# Properties

 Label 150.2.e.b.143.3 Level $150$ Weight $2$ Character 150.143 Analytic conductor $1.198$ Analytic rank $0$ Dimension $8$ CM no Inner twists $8$

# Related objects

## 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 143.3 Root $$0.258819 - 0.965926i$$ of defining polynomial Character $$\chi$$ $$=$$ 150.143 Dual form 150.2.e.b.107.3

## $q$-expansion

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

## Character values

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

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$3$$ 0.448288 1.67303i 0.258819 0.965926i
$$4$$ 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 −0.0716124 0.997433i $$-0.522814\pi$$
0.997433 + 0.0716124i $$0.0228145\pi$$
$$8$$ −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 $$0.713510\pi$$
$$12$$ 1.67303 + 0.448288i 0.482963 + 0.129410i
$$13$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$14$$ 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 $$-0.368522\pi$$
−0.915901 + 0.401405i $$0.868522\pi$$
$$18$$ −0.776457 2.89778i −0.183013 0.683013i
$$19$$ 1.00000i 0.229416i 0.993399 + 0.114708i $$0.0365932\pi$$
−0.993399 + 0.114708i $$0.963407\pi$$
$$20$$ 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 $$-0.965123\pi$$
0.109351 + 0.994003i $$0.465123\pi$$
$$24$$ 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
$$33$$ 8.69333 + 2.32937i 1.51331 + 0.405492i
$$34$$ 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 −0.879181 0.476488i $$-0.841910\pi$$
0.476488 + 0.879181i $$0.341910\pi$$
$$38$$ −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 $$-0.132990\pi$$
$$42$$ 1.55291 5.79555i 0.239620 0.894274i
$$43$$ −2.44949 2.44949i −0.373544 0.373544i 0.495222 0.868766i $$-0.335087\pi$$
−0.868766 + 0.495222i $$0.835087\pi$$
$$44$$ −5.19615 −0.783349
$$45$$ 0 0
$$46$$ −6.00000 −0.884652
$$47$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$48$$ −0.448288 + 1.67303i −0.0647048 + 0.241481i
$$49$$ 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 $$-0.614802\pi$$
0.935664 + 0.352892i $$0.114802\pi$$
$$54$$ −5.19615 −0.707107
$$55$$ 0 0
$$56$$ 3.46410i 0.462910i
$$57$$ 1.67303 + 0.448288i 0.221599 + 0.0593772i
$$58$$ 0 0
$$59$$ 10.3923 1.35296 0.676481 0.736460i $$-0.263504\pi$$
0.676481 + 0.736460i $$0.263504\pi$$
$$60$$ 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
$$63$$ −10.0382 + 2.68973i −1.26469 + 0.338874i
$$64$$ 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 −0.446103 0.894982i $$-0.647188\pi$$
0.894982 + 0.446103i $$0.147188\pi$$
$$68$$ 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 $$\pi$$
$$72$$ 2.89778 0.776457i 0.341506 0.0915064i
$$73$$ −6.12372 6.12372i −0.716728 0.716728i 0.251206 0.967934i $$-0.419173\pi$$
−0.967934 + 0.251206i $$0.919173\pi$$
$$74$$ −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 $$0.288657\pi$$
−0.616236 + 0.787562i $$0.711343\pi$$
$$80$$ 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 $$-0.697352\pi$$
0.813879 + 0.581034i $$0.197352\pi$$
$$84$$ 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 $$-0.809494\pi$$
−0.826187 + 0.563397i $$0.809494\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −4.24264 4.24264i −0.442326 0.442326i
$$93$$ −0.896575 + 3.34607i −0.0929705 + 0.346971i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.50000 + 0.866025i −0.153093 + 0.0883883i
