# Properties

 Label 168.2.q.b.25.1 Level $168$ Weight $2$ Character 168.25 Analytic conductor $1.341$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$168 = 2^{3} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 168.q (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.34148675396$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 25.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 168.25 Dual form 168.2.q.b.121.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(3.00000 - 5.19615i) q^{11} -3.00000 q^{13} -2.00000 q^{15} +(-2.00000 + 3.46410i) q^{17} +(2.50000 + 4.33013i) q^{19} +(2.00000 - 1.73205i) q^{21} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -4.00000 q^{29} +(-3.50000 + 6.06218i) q^{31} +(-3.00000 - 5.19615i) q^{33} +(-1.00000 - 5.19615i) q^{35} +(4.50000 + 7.79423i) q^{37} +(-1.50000 + 2.59808i) q^{39} -2.00000 q^{41} -1.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(-1.00000 - 1.73205i) q^{47} +(5.50000 + 4.33013i) q^{49} +(2.00000 + 3.46410i) q^{51} +(-4.00000 + 6.92820i) q^{53} -12.0000 q^{55} +5.00000 q^{57} +(-5.00000 - 8.66025i) q^{61} +(-0.500000 - 2.59808i) q^{63} +(3.00000 + 5.19615i) q^{65} +(7.50000 - 12.9904i) q^{67} +4.00000 q^{69} -6.00000 q^{71} +(5.50000 - 9.52628i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(12.0000 - 10.3923i) q^{77} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +6.00000 q^{83} +8.00000 q^{85} +(-2.00000 + 3.46410i) q^{87} +(4.00000 + 6.92820i) q^{89} +(-7.50000 - 2.59808i) q^{91} +(3.50000 + 6.06218i) q^{93} +(5.00000 - 8.66025i) q^{95} -14.0000 q^{97} -6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{3} - 2 q^{5} + 5 q^{7} - q^{9}+O(q^{10})$$ 2 * q + q^3 - 2 * q^5 + 5 * q^7 - q^9 $$2 q + q^{3} - 2 q^{5} + 5 q^{7} - q^{9} + 6 q^{11} - 6 q^{13} - 4 q^{15} - 4 q^{17} + 5 q^{19} + 4 q^{21} + 4 q^{23} + q^{25} - 2 q^{27} - 8 q^{29} - 7 q^{31} - 6 q^{33} - 2 q^{35} + 9 q^{37} - 3 q^{39} - 4 q^{41} - 2 q^{43} - 2 q^{45} - 2 q^{47} + 11 q^{49} + 4 q^{51} - 8 q^{53} - 24 q^{55} + 10 q^{57} - 10 q^{61} - q^{63} + 6 q^{65} + 15 q^{67} + 8 q^{69} - 12 q^{71} + 11 q^{73} - q^{75} + 24 q^{77} - q^{79} - q^{81} + 12 q^{83} + 16 q^{85} - 4 q^{87} + 8 q^{89} - 15 q^{91} + 7 q^{93} + 10 q^{95} - 28 q^{97} - 12 q^{99}+O(q^{100})$$ 2 * q + q^3 - 2 * q^5 + 5 * q^7 - q^9 + 6 * q^11 - 6 * q^13 - 4 * q^15 - 4 * q^17 + 5 * q^19 + 4 * q^21 + 4 * q^23 + q^25 - 2 * q^27 - 8 * q^29 - 7 * q^31 - 6 * q^33 - 2 * q^35 + 9 * q^37 - 3 * q^39 - 4 * q^41 - 2 * q^43 - 2 * q^45 - 2 * q^47 + 11 * q^49 + 4 * q^51 - 8 * q^53 - 24 * q^55 + 10 * q^57 - 10 * q^61 - q^63 + 6 * q^65 + 15 * q^67 + 8 * q^69 - 12 * q^71 + 11 * q^73 - q^75 + 24 * q^77 - q^79 - q^81 + 12 * q^83 + 16 * q^85 - 4 * q^87 + 8 * q^89 - 15 * q^91 + 7 * q^93 + 10 * q^95 - 28 * q^97 - 12 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$$.

