# Properties

 Label 336.2.q.b.289.1 Level $336$ Weight $2$ Character 336.289 Analytic conductor $2.683$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$336 = 2^{4} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 336.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.68297350792$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 42) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 289.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 336.289 Dual form 336.2.q.b.193.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +1.00000 q^{15} +(2.00000 + 3.46410i) q^{17} +(4.00000 - 6.92820i) q^{19} +(2.50000 - 0.866025i) q^{21} +(-2.00000 + 3.46410i) q^{23} +(2.00000 + 3.46410i) q^{25} +1.00000 q^{27} -5.00000 q^{29} +(1.50000 + 2.59808i) q^{31} +(2.50000 - 4.33013i) q^{33} +(-2.00000 - 1.73205i) q^{35} +(2.00000 - 3.46410i) q^{37} -2.00000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-3.00000 + 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{51} +(4.50000 + 7.79423i) q^{53} -5.00000 q^{55} -8.00000 q^{57} +(-5.50000 - 9.52628i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-2.00000 - 1.73205i) q^{63} +(-1.00000 - 1.73205i) q^{67} +4.00000 q^{69} -2.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(2.00000 - 3.46410i) q^{75} +(-12.5000 + 4.33013i) q^{77} +(1.50000 - 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.00000 q^{83} -4.00000 q^{85} +(2.50000 + 4.33013i) q^{87} +(3.00000 - 5.19615i) q^{89} +(1.50000 - 2.59808i) q^{93} +(4.00000 + 6.92820i) q^{95} +7.00000 q^{97} -5.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} - q^{5} - q^{7} - q^{9} + O(q^{10})$$ $$2q - q^{3} - q^{5} - q^{7} - q^{9} + 5q^{11} + 2q^{15} + 4q^{17} + 8q^{19} + 5q^{21} - 4q^{23} + 4q^{25} + 2q^{27} - 10q^{29} + 3q^{31} + 5q^{33} - 4q^{35} + 4q^{37} - 4q^{43} - q^{45} - 6q^{47} - 13q^{49} + 4q^{51} + 9q^{53} - 10q^{55} - 16q^{57} - 11q^{59} + 6q^{61} - 4q^{63} - 2q^{67} + 8q^{69} - 4q^{71} - 10q^{73} + 4q^{75} - 25q^{77} + 3q^{79} - q^{81} + 14q^{83} - 8q^{85} + 5q^{87} + 6q^{89} + 3q^{93} + 8q^{95} + 14q^{97} - 10q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$$.

 $$n$$ $$85$$ $$113$$ $$127$$ $$241$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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 0
$$3$$ −0.500000 0.866025i −0.288675 0.500000i
$$4$$ 0 0
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i −0.955901 0.293691i $$-0.905116\pi$$
0.732294 + 0.680989i $$0.238450\pi$$
$$6$$ 0 0
$$7$$ −0.500000 + 2.59808i −0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i $$0.105104\pi$$
−0.192201 + 0.981356i $$0.561563\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 1.00000 0.258199
$$16$$ 0 0
$$17$$ 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i $$-0.00546033\pi$$
−0.514782 + 0.857321i $$0.672127\pi$$
$$18$$ 0 0
$$19$$ 4.00000 6.92820i 0.917663 1.58944i 0.114708 0.993399i $$-0.463407\pi$$
0.802955 0.596040i $$-0.203260\pi$$
$$20$$ 0 0
$$21$$ 2.50000 0.866025i 0.545545 0.188982i
$$22$$ 0 0
$$23$$ −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i $$-0.970262\pi$$
0.578610 + 0.815604i $$0.303595\pi$$
$$24$$ 0 0
$$25$$ 2.00000 + 3.46410i 0.400000 + 0.692820i
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ 0 0
$$31$$ 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i $$-0.0798387\pi$$
−0.699301 + 0.714827i $$0.746505\pi$$
$$32$$ 0 0
$$33$$ 2.50000 4.33013i 0.435194 0.753778i
$$34$$ 0 0
$$35$$ −2.00000 1.73205i −0.338062 0.292770i
$$36$$ 0 0
$$37$$ 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i $$-0.726690\pi$$
0.982274 + 0.187453i $$0.0600231\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 0 0
$$45$$ −0.500000 0.866025i −0.0745356 0.129099i
$$46$$ 0 0
$$47$$ −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i $$-0.977503\pi$$
0.559908 + 0.828554i $$0.310836\pi$$
$$48$$ 0 0
