# Properties

 Label 1134.2.h.p.109.1 Level $1134$ Weight $2$ Character 1134.109 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.h (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 109.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.109 Dual form 1134.2.h.p.541.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{10} +3.00000 q^{11} +(2.00000 - 3.46410i) q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +4.00000 q^{25} +(-2.00000 - 3.46410i) q^{26} +(-0.500000 + 2.59808i) q^{28} +(-4.50000 - 7.79423i) q^{29} +(0.500000 + 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.00000 - 5.19615i) q^{35} +(-4.00000 - 6.92820i) q^{37} +4.00000 q^{38} -3.00000 q^{40} +(5.00000 + 8.66025i) q^{43} +(-1.50000 - 2.59808i) q^{44} +(3.00000 - 5.19615i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{50} -4.00000 q^{52} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(2.00000 + 1.73205i) q^{56} -9.00000 q^{58} +(-1.50000 - 2.59808i) q^{59} +(5.00000 - 8.66025i) q^{61} +1.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-7.50000 + 2.59808i) q^{70} -6.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} -8.00000 q^{74} +(2.00000 - 3.46410i) q^{76} +(-6.00000 - 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(4.50000 + 7.79423i) q^{83} +10.0000 q^{86} -3.00000 q^{88} +(-3.00000 - 5.19615i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(-3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(0.500000 + 0.866025i) q^{97} +(6.50000 + 2.59808i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{4} + 6q^{5} - 4q^{7} - 2q^{8} + O(q^{10})$$ $$2q + q^{2} - q^{4} + 6q^{5} - 4q^{7} - 2q^{8} + 3q^{10} + 6q^{11} + 4q^{13} - 5q^{14} - q^{16} + 4q^{19} - 3q^{20} + 3q^{22} + 8q^{25} - 4q^{26} - q^{28} - 9q^{29} + q^{31} + q^{32} - 12q^{35} - 8q^{37} + 8q^{38} - 6q^{40} + 10q^{43} - 3q^{44} + 6q^{47} + 2q^{49} + 4q^{50} - 8q^{52} + 3q^{53} + 18q^{55} + 4q^{56} - 18q^{58} - 3q^{59} + 10q^{61} + 2q^{62} + 2q^{64} + 12q^{65} + 10q^{67} - 15q^{70} - 12q^{71} - 2q^{73} - 16q^{74} + 4q^{76} - 12q^{77} + q^{79} - 3q^{80} + 9q^{83} + 20q^{86} - 6q^{88} - 6q^{89} - 20q^{91} - 6q^{94} + 12q^{95} + q^{97} + 13q^{98} + O(q^{100})$$

## Character values

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

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$5$$ 3.00000 1.34164 0.670820 0.741620i $$-0.265942\pi$$
0.670820 + 0.741620i $$0.265942\pi$$
$$6$$ 0 0
$$7$$ −2.00000 1.73205i −0.755929 0.654654i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 1.50000 2.59808i 0.474342 0.821584i
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 0 0
$$13$$ 2.00000 3.46410i 0.554700 0.960769i −0.443227 0.896410i $$-0.646166\pi$$
0.997927 0.0643593i $$-0.0205004\pi$$
$$14$$ −2.50000 + 0.866025i −0.668153 + 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$18$$ 0 0
$$19$$ 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i $$-0.0149348\pi$$
−0.540068 + 0.841621i $$0.681602\pi$$
$$20$$ −1.50000 2.59808i −0.335410 0.580948i
$$21$$ 0 0
$$22$$ 1.50000 2.59808i 0.319801 0.553912i
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 4.00000 0.800000
$$26$$ −2.00000 3.46410i −0.392232 0.679366i
$$27$$ 0 0
$$28$$ −0.500000 + 2.59808i −0.0944911 + 0.490990i
$$29$$ −4.50000 7.79423i −0.835629 1.44735i −0.893517 0.449029i $$-0.851770\pi$$
0.0578882 0.998323i $$-0.481563\pi$$
$$30$$ 0 0
$$31$$ 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i $$-0.138043\pi$$
−0.817625 + 0.575751i $$0.804710\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −6.00000 5.19615i −1.01419 0.878310i
$$36$$ 0 0
$$37$$ −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i $$-0.938240\pi$$
0.323640 0.946180i $$-0.395093\pi$$
$$38$$ 4.00000 0.648886
$$39$$ 0 0
$$40$$ −3.00000 −0.474342
$$41$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$42$$ 0 0
$$43$$ 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i $$0.109358\pi$$
−0.179069 + 0.983836i $$0.557309\pi$$
$$44$$ −1.50000 2.59808i −0.226134 0.391675i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ 0 0
$$49$$ 1.00000 + 6.92820i 0.142857 + 0.989743i
$$50$$ 2.00000 3.46410i 0.282843 0.489898i
$$51$$ 0 0
$$52$$ −4.00000 −0.554700
$$53$$ 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i $$-0.767275\pi$$
0.950464 + 0.310835i $$0.100609\pi$$
$$54$$ 0 0