$$97$$ 4.89898 4.89898i 0.497416 0.497416i −0.413217 0.910633i $$-0.635595\pi$$
0.910633 + 0.413217i $$0.135595\pi$$
$$98$$ 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 $$-0.172965\pi$$
$$102$$ −5.01910 1.34486i −0.496965 0.133161i
$$103$$ 9.79796 + 9.79796i 0.965422 + 0.965422i 0.999422 0.0340002i $$-0.0108247\pi$$
−0.0340002 + 0.999422i $$0.510825\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −6.36396 6.36396i −0.615227 0.615227i 0.329076 0.944303i $$-0.393263\pi$$
−0.944303 + 0.329076i $$0.893263\pi$$
$$108$$ −3.67423 3.67423i −0.353553 0.353553i
$$109$$ 10.0000i 0.957826i −0.877862 0.478913i $$-0.841031\pi$$
0.877862 0.478913i $$-0.158969\pi$$
$$110$$ 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 $$-0.610863\pi$$
0.939959 + 0.341288i $$0.110863\pi$$
$$114$$ 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
$$123$$ −8.69333 2.32937i −0.783851 0.210032i
$$124$$ 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 −0.953491 0.301420i $$-0.902539\pi$$
0.301420 + 0.953491i $$0.402539\pi$$
$$128$$ 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 $$-0.150000\pi$$
$$132$$ −2.32937 + 8.69333i −0.202746 + 0.756657i
$$133$$ 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 −0.946783 0.321874i $$-0.895687\pi$$
−0.321874 0.946783i $$-0.604313\pi$$
$$138$$ −2.68973 + 10.0382i −0.228965 + 0.854508i
$$139$$ 7.00000i 0.593732i 0.954919 + 0.296866i $$0.0959415\pi$$
−0.954919 + 0.296866i $$0.904058\pi$$
$$140$$ 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
$$147$$ −8.36516 2.24144i −0.689947 0.184871i
$$148$$ −2.44949 2.44949i −0.201347 0.201347i
$$149$$ 20.7846 1.70274 0.851371 0.524564i $$-0.175772\pi$$
0.851371 + 0.524564i $$0.175772\pi$$
$$150$$ 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
$$153$$ 2.32937 + 8.69333i 0.188319 + 0.702814i
$$154$$ 18.0000i 1.45048i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −12.2474 + 12.2474i −0.977453 + 0.977453i −0.999751 0.0222985i $$-0.992902\pi$$
0.0222985 + 0.999751i $$0.492902\pi$$
$$158$$ −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
$$162$$ −2.32937 + 8.69333i −0.183013 + 0.683013i
$$163$$ 3.67423 + 3.67423i 0.287788 + 0.287788i 0.836205 0.548417i $$-0.184769\pi$$
−0.548417 + 0.836205i $$0.684769\pi$$
$$164$$ 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 $$-0.0963081\pi$$
−0.297966 + 0.954577i $$0.596308\pi$$
$$168$$ 5.79555 + 1.55291i 0.447137 + 0.119810i
$$169$$ 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 $$-0.900780\pi$$
0.306687 + 0.951811i $$0.400780\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 5.19615i 0.391675i
$$177$$ 4.65874 17.3867i 0.350173 1.30686i
$$178$$ −11.0227 11.0227i −0.826187 0.826187i
$$179$$ −15.5885 −1.16514 −0.582568 0.812782i $$-0.697952\pi$$
−0.582568 + 0.812782i $$0.697952\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 6.27603 23.4225i 0.463937 1.73144i
$$184$$ 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 $$0.877306\pi$$
$$192$$ −1.67303 0.448288i −0.120741 0.0323524i
$$193$$ −6.12372 6.12372i −0.440795 0.440795i 0.451484 0.892279i $$-0.350895\pi$$
−0.892279 + 0.451484i $$0.850895\pi$$
$$194$$ 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 $$-0.318565\pi$$
−0.841904 + 0.539628i $$0.818565\pi$$