 $$n$$ $$73$$ $$85$$ $$113$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$1$$

## 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
$$5$$ −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i $$-0.314250\pi$$
−0.998203 + 0.0599153i $$0.980917\pi$$
$$6$$ 0 0
$$7$$ 2.50000 + 0.866025i 0.944911 + 0.327327i
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i $$-0.473552\pi$$
0.821541 0.570149i $$-0.193114\pi$$
$$12$$ 0 0
$$13$$ −3.00000 −0.832050 −0.416025 0.909353i $$-0.636577\pi$$
−0.416025 + 0.909353i $$0.636577\pi$$
$$14$$ 0 0
$$15$$ −2.00000 −0.516398
$$16$$ 0 0
$$17$$ −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i $$-0.994540\pi$$
0.514782 + 0.857321i $$0.327873\pi$$
$$18$$ 0 0
$$19$$ 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i $$0.0277634\pi$$
−0.422659 + 0.906289i $$0.638903\pi$$
$$20$$ 0 0
$$21$$ 2.00000 1.73205i 0.436436 0.377964i
$$22$$ 0 0
$$23$$ 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i $$-0.0297381\pi$$
−0.578610 + 0.815604i $$0.696405\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ −3.50000 + 6.06218i −0.628619 + 1.08880i 0.359211 + 0.933257i $$0.383046\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ 0 0
$$33$$ −3.00000 5.19615i −0.522233 0.904534i
$$34$$ 0 0
$$35$$ −1.00000 5.19615i −0.169031 0.878310i
$$36$$ 0 0
$$37$$ 4.50000 + 7.79423i 0.739795 + 1.28136i 0.952587 + 0.304266i $$0.0984111\pi$$
−0.212792 + 0.977098i $$0.568256\pi$$
$$38$$ 0 0
$$39$$ −1.50000 + 2.59808i −0.240192 + 0.416025i
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ −1.00000 −0.152499 −0.0762493 0.997089i $$-0.524294\pi$$
−0.0762493 + 0.997089i $$0.524294\pi$$
$$44$$ 0 0
$$45$$ −1.00000 + 1.73205i −0.149071 + 0.258199i
$$46$$ 0 0
$$47$$ −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i $$-0.213263\pi$$
−0.929695 + 0.368329i $$0.879930\pi$$
$$48$$ 0 0
$$49$$ 5.50000 + 4.33013i 0.785714 + 0.618590i
$$50$$ 0 0
$$51$$ 2.00000 + 3.46410i 0.280056 + 0.485071i
$$52$$ 0 0
$$53$$ −4.00000 + 6.92820i −0.549442 + 0.951662i 0.448871 + 0.893597i $$0.351826\pi$$
−0.998313 + 0.0580651i $$0.981507\pi$$
$$54$$ 0 0
$$55$$ −12.0000 −1.61808
$$56$$ 0 0
$$57$$ 5.00000 0.662266
$$58$$ 0 0
$$59$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$60$$ 0 0
$$61$$ −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i $$-0.945525\pi$$
0.345207 0.938527i $$-0.387809\pi$$
$$62$$ 0 0
$$63$$ −0.500000 2.59808i −0.0629941 0.327327i
$$64$$ 0 0
$$65$$ 3.00000 + 5.19615i 0.372104 + 0.644503i
$$66$$ 0 0
$$67$$ 7.50000 12.9904i 0.916271 1.58703i 0.111241 0.993793i $$-0.464517\pi$$
0.805030 0.593234i $$-0.202149\pi$$
$$68$$ 0 0
$$69$$ 4.00000 0.481543
$$70$$ 0 0
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 0 0