$$55$$ 9.00000 1.21356
$$56$$ 2.00000 + 1.73205i 0.267261 + 0.231455i
$$57$$ 0 0
$$58$$ −9.00000 −1.18176
$$59$$ −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i $$-0.229229\pi$$
−0.946993 + 0.321253i $$0.895896\pi$$
$$60$$ 0 0
$$61$$ 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i $$-0.612191\pi$$
0.985391 0.170305i $$-0.0544754\pi$$
$$62$$ 1.00000 0.127000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 10.3923i 0.744208 1.28901i
$$66$$ 0 0
$$67$$ 5.00000 + 8.66025i 0.610847 + 1.05802i 0.991098 + 0.133135i $$0.0425044\pi$$
−0.380251 + 0.924883i $$0.624162\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −7.50000 + 2.59808i −0.896421 + 0.310530i
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 0 0
$$73$$ −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i $$-0.870674\pi$$
0.801553 + 0.597924i $$0.204008\pi$$
$$74$$ −8.00000 −0.929981
$$75$$ 0 0
$$76$$ 2.00000 3.46410i 0.229416 0.397360i
$$77$$ −6.00000 5.19615i −0.683763 0.592157i
$$78$$ 0 0
$$79$$ 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i $$-0.815418\pi$$
0.892781 + 0.450490i $$0.148751\pi$$
$$80$$ −1.50000 + 2.59808i −0.167705 + 0.290474i
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i $$-0.00222321\pi$$
−0.506036 + 0.862512i $$0.668890\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 10.0000 1.07833
$$87$$ 0 0
$$88$$ −3.00000 −0.319801
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ 0 0
$$91$$ −10.0000 + 3.46410i −1.04828 + 0.363137i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −3.00000 5.19615i −0.309426 0.535942i
$$95$$ 6.00000 + 10.3923i 0.615587 + 1.06623i
$$96$$ 0 0
$$97$$ 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i $$-0.150500\pi$$
−0.839525 + 0.543321i $$0.817167\pi$$
$$98$$ 6.50000 + 2.59808i 0.656599 + 0.262445i
$$99$$ 0 0
$$100$$ −2.00000 3.46410i −0.200000 0.346410i
$$101$$ −18.0000 −1.79107 −0.895533 0.444994i $$-0.853206\pi$$
−0.895533 + 0.444994i $$0.853206\pi$$
$$102$$ 0 0
$$103$$ 8.00000 0.788263 0.394132 0.919054i $$-0.371045\pi$$
0.394132 + 0.919054i $$0.371045\pi$$
$$104$$ −2.00000 + 3.46410i −0.196116 + 0.339683i
$$105$$ 0 0
$$106$$ −1.50000 2.59808i −0.145693 0.252347i
$$107$$ 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i $$-0.120345\pi$$
−0.784366 + 0.620298i $$0.787012\pi$$
$$108$$ 0 0
$$109$$ −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i $$0.400578\pi$$
−0.977769 + 0.209687i $$0.932756\pi$$
$$110$$ 4.50000 7.79423i 0.429058 0.743151i
$$111$$ 0 0
$$112$$ 2.50000 0.866025i 0.236228 0.0818317i
$$113$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −4.50000 + 7.79423i −0.417815 + 0.723676i
$$117$$ 0 0
$$118$$ −3.00000 −0.276172
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ −5.00000 8.66025i −0.452679 0.784063i
$$123$$ 0 0
$$124$$ 0.500000 0.866025i 0.0449013 0.0777714i
$$125$$ −3.00000 −0.268328
$$126$$ 0 0
$$127$$ 5.00000 0.443678 0.221839 0.975083i $$-0.428794\pi$$
0.221839 + 0.975083i $$0.428794\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ −6.00000 10.3923i −0.526235 0.911465i
$$131$$ −9.00000 −0.786334 −0.393167 0.919467i $$-0.628621\pi$$
−0.393167 + 0.919467i $$0.628621\pi$$
$$132$$ 0 0
$$133$$ 2.00000 10.3923i 0.173422 0.901127i
$$134$$ 10.0000 0.863868
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 18.0000 1.53784 0.768922 0.639343i $$-0.220793\pi$$
0.768922 + 0.639343i $$0.220793\pi$$
$$138$$ 0 0
$$139$$ −1.00000 + 1.73205i −0.0848189 + 0.146911i −0.905314 0.424743i $$-0.860365\pi$$
0.820495 + 0.571654i $$0.193698\pi$$
$$140$$ −1.50000 + 7.79423i −0.126773 + 0.658733i
$$141$$ 0 0
$$142$$ −3.00000 + 5.19615i −0.251754 + 0.436051i
$$143$$ 6.00000 10.3923i 0.501745 0.869048i
$$144$$ 0 0
$$145$$ −13.5000 23.3827i −1.12111 1.94183i
$$146$$ 1.00000 + 1.73205i 0.0827606 + 0.143346i
$$147$$ 0 0
$$148$$ −4.00000 + 6.92820i −0.328798 + 0.569495i
$$149$$ 18.0000 1.47462 0.737309 0.675556i $$-0.236096\pi$$
0.737309 + 0.675556i $$0.236096\pi$$
$$150$$ 0 0
$$151$$ −1.00000 −0.0813788 −0.0406894 0.999172i $$-0.512955\pi$$
−0.0406894 + 0.999172i $$0.512955\pi$$
$$152$$ −2.00000 3.46410i −0.162221 0.280976i
$$153$$ 0 0
$$154$$ −7.50000 + 2.59808i −0.604367 + 0.209359i
$$155$$ 1.50000 + 2.59808i 0.120483 + 0.208683i
$$156$$ 0 0
$$157$$ 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i $$-0.115641\pi$$
