ 15.0000 + 25.9808i 0.691164 + 1.19713i
$$472$$ −7.34847 7.34847i −0.338241 0.338241i
$$473$$ −12.7279 12.7279i −0.585230 0.585230i
$$474$$ −12.1244 21.0000i −0.556890 0.964562i
$$475$$ 0 0
$$476$$ 10.3923i 0.476331i
$$477$$ −4.65874 17.3867i −0.213309 0.796081i
$$478$$ 14.6969 14.6969i 0.672222 0.672222i
$$479$$ −10.3923 −0.474837 −0.237418 0.971408i $$-0.576301\pi$$
−0.237418 + 0.971408i $$0.576301\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0.707107 0.707107i 0.0322078 0.0322078i
$$483$$ 9.31749 34.7733i 0.423960 1.58224i
$$484$$ 16.0000i 0.727273i
$$485$$ 0 0
$$486$$ 13.5000 + 7.79423i 0.612372 + 0.353553i
$$487$$ −22.0454 22.0454i −0.998973 0.998973i 0.00102669 0.999999i $$-0.499673\pi$$
−0.999999 + 0.00102669i $$0.999673\pi$$
$$488$$ 9.89949 + 9.89949i 0.448129 + 0.448129i
$$489$$ −7.79423 + 4.50000i −0.352467 + 0.203497i
$$490$$ 0 0
$$491$$ 31.1769i 1.40699i 0.710698 + 0.703497i $$0.248379\pi$$
−0.710698 + 0.703497i $$0.751621\pi$$
$$492$$ 8.69333 + 2.32937i 0.391926 + 0.105016i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 2.00000 0.0898027
$$497$$ 0 0
$$498$$ −5.01910 1.34486i −0.224911 0.0602648i
$$499$$ 20.0000i 0.895323i −0.894203 0.447661i $$-0.852257\pi$$
0.894203 0.447661i $$-0.147743\pi$$
$$500$$ 0 0
$$501$$ 18.0000 10.3923i 0.804181 0.464294i
$$502$$ −3.67423 3.67423i −0.163989 0.163989i
$$503$$ −8.48528 8.48528i −0.378340 0.378340i 0.492163 0.870503i $$-0.336206\pi$$
−0.870503 + 0.492163i $$0.836206\pi$$
$$504$$ −5.19615 + 9.00000i −0.231455 + 0.400892i
$$505$$ 0 0
$$506$$ 31.1769i 1.38598i
$$507$$ 5.82774 21.7494i 0.258819 0.965926i
$$508$$ −7.34847 + 7.34847i −0.326036 + 0.326036i
$$509$$ 10.3923 0.460631 0.230315 0.973116i $$-0.426024\pi$$
0.230315 + 0.973116i $$0.426024\pi$$
$$510$$ 0 0
$$511$$ −30.0000 −1.32712
$$512$$ −0.707107 + 0.707107i −0.0312500 + 0.0312500i
$$513$$ −3.67423 + 3.67423i −0.162221 + 0.162221i
$$514$$ 6.00000i 0.264649i
$$515$$ 0 0
$$516$$ −3.00000 5.19615i −0.132068 0.228748i
$$517$$ 0 0
$$518$$ 8.48528 + 8.48528i 0.372822 + 0.372822i
$$519$$ −10.3923 18.0000i −0.456172 0.790112i
$$520$$ 0 0
$$521$$ 36.3731i 1.59353i −0.604287 0.796766i $$-0.706542\pi$$
0.604287 0.796766i $$-0.293458\pi$$
$$522$$ 0 0
$$523$$ −30.6186 + 30.6186i −1.33886 + 1.33886i −0.441692 + 0.897167i $$0.645622\pi$$
−0.897167 + 0.441692i $$0.854378\pi$$
$$524$$ −10.3923 −0.453990
$$525$$ 0 0
$$526$$ 18.0000 0.784837
$$527$$ −4.24264 + 4.24264i −0.184812 + 0.184812i
$$528$$ −2.32937 + 8.69333i −0.101373 + 0.378329i
$$529$$ 13.0000i 0.565217i
$$530$$ 0 0
$$531$$ −27.0000 15.5885i −1.17170 0.676481i
$$532$$ −2.44949 2.44949i −0.106199 0.106199i
$$533$$ 0 0
$$534$$ 23.3827 13.5000i 1.01187 0.584202i
$$535$$ 0 0