$$73$$ 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i $$-0.610721\pi$$
0.984594 0.174855i $$-0.0559458\pi$$
$$74$$ 0 0
$$75$$ −0.500000 0.866025i −0.0577350 0.100000i
$$76$$ 0 0
$$77$$ 12.0000 10.3923i 1.36753 1.18431i
$$78$$ 0 0
$$79$$ −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i $$-0.184582\pi$$
−0.892781 + 0.450490i $$0.851249\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ 8.00000 0.867722
$$86$$ 0 0
$$87$$ −2.00000 + 3.46410i −0.214423 + 0.371391i
$$88$$ 0 0
$$89$$ 4.00000 + 6.92820i 0.423999 + 0.734388i 0.996326 0.0856373i $$-0.0272926\pi$$
−0.572327 + 0.820025i $$0.693959\pi$$
$$90$$ 0 0
$$91$$ −7.50000 2.59808i −0.786214 0.272352i
$$92$$ 0 0
$$93$$ 3.50000 + 6.06218i 0.362933 + 0.628619i
$$94$$ 0 0
$$95$$ 5.00000 8.66025i 0.512989 0.888523i
$$96$$ 0 0
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i $$-0.736843\pi$$
0.975796 + 0.218685i $$0.0701767\pi$$
$$102$$ 0 0
$$103$$ 4.50000 + 7.79423i 0.443398 + 0.767988i 0.997939 0.0641683i $$-0.0204394\pi$$
−0.554541 + 0.832156i $$0.687106\pi$$
$$104$$ 0 0
$$105$$ −5.00000 1.73205i −0.487950 0.169031i
$$106$$ 0 0
$$107$$ 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i $$0.0302972\pi$$
−0.415432 + 0.909624i $$0.636370\pi$$
$$108$$ 0 0
$$109$$ 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i $$-0.656723\pi$$
0.999512 0.0312328i $$-0.00994332\pi$$
$$110$$ 0 0
$$111$$ 9.00000 0.854242
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 4.00000 6.92820i 0.373002 0.646058i
$$116$$ 0 0
$$117$$ 1.50000 + 2.59808i 0.138675 + 0.240192i
$$118$$ 0 0
$$119$$ −8.00000 + 6.92820i −0.733359 + 0.635107i
$$120$$ 0 0
$$121$$ −12.5000 21.6506i −1.13636 1.96824i
$$122$$ 0 0
$$123$$ −1.00000 + 1.73205i −0.0901670 + 0.156174i
$$124$$ 0 0
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ −1.00000 −0.0887357 −0.0443678 0.999015i $$-0.514127\pi$$
−0.0443678 + 0.999015i $$0.514127\pi$$
$$128$$ 0 0
$$129$$ −0.500000 + 0.866025i −0.0440225 + 0.0762493i
$$130$$ 0 0
$$131$$ −7.00000 12.1244i −0.611593 1.05931i −0.990972 0.134069i $$-0.957196\pi$$
0.379379 0.925241i $$-0.376138\pi$$
$$132$$ 0 0
$$133$$ 2.50000 + 12.9904i 0.216777 + 1.12641i
$$134$$ 0 0
$$135$$ 1.00000 + 1.73205i 0.0860663 + 0.149071i
$$136$$ 0 0
$$137$$ −10.0000 + 17.3205i −0.854358 + 1.47979i 0.0228820 + 0.999738i $$0.492716\pi$$
−0.877240 + 0.480053i $$0.840618\pi$$
$$138$$ 0 0
$$139$$ −9.00000 −0.763370 −0.381685 0.924292i $$-0.624656\pi$$
−0.381685 + 0.924292i $$0.624656\pi$$
$$140$$ 0 0
$$141$$ −2.00000 −0.168430
$$142$$ 0 0
$$143$$ −9.00000 + 15.5885i −0.752618 + 1.30357i
$$144$$ 0 0
$$145$$ 4.00000 + 6.92820i 0.332182 + 0.575356i
$$146$$ 0 0
