# Properties

 Label 1134.2.f.j.757.1 Level $1134$ Weight $2$ Character 1134.757 Analytic conductor $9.055$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.f (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.05503558921$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 757.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.757 Dual form 1134.2.f.j.379.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -2.00000 q^{10} +(-2.00000 - 3.46410i) q^{11} +(-3.00000 + 5.19615i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} -4.00000 q^{19} +(-1.00000 - 1.73205i) q^{20} +(2.00000 - 3.46410i) q^{22} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} -6.00000 q^{26} -1.00000 q^{28} +(-1.00000 - 1.73205i) q^{29} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{34} -2.00000 q^{35} -10.0000 q^{37} +(-2.00000 - 3.46410i) q^{38} +(1.00000 - 1.73205i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +4.00000 q^{44} +8.00000 q^{46} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-3.00000 - 5.19615i) q^{52} -6.00000 q^{53} +8.00000 q^{55} +(-0.500000 - 0.866025i) q^{56} +(1.00000 - 1.73205i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-1.00000 - 1.73205i) q^{70} -8.00000 q^{71} +10.0000 q^{73} +(-5.00000 - 8.66025i) q^{74} +(2.00000 - 3.46410i) q^{76} +(2.00000 - 3.46410i) q^{77} +2.00000 q^{80} -6.00000 q^{82} +(-2.00000 - 3.46410i) q^{83} +(2.00000 - 3.46410i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(2.00000 + 3.46410i) q^{88} +6.00000 q^{89} -6.00000 q^{91} +(4.00000 + 6.92820i) q^{92} +(4.00000 - 6.92820i) q^{95} +(7.00000 + 12.1244i) q^{97} -1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{4} - 2q^{5} + q^{7} - 2q^{8} + O(q^{10})$$ $$2q + q^{2} - q^{4} - 2q^{5} + q^{7} - 2q^{8} - 4q^{10} - 4q^{11} - 6q^{13} - q^{14} - q^{16} - 4q^{17} - 8q^{19} - 2q^{20} + 4q^{22} + 8q^{23} + q^{25} - 12q^{26} - 2q^{28} - 2q^{29} + q^{32} - 2q^{34} - 4q^{35} - 20q^{37} - 4q^{38} + 2q^{40} - 6q^{41} + 4q^{43} + 8q^{44} + 16q^{46} - q^{49} - q^{50} - 6q^{52} - 12q^{53} + 16q^{55} - q^{56} + 2q^{58} + 4q^{59} - 6q^{61} + 2q^{64} - 12q^{65} - 4q^{67} + 2q^{68} - 2q^{70} - 16q^{71} + 20q^{73} - 10q^{74} + 4q^{76} + 4q^{77} + 4q^{80} - 12q^{82} - 4q^{83} + 4q^{85} - 4q^{86} + 4q^{88} + 12q^{89} - 12q^{91} + 8q^{92} + 8q^{95} + 14q^{97} - 2q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i $$-0.980917\pi$$
0.550990 + 0.834512i $$0.314250\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 0.866025i 0.188982 + 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ −2.00000 −0.632456
$$11$$ −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i $$-0.960630\pi$$
0.389338 0.921095i $$-0.372704\pi$$
$$12$$ 0 0
$$13$$ −3.00000 + 5.19615i −0.832050 + 1.44115i 0.0643593 + 0.997927i $$0.479500\pi$$
−0.896410 + 0.443227i $$0.853834\pi$$
$$14$$ −0.500000 + 0.866025i −0.133631 + 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ −4.00000 −0.917663 −0.458831 0.888523i $$-0.651732\pi$$
−0.458831 + 0.888523i $$0.651732\pi$$
$$20$$ −1.00000 1.73205i −0.223607 0.387298i
$$21$$ 0 0
$$22$$ 2.00000 3.46410i 0.426401 0.738549i
$$23$$ 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i $$-0.519345\pi$$
0.894795 0.446476i $$-0.147321\pi$$
$$24$$ 0 0
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ −6.00000 −1.17670
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ −1.00000 1.73205i −0.185695 0.321634i 0.758115 0.652121i $$-0.226120\pi$$
−0.943811 + 0.330487i $$0.892787\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ −1.00000 1.73205i −0.171499 0.297044i
$$35$$ −2.00000 −0.338062
$$36$$ 0 0
$$37$$ −10.0000 −1.64399 −0.821995 0.569495i $$-0.807139\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ −2.00000 3.46410i −0.324443 0.561951i
$$39$$ 0 0
$$40$$ 1.00000 1.73205i 0.158114 0.273861i
$$41$$ −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i $$-0.988546\pi$$
0.530831 + 0.847477i $$0.321880\pi$$
$$42$$ 0 0
$$43$$ 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i $$-0.0680112\pi$$
−0.672264 + 0.740312i $$0.734678\pi$$
$$44$$ 4.00000 0.603023
$$45$$ 0 0
$$46$$ 8.00000 1.17954
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 0 0
$$49$$ −0.500000 + 0.866025i −0.0714286 + 0.123718i