$$198$$ 15.0573 4.03459i 1.07008 0.286726i
$$199$$ 16.0000i 1.13421i −0.823646 0.567105i $$-0.808063\pi$$
0.823646 0.567105i $$-0.191937\pi$$
$$200$$ 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
$$207$$ 17.3867 4.65874i 1.20846 0.323805i
$$208$$ 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
$$222$$ −1.55291 + 5.79555i −0.104225 + 0.388972i
$$223$$ 9.79796 + 9.79796i 0.656120 + 0.656120i 0.954460 0.298340i $$-0.0964329\pi$$
−0.298340 + 0.954460i $$0.596433\pi$$
$$224$$ −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 $$-0.119623\pi$$
−0.367024 + 0.930212i $$0.619623\pi$$
$$228$$ −0.448288 + 1.67303i −0.0296886 + 0.110799i
$$229$$ 16.0000i 1.05731i 0.848837 + 0.528655i $$0.177303\pi$$
−0.848837 + 0.528655i $$0.822697\pi$$
$$230$$ 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 $$-0.950718\pi$$
0.154205 + 0.988039i $$0.450718\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 10.3923i 0.676481i
$$237$$ 23.4225 + 6.27603i 1.52145 + 0.407672i
$$238$$ −7.34847 7.34847i −0.476331 0.476331i
$$239$$ 20.7846 1.34444 0.672222 0.740349i $$-0.265340\pi$$
0.672222 + 0.740349i $$0.265340\pi$$
$$240$$ 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
$$243$$ 15.0573 4.03459i 0.965926 0.258819i
$$244$$ 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 $$0.947564\pi$$
$$252$$ −2.68973 10.0382i −0.169437 0.632347i
$$253$$ −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 $$-0.190080\pi$$
−0.562291 + 0.826940i $$0.690080\pi$$
$$258$$ −5.79555 1.55291i −0.360815 0.0966802i
$$259$$ 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 $$-0.562732\pi$$
0.980643 + 0.195805i $$0.0627321\pi$$
$$264$$ −7.79423 + 4.50000i −0.479702 + 0.276956i
$$265$$ 0 0
$$266$$ 3.46410i 0.212398i
$$267$$ −6.98811 + 26.0800i −0.427666 + 1.59607i
$$268$$ 3.67423 + 3.67423i 0.224440 + 0.224440i
$$269$$ 20.7846 1.26726 0.633630 0.773636i $$-0.281564\pi$$
0.633630 + 0.773636i $$0.281564\pi$$
$$270$$ 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 −0.937280 0.348578i $$-0.886665\pi$$
0.348578 + 0.937280i $$0.386665\pi$$
$$278$$ −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 0.865290 0.501272i $$-0.167134\pi$$
−0.501272 + 0.865290i $$0.667134\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −12.7279 12.7279i −0.751305 0.751305i
$$288$$ 0.776457 + 2.89778i 0.0457532 + 0.170753i
$$289$$ 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 −0.278996 + 0.960292i $$0.590002\pi$$
−0.960292 + 0.278996i $$0.909998\pi$$
$$294$$ −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
$$303$$ −17.3867 4.65874i −0.998838 0.267638i
$$304$$ 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 −0.741192 0.671293i $$-0.765739\pi$$
0.671293 + 0.741192i $$0.265739\pi$$
$$308$$ −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 0.987615 0.156895i $$-0.0501485\pi$$
−0.156895 + 0.987615i $$0.550148\pi$$
$$314$$ −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 $$-0.140590\pi$$
−0.427456 + 0.904036i $$0.640590\pi$$
$$318$$ 2.68973 10.0382i 0.150832 0.562914i
$$319$$ 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
$$327$$ −16.7303 4.48288i −0.925189 0.247904i
$$328$$ 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
$$333$$ 10.0382 2.68973i 0.550090 0.147396i