$$147$$ 6.50000 2.59808i 0.536111 0.214286i
$$148$$ 0 0
$$149$$ −2.00000 3.46410i −0.163846 0.283790i 0.772399 0.635138i $$-0.219057\pi$$
−0.936245 + 0.351348i $$0.885723\pi$$
$$150$$ 0 0
$$151$$ 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i $$-0.727796\pi$$
0.981617 + 0.190864i $$0.0611289\pi$$
$$152$$ 0 0
$$153$$ 4.00000 0.323381
$$154$$ 0 0
$$155$$ 14.0000 1.12451
$$156$$ 0 0
$$157$$ −9.00000 + 15.5885i −0.718278 + 1.24409i 0.243403 + 0.969925i $$0.421736\pi$$
−0.961681 + 0.274169i $$0.911597\pi$$
$$158$$ 0 0
$$159$$ 4.00000 + 6.92820i 0.317221 + 0.549442i
$$160$$ 0 0
$$161$$ 2.00000 + 10.3923i 0.157622 + 0.819028i
$$162$$ 0 0
$$163$$ −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i $$-0.216737\pi$$
−0.933659 + 0.358162i $$0.883403\pi$$
$$164$$ 0 0
$$165$$ −6.00000 + 10.3923i −0.467099 + 0.809040i
$$166$$ 0 0
$$167$$ 18.0000 1.39288 0.696441 0.717614i $$-0.254766\pi$$
0.696441 + 0.717614i $$0.254766\pi$$
$$168$$ 0 0
$$169$$ −4.00000 −0.307692
$$170$$ 0 0
$$171$$ 2.50000 4.33013i 0.191180 0.331133i
$$172$$ 0 0
$$173$$ −10.0000 17.3205i −0.760286 1.31685i −0.942703 0.333633i $$-0.891725\pi$$
0.182417 0.983221i $$-0.441608\pi$$
$$174$$ 0 0
$$175$$ 2.00000 1.73205i 0.151186 0.130931i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −13.0000 + 22.5167i −0.971666 + 1.68297i −0.281139 + 0.959667i $$0.590712\pi$$
−0.690526 + 0.723307i $$0.742621\pi$$
$$180$$ 0 0
$$181$$ −7.00000 −0.520306 −0.260153 0.965567i $$-0.583773\pi$$
−0.260153 + 0.965567i $$0.583773\pi$$
$$182$$ 0 0
$$183$$ −10.0000 −0.739221
$$184$$ 0 0
$$185$$ 9.00000 15.5885i 0.661693 1.14609i
$$186$$ 0 0
$$187$$ 12.0000 + 20.7846i 0.877527 + 1.51992i
$$188$$ 0 0
$$189$$ −2.50000 0.866025i −0.181848 0.0629941i
$$190$$ 0 0
$$191$$ −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i $$-0.284500\pi$$
−0.988255 + 0.152813i $$0.951167\pi$$
$$192$$ 0 0
$$193$$ −1.50000 + 2.59808i −0.107972 + 0.187014i −0.914949 0.403570i $$-0.867769\pi$$
0.806976 + 0.590584i $$0.201102\pi$$
$$194$$ 0 0
$$195$$ 6.00000 0.429669
$$196$$ 0 0
$$197$$ −12.0000 −0.854965 −0.427482 0.904024i $$-0.640599\pi$$
−0.427482 + 0.904024i $$0.640599\pi$$
$$198$$ 0 0
$$199$$ 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i $$-0.641397\pi$$
0.996850 0.0793045i $$-0.0252700\pi$$
$$200$$ 0 0
$$201$$ −7.50000 12.9904i −0.529009 0.916271i
$$202$$ 0 0
$$203$$ −10.0000 3.46410i −0.701862 0.243132i
$$204$$ 0 0
$$205$$ 2.00000 + 3.46410i 0.139686 + 0.241943i
$$206$$ 0 0
$$207$$ 2.00000 3.46410i 0.139010 0.240772i
$$208$$ 0 0
$$209$$ 30.0000 2.07514
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ −3.00000 + 5.19615i −0.205557 + 0.356034i
$$214$$ 0 0
$$215$$ 1.00000 + 1.73205i 0.0681994 + 0.118125i