$$49$$ −6.50000 2.59808i −0.928571 0.371154i
$$50$$ 0 0
$$51$$ 2.00000 3.46410i 0.280056 0.485071i
$$52$$ 0 0
$$53$$ 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i $$0.0454398\pi$$
−0.371706 + 0.928351i $$0.621227\pi$$
$$54$$ 0 0
$$55$$ −5.00000 −0.674200
$$56$$ 0 0
$$57$$ −8.00000 −1.05963
$$58$$ 0 0
$$59$$ −5.50000 9.52628i −0.716039 1.24022i −0.962557 0.271078i $$-0.912620\pi$$
0.246518 0.969138i $$-0.420713\pi$$
$$60$$ 0 0
$$61$$ 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i $$-0.707841\pi$$
0.991645 + 0.128994i $$0.0411748\pi$$
$$62$$ 0 0
$$63$$ −2.00000 1.73205i −0.251976 0.218218i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i $$-0.205652\pi$$
−0.920623 + 0.390453i $$0.872318\pi$$
$$68$$ 0 0
$$69$$ 4.00000 0.481543
$$70$$ 0 0
$$71$$ −2.00000 −0.237356 −0.118678 0.992933i $$-0.537866\pi$$
−0.118678 + 0.992933i $$0.537866\pi$$
$$72$$ 0 0
$$73$$ −5.00000 8.66025i −0.585206 1.01361i −0.994850 0.101361i $$-0.967680\pi$$
0.409644 0.912245i $$-0.365653\pi$$
$$74$$ 0 0
$$75$$ 2.00000 3.46410i 0.230940 0.400000i
$$76$$ 0 0
$$77$$ −12.5000 + 4.33013i −1.42451 + 0.493464i
$$78$$ 0 0
$$79$$ 1.50000 2.59808i 0.168763 0.292306i −0.769222 0.638982i $$-0.779356\pi$$
0.937985 + 0.346675i $$0.112689\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ 7.00000 0.768350 0.384175 0.923260i $$-0.374486\pi$$
0.384175 + 0.923260i $$0.374486\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ 0 0
$$87$$ 2.50000 + 4.33013i 0.268028 + 0.464238i
$$88$$ 0 0
$$89$$ 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i $$-0.730322\pi$$
0.980071 + 0.198650i $$0.0636557\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 1.50000 2.59808i 0.155543 0.269408i
$$94$$ 0 0
$$95$$ 4.00000 + 6.92820i 0.410391 + 0.710819i
$$96$$ 0 0
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ 0 0
$$99$$ −5.00000 −0.502519
$$100$$ 0 0
$$101$$ −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i $$-0.332422\pi$$
−0.999996 + 0.00286291i $$0.999089\pi$$
$$102$$ 0 0
$$103$$ 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i $$-0.704379\pi$$
0.992990 + 0.118199i $$0.0377120\pi$$
$$104$$ 0 0
$$105$$ −0.500000 + 2.59808i −0.0487950 + 0.253546i
$$106$$ 0 0
$$107$$ 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i $$-0.787012\pi$$
0.929377 + 0.369132i $$0.120345\pi$$
$$108$$ 0 0
$$109$$ 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i $$-0.136131\pi$$
−0.814152 + 0.580651i $$0.802798\pi$$
$$110$$ 0 0
$$111$$ −4.00000 −0.379663
$$112$$ 0 0
$$113$$ 16.0000 1.50515 0.752577 0.658505i $$-0.228811\pi$$
0.752577 + 0.658505i $$0.228811\pi$$
$$114$$ 0 0
$$115$$ −2.00000 3.46410i −0.186501 0.323029i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −10.0000 + 3.46410i −0.916698 + 0.317554i
$$120$$ 0 0
$$121$$ −7.00000 + 12.1244i −0.636364 + 1.10221i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −9.00000 −0.804984
$$126$$ 0 0
$$127$$ −9.00000 −0.798621 −0.399310 0.916816i $$-0.630750\pi$$
−0.399310 + 0.916816i $$0.630750\pi$$
$$128$$ 0 0
$$129$$ 1.00000 + 1.73205i 0.0880451 + 0.152499i
$$130$$ 0 0
$$131$$ 0.500000 0.866025i 0.0436852 0.0756650i −0.843356 0.537355i $$-0.819423\pi$$
0.887041 + 0.461690i $$0.152757\pi$$
$$132$$ 0 0
$$133$$ 16.0000 + 13.8564i 1.38738 + 1.20150i
$$134$$ 0 0
$$135$$ −0.500000 + 0.866025i −0.0430331 + 0.0745356i
$$136$$ 0 0
$$137$$ 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i $$-0.139438\pi$$
−0.820141 + 0.572161i $$0.806105\pi$$
$$138$$ 0 0
$$139$$ 14.0000 1.18746 0.593732 0.804663i $$-0.297654\pi$$
0.593732 + 0.804663i $$0.297654\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 2.50000 4.33013i 0.207614 0.359597i
$$146$$ 0 0
$$147$$ 1.00000 + 6.92820i 0.0824786 + 0.571429i
$$148$$ 0 0
$$149$$ 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i $$-0.569430\pi$$
0.953703 0.300750i $$-0.0972370\pi$$
$$150$$ 0 0