$$334$$ 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 −0.599915 0.800064i $$-0.704799\pi$$
0.800064 + 0.599915i $$0.204799\pi$$
$$338$$ 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
$$342$$ 2.89778 0.776457i 0.156694 0.0419860i
$$343$$ 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 $$-0.172337\pi$$
−0.515347 + 0.856982i $$0.672337\pi$$
$$348$$ 0 0
$$349$$ 22.0000i 1.17763i 0.808267 + 0.588817i $$0.200406\pi$$
−0.808267 + 0.588817i $$0.799594\pi$$
$$350$$ 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 $$-0.590992\pi$$
0.959420 + 0.281981i $$0.0909915\pi$$
$$354$$ 15.5885 9.00000i 0.828517 0.478345i
$$355$$ 0 0
$$356$$ 15.5885i 0.826187i
$$357$$ −4.65874 + 17.3867i −0.246567 + 0.920200i
$$358$$ −11.0227 11.0227i −0.582568 0.582568i
$$359$$ −10.3923 −0.548485 −0.274242 0.961661i $$-0.588427\pi$$
−0.274242 + 0.961661i $$0.588427\pi$$
$$360$$ 0 0
$$361$$ 18.0000 0.947368
$$362$$ −1.41421 1.41421i −0.0743294 0.0743294i
$$363$$ −7.17260 + 26.7685i −0.376464 + 1.40498i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 21.0000 12.1244i 1.09769 0.633750i
$$367$$ −14.6969 + 14.6969i −0.767174 + 0.767174i −0.977608 0.210434i $$-0.932512\pi$$
0.210434 + 0.977608i $$0.432512\pi$$
$$368$$ 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
$$372$$ −3.34607 0.896575i −0.173485 0.0464853i
$$373$$ 2.44949 + 2.44949i 0.126830 + 0.126830i 0.767672 0.640843i $$-0.221415\pi$$
−0.640843 + 0.767672i $$0.721415\pi$$
$$374$$ 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 $$-0.908831\pi$$
0.959263 0.282516i $$-0.0911690\pi$$
$$380$$ 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 $$-0.701012\pi$$
0.807144 + 0.590355i $$0.201012\pi$$
$$384$$ −0.866025 1.50000i −0.0441942 0.0765466i
$$385$$ 0 0
$$386$$ 8.66025i 0.440795i
$$387$$ 2.68973 + 10.0382i 0.136726 + 0.510270i
$$388$$ 4.89898 + 4.89898i 0.248708 + 0.248708i
$$389$$ −10.3923 −0.526911 −0.263455 0.964672i $$-0.584862\pi$$
−0.263455 + 0.964672i $$0.584862\pi$$
$$390$$ 0 0
$$391$$ 18.0000 0.910299
$$392$$ 3.53553 + 3.53553i 0.178571 + 0.178571i
$$393$$ −17.3867 4.65874i −0.877041 0.235002i
$$394$$ 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 −0.0163750 0.999866i $$-0.505213\pi$$
0.999866 + 0.0163750i $$0.00521255\pi$$
$$398$$ 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 $$0.958585\pi$$
$$402$$ 2.32937 8.69333i 0.116178 0.433584i
$$403$$ 0 0
$$404$$ 10.3923 0.517036
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −12.7279 12.7279i −0.630900 0.630900i
$$408$$ 1.34486 5.01910i 0.0665807 0.248482i
$$409$$ 5.00000i 0.247234i −0.992330 0.123617i $$-0.960551\pi$$
0.992330 0.123617i $$-0.0394494\pi$$
$$410$$ 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
$$417$$ 11.7112 + 3.13801i 0.573501 + 0.153669i
$$418$$ −3.67423 3.67423i −0.179713 0.179713i
$$419$$ −25.9808 −1.26924 −0.634622 0.772823i $$-0.718844\pi$$
−0.634622 + 0.772823i $$0.718844\pi$$
$$420$$ 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 0.212101 0.977248i $$-0.431970\pi$$
−0.977248 + 0.212101i $$0.931970\pi$$
$$434$$ −6.92820 −0.332564
$$435$$ 0 0
$$436$$ 10.0000 0.478913
$$437$$ −4.24264 4.24264i −0.202953 0.202953i
$$438$$ −14.4889 3.88229i −0.692306 0.185503i
$$439$$ 4.00000i 0.190910i −0.995434 0.0954548i $$-0.969569\pi$$
0.995434 0.0954548i $$-0.0304305\pi$$
$$440$$ 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 $$-0.916252\pi$$