$$216$$ 0 0
$$217$$ −14.0000 + 12.1244i −0.950382 + 0.823055i
$$218$$ 0 0
$$219$$ −5.50000 9.52628i −0.371656 0.643726i
$$220$$ 0 0
$$221$$ 6.00000 10.3923i 0.403604 0.699062i
$$222$$ 0 0
$$223$$ 24.0000 1.60716 0.803579 0.595198i $$-0.202926\pi$$
0.803579 + 0.595198i $$0.202926\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ 0 0
$$227$$ −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i $$-0.987137\pi$$
0.534577 + 0.845120i $$0.320471\pi$$
$$228$$ 0 0
$$229$$ 3.50000 + 6.06218i 0.231287 + 0.400600i 0.958187 0.286143i $$-0.0923732\pi$$
−0.726900 + 0.686743i $$0.759040\pi$$
$$230$$ 0 0
$$231$$ −3.00000 15.5885i −0.197386 1.02565i
$$232$$ 0 0
$$233$$ −13.0000 22.5167i −0.851658 1.47512i −0.879711 0.475509i $$-0.842264\pi$$
0.0280525 0.999606i $$-0.491069\pi$$
$$234$$ 0 0
$$235$$ −2.00000 + 3.46410i −0.130466 + 0.225973i
$$236$$ 0 0
$$237$$ −1.00000 −0.0649570
$$238$$ 0 0
$$239$$ 2.00000 0.129369 0.0646846 0.997906i $$-0.479396\pi$$
0.0646846 + 0.997906i $$0.479396\pi$$
$$240$$ 0 0
$$241$$ 1.00000 1.73205i 0.0644157 0.111571i −0.832019 0.554747i $$-0.812815\pi$$
0.896435 + 0.443176i $$0.146148\pi$$
$$242$$ 0 0
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ 2.00000 13.8564i 0.127775 0.885253i
$$246$$ 0 0
$$247$$ −7.50000 12.9904i −0.477214 0.826558i
$$248$$ 0 0
$$249$$ 3.00000 5.19615i 0.190117 0.329293i
$$250$$ 0 0
$$251$$ 4.00000 0.252478 0.126239 0.992000i $$-0.459709\pi$$
0.126239 + 0.992000i $$0.459709\pi$$
$$252$$ 0 0
$$253$$ 24.0000 1.50887
$$254$$ 0 0
$$255$$ 4.00000 6.92820i 0.250490 0.433861i
$$256$$ 0 0
$$257$$ 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i $$0.0230722\pi$$
−0.435970 + 0.899961i $$0.643595\pi$$
$$258$$ 0 0
$$259$$ 4.50000 + 23.3827i 0.279616 + 1.45293i
$$260$$ 0 0
$$261$$ 2.00000 + 3.46410i 0.123797 + 0.214423i
$$262$$ 0 0
$$263$$ 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i $$-0.712699\pi$$
0.989561 + 0.144112i $$0.0460326\pi$$
$$264$$ 0 0
$$265$$ 16.0000 0.982872
$$266$$ 0 0
$$267$$ 8.00000 0.489592
$$268$$ 0 0
$$269$$ 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i $$-0.648441\pi$$
0.998361 0.0572259i $$-0.0182255\pi$$
$$270$$ 0 0
$$271$$ −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i $$-0.244792\pi$$
−0.961563 + 0.274586i $$0.911459\pi$$
$$272$$ 0 0
$$273$$ −6.00000 + 5.19615i −0.363137 + 0.314485i
$$274$$ 0 0
$$275$$ −3.00000 5.19615i −0.180907 0.313340i
$$276$$ 0 0
$$277$$ −0.500000 + 0.866025i −0.0300421 + 0.0520344i −0.880656 0.473757i $$-0.842897\pi$$
0.850613 + 0.525792i $$0.176231\pi$$
$$278$$ 0 0
$$279$$ 7.00000 0.419079
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ 0.500000 0.866025i 0.0297219 0.0514799i −0.850782 0.525519i $$-0.823871\pi$$