$$151$$ 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i $$0.114628\pi$$
−0.162758 + 0.986666i $$0.552039\pi$$
$$152$$ 0 0
$$153$$ −4.00000 −0.323381
$$154$$ 0 0
$$155$$ −3.00000 −0.240966
$$156$$ 0 0
$$157$$ 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i $$-0.115641\pi$$
−0.775113 + 0.631822i $$0.782307\pi$$
$$158$$ 0 0
$$159$$ 4.50000 7.79423i 0.356873 0.618123i
$$160$$ 0 0
$$161$$ −8.00000 6.92820i −0.630488 0.546019i
$$162$$ 0 0
$$163$$ −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i $$-0.883403\pi$$
0.777007 + 0.629492i $$0.216737\pi$$
$$164$$ 0 0
$$165$$ 2.50000 + 4.33013i 0.194625 + 0.337100i
$$166$$ 0 0
$$167$$ 14.0000 1.08335 0.541676 0.840587i $$-0.317790\pi$$
0.541676 + 0.840587i $$0.317790\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 4.00000 + 6.92820i 0.305888 + 0.529813i
$$172$$ 0 0
$$173$$ −11.0000 + 19.0526i −0.836315 + 1.44854i 0.0566411 + 0.998395i $$0.481961\pi$$
−0.892956 + 0.450145i $$0.851372\pi$$
$$174$$ 0 0
$$175$$ −10.0000 + 3.46410i −0.755929 + 0.261861i
$$176$$ 0 0
$$177$$ −5.50000 + 9.52628i −0.413405 + 0.716039i
$$178$$ 0 0
$$179$$ 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i $$-0.0186389\pi$$
−0.549825 + 0.835280i $$0.685306\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ −6.00000 −0.443533
$$184$$ 0 0
$$185$$ 2.00000 + 3.46410i 0.147043 + 0.254686i
$$186$$ 0 0
$$187$$ −10.0000 + 17.3205i −0.731272 + 1.26660i
$$188$$ 0 0
$$189$$ −0.500000 + 2.59808i −0.0363696 + 0.188982i
$$190$$ 0 0
$$191$$ 12.0000 20.7846i 0.868290 1.50392i 0.00454614 0.999990i $$-0.498553\pi$$
0.863743 0.503932i $$-0.168114\pi$$
$$192$$ 0 0
$$193$$ −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i $$-0.224262\pi$$
−0.941865 + 0.335993i $$0.890928\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ 0 0
$$199$$ −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i $$-0.211948\pi$$
−0.928166 + 0.372168i $$0.878615\pi$$
$$200$$ 0 0
$$201$$ −1.00000 + 1.73205i −0.0705346 + 0.122169i
$$202$$ 0 0
$$203$$ 2.50000 12.9904i 0.175466 0.911746i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −2.00000 3.46410i −0.139010 0.240772i
$$208$$ 0 0
$$209$$ 40.0000 2.76686
$$210$$ 0 0
$$211$$ −2.00000 −0.137686 −0.0688428 0.997628i $$-0.521931\pi$$
−0.0688428 + 0.997628i $$0.521931\pi$$
$$212$$ 0 0
$$213$$ 1.00000 + 1.73205i 0.0685189 + 0.118678i
$$214$$ 0 0
$$215$$ 1.00000 1.73205i 0.0681994 0.118125i
$$216$$ 0 0
$$217$$ −7.50000 + 2.59808i −0.509133 + 0.176369i
$$218$$ 0 0
$$219$$ −5.00000 + 8.66025i −0.337869 + 0.585206i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 7.00000 0.468755 0.234377 0.972146i $$-0.424695\pi$$
0.234377 + 0.972146i $$0.424695\pi$$
$$224$$ 0 0
$$225$$ −4.00000 −0.266667
$$226$$ 0 0
$$227$$ 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i $$-0.134924\pi$$
−0.811943 + 0.583736i $$0.801590\pi$$
$$228$$ 0 0
$$229$$ 10.0000 17.3205i 0.660819 1.14457i −0.319582 0.947559i $$-0.603543\pi$$
0.980401 0.197013i $$-0.0631241\pi$$
$$230$$ 0 0
$$231$$ 10.0000 + 8.66025i 0.657952 + 0.569803i
$$232$$ 0 0
$$233$$ 2.00000 3.46410i 0.131024 0.226941i −0.793047 0.609160i $$-0.791507\pi$$
0.924072 + 0.382219i $$0.124840\pi$$
$$234$$ 0 0
$$235$$ −3.00000 5.19615i −0.195698 0.338960i
$$236$$ 0 0
$$237$$ −3.00000 −0.194871
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ 12.5000 + 21.6506i 0.805196 + 1.39464i 0.916159 + 0.400815i $$0.131273\pi$$
−0.110963 + 0.993825i $$0.535394\pi$$
$$242$$ 0 0
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ 5.50000 4.33013i 0.351382 0.276642i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −3.50000 6.06218i −0.221803 0.384175i
$$250$$ 0 0
$$251$$ −21.0000 −1.32551 −0.662754 0.748837i $$-0.730613\pi$$
−0.662754 + 0.748837i $$0.730613\pi$$
$$252$$ 0 0
$$253$$ −20.0000 −1.25739
$$254$$ 0 0
$$255$$ 2.00000 + 3.46410i 0.125245 + 0.216930i
$$256$$ 0 0
$$257$$ 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i $$-0.773413\pi$$