$$536$$ 5.19615i 0.224440i
$$537$$ −26.0800 6.98811i −1.12543 0.301559i
$$538$$ 14.6969 14.6969i 0.633630 0.633630i
$$539$$ −25.9808 −1.11907
$$540$$ 0 0
$$541$$ 8.00000 0.343947 0.171973 0.985102i $$-0.444986\pi$$
0.171973 + 0.985102i $$0.444986\pi$$
$$542$$ 7.07107 7.07107i 0.303728 0.303728i
$$543$$ 3.34607 + 0.896575i 0.143593 + 0.0384757i
$$544$$ 3.00000i 0.128624i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −8.57321 8.57321i −0.366564 0.366564i 0.499658 0.866223i $$-0.333459\pi$$
−0.866223 + 0.499658i $$0.833459\pi$$
$$548$$ −14.8492 14.8492i −0.634328 0.634328i
$$549$$ 36.3731 + 21.0000i 1.55236 + 0.896258i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 2.68973 10.0382i 0.114482 0.427254i
$$553$$ 34.2929 34.2929i 1.45828 1.45828i
$$554$$ 13.8564 0.588702
$$555$$ 0 0
$$556$$ −7.00000 −0.296866
$$557$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$558$$ 5.79555 1.55291i 0.245345 0.0657401i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −13.5000 23.3827i −0.569970 0.987218i
$$562$$ −14.6969 14.6969i −0.619953 0.619953i
$$563$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 8.66025i 0.364018i
$$567$$ −8.06918 + 30.1146i −0.338874 + 1.26469i
$$568$$ 0 0
$$569$$ −25.9808 −1.08917 −0.544585 0.838706i $$-0.683313\pi$$
−0.544585 + 0.838706i $$0.683313\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 0 0
$$573$$ 4.65874 17.3867i 0.194622 0.726338i
$$574$$ 18.0000i 0.751305i
$$575$$ 0 0
$$576$$ −1.50000 + 2.59808i −0.0625000 + 0.108253i
$$577$$ −13.4722 13.4722i −0.560855 0.560855i 0.368695 0.929550i $$-0.379805\pi$$
−0.929550 + 0.368695i $$0.879805\pi$$
$$578$$ −5.65685 5.65685i −0.235294 0.235294i
$$579$$ 12.9904 7.50000i 0.539862 0.311689i
$$580$$ 0 0
$$581$$ 10.3923i 0.431145i
$$582$$ 11.5911 + 3.10583i 0.480467 + 0.128741i
$$583$$ 22.0454 22.0454i 0.913027 0.913027i
$$584$$ −8.66025 −0.358364
$$585$$ 0 0
$$586$$ −30.0000 −1.23929
$$587$$ 14.8492 14.8492i 0.612894 0.612894i −0.330805 0.943699i $$-0.607320\pi$$
0.943699 + 0.330805i $$0.107320\pi$$
$$588$$ −8.36516 2.24144i −0.344974 0.0924354i
$$589$$ 2.00000i 0.0824086i
$$590$$ 0 0
$$591$$ −9.00000 + 5.19615i −0.370211 + 0.213741i
$$592$$ 2.44949 + 2.44949i 0.100673 + 0.100673i
$$593$$ 23.3345 + 23.3345i 0.958234 + 0.958234i 0.999162 0.0409281i $$-0.0130314\pi$$
−0.0409281 + 0.999162i $$0.513031\pi$$
$$594$$ 27.0000i 1.10782i
$$595$$ 0 0
$$596$$ 20.7846i 0.851371i
$$597$$ 7.17260 26.7685i 0.293555 1.09556i
$$598$$ 0 0
$$599$$ 10.3923 0.424618 0.212309 0.977203i $$-0.431902\pi$$
0.212309 + 0.977203i $$0.431902\pi$$
$$600$$ 0 0
$$601$$ −5.00000 −0.203954 −0.101977 0.994787i $$-0.532517\pi$$
−0.101977 + 0.994787i $$0.532517\pi$$
$$602$$ 8.48528 8.48528i 0.345834 0.345834i