0.880504 + 0.474039i $$0.157204\pi$$
$$284$$ 0 0
$$285$$ −5.00000 8.66025i −0.296174 0.512989i
$$286$$ 0 0
$$287$$ −5.00000 1.73205i −0.295141 0.102240i
$$288$$ 0 0
$$289$$ 0.500000 + 0.866025i 0.0294118 + 0.0509427i
$$290$$ 0 0
$$291$$ −7.00000 + 12.1244i −0.410347 + 0.710742i
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −3.00000 + 5.19615i −0.174078 + 0.301511i
$$298$$ 0 0
$$299$$ −6.00000 10.3923i −0.346989 0.601003i
$$300$$ 0 0
$$301$$ −2.50000 0.866025i −0.144098 0.0499169i
$$302$$ 0 0
$$303$$ −3.00000 5.19615i −0.172345 0.298511i
$$304$$ 0 0
$$305$$ −10.0000 + 17.3205i −0.572598 + 0.991769i
$$306$$ 0 0
$$307$$ −11.0000 −0.627803 −0.313902 0.949456i $$-0.601636\pi$$
−0.313902 + 0.949456i $$0.601636\pi$$
$$308$$ 0 0
$$309$$ 9.00000 0.511992
$$310$$ 0 0
$$311$$ 9.00000 15.5885i 0.510343 0.883940i −0.489585 0.871956i $$-0.662852\pi$$
0.999928 0.0119847i $$-0.00381495\pi$$
$$312$$ 0 0
$$313$$ 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i $$-0.157669\pi$$
−0.851549 + 0.524276i $$0.824336\pi$$
$$314$$ 0 0
$$315$$ −4.00000 + 3.46410i −0.225374 + 0.195180i
$$316$$ 0 0
$$317$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$318$$ 0 0
$$319$$ −12.0000 + 20.7846i −0.671871 + 1.16371i
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ −20.0000 −1.11283
$$324$$ 0 0
$$325$$ −1.50000 + 2.59808i −0.0832050 + 0.144115i
$$326$$ 0 0
$$327$$ −5.50000 9.52628i −0.304151 0.526804i
$$328$$ 0 0
$$329$$ −1.00000 5.19615i −0.0551318 0.286473i
$$330$$ 0 0
$$331$$ −2.50000 4.33013i −0.137412 0.238005i 0.789104 0.614260i $$-0.210545\pi$$
−0.926516 + 0.376254i $$0.877212\pi$$
$$332$$ 0 0
$$333$$ 4.50000 7.79423i 0.246598 0.427121i
$$334$$ 0 0
$$335$$ −30.0000 −1.63908
$$336$$ 0 0
$$337$$ 29.0000 1.57973 0.789865 0.613280i $$-0.210150\pi$$
0.789865 + 0.613280i $$0.210150\pi$$
$$338$$ 0 0
$$339$$ 3.00000 5.19615i 0.162938 0.282216i
$$340$$ 0 0
$$341$$ 21.0000 + 36.3731i 1.13721 + 1.96971i
$$342$$ 0 0
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ −4.00000 6.92820i −0.215353 0.373002i
$$346$$ 0 0
$$347$$ −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i $$-0.937721\pi$$
0.658824 + 0.752297i $$0.271054\pi$$
$$348$$ 0 0
$$349$$ −22.0000 −1.17763 −0.588817 0.808267i $$-0.700406\pi$$
−0.588817 + 0.808267i $$0.700406\pi$$
$$350$$ 0 0
$$351$$ 3.00000 0.160128
$$352$$ 0 0
$$353$$ −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i $$-0.884378\pi$$
0.775077 + 0.631867i $$0.217711\pi$$
$$354$$ 0 0
$$355$$ 6.00000 + 10.3923i 0.318447 + 0.551566i
$$356$$ 0 0
$$357$$ 2.00000 + 10.3923i 0.105851 + 0.550019i
$$358$$ 0 0
$$359$$ 6.00000 + 10.3923i 0.316668 + 0.548485i 0.979791 0.200026i $$-0.0641026\pi$$