0.944294 + 0.329104i $$0.106747\pi$$
$$258$$ 0 0
$$259$$ 8.00000 + 6.92820i 0.497096 + 0.430498i
$$260$$ 0 0
$$261$$ 2.50000 4.33013i 0.154746 0.268028i
$$262$$ 0 0
$$263$$ −15.0000 25.9808i −0.924940 1.60204i −0.791658 0.610964i $$-0.790782\pi$$
−0.133281 0.991078i $$-0.542551\pi$$
$$264$$ 0 0
$$265$$ −9.00000 −0.552866
$$266$$ 0 0
$$267$$ −6.00000 −0.367194
$$268$$ 0 0
$$269$$ −15.5000 26.8468i −0.945052 1.63688i −0.755648 0.654978i $$-0.772678\pi$$
−0.189404 0.981899i $$-0.560656\pi$$
$$270$$ 0 0
$$271$$ 7.50000 12.9904i 0.455593 0.789109i −0.543130 0.839649i $$-0.682761\pi$$
0.998722 + 0.0505395i $$0.0160941\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −10.0000 + 17.3205i −0.603023 + 1.04447i
$$276$$ 0 0
$$277$$ 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i $$-0.00705893\pi$$
−0.519081 + 0.854725i $$0.673726\pi$$
$$278$$ 0 0
$$279$$ −3.00000 −0.179605
$$280$$ 0 0
$$281$$ 2.00000 0.119310 0.0596550 0.998219i $$-0.481000\pi$$
0.0596550 + 0.998219i $$0.481000\pi$$
$$282$$ 0 0
$$283$$ 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i $$-0.0706075\pi$$
−0.678280 + 0.734804i $$0.737274\pi$$
$$284$$ 0 0
$$285$$ 4.00000 6.92820i 0.236940 0.410391i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 0.500000 0.866025i 0.0294118 0.0509427i
$$290$$ 0 0
$$291$$ −3.50000 6.06218i −0.205174 0.355371i
$$292$$ 0 0
$$293$$ −21.0000 −1.22683 −0.613417 0.789760i $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 0 0
$$295$$ 11.0000 0.640445
$$296$$ 0 0
$$297$$ 2.50000 + 4.33013i 0.145065 + 0.251259i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 1.00000 5.19615i 0.0576390 0.299501i
$$302$$ 0 0
$$303$$ −5.00000 + 8.66025i −0.287242 + 0.497519i
$$304$$ 0 0
$$305$$ 3.00000 + 5.19615i 0.171780 + 0.297531i
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 0 0
$$309$$ −8.00000 −0.455104
$$310$$ 0 0
$$311$$ −16.0000 27.7128i −0.907277 1.57145i −0.817832 0.575458i $$-0.804824\pi$$
−0.0894452 0.995992i $$-0.528509\pi$$
$$312$$ 0 0
$$313$$ −0.500000 + 0.866025i −0.0282617 + 0.0489506i −0.879810 0.475325i $$-0.842331\pi$$
0.851549 + 0.524276i $$0.175664\pi$$
$$314$$ 0 0
$$315$$ 2.50000 0.866025i 0.140859 0.0487950i
$$316$$ 0 0
$$317$$ −1.50000 + 2.59808i −0.0842484 + 0.145922i −0.905071 0.425261i $$-0.860182\pi$$
0.820822 + 0.571184i $$0.193516\pi$$
$$318$$ 0 0
$$319$$ −12.5000 21.6506i −0.699866 1.21220i
$$320$$ 0 0
$$321$$ −3.00000 −0.167444
$$322$$ 0 0
$$323$$ 32.0000 1.78053
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 1.00000 1.73205i 0.0553001 0.0957826i
$$328$$ 0 0
$$329$$ −12.0000 10.3923i −0.661581 0.572946i
$$330$$ 0 0
$$331$$ −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i $$-0.868396\pi$$
0.805812 + 0.592172i $$0.201729\pi$$
$$332$$ 0 0
$$333$$ 2.00000 + 3.46410i 0.109599 + 0.189832i
$$334$$ 0 0
$$335$$ 2.00000 0.109272
$$336$$ 0 0
$$337$$ 9.00000 0.490261 0.245131 0.969490i $$-0.421169\pi$$
0.245131 + 0.969490i $$0.421169\pi$$
$$338$$ 0 0
$$339$$ −8.00000 13.8564i −0.434500 0.752577i
$$340$$ 0 0
$$341$$ −7.50000 + 12.9904i −0.406148 + 0.703469i
$$342$$ 0 0
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ 0 0
$$345$$ −2.00000 + 3.46410i −0.107676 + 0.186501i
$$346$$ 0 0
$$347$$ 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i $$-0.0622790\pi$$
−0.658824 + 0.752297i $$0.728946\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i $$-0.946141\pi$$
0.347024 0.937856i $$-0.387192\pi$$
$$354$$ 0 0
$$355$$ 1.00000 1.73205i 0.0530745 0.0919277i
$$356$$ 0 0
$$357$$ 8.00000 + 6.92820i 0.423405 + 0.366679i
$$358$$ 0 0
$$359$$ 5.00000 8.66025i 0.263890 0.457071i −0.703382 0.710812i $$-0.748328\pi$$
0.967272 + 0.253741i $$0.0816611\pi$$
$$360$$ 0 0
$$361$$ −22.5000 38.9711i −1.18421 2.05111i
$$362$$ 0 0
$$363$$ 14.0000 0.734809
$$364$$ 0 0
$$365$$ 10.0000 0.523424
$$366$$ 0 0