−0.775113 + 0.631822i $$0.782307\pi$$
$$158$$ −0.500000 0.866025i −0.0397779 0.0688973i
$$159$$ 0 0
$$160$$ 1.50000 + 2.59808i 0.118585 + 0.205396i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 8.00000 + 13.8564i 0.626608 + 1.08532i 0.988227 + 0.152992i $$0.0488907\pi$$
−0.361619 + 0.932326i $$0.617776\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 9.00000 0.698535
$$167$$ −3.00000 + 5.19615i −0.232147 + 0.402090i −0.958440 0.285295i $$-0.907908\pi$$
0.726293 + 0.687386i $$0.241242\pi$$
$$168$$ 0 0
$$169$$ −1.50000 2.59808i −0.115385 0.199852i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 5.00000 8.66025i 0.381246 0.660338i
$$173$$ −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i $$0.406540\pi$$
−0.973670 + 0.227964i $$0.926793\pi$$
$$174$$ 0 0
$$175$$ −8.00000 6.92820i −0.604743 0.523723i
$$176$$ −1.50000 + 2.59808i −0.113067 + 0.195837i
$$177$$ 0 0
$$178$$ −6.00000 −0.449719
$$179$$ −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i $$-0.981361\pi$$
0.549825 + 0.835280i $$0.314694\pi$$
$$180$$ 0 0
$$181$$ 8.00000 0.594635 0.297318 0.954779i $$-0.403908\pi$$
0.297318 + 0.954779i $$0.403908\pi$$
$$182$$ −2.00000 + 10.3923i −0.148250 + 0.770329i
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −12.0000 20.7846i −0.882258 1.52811i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −6.00000 −0.437595
$$189$$ 0 0
$$190$$ 12.0000 0.870572
$$191$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$192$$ 0 0
$$193$$ 9.50000 + 16.4545i 0.683825 + 1.18442i 0.973805 + 0.227387i $$0.0730182\pi$$
−0.289980 + 0.957033i $$0.593649\pi$$
$$194$$ 1.00000 0.0717958
$$195$$ 0 0
$$196$$ 5.50000 4.33013i 0.392857 0.309295i
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i $$0.417466\pi$$
−0.965272 + 0.261245i $$0.915867\pi$$
$$200$$ −4.00000 −0.282843
$$201$$ 0 0
$$202$$ −9.00000 + 15.5885i −0.633238 + 1.09680i
$$203$$ −4.50000 + 23.3827i −0.315838 + 1.64114i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 4.00000 6.92820i 0.278693 0.482711i
$$207$$ 0 0
$$208$$ 2.00000 + 3.46410i 0.138675 + 0.240192i
$$209$$ 6.00000 + 10.3923i 0.415029 + 0.718851i
$$210$$ 0 0
$$211$$ −7.00000 + 12.1244i −0.481900 + 0.834675i −0.999784 0.0207756i $$-0.993386\pi$$
0.517884 + 0.855451i $$0.326720\pi$$
$$212$$ −3.00000 −0.206041
$$213$$ 0 0
$$214$$ 3.00000 0.205076
$$215$$ 15.0000 + 25.9808i 1.02299 + 1.77187i
$$216$$ 0 0
$$217$$ 0.500000 2.59808i 0.0339422 0.176369i
$$218$$ 7.00000 + 12.1244i 0.474100 + 0.821165i
$$219$$ 0 0
$$220$$ −4.50000 7.79423i −0.303390 0.525487i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 9.50000 + 16.4545i 0.636167 + 1.10187i 0.986267 + 0.165161i $$0.0528144\pi$$
−0.350100 + 0.936713i $$0.613852\pi$$
$$224$$ 0.500000 2.59808i 0.0334077 0.173591i
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −27.0000 −1.79205 −0.896026 0.444001i $$-0.853559\pi$$
−0.896026 + 0.444001i $$0.853559\pi$$
$$228$$ 0 0
$$229$$ −4.00000 −0.264327 −0.132164 0.991228i $$-0.542192\pi$$
−0.132164 + 0.991228i $$0.542192\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 4.50000 + 7.79423i 0.295439 + 0.511716i
$$233$$ 12.0000 + 20.7846i 0.786146 + 1.36165i 0.928312 + 0.371802i $$0.121260\pi$$
−0.142166 + 0.989843i $$0.545407\pi$$
$$234$$ 0 0
$$235$$ 9.00000 15.5885i 0.587095 1.01688i
$$236$$ −1.50000 + 2.59808i −0.0976417 + 0.169120i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i $$-0.550470\pi$$
0.934109 0.356988i $$-0.116196\pi$$
$$240$$ 0 0
$$241$$ −1.00000 −0.0644157 −0.0322078 0.999481i $$-0.510254\pi$$
−0.0322078 + 0.999481i $$0.510254\pi$$
$$242$$ −1.00000 + 1.73205i −0.0642824 + 0.111340i
$$243$$ 0 0
$$244$$ −10.0000 −0.640184
$$245$$ 3.00000 + 20.7846i 0.191663 + 1.32788i
$$246$$ 0 0
$$247$$ 16.0000 1.01806
$$248$$ −0.500000 0.866025i −0.0317500 0.0549927i
$$249$$ 0 0
$$250$$ −1.50000 + 2.59808i −0.0948683 + 0.164317i
$$251$$ 27.0000 1.70422 0.852112 0.523359i $$-0.175321\pi$$
0.852112 + 0.523359i $$0.175321\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 2.50000 4.33013i 0.156864 0.271696i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 0 0
$$259$$ −4.00000 + 20.7846i −0.248548 + 1.29149i
$$260$$ −12.0000 −0.744208
$$261$$ 0 0
$$262$$ −4.50000 + 7.79423i −0.278011 + 0.481529i
$$263$$ −6.00000 −0.369976 −0.184988 0.982741i $$-0.559225\pi$$