$$50$$ −0.500000 + 0.866025i −0.0707107 + 0.122474i
$$51$$ 0 0
$$52$$ −3.00000 5.19615i −0.416025 0.720577i
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ 8.00000 1.07872
$$56$$ −0.500000 0.866025i −0.0668153 0.115728i
$$57$$ 0 0
$$58$$ 1.00000 1.73205i 0.131306 0.227429i
$$59$$ 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i $$-0.749486\pi$$
0.966342 + 0.257260i $$0.0828195\pi$$
$$60$$ 0 0
$$61$$ −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i $$-0.292159\pi$$
−0.991645 + 0.128994i $$0.958825\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −6.00000 10.3923i −0.744208 1.28901i
$$66$$ 0 0
$$67$$ −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i $$-0.911904\pi$$
0.717607 + 0.696449i $$0.245238\pi$$
$$68$$ 1.00000 1.73205i 0.121268 0.210042i
$$69$$ 0 0
$$70$$ −1.00000 1.73205i −0.119523 0.207020i
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ 0 0
$$73$$ 10.0000 1.17041 0.585206 0.810885i $$-0.301014\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ −5.00000 8.66025i −0.581238 1.00673i
$$75$$ 0 0
$$76$$ 2.00000 3.46410i 0.229416 0.397360i
$$77$$ 2.00000 3.46410i 0.227921 0.394771i
$$78$$ 0 0
$$79$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$80$$ 2.00000 0.223607
$$81$$ 0 0
$$82$$ −6.00000 −0.662589
$$83$$ −2.00000 3.46410i −0.219529 0.380235i 0.735135 0.677920i $$-0.237119\pi$$
−0.954664 + 0.297686i $$0.903785\pi$$
$$84$$ 0 0
$$85$$ 2.00000 3.46410i 0.216930 0.375735i
$$86$$ −2.00000 + 3.46410i −0.215666 + 0.373544i
$$87$$ 0 0
$$88$$ 2.00000 + 3.46410i 0.213201 + 0.369274i
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ −6.00000 −0.628971
$$92$$ 4.00000 + 6.92820i 0.417029 + 0.722315i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 4.00000 6.92820i 0.410391 0.710819i
$$96$$ 0 0
$$97$$ 7.00000 + 12.1244i 0.710742 + 1.23104i 0.964579 + 0.263795i $$0.0849741\pi$$
−0.253837 + 0.967247i $$0.581693\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 0 0
$$100$$ −1.00000 −0.100000
$$101$$ −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i $$-0.198392\pi$$
−0.911479 + 0.411346i $$0.865059\pi$$
$$102$$ 0 0
$$103$$ −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i $$-0.962288\pi$$
0.598858 + 0.800855i $$0.295621\pi$$
$$104$$ 3.00000 5.19615i 0.294174 0.509525i
$$105$$ 0 0
$$106$$ −3.00000 5.19615i −0.291386 0.504695i
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 0 0
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 4.00000 + 6.92820i 0.381385 + 0.660578i
$$111$$ 0 0
$$112$$ 0.500000 0.866025i 0.0472456 0.0818317i
$$113$$ −7.00000 + 12.1244i −0.658505 + 1.14056i 0.322498 + 0.946570i $$0.395477\pi$$
−0.981003 + 0.193993i $$0.937856\pi$$
$$114$$ 0 0
$$115$$ 8.00000 + 13.8564i 0.746004 + 1.29212i
$$116$$ 2.00000 0.185695
$$117$$ 0 0
$$118$$ 4.00000 0.368230
$$119$$ −1.00000 1.73205i −0.0916698 0.158777i
$$120$$ 0 0
$$121$$ −2.50000 + 4.33013i −0.227273 + 0.393648i
$$122$$ 3.00000 5.19615i 0.271607 0.470438i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 6.00000 10.3923i 0.526235 0.911465i
$$131$$ −10.0000 + 17.3205i −0.873704 + 1.51330i −0.0155672 + 0.999879i $$0.504955\pi$$
−0.858137 + 0.513421i $$0.828378\pi$$
$$132$$ 0 0
$$133$$ −2.00000 3.46410i −0.173422 0.300376i
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ 2.00000 0.171499
$$137$$ 5.00000 + 8.66025i 0.427179 + 0.739895i 0.996621 0.0821359i $$-0.0261741\pi$$
−0.569442 + 0.822031i $$0.692841\pi$$
$$138$$ 0 0
$$139$$ −2.00000 + 3.46410i −0.169638 + 0.293821i −0.938293 0.345843i $$-0.887593\pi$$
0.768655 + 0.639664i $$0.220926\pi$$
$$140$$ 1.00000 1.73205i 0.0845154 0.146385i
$$141$$ 0 0
$$142$$ −4.00000 6.92820i −0.335673 0.581402i
$$143$$ 24.0000 2.00698
$$144$$ 0 0
$$145$$ 4.00000 0.332182
$$146$$ 5.00000 + 8.66025i 0.413803 + 0.716728i
$$147$$ 0 0
$$148$$ 5.00000 8.66025i 0.410997 0.711868i
$$149$$ 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i $$-0.754293\pi$$
0.962348 + 0.271821i $$0.0876260\pi$$
$$150$$ 0 0
$$151$$ 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i $$-0.0611289\pi$$
−0.656101 + 0.754673i $$0.727796\pi$$
$$152$$ 4.00000 0.324443
$$153$$ 0 0
$$154$$ 4.00000 0.322329
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 5.00000 8.66025i 0.399043 0.691164i −0.594565 0.804048i $$-0.702676\pi$$