$$367$$ 8.50000 + 14.7224i 0.443696 + 0.768505i 0.997960 0.0638362i $$-0.0203335\pi$$
−0.554264 + 0.832341i $$0.687000\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −22.5000 + 7.79423i −1.16814 + 0.404656i
$$372$$ 0 0
$$373$$ 16.0000 27.7128i 0.828449 1.43492i −0.0708063 0.997490i $$-0.522557\pi$$
0.899255 0.437425i $$-0.144109\pi$$
$$374$$ 0 0
$$375$$ 4.50000 + 7.79423i 0.232379 + 0.402492i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −16.0000 −0.821865 −0.410932 0.911666i $$-0.634797\pi$$
−0.410932 + 0.911666i $$0.634797\pi$$
$$380$$ 0 0
$$381$$ 4.50000 + 7.79423i 0.230542 + 0.399310i
$$382$$ 0 0
$$383$$ −17.0000 + 29.4449i −0.868659 + 1.50456i −0.00529229 + 0.999986i $$0.501685\pi$$
−0.863367 + 0.504576i $$0.831649\pi$$
$$384$$ 0 0
$$385$$ 2.50000 12.9904i 0.127412 0.662051i
$$386$$ 0 0
$$387$$ 1.00000 1.73205i 0.0508329 0.0880451i
$$388$$ 0 0
$$389$$ 1.00000 + 1.73205i 0.0507020 + 0.0878185i 0.890263 0.455448i $$-0.150521\pi$$
−0.839561 + 0.543266i $$0.817187\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ −1.00000 −0.0504433
$$394$$ 0 0
$$395$$ 1.50000 + 2.59808i 0.0754732 + 0.130723i
$$396$$ 0 0
$$397$$ −18.0000 + 31.1769i −0.903394 + 1.56472i −0.0803356 + 0.996768i $$0.525599\pi$$
−0.823058 + 0.567957i $$0.807734\pi$$
$$398$$ 0 0
$$399$$ 4.00000 20.7846i 0.200250 1.04053i
$$400$$ 0 0
$$401$$ −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i $$0.371202\pi$$
−0.992932 + 0.118686i $$0.962132\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 1.00000 0.0496904
$$406$$ 0 0
$$407$$ 20.0000 0.991363
$$408$$ 0 0
$$409$$ 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i $$0.0454247\pi$$
−0.371750 + 0.928333i $$0.621242\pi$$
$$410$$ 0 0
$$411$$ 1.00000 1.73205i 0.0493264 0.0854358i
$$412$$ 0 0
$$413$$ 27.5000 9.52628i 1.35319 0.468758i
$$414$$ 0 0
$$415$$ −3.50000 + 6.06218i −0.171808 + 0.297581i
$$416$$ 0 0
$$417$$ −7.00000 12.1244i −0.342791 0.593732i
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ 0 0
$$423$$ −3.00000 5.19615i −0.145865 0.252646i
$$424$$ 0 0
$$425$$ −8.00000 + 13.8564i −0.388057 + 0.672134i
$$426$$ 0 0
$$427$$ 12.0000 + 10.3923i 0.580721 + 0.502919i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i $$-0.0733406\pi$$
−0.684564 + 0.728953i $$0.740007\pi$$
$$432$$ 0 0
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 0 0
$$435$$ −5.00000 −0.239732
$$436$$ 0 0
$$437$$ 16.0000 + 27.7128i 0.765384 + 1.32568i
$$438$$ 0 0
$$439$$ 7.50000 12.9904i 0.357955 0.619997i −0.629664 0.776868i $$-0.716807\pi$$
0.987619 + 0.156871i $$0.0501406\pi$$
$$440$$ 0 0
$$441$$ 5.50000 4.33013i 0.261905 0.206197i
$$442$$ 0 0
$$443$$ 8.50000 14.7224i 0.403847 0.699484i −0.590339 0.807155i $$-0.701006\pi$$
0.994187 + 0.107671i $$0.0343394\pi$$
$$444$$ 0 0
$$445$$ 3.00000 + 5.19615i 0.142214 + 0.246321i
$$446$$ 0 0
$$447$$ −18.0000 −0.851371
$$448$$ 0 0
$$449$$ 16.0000 0.755087 0.377543 0.925992i $$-0.376769\pi$$
0.377543 + 0.925992i $$0.376769\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 9.50000 16.4545i 0.446349 0.773099i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −15.5000 + 26.8468i −0.725059 + 1.25584i 0.233890 + 0.972263i $$0.424854\pi$$
−0.958950 + 0.283577i $$0.908479\pi$$
$$458$$ 0 0
$$459$$ 2.00000 + 3.46410i 0.0933520 + 0.161690i
$$460$$ 0 0
$$461$$ −14.0000 −0.652045 −0.326023 0.945362i $$-0.605709\pi$$
−0.326023 + 0.945362i $$0.605709\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 1.50000 + 2.59808i 0.0695608 + 0.120483i
$$466$$ 0 0
$$467$$ −10.0000 + 17.3205i −0.462745 + 0.801498i −0.999097 0.0424970i $$-0.986469\pi$$
0.536352 + 0.843995i $$0.319802\pi$$
$$468$$ 0 0
$$469$$ 5.00000 1.73205i 0.230879 0.0799787i
$$470$$ 0 0
$$471$$ 2.00000 3.46410i 0.0921551 0.159617i
$$472$$ 0 0
$$473$$ −5.00000 8.66025i −0.229900 0.398199i
$$474$$ 0 0
$$475$$ 32.0000 1.46826
$$476$$ 0 0
$$477$$ −9.00000 −0.412082
$$478$$ 0 0