$$603$$ 4.03459 + 15.0573i 0.164301 + 0.613180i
$$604$$ 14.0000i 0.569652i
$$605$$ 0 0
$$606$$ −9.00000 15.5885i −0.365600 0.633238i
$$607$$ 4.89898 + 4.89898i 0.198843 + 0.198843i 0.799504 0.600661i $$-0.205096\pi$$
−0.600661 + 0.799504i $$0.705096\pi$$
$$608$$ −0.707107 0.707107i −0.0286770 0.0286770i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −2.32937 8.69333i −0.0941593 0.351407i
$$613$$ 17.1464 17.1464i 0.692538 0.692538i −0.270252 0.962790i $$-0.587107\pi$$
0.962790 + 0.270252i $$0.0871070\pi$$
$$614$$ 1.73205 0.0698999
$$615$$ 0 0
$$616$$ −18.0000 −0.725241
$$617$$ 21.2132 21.2132i 0.854011 0.854011i −0.136613 0.990624i $$-0.543622\pi$$
0.990624 + 0.136613i $$0.0436217\pi$$
$$618$$ 6.21166 23.1822i 0.249869 0.932526i
$$619$$ 4.00000i 0.160774i 0.996764 + 0.0803868i $$0.0256155\pi$$
−0.996764 + 0.0803868i $$0.974384\pi$$
$$620$$ 0 0
$$621$$ 31.1769i 1.25109i
$$622$$ 22.0454 + 22.0454i 0.883940 + 0.883940i
$$623$$ 38.1838 + 38.1838i 1.52980 + 1.52980i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 20.7846i 0.830720i
$$627$$ −8.69333 2.32937i −0.347178 0.0930261i
$$628$$ −12.2474 + 12.2474i −0.488726 + 0.488726i
$$629$$ −10.3923 −0.414368
$$630$$ 0 0
$$631$$ −34.0000 −1.35352 −0.676759 0.736204i $$-0.736616\pi$$
−0.676759 + 0.736204i $$0.736616\pi$$
$$632$$ 9.89949 9.89949i 0.393781 0.393781i
$$633$$ −38.4797 10.3106i −1.52943 0.409810i
$$634$$ 12.0000i 0.476581i
$$635$$ 0 0
$$636$$ 9.00000 5.19615i 0.356873 0.206041i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 20.7846i 0.820943i −0.911873 0.410471i $$-0.865364\pi$$
0.911873 0.410471i $$-0.134636\pi$$
$$642$$ 4.03459 15.0573i 0.159233 0.594264i
$$643$$ −22.0454 + 22.0454i −0.869386 + 0.869386i −0.992404 0.123018i $$-0.960743\pi$$
0.123018 + 0.992404i $$0.460743\pi$$
$$644$$ 20.7846 0.819028
$$645$$ 0 0
$$646$$ 3.00000 0.118033
$$647$$ −33.9411 + 33.9411i −1.33436 + 1.33436i −0.432941 + 0.901422i $$0.642524\pi$$
−0.901422 + 0.432941i $$0.857476\pi$$
$$648$$ −2.32937 + 8.69333i −0.0915064 + 0.341506i
$$649$$ 54.0000i 2.11969i
$$650$$ 0 0
$$651$$ 6.00000 + 10.3923i 0.235159 + 0.407307i
$$652$$ −3.67423 3.67423i −0.143894 0.143894i
$$653$$ −4.24264 4.24264i −0.166027 0.166027i 0.619203 0.785231i $$-0.287456\pi$$
−0.785231 + 0.619203i $$0.787456\pi$$
$$654$$ 8.66025 + 15.0000i 0.338643 + 0.586546i
$$655$$ 0 0
$$656$$ 5.19615i 0.202876i
$$657$$ −25.0955 + 6.72432i −0.979068 + 0.262341i
$$658$$ 0 0
$$659$$ −25.9808 −1.01207 −0.506033 0.862514i $$-0.668889\pi$$
−0.506033 + 0.862514i $$0.668889\pi$$
$$660$$ 0 0
$$661$$ −20.0000 −0.777910 −0.388955 0.921257i $$-0.627164\pi$$
−0.388955 + 0.921257i $$0.627164\pi$$
$$662$$ 9.19239 9.19239i 0.357272 0.357272i
$$663$$ 0 0