0.993608 + 0.112884i $$0.0360089\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 1.00000 + 1.73205i 0.0790569 + 0.136931i
$$161$$ 8.00000 0.630488
$$162$$ 0 0
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ −3.00000 5.19615i −0.234261 0.405751i
$$165$$ 0 0
$$166$$ 2.00000 3.46410i 0.155230 0.268866i
$$167$$ −4.00000 + 6.92820i −0.309529 + 0.536120i −0.978259 0.207385i $$-0.933505\pi$$
0.668730 + 0.743505i $$0.266838\pi$$
$$168$$ 0 0
$$169$$ −11.5000 19.9186i −0.884615 1.53220i
$$170$$ 4.00000 0.306786
$$171$$ 0 0
$$172$$ −4.00000 −0.304997
$$173$$ 11.0000 + 19.0526i 0.836315 + 1.44854i 0.892956 + 0.450145i $$0.148628\pi$$
−0.0566411 + 0.998395i $$0.518039\pi$$
$$174$$ 0 0
$$175$$ −0.500000 + 0.866025i −0.0377964 + 0.0654654i
$$176$$ −2.00000 + 3.46410i −0.150756 + 0.261116i
$$177$$ 0 0
$$178$$ 3.00000 + 5.19615i 0.224860 + 0.389468i
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −18.0000 −1.33793 −0.668965 0.743294i $$-0.733262\pi$$
−0.668965 + 0.743294i $$0.733262\pi$$
$$182$$ −3.00000 5.19615i −0.222375 0.385164i
$$183$$ 0 0
$$184$$ −4.00000 + 6.92820i −0.294884 + 0.510754i
$$185$$ 10.0000 17.3205i 0.735215 1.27343i
$$186$$ 0 0
$$187$$ 4.00000 + 6.92820i 0.292509 + 0.506640i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 8.00000 0.580381
$$191$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$192$$ 0 0
$$193$$ −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i $$-0.856266\pi$$
0.827788 + 0.561041i $$0.189599\pi$$
$$194$$ −7.00000 + 12.1244i −0.502571 + 0.870478i
$$195$$ 0 0
$$196$$ −0.500000 0.866025i −0.0357143 0.0618590i
$$197$$ 10.0000 0.712470 0.356235 0.934396i $$-0.384060\pi$$
0.356235 + 0.934396i $$0.384060\pi$$
$$198$$ 0 0
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ −0.500000 0.866025i −0.0353553 0.0612372i
$$201$$ 0 0
$$202$$ 1.00000 1.73205i 0.0703598 0.121867i
$$203$$ 1.00000 1.73205i 0.0701862 0.121566i
$$204$$ 0 0
$$205$$ −6.00000 10.3923i −0.419058 0.725830i
$$206$$ −8.00000 −0.557386
$$207$$ 0 0
$$208$$ 6.00000 0.416025
$$209$$ 8.00000 + 13.8564i 0.553372 + 0.958468i
$$210$$ 0 0
$$211$$ −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i $$0.408366\pi$$
−0.972346 + 0.233544i $$0.924968\pi$$
$$212$$ 3.00000 5.19615i 0.206041 0.356873i
$$213$$ 0 0
$$214$$ −6.00000 10.3923i −0.410152 0.710403i
$$215$$ −8.00000 −0.545595
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −1.00000 1.73205i −0.0677285 0.117309i
$$219$$ 0 0
$$220$$ −4.00000 + 6.92820i −0.269680 + 0.467099i
$$221$$ 6.00000 10.3923i 0.403604 0.699062i
$$222$$ 0 0
$$223$$ 8.00000 + 13.8564i 0.535720 + 0.927894i 0.999128 + 0.0417488i $$0.0132929\pi$$
−0.463409 + 0.886145i $$0.653374\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −14.0000 −0.931266
$$227$$ 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i $$-0.0362899\pi$$
−0.595274 + 0.803523i $$0.702957\pi$$
$$228$$ 0 0
$$229$$ 1.00000 1.73205i 0.0660819 0.114457i −0.831092 0.556136i $$-0.812283\pi$$
0.897173 + 0.441679i $$0.145617\pi$$
$$230$$ −8.00000 + 13.8564i −0.527504 + 0.913664i
$$231$$ 0 0
$$232$$ 1.00000 + 1.73205i 0.0656532 + 0.113715i
$$233$$ 22.0000 1.44127 0.720634 0.693316i $$-0.243851\pi$$
0.720634 + 0.693316i $$0.243851\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 2.00000 + 3.46410i 0.130189 + 0.225494i
$$237$$ 0 0
$$238$$ 1.00000 1.73205i 0.0648204 0.112272i
$$239$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$240$$ 0 0
$$241$$ −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i $$-0.187185\pi$$
−0.896435 + 0.443176i $$0.853852\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ 0 0
$$244$$ 6.00000 0.384111
$$245$$ −1.00000 1.73205i −0.0638877 0.110657i
$$246$$ 0 0
$$247$$ 12.0000 20.7846i 0.763542 1.32249i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −6.00000 10.3923i −0.379473 0.657267i
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ −32.0000 −2.01182
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −15.0000 + 25.9808i −0.935674 + 1.62064i −0.162247 + 0.986750i $$0.551874\pi$$
−0.773427 + 0.633885i $$0.781459\pi$$
$$258$$ 0 0
$$259$$ −5.00000 8.66025i −0.310685 0.538122i
$$260$$ 12.0000 0.744208
$$261$$ 0 0
$$262$$ −20.0000 −1.23560