−0.184988 + 0.982741i $$0.559225\pi$$
$$264$$ 0 0
$$265$$ 4.50000 7.79423i 0.276433 0.478796i
$$266$$ −8.00000 6.92820i −0.490511 0.424795i
$$267$$ 0 0
$$268$$ 5.00000 8.66025i 0.305424 0.529009i
$$269$$ −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i $$0.387814\pi$$
−0.985389 + 0.170321i $$0.945520\pi$$
$$270$$ 0 0
$$271$$ −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i $$-0.275099\pi$$
−0.983312 + 0.181928i $$0.941766\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 9.00000 15.5885i 0.543710 0.941733i
$$275$$ 12.0000 0.723627
$$276$$ 0 0
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ 1.00000 + 1.73205i 0.0599760 + 0.103882i
$$279$$ 0 0
$$280$$ 6.00000 + 5.19615i 0.358569 + 0.310530i
$$281$$ −3.00000 5.19615i −0.178965 0.309976i 0.762561 0.646916i $$-0.223942\pi$$
−0.941526 + 0.336939i $$0.890608\pi$$
$$282$$ 0 0
$$283$$ −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i $$-0.303272\pi$$
−0.995544 + 0.0942988i $$0.969939\pi$$
$$284$$ 3.00000 + 5.19615i 0.178017 + 0.308335i
$$285$$ 0 0
$$286$$ −6.00000 10.3923i −0.354787 0.614510i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 8.50000 + 14.7224i 0.500000 + 0.866025i
$$290$$ −27.0000 −1.58549
$$291$$ 0 0
$$292$$ 2.00000 0.117041
$$293$$ −16.5000 + 28.5788i −0.963940 + 1.66959i −0.251505 + 0.967856i $$0.580925\pi$$
−0.712436 + 0.701737i $$0.752408\pi$$
$$294$$ 0 0
$$295$$ −4.50000 7.79423i −0.262000 0.453798i
$$296$$ 4.00000 + 6.92820i 0.232495 + 0.402694i
$$297$$ 0 0
$$298$$ 9.00000 15.5885i 0.521356 0.903015i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 5.00000 25.9808i 0.288195 1.49751i
$$302$$ −0.500000 + 0.866025i −0.0287718 + 0.0498342i
$$303$$ 0 0
$$304$$ −4.00000 −0.229416
$$305$$ 15.0000 25.9808i 0.858898 1.48765i
$$306$$ 0 0
$$307$$ 8.00000 0.456584 0.228292 0.973593i $$-0.426686\pi$$
0.228292 + 0.973593i $$0.426686\pi$$
$$308$$ −1.50000 + 7.79423i −0.0854704 + 0.444117i
$$309$$ 0 0
$$310$$ 3.00000 0.170389
$$311$$ −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i $$-0.928448\pi$$
0.294384 0.955687i $$-0.404886\pi$$
$$312$$ 0 0
$$313$$ 15.5000 26.8468i 0.876112 1.51747i 0.0205381 0.999789i $$-0.493462\pi$$
0.855574 0.517681i $$-0.173205\pi$$
$$314$$ 4.00000 0.225733
$$315$$ 0 0
$$316$$ −1.00000 −0.0562544
$$317$$ −4.50000 + 7.79423i −0.252745 + 0.437767i −0.964281 0.264883i $$-0.914667\pi$$
0.711535 + 0.702650i $$0.248000\pi$$
$$318$$ 0 0
$$319$$ −13.5000 23.3827i −0.755855 1.30918i
$$320$$ 3.00000 0.167705
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 8.00000 13.8564i 0.443760 0.768615i
$$326$$ 16.0000 0.886158
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −15.0000 + 5.19615i −0.826977 + 0.286473i
$$330$$ 0 0
$$331$$ −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i $$0.351905\pi$$
−0.998298 + 0.0583130i $$0.981428\pi$$
$$332$$ 4.50000 7.79423i 0.246970 0.427764i
$$333$$ 0 0
$$334$$ 3.00000 + 5.19615i 0.164153 + 0.284321i
$$335$$ 15.0000 + 25.9808i 0.819538 + 1.41948i
$$336$$ 0 0
$$337$$ 3.50000 6.06218i 0.190657 0.330228i −0.754811 0.655942i $$-0.772271\pi$$
0.945468 + 0.325714i $$0.105605\pi$$
$$338$$ −3.00000 −0.163178
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.50000 + 2.59808i 0.0812296 + 0.140694i
$$342$$ 0 0
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ −5.00000 8.66025i −0.269582 0.466930i
$$345$$ 0 0
$$346$$ 9.00000 + 15.5885i 0.483843 + 0.838041i
$$347$$ −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i $$-0.271054\pi$$
−0.980921 + 0.194409i $$0.937721\pi$$
$$348$$ 0 0
$$349$$ −13.0000 22.5167i −0.695874 1.20529i −0.969885 0.243563i $$-0.921684\pi$$
0.274011 0.961727i $$-0.411649\pi$$
$$350$$ −10.0000 + 3.46410i −0.534522 + 0.185164i
$$351$$ 0 0
$$352$$ 1.50000 + 2.59808i 0.0799503 + 0.138478i
$$353$$ 24.0000 1.27739 0.638696 0.769460i $$-0.279474\pi$$
0.638696 + 0.769460i $$0.279474\pi$$
$$354$$ 0 0
$$355$$ −18.0000 −0.955341
$$356$$ −3.00000 + 5.19615i −0.159000 + 0.275396i
$$357$$ 0 0
$$358$$ 6.00000 + 10.3923i 0.317110 + 0.549250i
$$359$$ −15.0000 25.9808i −0.791670 1.37121i −0.924932 0.380131i $$-0.875879\pi$$
0.133263 0.991081i $$-0.457455\pi$$
$$360$$ 0 0
$$361$$ 1.50000 2.59808i 0.0789474 0.136741i
$$362$$ 4.00000 6.92820i 0.210235 0.364138i
$$363$$ 0 0
$$364$$ 8.00000 + 6.92820i 0.419314 + 0.363137i