$$664$$ 3.00000i 0.116423i
$$665$$ 0 0
$$666$$ 9.00000 + 5.19615i 0.348743 + 0.201347i
$$667$$ 0 0
$$668$$ 8.48528 + 8.48528i 0.328305 + 0.328305i
$$669$$ −20.7846 + 12.0000i −0.803579 + 0.463947i
$$670$$ 0 0
$$671$$ 72.7461i 2.80833i
$$672$$ −5.79555 1.55291i −0.223568 0.0599050i
$$673$$ 4.89898 4.89898i 0.188842 0.188842i −0.606353 0.795195i $$-0.707368\pi$$
0.795195 + 0.606353i $$0.207368\pi$$
$$674$$ −5.19615 −0.200148
$$675$$ 0 0
$$676$$ 13.0000 0.500000
$$677$$ −25.4558 + 25.4558i −0.978348 + 0.978348i −0.999771 0.0214229i $$-0.993180\pi$$
0.0214229 + 0.999771i $$0.493180\pi$$
$$678$$ −15.0573 4.03459i −0.578272 0.154947i
$$679$$ 24.0000i 0.921035i
$$680$$ 0 0
$$681$$ 18.0000 10.3923i 0.689761 0.398234i
$$682$$ 7.34847 + 7.34847i 0.281387 + 0.281387i
$$683$$ 14.8492 + 14.8492i 0.568190 + 0.568190i 0.931621 0.363431i $$-0.118395\pi$$
−0.363431 + 0.931621i $$0.618395\pi$$
$$684$$ −2.59808 1.50000i −0.0993399 0.0573539i
$$685$$ 0 0
$$686$$ 6.92820i 0.264520i
$$687$$ −7.17260 + 26.7685i −0.273652 + 1.02128i
$$688$$ 2.44949 2.44949i 0.0933859 0.0933859i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 37.0000 1.40755 0.703773 0.710425i $$-0.251497\pi$$
0.703773 + 0.710425i $$0.251497\pi$$
$$692$$ 8.48528 8.48528i 0.322562 0.322562i
$$693$$ −52.1600 + 13.9762i −1.98139 + 0.530913i
$$694$$ 9.00000i 0.341635i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −11.0227 11.0227i −0.417515 0.417515i
$$698$$ 15.5563 + 15.5563i 0.588817 + 0.588817i
$$699$$ −15.5885 27.0000i −0.589610 1.02123i
$$700$$ 0 0
$$701$$ 20.7846i 0.785024i 0.919747 + 0.392512i $$0.128394\pi$$
−0.919747 + 0.392512i $$0.871606\pi$$
$$702$$ 0 0
$$703$$ −2.44949 + 2.44949i −0.0923843 + 0.0923843i
$$704$$ −5.19615 −0.195837
$$705$$ 0 0
$$706$$ 18.0000 0.677439
$$707$$ 25.4558 25.4558i 0.957366 0.957366i
$$708$$ 4.65874 17.3867i 0.175086 0.653431i
$$709$$ 40.0000i 1.50223i −0.660171 0.751116i $$-0.729516\pi$$
0.660171 0.751116i $$-0.270484\pi$$
$$710$$ 0 0
$$711$$ 21.0000 36.3731i 0.787562 1.36410i
$$712$$ 11.0227 + 11.0227i 0.413093 + 0.413093i
$$713$$ −8.48528 8.48528i −0.317776 0.317776i
$$714$$ 15.5885 9.00000i 0.583383 0.336817i
$$715$$ 0 0
$$716$$ 15.5885i 0.582568i
$$717$$ 34.7733 + 9.31749i 1.29863 + 0.347968i
$$718$$ −7.34847 + 7.34847i −0.274242 + 0.274242i
$$719$$ −31.1769 −1.16270 −0.581351 0.813653i $$-0.697476\pi$$
−0.581351 + 0.813653i $$0.697476\pi$$
$$720$$ 0 0
$$721$$ 48.0000 1.78761
$$722$$ −12.7279 + 12.7279i −0.473684 + 0.473684i
$$723$$ 1.67303 + 0.448288i 0.0622208 + 0.0166720i
$$724$$ 2.00000i 0.0743294i
$$725$$ 0 0
$$726$$ −24.0000 + 13.8564i −0.890724 + 0.514259i
$$727$$ −4.89898 4.89898i −0.181693 0.181693i 0.610400 0.792093i $$-0.291009\pi$$