−0.663123 + 0.748511i $$0.730769\pi$$
$$360$$ 0 0
$$361$$ −3.00000 + 5.19615i −0.157895 + 0.273482i
$$362$$ 0 0
$$363$$ −25.0000 −1.31216
$$364$$ 0 0
$$365$$ −22.0000 −1.15153
$$366$$ 0 0
$$367$$ 3.50000 6.06218i 0.182699 0.316443i −0.760100 0.649806i $$-0.774850\pi$$
0.942799 + 0.333363i $$0.108183\pi$$
$$368$$ 0 0
$$369$$ 1.00000 + 1.73205i 0.0520579 + 0.0901670i
$$370$$ 0 0
$$371$$ −16.0000 + 13.8564i −0.830679 + 0.719389i
$$372$$ 0 0
$$373$$ 6.50000 + 11.2583i 0.336557 + 0.582934i 0.983783 0.179364i $$-0.0574041\pi$$
−0.647225 + 0.762299i $$0.724071\pi$$
$$374$$ 0 0
$$375$$ −6.00000 + 10.3923i −0.309839 + 0.536656i
$$376$$ 0 0
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ −15.0000 −0.770498 −0.385249 0.922813i $$-0.625884\pi$$
−0.385249 + 0.922813i $$0.625884\pi$$
$$380$$ 0 0
$$381$$ −0.500000 + 0.866025i −0.0256158 + 0.0443678i
$$382$$ 0 0
$$383$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$384$$ 0 0
$$385$$ −30.0000 10.3923i −1.52894 0.529641i
$$386$$ 0 0
$$387$$ 0.500000 + 0.866025i 0.0254164 + 0.0440225i
$$388$$ 0 0
$$389$$ 13.0000 22.5167i 0.659126 1.14164i −0.321716 0.946836i $$-0.604260\pi$$
0.980842 0.194804i $$-0.0624070\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ −14.0000 −0.706207
$$394$$ 0 0
$$395$$ −1.00000 + 1.73205i −0.0503155 + 0.0871489i
$$396$$ 0 0
$$397$$ 2.50000 + 4.33013i 0.125471 + 0.217323i 0.921917 0.387387i $$-0.126622\pi$$
−0.796446 + 0.604710i $$0.793289\pi$$
$$398$$ 0 0
$$399$$ 12.5000 + 4.33013i 0.625783 + 0.216777i
$$400$$ 0 0
$$401$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$402$$ 0 0
$$403$$ 10.5000 18.1865i 0.523042 0.905936i
$$404$$ 0 0
$$405$$ 2.00000 0.0993808
$$406$$ 0 0
$$407$$ 54.0000 2.67668
$$408$$ 0 0
$$409$$ 1.50000 2.59808i 0.0741702 0.128467i −0.826555 0.562856i $$-0.809703\pi$$
0.900725 + 0.434389i $$0.143036\pi$$
$$410$$ 0 0
$$411$$ 10.0000 + 17.3205i 0.493264 + 0.854358i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −6.00000 10.3923i −0.294528 0.510138i
$$416$$ 0 0
$$417$$ −4.50000 + 7.79423i −0.220366 + 0.381685i
$$418$$ 0 0
$$419$$ 26.0000 1.27018 0.635092 0.772437i $$-0.280962\pi$$
0.635092 + 0.772437i $$0.280962\pi$$
$$420$$ 0 0
$$421$$ −35.0000 −1.70580 −0.852898 0.522078i $$-0.825157\pi$$
−0.852898 + 0.522078i $$0.825157\pi$$
$$422$$ 0 0
$$423$$ −1.00000 + 1.73205i −0.0486217 + 0.0842152i
$$424$$ 0 0
$$425$$ 2.00000 + 3.46410i 0.0970143 + 0.168034i
$$426$$ 0 0
$$427$$ −5.00000 25.9808i −0.241967 1.25730i
$$428$$ 0 0
$$429$$ 9.00000 + 15.5885i 0.434524 + 0.752618i
$$430$$ 0 0
$$431$$ 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i $$-0.690607\pi$$
0.997173 + 0.0751385i $$0.0239399\pi$$
$$432$$ 0 0