$$365$$ −3.00000 + 5.19615i −0.157027 + 0.271979i
$$366$$ 0 0
$$367$$ −19.0000 −0.991792 −0.495896 0.868382i $$-0.665160\pi$$
−0.495896 + 0.868382i $$0.665160\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ −24.0000 −1.24770
$$371$$ −7.50000 + 2.59808i −0.389381 + 0.134885i
$$372$$ 0 0
$$373$$ 8.00000 0.414224 0.207112 0.978317i $$-0.433593\pi$$
0.207112 + 0.978317i $$0.433593\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −3.00000 + 5.19615i −0.154713 + 0.267971i
$$377$$ −36.0000 −1.85409
$$378$$ 0 0
$$379$$ 8.00000 0.410932 0.205466 0.978664i $$-0.434129\pi$$
0.205466 + 0.978664i $$0.434129\pi$$
$$380$$ 6.00000 10.3923i 0.307794 0.533114i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 18.0000 0.919757 0.459879 0.887982i $$-0.347893\pi$$
0.459879 + 0.887982i $$0.347893\pi$$
$$384$$ 0 0
$$385$$ −18.0000 15.5885i −0.917365 0.794461i
$$386$$ 19.0000 0.967075
$$387$$ 0 0
$$388$$ 0.500000 0.866025i 0.0253837 0.0439658i
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −1.00000 6.92820i −0.0505076 0.349927i
$$393$$ 0 0
$$394$$ 3.00000 5.19615i 0.151138 0.261778i
$$395$$ 1.50000 2.59808i 0.0754732 0.130723i
$$396$$ 0 0
$$397$$ 2.00000 + 3.46410i 0.100377 + 0.173858i 0.911840 0.410546i $$-0.134662\pi$$
−0.811463 + 0.584404i $$0.801328\pi$$
$$398$$ 10.0000 + 17.3205i 0.501255 + 0.868199i
$$399$$ 0 0
$$400$$ −2.00000 + 3.46410i −0.100000 + 0.173205i
$$401$$ 24.0000 1.19850 0.599251 0.800561i $$-0.295465\pi$$
0.599251 + 0.800561i $$0.295465\pi$$
$$402$$ 0 0
$$403$$ 4.00000 0.199254
$$404$$ 9.00000 + 15.5885i 0.447767 + 0.775555i
$$405$$ 0 0
$$406$$ 18.0000 + 15.5885i 0.893325 + 0.773642i
$$407$$ −12.0000 20.7846i −0.594818 1.03025i
$$408$$ 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
$$411$$ 0 0
$$412$$ −4.00000 6.92820i −0.197066 0.341328i
$$413$$ −1.50000 + 7.79423i −0.0738102 + 0.383529i
$$414$$ 0 0
$$415$$ 13.5000 + 23.3827i 0.662689 + 1.14781i
$$416$$ 4.00000 0.196116
$$417$$ 0 0
$$418$$ 12.0000 0.586939
$$419$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$420$$ 0 0
$$421$$ 11.0000 + 19.0526i 0.536107 + 0.928565i 0.999109 + 0.0422075i $$0.0134391\pi$$
−0.463002 + 0.886357i $$0.653228\pi$$
$$422$$ 7.00000 + 12.1244i 0.340755 + 0.590204i
$$423$$ 0 0
$$424$$ −1.50000 + 2.59808i −0.0728464 + 0.126174i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −25.0000 + 8.66025i −1.20983 + 0.419099i
$$428$$ 1.50000 2.59808i 0.0725052 0.125583i
$$429$$ 0 0
$$430$$ 30.0000 1.44673
$$431$$ −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i $$-0.926659\pi$$
0.684564 + 0.728953i $$0.259993\pi$$
$$432$$ 0 0
$$433$$ −34.0000 −1.63394 −0.816968 0.576683i $$-0.804347\pi$$
−0.816968 + 0.576683i $$0.804347\pi$$
$$434$$ −2.00000 1.73205i −0.0960031 0.0831411i
$$435$$ 0 0
$$436$$ 14.0000 0.670478
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −17.5000 + 30.3109i −0.835229 + 1.44666i 0.0586141 + 0.998281i $$0.481332\pi$$
−0.893843 + 0.448379i $$0.852001\pi$$
$$440$$ −9.00000 −0.429058
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 16.5000 28.5788i 0.783939 1.35782i −0.145692 0.989330i $$-0.546541\pi$$
0.929631 0.368492i $$-0.120126\pi$$
$$444$$ 0 0
$$445$$ −9.00000 15.5885i −0.426641 0.738964i
$$446$$ 19.0000 0.899676
$$447$$ 0 0
$$448$$ −2.00000 1.73205i −0.0944911 0.0818317i
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −13.5000 + 23.3827i −0.633586 + 1.09740i
$$455$$ −30.0000 + 10.3923i −1.40642 + 0.487199i
$$456$$ 0 0
$$457$$ 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i $$-0.825888\pi$$
0.877483 + 0.479608i $$0.159221\pi$$
$$458$$ −2.00000 + 3.46410i −0.0934539 + 0.161867i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i $$-0.920465\pi$$
0.270326 0.962769i $$-0.412869\pi$$
$$462$$ 0 0
$$463$$ −4.00000 + 6.92820i −0.185896 + 0.321981i −0.943878 0.330294i $$-0.892852\pi$$
0.757982 + 0.652275i $$0.226185\pi$$
$$464$$ 9.00000 0.417815
$$465$$ 0 0
$$466$$ 24.0000 1.11178
$$467$$ −18.0000 31.1769i −0.832941 1.44270i −0.895696 0.444667i $$-0.853322\pi$$
0.0627555 0.998029i $$-0.480011\pi$$
$$468$$ 0 0
$$469$$ 5.00000 25.9808i 0.230879 1.19968i
$$470$$ −9.00000 15.5885i −0.415139 0.719042i
$$471$$ 0 0
$$472$$ 1.50000 + 2.59808i 0.0690431 + 0.119586i
$$473$$ 15.0000 + 25.9808i 0.689701 + 1.19460i
$$474$$ 0 0