−0.792093 + 0.610400i $$0.791009\pi$$
$$728$$ 0 0
$$729$$ 27.0000i 1.00000i
$$730$$ 0 0
$$731$$ 10.3923i 0.384373i
$$732$$ −6.27603 + 23.4225i −0.231969 + 0.865719i
$$733$$ 14.6969 14.6969i 0.542844 0.542844i −0.381518 0.924362i $$-0.624598\pi$$
0.924362 + 0.381518i $$0.124598\pi$$
$$734$$ 20.7846 0.767174
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ −19.0919 + 19.0919i −0.703259 + 0.703259i
$$738$$ 4.03459 + 15.0573i 0.148515 + 0.554267i
$$739$$ 20.0000i 0.735712i 0.929883 + 0.367856i $$0.119908\pi$$
−0.929883 + 0.367856i $$0.880092\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 14.6969 + 14.6969i 0.539542 + 0.539542i
$$743$$ −12.7279 12.7279i −0.466942 0.466942i 0.433980 0.900922i $$-0.357109\pi$$
−0.900922 + 0.433980i $$0.857109\pi$$
$$744$$ 1.73205 + 3.00000i 0.0635001 + 0.109985i
$$745$$ 0 0
$$746$$ 3.46410i 0.126830i
$$747$$ −2.32937 8.69333i −0.0852272 0.318072i
$$748$$ 11.0227 11.0227i 0.403030 0.403030i
$$749$$ 31.1769 1.13918
$$750$$ 0 0
$$751$$ −20.0000 −0.729810 −0.364905 0.931045i $$-0.618899\pi$$
−0.364905 + 0.931045i $$0.618899\pi$$
$$752$$ 0 0
$$753$$ 2.32937 8.69333i 0.0848870 0.316803i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −18.0000 −0.654654
$$757$$ 24.4949 + 24.4949i 0.890282 + 0.890282i 0.994549 0.104267i $$-0.0332497\pi$$
−0.104267 + 0.994549i $$0.533250\pi$$
$$758$$ −7.77817 7.77817i −0.282516 0.282516i
$$759$$ 46.7654 27.0000i 1.69748 0.980038i
$$760$$ 0 0
$$761$$ 5.19615i 0.188360i −0.995555 0.0941802i $$-0.969977\pi$$
0.995555 0.0941802i $$-0.0300230\pi$$
$$762$$ −17.3867 4.65874i −0.629852 0.168768i
$$763$$ −24.4949 + 24.4949i −0.886775 + 0.886775i
$$764$$ 10.3923 0.375980
$$765$$ 0 0
$$766$$ 6.00000 0.216789
$$767$$ 0 0
$$768$$ −1.67303 0.448288i −0.0603704 0.0161762i
$$769$$ 13.0000i 0.468792i 0.972141 + 0.234396i $$0.0753112\pi$$
−0.972141 + 0.234396i $$0.924689\pi$$
$$770$$ 0 0
$$771$$ 9.00000 5.19615i 0.324127 0.187135i
$$772$$ 6.12372 + 6.12372i 0.220398 + 0.220398i
$$773$$ −8.48528 8.48528i −0.305194 0.305194i 0.537848 0.843042i $$-0.319238\pi$$
−0.843042 + 0.537848i $$0.819238\pi$$
$$774$$ 5.19615 9.00000i 0.186772 0.323498i
$$775$$ 0 0
$$776$$ 6.92820i 0.248708i
$$777$$ −5.37945 + 20.0764i −0.192987 + 0.720237i
$$778$$ −7.34847 + 7.34847i −0.263455 + 0.263455i
$$779$$ −5.19615 −0.186171
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −12.7279 + 12.7279i −0.455150 + 0.455150i
$$783$$ 0 0
$$784$$ 5.00000i 0.178571i
$$785$$ 0 0
$$786$$ −9.00000 15.5885i −0.321019 0.556022i
$$787$$ 17.1464 + 17.1464i 0.611204 + 0.611204i 0.943260 0.332056i $$-0.107742\pi$$
−0.332056 + 0.943260i $$0.607742\pi$$
$$788$$ −4.24264 4.24264i −0.151138 0.151138i
$$789$$ 15.5885 + 27.0000i 0.554964 + 0.961225i