$$479$$ 19.0000 + 32.9090i 0.868132 + 1.50365i 0.863903 + 0.503658i $$0.168013\pi$$
0.00422900 + 0.999991i $$0.498654\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ −2.00000 + 10.3923i −0.0910032 + 0.472866i
$$484$$ 0 0
$$485$$ −3.50000 + 6.06218i −0.158927 + 0.275269i
$$486$$ 0 0
$$487$$ 2.50000 + 4.33013i 0.113286 + 0.196217i 0.917093 0.398673i $$-0.130529\pi$$
−0.803807 + 0.594890i $$0.797196\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ −9.00000 −0.406164 −0.203082 0.979162i $$-0.565096\pi$$
−0.203082 + 0.979162i $$0.565096\pi$$
$$492$$ 0 0
$$493$$ −10.0000 17.3205i −0.450377 0.780076i
$$494$$ 0 0
$$495$$ 2.50000 4.33013i 0.112367 0.194625i
$$496$$ 0 0
$$497$$ 1.00000 5.19615i 0.0448561 0.233079i
$$498$$ 0 0
$$499$$ 5.00000 8.66025i 0.223831 0.387686i −0.732137 0.681157i $$-0.761477\pi$$
0.955968 + 0.293471i $$0.0948104\pi$$
$$500$$ 0 0
$$501$$ −7.00000 12.1244i −0.312737 0.541676i
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 10.0000 0.444994
$$506$$ 0 0
$$507$$ 6.50000 + 11.2583i 0.288675 + 0.500000i
$$508$$ 0 0
$$509$$ −7.50000 + 12.9904i −0.332432 + 0.575789i −0.982988 0.183669i $$-0.941202\pi$$
0.650556 + 0.759458i $$0.274536\pi$$
$$510$$ 0 0
$$511$$ 25.0000 8.66025i 1.10593 0.383107i
$$512$$ 0 0
$$513$$ 4.00000 6.92820i 0.176604 0.305888i
$$514$$ 0 0
$$515$$ 4.00000 + 6.92820i 0.176261 + 0.305293i
$$516$$ 0 0
$$517$$ −30.0000 −1.31940
$$518$$ 0 0
$$519$$ 22.0000 0.965693
$$520$$ 0 0
$$521$$ 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i $$-0.0376547\pi$$
−0.598714 + 0.800963i $$0.704321\pi$$
$$522$$ 0 0
$$523$$ 4.00000 6.92820i 0.174908 0.302949i −0.765222 0.643767i $$-0.777371\pi$$
0.940129 + 0.340818i $$0.110704\pi$$
$$524$$ 0 0
$$525$$ 8.00000 + 6.92820i 0.349149 + 0.302372i
$$526$$ 0 0
$$527$$ −6.00000 + 10.3923i −0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ 3.50000 + 6.06218i 0.152174 + 0.263573i
$$530$$ 0 0
$$531$$ 11.0000 0.477359
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 1.50000 + 2.59808i 0.0648507 + 0.112325i
$$536$$ 0 0
$$537$$ 6.00000 10.3923i 0.258919 0.448461i
$$538$$ 0 0
$$539$$ −5.00000 34.6410i −0.215365 1.49209i
$$540$$ 0 0
$$541$$ 9.00000 15.5885i 0.386940 0.670200i −0.605096 0.796152i $$-0.706865\pi$$
0.992036 + 0.125952i $$0.0401986\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −2.00000 −0.0856706
$$546$$ 0 0
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ 0 0
$$549$$ 3.00000 + 5.19615i 0.128037 + 0.221766i
$$550$$ 0 0
$$551$$ −20.0000 + 34.6410i −0.852029 + 1.47576i
$$552$$ 0 0
$$553$$ 6.00000 + 5.19615i 0.255146 + 0.220963i
$$554$$ 0 0
$$555$$ 2.00000 3.46410i 0.0848953 0.147043i
$$556$$ 0 0
$$557$$ 11.5000 + 19.9186i 0.487271 + 0.843978i 0.999893 0.0146368i $$-0.00465919\pi$$
−0.512622 + 0.858614i $$0.671326\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 20.0000 0.844401
$$562$$ 0 0
$$563$$ 8.50000 + 14.7224i 0.358232 + 0.620477i 0.987666 0.156578i $$-0.0500463\pi$$
−0.629433 + 0.777055i $$0.716713\pi$$
$$564$$ 0 0
$$565$$ −8.00000 + 13.8564i −0.336563 + 0.582943i
$$566$$ 0 0
$$567$$ 2.50000 0.866025i 0.104990 0.0363696i
$$568$$ 0 0
$$569$$ −12.0000 + 20.7846i −0.503066 + 0.871336i 0.496928 + 0.867792i $$0.334461\pi$$
−0.999994 + 0.00354413i $$0.998872\pi$$
$$570$$ 0 0
$$571$$ −15.0000 25.9808i −0.627730 1.08726i −0.988006 0.154415i $$-0.950651\pi$$
0.360276 0.932846i $$-0.382683\pi$$
$$572$$ 0 0
$$573$$ −24.0000 −1.00261
$$574$$ 0 0
$$575$$ −16.0000 −0.667246
$$576$$ 0 0
$$577$$ −15.5000 26.8468i −0.645273 1.11765i −0.984238 0.176847i $$-0.943410\pi$$
0.338965 0.940799i $$-0.389923\pi$$
$$578$$ 0 0
$$579$$ −2.50000 + 4.33013i −0.103896 + 0.179954i
$$580$$ 0 0
$$581$$ −3.50000 + 18.1865i −0.145204 + 0.754505i
$$582$$ 0 0
$$583$$ −22.5000 + 38.9711i −0.931855 + 1.61402i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −35.0000 −1.44460 −0.722302 0.691577i $$-0.756916\pi$$