$$475$$ 8.00000 + 13.8564i 0.367065 + 0.635776i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −12.0000 20.7846i −0.548867 0.950666i
$$479$$ −18.0000 −0.822441 −0.411220 0.911536i $$-0.634897\pi$$
−0.411220 + 0.911536i $$0.634897\pi$$
$$480$$ 0 0
$$481$$ −32.0000 −1.45907
$$482$$ −0.500000 + 0.866025i −0.0227744 + 0.0394464i
$$483$$ 0 0
$$484$$ 1.00000 + 1.73205i 0.0454545 + 0.0787296i
$$485$$ 1.50000 + 2.59808i 0.0681115 + 0.117973i
$$486$$ 0 0
$$487$$ −20.5000 + 35.5070i −0.928944 + 1.60898i −0.143851 + 0.989599i $$0.545949\pi$$
−0.785093 + 0.619378i $$0.787385\pi$$
$$488$$ −5.00000 + 8.66025i −0.226339 + 0.392031i
$$489$$ 0 0
$$490$$ 19.5000 + 7.79423i 0.880920 + 0.352107i
$$491$$ 16.5000 28.5788i 0.744635 1.28974i −0.205731 0.978609i $$-0.565957\pi$$
0.950365 0.311136i $$-0.100710\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 8.00000 13.8564i 0.359937 0.623429i
$$495$$ 0 0
$$496$$ −1.00000 −0.0449013
$$497$$ 12.0000 + 10.3923i 0.538274 + 0.466159i
$$498$$ 0 0
$$499$$ 2.00000 0.0895323 0.0447661 0.998997i $$-0.485746\pi$$
0.0447661 + 0.998997i $$0.485746\pi$$
$$500$$ 1.50000 + 2.59808i 0.0670820 + 0.116190i
$$501$$ 0 0
$$502$$ 13.5000 23.3827i 0.602534 1.04362i
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ −54.0000 −2.40297
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −2.50000 4.33013i −0.110920 0.192118i
$$509$$ −3.00000 −0.132973 −0.0664863 0.997787i $$-0.521179\pi$$
−0.0664863 + 0.997787i $$0.521179\pi$$
$$510$$ 0 0
$$511$$ 5.00000 1.73205i 0.221187 0.0766214i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 3.00000 5.19615i 0.132324 0.229192i
$$515$$ 24.0000 1.05757
$$516$$ 0 0
$$517$$ 9.00000 15.5885i 0.395820 0.685580i
$$518$$ 16.0000 + 13.8564i 0.703000 + 0.608816i
$$519$$ 0 0
$$520$$ −6.00000 + 10.3923i −0.263117 + 0.455733i
$$521$$ 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i $$-0.704321\pi$$
0.993011 + 0.118020i $$0.0376547\pi$$
$$522$$ 0 0
$$523$$ 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i $$-0.138794\pi$$
−0.818980 + 0.573822i $$0.805460\pi$$
$$524$$ 4.50000 + 7.79423i 0.196583 + 0.340492i
$$525$$ 0 0
$$526$$ −3.00000 + 5.19615i −0.130806 + 0.226563i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ −4.50000 7.79423i −0.195468 0.338560i
$$531$$ 0 0
$$532$$ −10.0000 + 3.46410i −0.433555 + 0.150188i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 4.50000 + 7.79423i 0.194552 + 0.336974i
$$536$$ −5.00000 8.66025i −0.215967 0.374066i
$$537$$ 0 0
$$538$$ 10.5000 + 18.1865i 0.452687 + 0.784077i
$$539$$ 3.00000 + 20.7846i 0.129219 + 0.895257i
$$540$$ 0 0
$$541$$ −13.0000 22.5167i −0.558914 0.968067i −0.997587 0.0694205i $$-0.977885\pi$$
0.438674 0.898646i $$-0.355448\pi$$
$$542$$ −11.0000 −0.472490
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −21.0000 + 36.3731i −0.899541 + 1.55805i
$$546$$ 0 0
$$547$$ −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i $$-0.221375\pi$$
−0.938779 + 0.344519i $$0.888042\pi$$
$$548$$ −9.00000 15.5885i −0.384461 0.665906i
$$549$$ 0 0
$$550$$ 6.00000 10.3923i 0.255841 0.443129i
$$551$$ 18.0000 31.1769i 0.766826 1.32818i
$$552$$ 0 0
$$553$$ −2.50000 + 0.866025i −0.106311 + 0.0368271i
$$554$$ 4.00000 6.92820i 0.169944 0.294351i
$$555$$ 0 0
$$556$$ 2.00000 0.0848189
$$557$$ −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i $$-0.853578\pi$$
0.832496 + 0.554031i $$0.186911\pi$$
$$558$$ 0 0
$$559$$ 40.0000 1.69182
$$560$$ 7.50000 2.59808i 0.316933 0.109789i
$$561$$ 0 0
$$562$$ −6.00000 −0.253095
$$563$$ −19.5000 33.7750i −0.821827 1.42345i −0.904320 0.426855i $$-0.859622\pi$$
0.0824933 0.996592i $$-0.473712\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −14.0000 −0.588464
$$567$$ 0 0
$$568$$ 6.00000 0.251754
$$569$$ 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i $$-0.561165\pi$$
0.945573 0.325409i $$-0.105502\pi$$
$$570$$ 0 0
$$571$$ 17.0000 + 29.4449i 0.711428 + 1.23223i 0.964321 + 0.264735i $$0.0852845\pi$$
−0.252893 + 0.967494i $$0.581382\pi$$
$$572$$ −12.0000 −0.501745
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −11.5000 + 19.9186i −0.478751 + 0.829222i −0.999703 0.0243645i $$-0.992244\pi$$
0.520952 + 0.853586i $$0.325577\pi$$
$$578$$ 17.0000 0.707107
$$579$$ 0 0
$$580$$ −13.5000 + 23.3827i −0.560557 + 0.970913i
$$581$$ 4.50000 23.3827i 0.186691 0.970077i
$$582$$ 0 0
$$583$$ 4.50000 7.79423i 0.186371 0.322804i