0.260079 + 0.965587i $$0.416252\pi$$
$$444$$ −5.19615 + 3.00000i −0.246598 + 0.142374i
$$445$$ 0 0
$$446$$ 13.8564i 0.656120i
$$447$$ 9.31749 34.7733i 0.440702 1.64472i
$$448$$ −2.44949 2.44949i −0.115728 0.115728i
$$449$$ −25.9808 −1.22611 −0.613054 0.790041i $$-0.710059\pi$$
−0.613054 + 0.790041i $$0.710059\pi$$
$$450$$ 0 0
$$451$$ 27.0000 1.27138
$$452$$ 6.36396 + 6.36396i 0.299336 + 0.299336i
$$453$$ −6.27603 + 23.4225i −0.294874 + 1.10048i
$$454$$ 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 −0.131896 0.991264i $$-0.542107\pi$$
0.991264 + 0.131896i $$0.0421066\pi$$
$$458$$ −11.3137 + 11.3137i −0.528655 + 0.528655i
$$459$$ 15.5885 0.727607
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 30.1146 + 8.06918i 1.40106 + 0.375412i
$$463$$ −24.4949 24.4949i −1.13837 1.13837i −0.988742 0.149633i $$-0.952191\pi$$
−0.149633 0.988742i $$-0.547809\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −18.0000 −0.833834
$$467$$ 8.48528 + 8.48528i 0.392652 + 0.392652i 0.875632 0.482980i $$-0.160445\pi$$
−0.482980 + 0.875632i $$0.660445\pi$$
$$468$$ 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
$$477$$ −17.3867 + 4.65874i −0.796081 + 0.213309i
$$478$$ 14.6969 + 14.6969i 0.672222 + 0.672222i
$$479$$ 10.3923 0.474837 0.237418 0.971408i $$-0.423699\pi$$
0.237418 + 0.971408i $$0.423699\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −0.707107 0.707107i −0.0322078 0.0322078i
$$483$$ 34.7733 + 9.31749i 1.58224 + 0.423960i
$$484$$ 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 −0.999999 0.00102669i $$-0.999673\pi$$
0.00102669 + 0.999999i $$0.499673\pi$$
$$488$$ −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 $$0.751621\pi$$
$$492$$ 2.32937 8.69333i 0.105016 0.391926i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 2.00000 0.0898027
$$497$$ 0 0
$$498$$ 1.34486 5.01910i 0.0602648 0.224911i
$$499$$ 20.0000i 0.895323i 0.894203 + 0.447661i $$0.147743\pi$$
−0.894203 + 0.447661i $$0.852257\pi$$
$$500$$ 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 $$-0.663794\pi$$
0.870503 + 0.492163i $$0.163794\pi$$
$$504$$ 5.19615 9.00000i 0.231455 0.400892i
$$505$$ 0 0
$$506$$ 31.1769i 1.38598i
$$507$$ −21.7494 5.82774i −0.965926 0.258819i
$$508$$ −7.34847 7.34847i −0.326036 0.326036i
$$509$$ −10.3923 −0.460631 −0.230315 0.973116i $$-0.573976\pi$$
−0.230315 + 0.973116i $$0.573976\pi$$
$$510$$ 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 −0.897167 0.441692i $$-0.854378\pi$$
−0.441692 0.897167i $$-0.645622\pi$$
$$524$$ 10.3923 0.453990
$$525$$ 0 0
$$526$$ 18.0000 0.784837
$$527$$ 4.24264 + 4.24264i 0.184812 + 0.184812i
$$528$$ −8.69333 2.32937i −0.378329 0.101373i
$$529$$ 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
$$537$$ −6.98811 + 26.0800i −0.301559 + 1.12543i
$$538$$ 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
$$543$$ −0.896575 + 3.34607i −0.0384757 + 0.143593i
$$544$$ 3.00000i 0.128624i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −8.57321 + 8.57321i −0.366564 + 0.366564i −0.866223 0.499658i $$-0.833459\pi$$
0.499658 + 0.866223i $$0.333459\pi$$
$$548$$ 14.8492 14.8492i 0.634328 0.634328i
$$549$$ −36.3731 21.0000i −1.55236 0.896258i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −10.0382 2.68973i −0.427254 0.114482i