−0.722302 + 0.691577i $$0.756916\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ 0 0
$$591$$ −1.00000 1.73205i −0.0411345 0.0712470i
$$592$$ 0 0
$$593$$ −18.0000 + 31.1769i −0.739171 + 1.28028i 0.213697 + 0.976900i $$0.431449\pi$$
−0.952869 + 0.303383i $$0.901884\pi$$
$$594$$ 0 0
$$595$$ 2.00000 10.3923i 0.0819920 0.426043i
$$596$$ 0 0
$$597$$ −2.00000 + 3.46410i −0.0818546 + 0.141776i
$$598$$ 0 0
$$599$$ −15.0000 25.9808i −0.612883 1.06155i −0.990752 0.135686i $$-0.956676\pi$$
0.377869 0.925859i $$-0.376657\pi$$
$$600$$ 0 0
$$601$$ 35.0000 1.42768 0.713840 0.700309i $$-0.246954\pi$$
0.713840 + 0.700309i $$0.246954\pi$$
$$602$$ 0 0
$$603$$ 2.00000 0.0814463
$$604$$ 0 0
$$605$$ −7.00000 12.1244i −0.284590 0.492925i
$$606$$ 0 0
$$607$$ −13.5000 + 23.3827i −0.547948 + 0.949074i 0.450467 + 0.892793i $$0.351258\pi$$
−0.998415 + 0.0562808i $$0.982076\pi$$
$$608$$ 0 0
$$609$$ −12.5000 + 4.33013i −0.506526 + 0.175466i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −6.00000 10.3923i −0.242338 0.419741i 0.719042 0.694967i $$-0.244581\pi$$
−0.961380 + 0.275225i $$0.911248\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 2.00000 0.0805170 0.0402585 0.999189i $$-0.487182\pi$$
0.0402585 + 0.999189i $$0.487182\pi$$
$$618$$ 0 0
$$619$$ 5.00000 + 8.66025i 0.200967 + 0.348085i 0.948840 0.315757i $$-0.102258\pi$$
−0.747873 + 0.663842i $$0.768925\pi$$
$$620$$ 0 0
$$621$$ −2.00000 + 3.46410i −0.0802572 + 0.139010i
$$622$$ 0 0
$$623$$ 12.0000 + 10.3923i 0.480770 + 0.416359i
$$624$$ 0 0
$$625$$ −5.50000 + 9.52628i −0.220000 + 0.381051i
$$626$$ 0 0
$$627$$ −20.0000 34.6410i −0.798723 1.38343i
$$628$$ 0 0
$$629$$ 16.0000 0.637962
$$630$$ 0 0
$$631$$ 19.0000 0.756378 0.378189 0.925728i $$-0.376547\pi$$
0.378189 + 0.925728i $$0.376547\pi$$
$$632$$ 0 0
$$633$$ 1.00000 + 1.73205i 0.0397464 + 0.0688428i
$$634$$ 0 0
$$635$$ 4.50000 7.79423i 0.178577 0.309305i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 1.00000 1.73205i 0.0395594 0.0685189i
$$640$$ 0 0
$$641$$ −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i $$-0.995027\pi$$
0.486409 0.873731i $$-0.338307\pi$$
$$642$$ 0 0
$$643$$ −14.0000 −0.552106 −0.276053 0.961142i $$-0.589027\pi$$
−0.276053 + 0.961142i $$0.589027\pi$$
$$644$$ 0 0
$$645$$ −2.00000 −0.0787499
$$646$$ 0 0
$$647$$ −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i $$-0.281786\pi$$
−0.986916 + 0.161233i $$0.948453\pi$$
$$648$$ 0 0
$$649$$ 27.5000 47.6314i 1.07947 1.86970i
$$650$$ 0 0
$$651$$ 6.00000 + 5.19615i 0.235159 + 0.203653i
$$652$$ 0 0
$$653$$ 19.5000 33.7750i 0.763094 1.32172i −0.178154 0.984003i $$-0.557013\pi$$
0.941248 0.337715i $$-0.109654\pi$$
$$654$$ 0 0
$$655$$ 0.500000 + 0.866025i 0.0195366 + 0.0338384i
$$656$$ 0 0
$$657$$ 10.0000 0.390137
$$658$$ 0 0
$$659$$ 40.0000 1.55818 0.779089 0.626913i $$-0.215682\pi$$
0.779089 + 0.626913i $$0.215682\pi$$
$$660$$ 0 0
$$661$$ −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i $$-0.228968\pi$$
−0.946729 + 0.322031i $$0.895634\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −20.0000 + 6.92820i −0.775567 + 0.268664i
$$666$$ 0 0
$$667$$ 10.0000 17.3205i 0.387202 0.670653i
$$668$$ 0 0
$$669$$ −3.50000 6.06218i −0.135318 0.234377i
$$670$$ 0 0
$$671$$ 30.0000 1.15814
$$672$$ 0 0
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ 0 0
$$675$$ 2.00000 + 3.46410i 0.0769800 + 0.133333i
$$676$$ 0 0
$$677$$ 13.5000 23.3827i 0.518847 0.898670i −0.480913 0.876768i $$-0.659695\pi$$
0.999760 0.0219013i $$-0.00697196\pi$$
$$678$$ 0 0
$$679$$ −3.50000 + 18.1865i −0.134318 + 0.697935i
$$680$$ 0 0
$$681$$ 1.50000 2.59808i 0.0574801 0.0995585i
$$682$$ 0 0
$$683$$ −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i $$-0.221750\pi$$
−0.939184 + 0.343413i $$0.888417\pi$$
$$684$$ 0 0
$$685$$ −2.00000 −0.0764161
$$686$$ 0 0
$$687$$ −20.0000 −0.763048