$$584$$ 1.00000 1.73205i 0.0413803 0.0716728i
$$585$$ 0 0
$$586$$ 16.5000 + 28.5788i 0.681609 + 1.18058i
$$587$$ −10.5000 18.1865i −0.433381 0.750639i 0.563781 0.825925i $$-0.309346\pi$$
−0.997162 + 0.0752860i $$0.976013\pi$$
$$588$$ 0 0
$$589$$ −2.00000 + 3.46410i −0.0824086 + 0.142736i
$$590$$ −9.00000 −0.370524
$$591$$ 0 0
$$592$$ 8.00000 0.328798
$$593$$ −12.0000 20.7846i −0.492781 0.853522i 0.507184 0.861838i $$-0.330686\pi$$
−0.999965 + 0.00831589i $$0.997353\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −9.00000 15.5885i −0.368654 0.638528i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 9.00000 + 15.5885i 0.367730 + 0.636927i 0.989210 0.146503i $$-0.0468017\pi$$
−0.621480 + 0.783430i $$0.713468\pi$$
$$600$$ 0 0
$$601$$ −5.50000 9.52628i −0.224350 0.388585i 0.731774 0.681547i $$-0.238692\pi$$
−0.956124 + 0.292962i $$0.905359\pi$$
$$602$$ −20.0000 17.3205i −0.815139 0.705931i
$$603$$ 0 0
$$604$$ 0.500000 + 0.866025i 0.0203447 + 0.0352381i
$$605$$ −6.00000 −0.243935
$$606$$ 0 0
$$607$$ −7.00000 −0.284121 −0.142061 0.989858i $$-0.545373\pi$$
−0.142061 + 0.989858i $$0.545373\pi$$
$$608$$ −2.00000 + 3.46410i −0.0811107 + 0.140488i
$$609$$ 0 0
$$610$$ −15.0000 25.9808i −0.607332 1.05193i
$$611$$ −12.0000 20.7846i −0.485468 0.840855i
$$612$$ 0 0
$$613$$ 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i $$-0.728603\pi$$
0.981129 + 0.193352i $$0.0619359\pi$$
$$614$$ 4.00000 6.92820i 0.161427 0.279600i
$$615$$ 0 0
$$616$$ 6.00000 + 5.19615i 0.241747 + 0.209359i
$$617$$ 3.00000 5.19615i 0.120775 0.209189i −0.799298 0.600935i $$-0.794795\pi$$
0.920074 + 0.391745i $$0.128129\pi$$
$$618$$ 0 0
$$619$$ −34.0000 −1.36658 −0.683288 0.730149i $$-0.739451\pi$$
−0.683288 + 0.730149i $$0.739451\pi$$
$$620$$ 1.50000 2.59808i 0.0602414 0.104341i
$$621$$ 0 0
$$622$$ −24.0000 −0.962312
$$623$$ −3.00000 + 15.5885i −0.120192 + 0.624538i
$$624$$ 0 0
$$625$$ −29.0000 −1.16000
$$626$$ −15.5000 26.8468i −0.619505 1.07301i
$$627$$ 0 0
$$628$$ 2.00000 3.46410i 0.0798087 0.138233i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −7.00000 −0.278666 −0.139333 0.990246i $$-0.544496\pi$$
−0.139333 + 0.990246i $$0.544496\pi$$
$$632$$ −0.500000 + 0.866025i −0.0198889 + 0.0344486i
$$633$$ 0 0
$$634$$ 4.50000 + 7.79423i 0.178718 + 0.309548i
$$635$$ 15.0000 0.595257
$$636$$ 0 0
$$637$$ 26.0000 + 10.3923i 1.03016 + 0.411758i
$$638$$ −27.0000 −1.06894
$$639$$ 0 0
$$640$$ 1.50000 2.59808i 0.0592927 0.102698i
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ 0 0
$$643$$ 17.0000 29.4449i 0.670415 1.16119i −0.307372 0.951589i $$-0.599450\pi$$
0.977787 0.209603i $$-0.0672170\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i $$-0.718214\pi$$
0.986916 + 0.161233i $$0.0515470\pi$$
$$648$$ 0 0
$$649$$ −4.50000 7.79423i −0.176640 0.305950i
$$650$$ −8.00000 13.8564i −0.313786 0.543493i
$$651$$ 0 0
$$652$$ 8.00000 13.8564i 0.313304 0.542659i
$$653$$ 3.00000 0.117399 0.0586995 0.998276i $$-0.481305\pi$$
0.0586995 + 0.998276i $$0.481305\pi$$
$$654$$ 0 0
$$655$$ −27.0000 −1.05498
$$656$$ 0 0
$$657$$ 0 0
$$658$$ −3.00000 + 15.5885i −0.116952 + 0.607701i
$$659$$ 12.0000 + 20.7846i 0.467454 + 0.809653i 0.999309 0.0371821i $$-0.0118382\pi$$
−0.531855 + 0.846836i $$0.678505\pi$$
$$660$$ 0 0
$$661$$ −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i $$-0.254441\pi$$
−0.969442 + 0.245319i $$0.921107\pi$$
$$662$$ 10.0000 + 17.3205i 0.388661 + 0.673181i
$$663$$ 0 0
$$664$$ −4.50000 7.79423i −0.174634 0.302475i
$$665$$ 6.00000 31.1769i 0.232670 1.20899i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 6.00000 0.232147
$$669$$ 0 0
$$670$$ 30.0000 1.15900
$$671$$ 15.0000 25.9808i 0.579069 1.00298i
$$672$$ 0 0
$$673$$ −14.5000 25.1147i −0.558934 0.968102i −0.997586 0.0694449i $$-0.977877\pi$$
0.438652 0.898657i $$-0.355456\pi$$
$$674$$ −3.50000 6.06218i −0.134815 0.233506i
$$675$$ 0 0
$$676$$ −1.50000 + 2.59808i −0.0576923 + 0.0999260i
$$677$$ 16.5000 28.5788i 0.634147 1.09837i −0.352549 0.935793i $$-0.614685\pi$$
0.986695 0.162581i $$-0.0519817\pi$$
$$678$$ 0 0
$$679$$ 0.500000 2.59808i 0.0191882 0.0997050i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 3.00000 0.114876
$$683$$ −16.5000 + 28.5788i −0.631355 + 1.09354i 0.355920 + 0.934516i $$0.384168\pi$$
−0.987275 + 0.159022i $$0.949166\pi$$
$$684$$ 0 0
$$685$$ 54.0000 2.06323