$$263$$ −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i $$-0.901515\pi$$
0.212565 0.977147i $$-0.431818\pi$$
$$264$$ 0 0
$$265$$ 6.00000 10.3923i 0.368577 0.638394i
$$266$$ 2.00000 3.46410i 0.122628 0.212398i
$$267$$ 0 0
$$268$$ −2.00000 3.46410i −0.122169 0.211604i
$$269$$ −22.0000 −1.34136 −0.670682 0.741745i $$-0.733998\pi$$
−0.670682 + 0.741745i $$0.733998\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 1.00000 + 1.73205i 0.0606339 + 0.105021i
$$273$$ 0 0
$$274$$ −5.00000 + 8.66025i −0.302061 + 0.523185i
$$275$$ 2.00000 3.46410i 0.120605 0.208893i
$$276$$ 0 0
$$277$$ 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i $$-0.0695395\pi$$
−0.675810 + 0.737075i $$0.736206\pi$$
$$278$$ −4.00000 −0.239904
$$279$$ 0 0
$$280$$ 2.00000 0.119523
$$281$$ 13.0000 + 22.5167i 0.775515 + 1.34323i 0.934505 + 0.355951i $$0.115843\pi$$
−0.158990 + 0.987280i $$0.550824\pi$$
$$282$$ 0 0
$$283$$ −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i $$-0.871266\pi$$
0.800439 + 0.599414i $$0.204600\pi$$
$$284$$ 4.00000 6.92820i 0.237356 0.411113i
$$285$$ 0 0
$$286$$ 12.0000 + 20.7846i 0.709575 + 1.22902i
$$287$$ −6.00000 −0.354169
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 2.00000 + 3.46410i 0.117444 + 0.203419i
$$291$$ 0 0
$$292$$ −5.00000 + 8.66025i −0.292603 + 0.506803i
$$293$$ 15.0000 25.9808i 0.876309 1.51781i 0.0209480 0.999781i $$-0.493332\pi$$
0.855361 0.518032i $$-0.173335\pi$$
$$294$$ 0 0
$$295$$ 4.00000 + 6.92820i 0.232889 + 0.403376i
$$296$$ 10.0000 0.581238
$$297$$ 0 0
$$298$$ 6.00000 0.347571
$$299$$ 24.0000 + 41.5692i 1.38796 + 2.40401i
$$300$$ 0 0
$$301$$ −2.00000 + 3.46410i −0.115278 + 0.199667i
$$302$$ −4.00000 + 6.92820i −0.230174 + 0.398673i
$$303$$ 0 0
$$304$$ 2.00000 + 3.46410i 0.114708 + 0.198680i
$$305$$ 12.0000 0.687118
$$306$$ 0 0
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 2.00000 + 3.46410i 0.113961 + 0.197386i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −4.00000 + 6.92820i −0.226819 + 0.392862i −0.956864 0.290537i $$-0.906166\pi$$
0.730044 + 0.683400i $$0.239499\pi$$
$$312$$ 0 0
$$313$$ −5.00000 8.66025i −0.282617 0.489506i 0.689412 0.724370i $$-0.257869\pi$$
−0.972028 + 0.234863i $$0.924536\pi$$
$$314$$ 10.0000 0.564333
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i $$-0.997978\pi$$
0.494489 0.869184i $$-0.335355\pi$$
$$318$$ 0 0
$$319$$ −4.00000 + 6.92820i −0.223957 + 0.387905i
$$320$$ −1.00000 + 1.73205i −0.0559017 + 0.0968246i
$$321$$ 0 0
$$322$$ 4.00000 + 6.92820i 0.222911 + 0.386094i
$$323$$ 8.00000 0.445132
$$324$$ 0 0
$$325$$ −6.00000 −0.332820
$$326$$ 10.0000 + 17.3205i 0.553849 + 0.959294i
$$327$$ 0 0
$$328$$ 3.00000 5.19615i 0.165647 0.286910i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i $$-0.131604\pi$$
−0.805812 + 0.592172i $$0.798271\pi$$
$$332$$ 4.00000 0.219529
$$333$$ 0 0
$$334$$ −8.00000 −0.437741
$$335$$ −4.00000 6.92820i −0.218543 0.378528i
$$336$$ 0 0
$$337$$ −9.00000 + 15.5885i −0.490261 + 0.849157i −0.999937 0.0112091i $$-0.996432\pi$$
0.509676 + 0.860366i $$0.329765\pi$$
$$338$$ 11.5000 19.9186i 0.625518 1.08343i
$$339$$ 0 0
$$340$$ 2.00000 + 3.46410i 0.108465 + 0.187867i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ −2.00000 3.46410i −0.107833 0.186772i
$$345$$ 0 0
$$346$$ −11.0000 + 19.0526i −0.591364 + 1.02427i
$$347$$ 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i $$-0.728946\pi$$
0.980921 + 0.194409i $$0.0622790\pi$$
$$348$$ 0 0
$$349$$ −11.0000 19.0526i −0.588817 1.01986i −0.994388 0.105797i $$-0.966261\pi$$
0.405571 0.914063i $$-0.367073\pi$$
$$350$$ −1.00000 −0.0534522
$$351$$ 0 0
$$352$$ −4.00000 −0.213201
$$353$$ −15.0000 25.9808i −0.798369 1.38282i −0.920677 0.390324i $$-0.872363\pi$$
0.122308 0.992492i $$-0.460970\pi$$
$$354$$ 0 0
$$355$$ 8.00000 13.8564i 0.424596 0.735422i
$$356$$ −3.00000 + 5.19615i −0.159000 + 0.275396i
$$357$$ 0 0
$$358$$ 6.00000 + 10.3923i 0.317110 + 0.549250i
$$359$$ 8.00000 0.422224 0.211112 0.977462i $$-0.432292\pi$$
0.211112 + 0.977462i $$0.432292\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ −9.00000 15.5885i −0.473029 0.819311i
$$363$$ 0 0
$$364$$ 3.00000 5.19615i 0.157243 0.272352i
$$365$$ −10.0000 + 17.3205i −0.523424 + 0.906597i
$$366$$ 0 0
$$367$$ −16.0000 27.7128i −0.835193 1.44660i −0.893873 0.448320i $$-0.852022\pi$$