$$553$$ 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 $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$558$$ 1.55291 + 5.79555i 0.0657401 + 0.245345i
$$559$$ 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 $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 8.66025i 0.364018i
$$567$$ 30.1146 + 8.06918i 1.26469 + 0.338874i
$$568$$ 0 0
$$569$$ 25.9808 1.08917 0.544585 0.838706i $$-0.316687\pi$$
0.544585 + 0.838706i $$0.316687\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 0 0
$$573$$ 17.3867 + 4.65874i 0.726338 + 0.194622i
$$574$$ 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 −0.929550 0.368695i $$-0.879805\pi$$
0.368695 + 0.929550i $$0.379805\pi$$
$$578$$ 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
$$582$$ 3.10583 11.5911i 0.128741 0.480467i
$$583$$ 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 $$-0.392680\pi$$
−0.943699 + 0.330805i $$0.892680\pi$$
$$588$$ 2.24144 8.36516i 0.0924354 0.344974i
$$589$$ 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 $$-0.986969\pi$$
0.0409281 + 0.999162i $$0.486969\pi$$
$$594$$ 27.0000i 1.10782i
$$595$$ 0 0
$$596$$ 20.7846i 0.851371i
$$597$$ −26.7685 7.17260i −1.09556 0.293555i
$$598$$ 0 0
$$599$$ −10.3923 −0.424618 −0.212309 0.977203i $$-0.568098\pi$$
−0.212309 + 0.977203i $$0.568098\pi$$
$$600$$ 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
$$603$$ −15.0573 + 4.03459i −0.613180 + 0.164301i
$$604$$ 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 −0.600661 0.799504i $$-0.705096\pi$$
0.799504 + 0.600661i $$0.205096\pi$$
$$608$$ 0.707107 0.707107i 0.0286770 0.0286770i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −8.69333 + 2.32937i −0.351407 + 0.0941593i
$$613$$ 17.1464 + 17.1464i 0.692538 + 0.692538i 0.962790 0.270252i $$-0.0871070\pi$$
−0.270252 + 0.962790i $$0.587107\pi$$
$$614$$ −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 $$-0.456378\pi$$
−0.990624 + 0.136613i $$0.956378\pi$$
$$618$$ 23.1822 + 6.21166i 0.932526 + 0.249869i
$$619$$ 4.00000i 0.160774i −0.996764 0.0803868i $$-0.974384\pi$$
0.996764 0.0803868i $$-0.0256155\pi$$
$$620$$ 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
$$627$$ −2.32937 + 8.69333i −0.0930261 + 0.347178i
$$628$$ −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
$$633$$ 10.3106 38.4797i 0.409810 1.52943i
$$634$$ 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 $$-0.134636\pi$$
$$642$$ −15.0573 4.03459i −0.594264 0.159233i
$$643$$ −22.0454 22.0454i −0.869386 0.869386i 0.123018 0.992404i $$-0.460743\pi$$
−0.992404 + 0.123018i $$0.960743\pi$$
$$644$$ −20.7846 −0.819028
$$645$$ 0 0
$$646$$ 3.00000 0.118033
$$647$$ 33.9411 + 33.9411i 1.33436 + 1.33436i 0.901422 + 0.432941i $$0.142524\pi$$
0.432941 + 0.901422i $$0.357476\pi$$
$$648$$ −8.69333 2.32937i −0.341506 0.0915064i
$$649$$ 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 $$-0.712544\pi$$
0.785231 + 0.619203i $$0.212544\pi$$
$$654$$ −8.66025 15.0000i −0.338643 0.586546i
$$655$$ 0 0
$$656$$ 5.19615i 0.202876i
$$657$$ 6.72432 + 25.0955i 0.262341 + 0.979068i
$$658$$ 0 0
$$659$$ 25.9808 1.01207 0.506033 0.862514i $$-0.331111\pi$$
0.506033 + 0.862514i $$0.331111\pi$$
$$660$$ 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
$$672$$ −1.55291 + 5.79555i −0.0599050 + 0.223568i
$$673$$ 4.89898 + 4.89898i 0.188842 + 0.188842i 0.795195 0.606353i $$-0.207368\pi$$