$$686$$ −8.50000 16.4545i −0.324532 0.628235i
$$687$$ 0 0
$$688$$ −10.0000 −0.381246
$$689$$ −6.00000 10.3923i −0.228582 0.395915i
$$690$$ 0 0
$$691$$ −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i $$-0.881959\pi$$
0.779857 + 0.625958i $$0.215292\pi$$
$$692$$ 18.0000 0.684257
$$693$$ 0 0
$$694$$ −12.0000 −0.455514
$$695$$ −3.00000 + 5.19615i −0.113796 + 0.197101i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −26.0000 −0.984115
$$699$$ 0 0
$$700$$ −2.00000 + 10.3923i −0.0755929 + 0.392792i
$$701$$ −15.0000 −0.566542 −0.283271 0.959040i $$-0.591420\pi$$
−0.283271 + 0.959040i $$0.591420\pi$$
$$702$$ 0 0
$$703$$ 16.0000 27.7128i 0.603451 1.04521i
$$704$$ 3.00000 0.113067
$$705$$ 0 0
$$706$$ 12.0000 20.7846i 0.451626 0.782239i
$$707$$ 36.0000 + 31.1769i 1.35392 + 1.17253i
$$708$$ 0 0
$$709$$ 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i $$-0.773204\pi$$
0.944509 + 0.328484i $$0.106538\pi$$
$$710$$ −9.00000 + 15.5885i −0.337764 + 0.585024i
$$711$$ 0 0
$$712$$ 3.00000 + 5.19615i 0.112430 + 0.194734i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 18.0000 31.1769i 0.673162 1.16595i
$$716$$ 12.0000 0.448461
$$717$$ 0 0
$$718$$ −30.0000 −1.11959
$$719$$ 9.00000 + 15.5885i 0.335643 + 0.581351i 0.983608 0.180319i $$-0.0577130\pi$$
−0.647965 + 0.761670i $$0.724380\pi$$
$$720$$ 0 0
$$721$$ −16.0000 13.8564i −0.595871 0.516040i
$$722$$ −1.50000 2.59808i −0.0558242 0.0966904i
$$723$$ 0 0
$$724$$ −4.00000 6.92820i −0.148659 0.257485i
$$725$$ −18.0000 31.1769i −0.668503 1.15788i
$$726$$ 0 0
$$727$$ 6.50000 + 11.2583i 0.241072 + 0.417548i 0.961020 0.276479i $$-0.0891678\pi$$
−0.719948 + 0.694028i $$0.755834\pi$$
$$728$$ 10.0000 3.46410i 0.370625 0.128388i
$$729$$ 0 0
$$730$$ 3.00000 + 5.19615i 0.111035 + 0.192318i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −10.0000 −0.369358 −0.184679 0.982799i $$-0.559125\pi$$
−0.184679 + 0.982799i $$0.559125\pi$$
$$734$$ −9.50000 + 16.4545i −0.350651 + 0.607346i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 15.0000 + 25.9808i 0.552532 + 0.957014i
$$738$$ 0 0
$$739$$ −25.0000 + 43.3013i −0.919640 + 1.59286i −0.119677 + 0.992813i $$0.538186\pi$$
−0.799962 + 0.600050i $$0.795147\pi$$
$$740$$ −12.0000 + 20.7846i −0.441129 + 0.764057i
$$741$$ 0 0
$$742$$ −1.50000 + 7.79423i −0.0550667 + 0.286135i
$$743$$ −21.0000 + 36.3731i −0.770415 + 1.33440i 0.166920 + 0.985970i $$0.446618\pi$$
−0.937336 + 0.348428i $$0.886716\pi$$
$$744$$ 0 0
$$745$$ 54.0000 1.97841
$$746$$ 4.00000 6.92820i 0.146450 0.253660i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 1.50000 7.79423i 0.0548088 0.284795i
$$750$$ 0 0
$$751$$ −7.00000 −0.255434 −0.127717 0.991811i $$-0.540765\pi$$
−0.127717 + 0.991811i $$0.540765\pi$$
$$752$$ 3.00000 + 5.19615i 0.109399 + 0.189484i
$$753$$ 0 0
$$754$$ −18.0000 + 31.1769i −0.655521 + 1.13540i
$$755$$ −3.00000 −0.109181
$$756$$ 0 0
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ 4.00000 6.92820i 0.145287 0.251644i
$$759$$ 0 0
$$760$$ −6.00000 10.3923i −0.217643 0.376969i
$$761$$ 12.0000 0.435000 0.217500 0.976060i $$-0.430210\pi$$
0.217500 + 0.976060i $$0.430210\pi$$
$$762$$ 0 0
$$763$$ 35.0000 12.1244i 1.26709 0.438931i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 9.00000 15.5885i 0.325183 0.563234i
$$767$$ −12.0000 −0.433295
$$768$$ 0 0
$$769$$ 9.50000 16.4545i 0.342579 0.593364i −0.642332 0.766426i $$-0.722033\pi$$
0.984911 + 0.173063i $$0.0553663\pi$$
$$770$$ −22.5000 + 7.79423i −0.810844 + 0.280885i
$$771$$ 0 0
$$772$$ 9.50000 16.4545i 0.341912 0.592210i
$$773$$ −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i $$-0.867747\pi$$
0.807018 + 0.590527i $$0.201080\pi$$
$$774$$ 0 0
$$775$$ 2.00000 + 3.46410i 0.0718421 + 0.124434i
$$776$$ −0.500000 0.866025i −0.0179490 0.0310885i
$$777$$ 0 0
$$778$$ −3.00000 + 5.19615i −0.107555 + 0.186291i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −18.0000 −0.644091
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −6.50000 2.59808i −0.232143 0.0927884i
$$785$$ 6.00000 + 10.3923i 0.214149 + 0.370917i
$$786$$ 0 0
$$787$$ −25.0000 43.3013i −0.891154 1.54352i −0.838494 0.544911i $$-0.816563\pi$$
−0.0526599 0.998613i $$-0.516770\pi$$
$$788$$ −3.00000 5.19615i −0.106871 0.185105i
$$789$$ 0 0
$$790$$ −1.50000 2.59808i −0.0533676 0.0924354i
$$791$$ 0 0
$$792$$ 0 0