0.0586798 0.998277i $$-0.481311\pi$$
$$368$$ −8.00000 −0.417029
$$369$$ 0 0
$$370$$ 20.0000 1.03975
$$371$$ −3.00000 5.19615i −0.155752 0.269771i
$$372$$ 0 0
$$373$$ −11.0000 + 19.0526i −0.569558 + 0.986504i 0.427051 + 0.904227i $$0.359552\pi$$
−0.996610 + 0.0822766i $$0.973781\pi$$
$$374$$ −4.00000 + 6.92820i −0.206835 + 0.358249i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 4.00000 + 6.92820i 0.205196 + 0.355409i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −8.00000 + 13.8564i −0.408781 + 0.708029i −0.994753 0.102302i $$-0.967379\pi$$
0.585973 + 0.810331i $$0.300713\pi$$
$$384$$ 0 0
$$385$$ 4.00000 + 6.92820i 0.203859 + 0.353094i
$$386$$ −2.00000 −0.101797
$$387$$ 0 0
$$388$$ −14.0000 −0.710742
$$389$$ −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i $$-0.937593\pi$$
0.321716 0.946836i $$-0.395740\pi$$
$$390$$ 0 0
$$391$$ −8.00000 + 13.8564i −0.404577 + 0.700749i
$$392$$ 0.500000 0.866025i 0.0252538 0.0437409i
$$393$$ 0 0
$$394$$ 5.00000 + 8.66025i 0.251896 + 0.436297i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 6.00000 0.301131 0.150566 0.988600i $$-0.451890\pi$$
0.150566 + 0.988600i $$0.451890\pi$$
$$398$$ 4.00000 + 6.92820i 0.200502 + 0.347279i
$$399$$ 0 0
$$400$$ 0.500000 0.866025i 0.0250000 0.0433013i
$$401$$ 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i $$-0.684957\pi$$
0.998350 + 0.0574304i $$0.0182907\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 2.00000 0.0995037
$$405$$ 0 0
$$406$$ 2.00000 0.0992583
$$407$$ 20.0000 + 34.6410i 0.991363 + 1.71709i
$$408$$ 0 0
$$409$$ 11.0000 19.0526i 0.543915 0.942088i −0.454759 0.890614i $$-0.650275\pi$$
0.998674 0.0514740i $$-0.0163919\pi$$
$$410$$ 6.00000 10.3923i 0.296319 0.513239i
$$411$$ 0 0
$$412$$ −4.00000 6.92820i −0.197066 0.341328i
$$413$$ 4.00000 0.196827
$$414$$ 0 0
$$415$$ 8.00000 0.392705
$$416$$ 3.00000 + 5.19615i 0.147087 + 0.254762i
$$417$$ 0 0
$$418$$ −8.00000 + 13.8564i −0.391293 + 0.677739i
$$419$$ −18.0000 + 31.1769i −0.879358 + 1.52309i −0.0273103 + 0.999627i $$0.508694\pi$$
−0.852047 + 0.523465i $$0.824639\pi$$
$$420$$ 0 0
$$421$$ −3.00000 5.19615i −0.146211 0.253245i 0.783613 0.621249i $$-0.213375\pi$$
−0.929824 + 0.368004i $$0.880041\pi$$
$$422$$ −20.0000 −0.973585
$$423$$ 0 0
$$424$$ 6.00000 0.291386
$$425$$ −1.00000 1.73205i −0.0485071 0.0840168i
$$426$$ 0 0
$$427$$ 3.00000 5.19615i 0.145180 0.251459i
$$428$$ 6.00000 10.3923i 0.290021 0.502331i
$$429$$ 0 0
$$430$$ −4.00000 6.92820i −0.192897 0.334108i
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1.00000 1.73205i 0.0478913 0.0829502i
$$437$$ −16.0000 + 27.7128i −0.765384 + 1.32568i
$$438$$ 0 0
$$439$$ 12.0000 + 20.7846i 0.572729 + 0.991995i 0.996284 + 0.0861252i $$0.0274485\pi$$
−0.423556 + 0.905870i $$0.639218\pi$$
$$440$$ −8.00000 −0.381385
$$441$$ 0 0
$$442$$ 12.0000 0.570782
$$443$$ −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i $$-0.196959\pi$$
−0.909618 + 0.415445i $$0.863626\pi$$
$$444$$ 0 0
$$445$$ −6.00000 + 10.3923i −0.284427 + 0.492642i
$$446$$ −8.00000 + 13.8564i −0.378811 + 0.656120i
$$447$$ 0 0
$$448$$ 0.500000 + 0.866025i 0.0236228 + 0.0409159i
$$449$$ −34.0000 −1.60456 −0.802280 0.596948i $$-0.796380\pi$$
−0.802280 + 0.596948i $$0.796380\pi$$
$$450$$ 0 0
$$451$$ 24.0000 1.13012
$$452$$ −7.00000 12.1244i −0.329252 0.570282i
$$453$$ 0 0
$$454$$ −6.00000 + 10.3923i −0.281594 + 0.487735i
$$455$$ 6.00000 10.3923i 0.281284 0.487199i
$$456$$ 0 0
$$457$$ −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i $$-0.241812\pi$$
−0.958950 + 0.283577i $$0.908479\pi$$
$$458$$ 2.00000 0.0934539
$$459$$ 0 0
$$460$$ −16.0000 −0.746004
$$461$$ 11.0000 + 19.0526i 0.512321 + 0.887366i 0.999898 + 0.0142861i $$0.00454755\pi$$
−0.487577 + 0.873080i $$0.662119\pi$$
$$462$$ 0 0
$$463$$ 16.0000 27.7128i 0.743583 1.28792i −0.207271 0.978284i $$-0.566458\pi$$
0.950854 0.309640i $$-0.100209\pi$$
$$464$$ −1.00000 + 1.73205i −0.0464238 + 0.0804084i
$$465$$ 0 0
$$466$$ 11.0000 + 19.0526i 0.509565 + 0.882593i
$$467$$ −28.0000 −1.29569 −0.647843 0.761774i $$-0.724329\pi$$
−0.647843 + 0.761774i $$0.724329\pi$$
$$468$$ 0 0
$$469$$ −4.00000 −0.184703
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −2.00000 + 3.46410i −0.0920575 + 0.159448i