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 4.00000 6.92820i 0.152167 0.263561i −0.779857 0.625958i $$-0.784708\pi$$
0.932024 + 0.362397i $$0.118041\pi$$
$$692$$ 0 0
$$693$$ 2.50000 12.9904i 0.0949671 0.493464i
$$694$$ 0 0
$$695$$ −7.00000 + 12.1244i −0.265525 + 0.459903i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ −4.00000 −0.151294
$$700$$ 0 0
$$701$$ −5.00000 −0.188847 −0.0944237 0.995532i $$-0.530101\pi$$
−0.0944237 + 0.995532i $$0.530101\pi$$
$$702$$ 0 0
$$703$$ −16.0000 27.7128i −0.603451 1.04521i
$$704$$ 0 0
$$705$$ −3.00000 + 5.19615i −0.112987 + 0.195698i
$$706$$ 0 0
$$707$$ 25.0000 8.66025i 0.940222 0.325702i
$$708$$ 0 0
$$709$$ −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i $$0.419585\pi$$
−0.963512 + 0.267664i $$0.913748\pi$$
$$710$$ 0 0
$$711$$ 1.50000 + 2.59808i 0.0562544 + 0.0974355i
$$712$$ 0 0
$$713$$ −12.0000 −0.449404
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −6.00000 10.3923i −0.224074 0.388108i
$$718$$ 0 0
$$719$$ −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i $$-0.869021\pi$$
0.804648 + 0.593753i $$0.202354\pi$$
$$720$$ 0 0
$$721$$ 16.0000 + 13.8564i 0.595871 + 0.516040i
$$722$$ 0 0
$$723$$ 12.5000 21.6506i 0.464880 0.805196i
$$724$$ 0 0
$$725$$ −10.0000 17.3205i −0.371391 0.643268i
$$726$$ 0 0
$$727$$ −7.00000 −0.259616 −0.129808 0.991539i $$-0.541436\pi$$
−0.129808 + 0.991539i $$0.541436\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −4.00000 6.92820i −0.147945 0.256249i
$$732$$ 0 0
$$733$$ 3.00000 5.19615i 0.110808 0.191924i −0.805289 0.592883i $$-0.797990\pi$$
0.916096 + 0.400959i $$0.131323\pi$$
$$734$$ 0 0
$$735$$ −6.50000 2.59808i −0.239756 0.0958315i
$$736$$ 0 0
$$737$$ 5.00000 8.66025i 0.184177 0.319005i
$$738$$ 0 0
$$739$$ −15.0000 25.9808i −0.551784 0.955718i −0.998146 0.0608653i $$-0.980614\pi$$
0.446362 0.894852i $$-0.352719\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −30.0000 −1.10059 −0.550297 0.834969i $$-0.685485\pi$$
−0.550297 + 0.834969i $$0.685485\pi$$
$$744$$ 0 0
$$745$$ 9.00000 + 15.5885i 0.329734 + 0.571117i
$$746$$ 0 0
$$747$$ −3.50000 + 6.06218i −0.128058 + 0.221803i
$$748$$ 0 0
$$749$$ 6.00000 + 5.19615i 0.219235 + 0.189863i
$$750$$ 0 0
$$751$$ 22.5000 38.9711i 0.821037 1.42208i −0.0838743 0.996476i $$-0.526729\pi$$
0.904911 0.425601i $$-0.139937\pi$$
$$752$$ 0 0
$$753$$ 10.5000 + 18.1865i 0.382641 + 0.662754i
$$754$$ 0 0
$$755$$ −19.0000 −0.691481
$$756$$ 0 0
$$757$$ −54.0000 −1.96266 −0.981332 0.192323i $$-0.938398\pi$$
−0.981332 + 0.192323i $$0.938398\pi$$
$$758$$ 0 0
$$759$$ 10.0000 + 17.3205i 0.362977 + 0.628695i
$$760$$ 0 0
$$761$$ −4.00000 + 6.92820i −0.145000 + 0.251147i −0.929373 0.369142i $$-0.879652\pi$$
0.784373 + 0.620289i $$0.212985\pi$$
$$762$$ 0 0
$$763$$ −5.00000 + 1.73205i −0.181012 + 0.0627044i
$$764$$ 0 0
$$765$$ 2.00000 3.46410i 0.0723102 0.125245i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −35.0000 −1.26213 −0.631066 0.775729i $$-0.717382\pi$$
−0.631066 + 0.775729i $$0.717382\pi$$
$$770$$ 0 0
$$771$$ −6.00000 −0.216085
$$772$$ 0 0
$$773$$ −5.00000 8.66025i −0.179838 0.311488i 0.761987 0.647592i $$-0.224224\pi$$
−0.941825 + 0.336104i $$0.890891\pi$$
$$774$$ 0 0
$$775$$ −6.00000 + 10.3923i −0.215526 + 0.373303i
$$776$$ 0 0
$$777$$ 2.00000 10.3923i 0.0717496 0.372822i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −5.00000 8.66025i −0.178914 0.309888i
$$782$$ 0 0
$$783$$ −5.00000 −0.178685
$$784$$ 0 0
$$785$$ −4.00000 −0.142766
$$786$$ 0 0
$$787$$ −9.00000 15.5885i −0.320815 0.555668i 0.659841 0.751405i $$-0.270624\pi$$
−0.980656 + 0.195737i $$0.937290\pi$$
$$788$$ 0 0
$$789$$ −15.0000 + 25.9808i −0.534014 + 0.924940i
$$790$$ 0 0
$$791$$ −8.00000 + 41.5692i −0.284447 + 1.47803i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 4.50000 + 7.79423i 0.159599 + 0.276433i
$$796$$ 0 0
$$797$$ 21.0000 0.743858 0.371929 0.928261i $$-0.378696\pi$$
0.371929 + 0.928261i $$0.378696\pi$$
$$798$$