−0.606353 + 0.795195i $$0.707368\pi$$
$$674$$ 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 $$-0.00681965\pi$$
−0.0214229 + 0.999771i $$0.506820\pi$$
$$678$$ 4.03459 15.0573i 0.154947 0.578272i
$$679$$ 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 $$-0.881605\pi$$
0.363431 + 0.931621i $$0.381605\pi$$
$$684$$ 2.59808 + 1.50000i 0.0993399 + 0.0573539i
$$685$$ 0 0
$$686$$ 6.92820i 0.264520i
$$687$$ 26.7685 + 7.17260i 1.02128 + 0.273652i
$$688$$ 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
$$693$$ −13.9762 52.1600i −0.530913 1.98139i
$$694$$ 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
$$708$$ 17.3867 + 4.65874i 0.653431 + 0.175086i
$$709$$ 40.0000i 1.50223i 0.660171 + 0.751116i $$0.270484\pi$$
−0.660171 + 0.751116i $$0.729516\pi$$
$$710$$ 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
$$717$$ 9.31749 34.7733i 0.347968 1.29863i
$$718$$ −7.34847 7.34847i −0.274242 0.274242i
$$719$$ 31.1769 1.16270 0.581351 0.813653i $$-0.302524\pi$$
0.581351 + 0.813653i $$0.302524\pi$$
$$720$$ 0 0
$$721$$ 48.0000 1.78761
$$722$$ 12.7279 + 12.7279i 0.473684 + 0.473684i
$$723$$ −0.448288 + 1.67303i −0.0166720 + 0.0622208i
$$724$$ 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 −0.792093 0.610400i $$-0.791009\pi$$
0.610400 + 0.792093i $$0.291009\pi$$
$$728$$ 0 0
$$729$$ 27.0000i 1.00000i
$$730$$ 0 0
$$731$$ 10.3923i 0.384373i
$$732$$ 23.4225 + 6.27603i 0.865719 + 0.231969i
$$733$$ 14.6969 + 14.6969i 0.542844 + 0.542844i 0.924362 0.381518i $$-0.124598\pi$$
−0.381518 + 0.924362i $$0.624598\pi$$
$$734$$ −20.7846 −0.767174
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ 19.0919 + 19.0919i 0.703259 + 0.703259i
$$738$$ −15.0573 + 4.03459i −0.554267 + 0.148515i
$$739$$ 20.0000i 0.735712i −0.929883 0.367856i $$-0.880092\pi$$
0.929883 0.367856i $$-0.119908\pi$$
$$740$$ 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 $$-0.642891\pi$$
0.900922 + 0.433980i $$0.142891\pi$$
$$744$$ −1.73205 3.00000i −0.0635001 0.109985i
$$745$$ 0 0
$$746$$ 3.46410i 0.126830i
$$747$$ −8.69333 + 2.32937i −0.318072 + 0.0852272i
$$748$$ 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
$$753$$ 8.69333 + 2.32937i 0.316803 + 0.0848870i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −18.0000 −0.654654
$$757$$ 24.4949 24.4949i 0.890282 0.890282i −0.104267 0.994549i $$-0.533250\pi$$
0.994549 + 0.104267i $$0.0332497\pi$$
$$758$$ 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 $$-0.0300230\pi$$
$$762$$ −4.65874 + 17.3867i −0.168768 + 0.629852i
$$763$$ −24.4949 24.4949i −0.886775 0.886775i
$$764$$ −10.3923 −0.375980
$$765$$ 0 0
$$766$$ 6.00000 0.216789
$$767$$ 0 0
$$768$$ 0.448288 1.67303i 0.0161762 0.0603704i
$$769$$ 13.0000i 0.468792i −0.972141 0.234396i $$-0.924689\pi$$
0.972141 0.234396i $$-0.0753112\pi$$
$$770$$ 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 $$-0.680762\pi$$
0.843042 + 0.537848i $$0.180762\pi$$
$$774$$ −5.19615 + 9.00000i −0.186772 + 0.323498i
$$775$$ 0 0
$$776$$ 6.92820i 0.248708i
$$777$$ 20.0764 + 5.37945i 0.720237 + 0.192987i
$$778$$ −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 −0.332056 0.943260i $$-0.607742\pi$$
0.943260 + 0.332056i $$0.107742\pi$$
$$788$$ 4.24264 4.24264i 0.151138 0.151138i
$$789$$ −15.5885 27.0000i −0.554964 0.961225i