$$473$$ 8.00000 13.8564i 0.367840 0.637118i
$$474$$ 0 0
$$475$$ −2.00000 3.46410i −0.0917663 0.158944i
$$476$$ 2.00000 0.0916698
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i $$-0.285779\pi$$
−0.988861 + 0.148842i $$0.952445\pi$$
$$480$$ 0 0
$$481$$ 30.0000 51.9615i 1.36788 2.36924i
$$482$$ 1.00000 1.73205i 0.0455488 0.0788928i
$$483$$ 0 0
$$484$$ −2.50000 4.33013i −0.113636 0.196824i
$$485$$ −28.0000 −1.27141
$$486$$ 0 0
$$487$$ 8.00000 0.362515 0.181257 0.983436i $$-0.441983\pi$$
0.181257 + 0.983436i $$0.441983\pi$$
$$488$$ 3.00000 + 5.19615i 0.135804 + 0.235219i
$$489$$ 0 0
$$490$$ 1.00000 1.73205i 0.0451754 0.0782461i
$$491$$ 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i $$-0.746053\pi$$
0.969061 + 0.246822i $$0.0793863\pi$$
$$492$$ 0 0
$$493$$ 2.00000 + 3.46410i 0.0900755 + 0.156015i
$$494$$ 24.0000 1.07981
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −4.00000 6.92820i −0.179425 0.310772i
$$498$$ 0 0
$$499$$ 22.0000 38.1051i 0.984855 1.70582i 0.342277 0.939599i $$-0.388802\pi$$
0.642578 0.766220i $$-0.277865\pi$$
$$500$$ 6.00000 10.3923i 0.268328 0.464758i
$$501$$ 0 0
$$502$$ 6.00000 + 10.3923i 0.267793 + 0.463831i
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ 4.00000 0.177998
$$506$$ −16.0000 27.7128i −0.711287 1.23198i
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i $$-0.790881\pi$$
0.924821 + 0.380402i $$0.124214\pi$$
$$510$$ 0 0
$$511$$ 5.00000 + 8.66025i 0.221187 + 0.383107i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −30.0000 −1.32324
$$515$$ −8.00000 13.8564i −0.352522 0.610586i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 5.00000 8.66025i 0.219687 0.380510i
$$519$$ 0 0
$$520$$ 6.00000 + 10.3923i 0.263117 + 0.455733i
$$521$$ 6.00000 0.262865 0.131432 0.991325i $$-0.458042\pi$$
0.131432 + 0.991325i $$0.458042\pi$$
$$522$$ 0 0
$$523$$ 20.0000 0.874539 0.437269 0.899331i $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ −10.0000 17.3205i −0.436852 0.756650i
$$525$$ 0 0
$$526$$ 12.0000 20.7846i 0.523225 0.906252i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −20.5000 35.5070i −0.891304 1.54378i
$$530$$ 12.0000 0.521247
$$531$$ 0 0
$$532$$ 4.00000 0.173422
$$533$$ −18.0000 31.1769i −0.779667 1.35042i
$$534$$ 0 0
$$535$$ 12.0000 20.7846i 0.518805 0.898597i
$$536$$ 2.00000 3.46410i 0.0863868 0.149626i
$$537$$ 0 0
$$538$$ −11.0000 19.0526i −0.474244 0.821414i
$$539$$ 4.00000 0.172292
$$540$$ 0 0
$$541$$ 30.0000 1.28980 0.644900 0.764267i $$-0.276899\pi$$
0.644900 + 0.764267i $$0.276899\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −1.00000 + 1.73205i −0.0428746 + 0.0742611i
$$545$$ 2.00000 3.46410i 0.0856706 0.148386i
$$546$$ 0 0
$$547$$ 6.00000 + 10.3923i 0.256541 + 0.444343i 0.965313 0.261095i $$-0.0840836\pi$$
−0.708772 + 0.705438i $$0.750750\pi$$
$$548$$ −10.0000 −0.427179
$$549$$ 0 0
$$550$$ 4.00000 0.170561
$$551$$ 4.00000 + 6.92820i 0.170406 + 0.295151i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −5.00000 + 8.66025i −0.212430 + 0.367939i
$$555$$ 0 0
$$556$$ −2.00000 3.46410i −0.0848189 0.146911i
$$557$$ 2.00000 0.0847427 0.0423714 0.999102i $$-0.486509\pi$$
0.0423714 + 0.999102i $$0.486509\pi$$
$$558$$ 0 0
$$559$$ −24.0000 −1.01509
$$560$$ 1.00000 + 1.73205i 0.0422577 + 0.0731925i
$$561$$ 0 0
$$562$$ −13.0000 + 22.5167i −0.548372 + 0.949808i
$$563$$ 22.0000 38.1051i 0.927189 1.60594i 0.139188 0.990266i $$-0.455551\pi$$
0.788002 0.615673i $$-0.211116\pi$$
$$564$$ 0 0
$$565$$ −14.0000 24.2487i −0.588984 1.02015i
$$566$$ −4.00000 −0.168133
$$567$$ 0 0
$$568$$ 8.00000 0.335673
$$569$$ −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i $$-0.206806\pi$$
−0.922032 + 0.387113i $$0.873472\pi$$
$$570$$ 0 0
$$571$$ −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i $$-0.914123\pi$$
0.712735 + 0.701434i $$0.247456\pi$$
$$572$$ −12.0000 + 20.7846i −0.501745 + 0.869048i
$$573$$ 0 0
$$574$$ −3.00000 5.19615i −0.125218 0.216883i
$$575$$ 8.00000 0.333623
$$576$$ 0 0
$$577$$ 34.0000 1.41544 0.707719 0.706494i $$-0.249724\pi$$
0.707719 + 0.706494i $$0.249724\pi$$
$$578$$ −6.50000 11.2583i −0.270364 0.468285i
$$579$$ 0 0
$$580$$ −2.00000 + 3.46410i −0.0830455 + 0.143839i
$$581$$ 2.00000 3.46410i 0.0829740 0.143715i
$$582$$ 0 0
$$583$$ 12.0000 + 20.7846i 0.496989 + 0.860811i
$$584$$ −10.0000 −0.413803
$$585$$ 0 0
$$586$$ 30.0000 1.23929
$$587$$ −14.0000 24.2487i −0.577842 1.00085i −0.995726 0.0923513i $$-0.970562\pi$$
0.417885 0.908500i $$-0.362772\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −4.00000 + 6.92820i −0.164677 + 0.285230i
$$591$$ 0 0
$$592$$ 5.00000 + 8.66025i 0.205499 + 0.355934i
$$593$$ −18.0000 −0.739171 −0.369586 0.929197i $$-0.620500\pi$$
−0.369586 + 0.929197i $$0.620500\pi$$
$$594$$ 0 0
$$595$$ 4.00000 0.163984
$$596$$ 3.00000 + 5.19615i 0.122885 + 0.212843i
$$597$$ 0 0
$$598$$ −24.0000 + 41.5692i −0.981433 + 1.69989i
$$599$$ 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i $$-0.670218\pi$$
0.999938 + 0.0111569i $$0.00355143\pi$$
$$600$$ 0 0
$$601$$ −13.0000 22.5167i −0.530281 0.918474i −0.999376 0.0353259i $$-0.988753\pi$$
0.469095 0.883148i $$-0.344580\pi$$
$$602$$ −4.00000 −0.163028
$$603$$ 0 0
$$604$$ −8.00000 −0.325515
$$605$$ −5.00000 8.66025i −0.203279 0.352089i
$$606$$ 0 0
$$607$$ −24.0000 + 41.5692i −0.974130 + 1.68724i −0.291353 + 0.956616i $$0.594105\pi$$
−0.682777 + 0.730627i $$0.739228\pi$$
$$608$$ −2.00000 + 3.46410i −0.0811107 + 0.140488i
$$609$$ 0 0
$$610$$ 6.00000 + 10.3923i 0.242933 + 0.420772i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −42.0000 −1.69636 −0.848182 0.529705i $$-0.822303\pi$$
−0.848182 + 0.529705i $$0.822303\pi$$
$$614$$ 14.0000 + 24.2487i 0.564994 + 0.978598i
$$615$$ 0 0
$$616$$ −2.00000 + 3.46410i −0.0805823 + 0.139573i
$$617$$ −11.0000 + 19.0526i −0.442843 + 0.767027i −0.997899 0.0647859i $$-0.979364\pi$$
0.555056 + 0.831813i $$0.312697\pi$$
$$618$$ 0 0
$$619$$ 22.0000 + 38.1051i 0.884255 + 1.53157i 0.846566 + 0.532284i $$0.178666\pi$$
0.0376891 + 0.999290i $$0.488000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −8.00000 −0.320771
$$623$$ 3.00000 + 5.19615i 0.120192 + 0.208179i
$$624$$ 0 0
$$625$$ 9.50000 16.4545i 0.380000 0.658179i
$$626$$ 5.00000 8.66025i 0.199840 0.346133i
$$627$$ 0 0
$$628$$ 5.00000 + 8.66025i 0.199522 + 0.345582i
$$629$$ 20.0000 0.797452
$$630$$ 0 0
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 9.00000 15.5885i 0.357436 0.619097i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −3.00000 5.19615i −0.118864 0.205879i
$$638$$ −8.00000 −0.316723
$$639$$ 0 0
$$640$$ −2.00000 −0.0790569
$$641$$ 1.00000 + 1.73205i 0.0394976 + 0.0684119i 0.885098 0.465404i $$-0.154091\pi$$
−0.845601 + 0.533816i $$0.820758\pi$$
$$642$$ 0 0
$$643$$ 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i $$-0.808201\pi$$
0.902764 + 0.430137i $$0.141535\pi$$
$$644$$ −4.00000 + 6.92820i −0.157622 + 0.273009i
$$645$$ 0 0
$$646$$ 4.00000 + 6.92820i 0.157378 + 0.272587i
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ 0 0
$$649$$ −16.0000 −0.628055
$$650$$ −3.00000 5.19615i −0.117670 0.203810i
$$651$$ 0 0
$$652$$ −10.0000 + 17.3205i −0.391630 + 0.678323i
$$653$$ −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i $$-0.947899\pi$$
0.634437 + 0.772975i $$0.281232\pi$$
$$654$$ 0 0
$$655$$ −20.0000 34.6410i −0.781465 1.35354i
$$656$$ 6.00000 0.234261
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −14.0000 24.2487i −0.545363 0.944596i −0.998584 0.0531977i $$-0.983059\pi$$
0.453221 0.891398i $$-0.350275\pi$$
$$660$$ 0 0
$$661$$ 1.00000 1.73205i 0.0388955 0.0673690i −0.845922 0.533306i $$-0.820949\pi$$
0.884818 + 0.465937i $$0.154283\pi$$
$$662$$ −2.00000 + 3.46410i −0.0777322 + 0.134636i
$$663$$ 0 0
$$664$$ 2.00000 + 3.46410i 0.0776151 + 0.134433i
$$665$$ 8.00000 0.310227
$$666$$ 0 0
$$667$$ −16.0000 −0.619522
$$668$$ −4.00000 6.92820i −0.154765 0.268060i
$$669$$ 0 0
$$670$$ 4.00000 6.92820i 0.154533 0.267660i
$$671$$ −12.0000 + 20.7846i −0.463255 + 0.802381i
$$672$$ 0 0
$$673$$ −1.00000 1.73205i −0.0385472 0.0667657i 0.846108 0.533011i $$-0.178940\pi$$
−0.884655 + 0.466246i $$0.845606\pi$$
$$674$$ −18.0000 −0.693334
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ −9.00000 15.5885i −0.345898 0.599113i 0.639618 0.768693i $$-0.279092\pi$$
−0.985517 + 0.169580i $$0.945759\pi$$
$$678$$ 0 0
$$679$$ −7.00000 + 12.1244i −0.268635 + 0.465290i
$$680$$ −2.00000 + 3.46410i −0.0766965 + 0.132842i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ −20.0000 −0.764161
$$686$$ −0.500000 0.866025i −0.0190901 0.0330650i
$$687$$ 0 0
$$688$$ 2.00000 3.46410i 0.0762493 0.132068i
$$689$$ 18.0000 31.1769i 0.685745 1.18775i
$$690$$ 0 0
$$691$$ 2.00000 + 3.46410i 0.0760836 + 0.131781i 0.901557 0.432660i $$-0.142425\pi$$
−0.825473 + 0.564441i $$0.809092\pi$$
$$692$$ −22.0000 −0.836315
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ −4.00000 6.92820i −0.151729 0.262802i
$$696$$ 0 0
$$697$$ 6.00000 10.3923i 0.227266 0.393637i
$$698$$ 11.0000 19.0526i 0.416356 0.721150i
$$699$$ 0 0
$$700$$ −0.500000 0.866025i −0.0188982 0.0327327i
$$701$$ 2.00000 0.0755390 0.0377695 0.999286i $$-0.487975\pi$$
0.0377695 + 0.999286i $$0.487975\pi$$
$$702$$ 0 0
$$703$$ 40.0000 1.50863
$$704$$ −2.00000 3.46410i −0.0753778 0.130558i
$$705$$ 0 0
$$706$$ 15.0000 25.9808i 0.564532 0.977799i
$$707$$ 1.00000 1.73205i 0.0376089 0.0651405i
$$708$$ 0 0
$$709$$ 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i $$-0.106538\pi$$
−0.756730 + 0.653727i $$0.773204\pi$$
$$710$$ 16.0000 0.600469
$$711$$ 0 0
$$712$$ −6.00000 −0.224860
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −24.0000 + 41.5692i −0.897549 + 1.55460i
$$716$$ −6.00000 + 10.3923i −0.224231 + 0.388379i
$$717$$ 0 0
$$718$$ 4.00000 + 6.92820i 0.149279 + 0.258558i
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ −1.50000 2.59808i −0.0558242 0.0966904i
$$723$$ 0 0
$$724$$ 9.00000 15.5885i 0.334482 0.579340i
$$725$$ 1.00000 1.73205i 0.0371391 0.0643268i
$$726$$ 0 0
$$727$$ 4.00000 + 6.92820i 0.148352 + 0.256953i 0.930618 0.365991i $$-0.119270\pi$$
−0.782267 + 0.622944i $$0.785937\pi$$
$$728$$ 6.00000 0.222375
$$729$$ 0 0
$$730$$ −20.0000 −0.740233
$$731$$ −4.00000 6.92820i −0.147945 0.256249i
$$732$$ 0 0
$$733$$ −3.00000 + 5.19615i −0.110808 + 0.191924i −0.916096 0.400959i $$-0.868677\pi$$
0.805289 + 0.592883i $$0.202010\pi$$
$$734$$ 16.0000 27.7128i 0.590571 1.02290i
$$735$$ 0 0
$$736$$ −4.00000 6.92820i −0.147442 0.255377i
$$737$$ 16.0000 0.589368
$$738$$ 0 0
$$739$$ −12.0000 −0.441427 −0.220714 0.975339i $$-0.570839\pi$$
−0.220714 + 0.975339i $$0.570839\pi$$
$$740$$ 10.0000 + 17.3205i 0.367607 + 0.636715i
$$741$$ 0 0
$$742$$ 3.00000 5.19615i 0.110133 0.190757i
$$743$$ 12.0000 20.7846i 0.440237 0.762513i −0.557470 0.830197i $$-0.688228\pi$$
0.997707 + 0.0676840i $$0.0215610\pi$$
$$744$$ 0 0
$$745$$ 6.00000 + 10.3923i 0.219823 + 0.380745i
$$746$$ −22.0000 −0.805477
$$747$$ 0 0
$$748$$ −8.00000 −0.292509
$$749$$ −6.00000 10.3923i −0.219235 0.379727i
$$750$$ 0 0
$$751$$ −24.0000 + 41.5692i −0.875772 + 1.51688i −0.0198348 + 0.999803i $$0.506314\pi$$
−0.855938 + 0.517079i $$0.827019\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 6.00000 + 10.3923i 0.218507 + 0.378465i
$$755$$ −16.0000 −0.582300
$$756$$ 0 0
$$757$$ 6.00000 0.218074 0.109037 0.994038i $$-0.465223\pi$$
0.109037 + 0.994038i $$0.465223\pi$$
$$758$$ −10.0000 17.3205i −0.363216 0.629109i
$$759$$ 0 0
$$760$$ −4.00000 + 6.92820i −0.145095 + 0.251312i
$$761$$ −11.0000 + 19.0526i −0.398750 + 0.690655i −0.993572 0.113203i $$-0.963889\pi$$
0.594822 + 0.803857i $$0.297222\pi$$
$$762$$ 0 0
$$763$$ −1.00000 1.73205i −0.0362024 0.0627044i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −16.0000 −0.578103
$$767$$ 12.0000 + 20.7846i 0.433295 + 0.750489i
$$768$$ 0 0
$$769$$ 7.00000 12.1244i 0.252426 0.437215i −0.711767 0.702416i $$-0.752105\pi$$
0.964193 + 0.265200i $$0.0854381\pi$$
$$770$$ −4.00000 + 6.92820i −0.144150 + 0.249675i
$$771$$ 0 0
$$772$$ −1.00000 1.73205i −0.0359908 0.0623379i
$$773$$ 2.00000 0.0719350 0.0359675 0.999353i $$-0.488549\pi$$
0.0359675 + 0.999353i $$0.488549\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −7.00000 12.1244i −0.251285 0.435239i
$$777$$ 0 0
$$778$$ 13.0000 22.5167i 0.466073 0.807261i
$$779$$ 12.0000 20.7846i 0.429945 0.744686i
$$780$$ 0 0
$$781$$ 16.0000 + 27.7128i 0.572525 + 0.991642i
$$782$$ −16.0000 −0.572159
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 10.0000 + 17.3205i 0.356915 + 0.618195i
$$786$$ 0 0
$$787$$ 18.0000 31.1769i 0.641631 1.11134i −0.343438 0.939175i $$-0.611592\pi$$
0.985069 0.172162i $$-0.0550751\pi$$
$$788$$ −5.00000 + 8.66025i −0.178118 + 0.308509i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −14.0000 −0.497783
$$792$$ 0 0
$$793$$ 36.0000 1.27840