$$433$$ 31.0000 1.48976 0.744882 0.667196i $$-0.232506\pi$$
0.744882 + 0.667196i $$0.232506\pi$$
$$434$$ 0 0
$$435$$ 8.00000 0.383571
$$436$$ 0 0
$$437$$ −10.0000 + 17.3205i −0.478365 + 0.828552i
$$438$$ 0 0
$$439$$ −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i $$-0.972552\pi$$
0.423556 0.905870i $$-0.360782\pi$$
$$440$$ 0 0
$$441$$ 1.00000 6.92820i 0.0476190 0.329914i
$$442$$ 0 0
$$443$$ 8.00000 + 13.8564i 0.380091 + 0.658338i 0.991075 0.133306i $$-0.0425592\pi$$
−0.610984 + 0.791643i $$0.709226\pi$$
$$444$$ 0 0
$$445$$ 8.00000 13.8564i 0.379236 0.656857i
$$446$$ 0 0
$$447$$ −4.00000 −0.189194
$$448$$ 0 0
$$449$$ −38.0000 −1.79333 −0.896665 0.442709i $$-0.854018\pi$$
−0.896665 + 0.442709i $$0.854018\pi$$
$$450$$ 0 0
$$451$$ −6.00000 + 10.3923i −0.282529 + 0.489355i
$$452$$ 0 0
$$453$$ −4.00000 6.92820i −0.187936 0.325515i
$$454$$ 0 0
$$455$$ 3.00000 + 15.5885i 0.140642 + 0.730798i
$$456$$ 0 0
$$457$$ −6.50000 11.2583i −0.304057 0.526642i 0.672994 0.739648i $$-0.265008\pi$$
−0.977051 + 0.213006i $$0.931675\pi$$
$$458$$ 0 0
$$459$$ 2.00000 3.46410i 0.0933520 0.161690i
$$460$$ 0 0
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ 17.0000 0.790057 0.395029 0.918669i $$-0.370735\pi$$
0.395029 + 0.918669i $$0.370735\pi$$
$$464$$ 0 0
$$465$$ 7.00000 12.1244i 0.324617 0.562254i
$$466$$ 0 0
$$467$$ −15.0000 25.9808i −0.694117 1.20225i −0.970477 0.241192i $$-0.922462\pi$$
0.276360 0.961054i $$-0.410872\pi$$
$$468$$ 0 0
$$469$$ 30.0000 25.9808i 1.38527 1.19968i
$$470$$ 0 0
$$471$$ 9.00000 + 15.5885i 0.414698 + 0.718278i
$$472$$ 0 0
$$473$$ −3.00000 + 5.19615i −0.137940 + 0.238919i
$$474$$ 0 0
$$475$$ 5.00000 0.229416
$$476$$ 0 0
$$477$$ 8.00000 0.366295
$$478$$ 0 0
$$479$$ −8.00000 + 13.8564i −0.365529 + 0.633115i −0.988861 0.148842i $$-0.952445\pi$$
0.623332 + 0.781958i $$0.285779\pi$$
$$480$$ 0 0
$$481$$ −13.5000 23.3827i −0.615547 1.06616i
$$482$$ 0 0
$$483$$ 10.0000 + 3.46410i 0.455016 + 0.157622i
$$484$$ 0 0
$$485$$ 14.0000 + 24.2487i 0.635707 + 1.10108i
$$486$$ 0 0
$$487$$ −12.5000 + 21.6506i −0.566429 + 0.981084i 0.430486 + 0.902597i $$0.358342\pi$$
−0.996915 + 0.0784867i $$0.974991\pi$$
$$488$$ 0 0
$$489$$ −4.00000 −0.180886
$$490$$ 0 0
$$491$$ 36.0000 1.62466 0.812329 0.583200i $$-0.198200\pi$$
0.812329 + 0.583200i $$0.198200\pi$$
$$492$$ 0 0
$$493$$ 8.00000 13.8564i 0.360302 0.624061i
$$494$$ 0 0
$$495$$ 6.00000 + 10.3923i 0.269680 + 0.467099i
$$496$$ 0 0
$$497$$ −15.0000 5.19615i −0.672842 0.233079i
$$498$$ 0 0
$$499$$ 8.50000 + 14.7224i 0.380512 + 0.659067i 0.991136 0.132855i $$-0.0424144\pi$$
−0.610623 + 0.791921i $$0.709081\pi$$
$$500$$ 0 0
$$501$$ 9.00000 15.5885i 0.402090 0.696441i
$$502$$ 0 0
$$503$$ −14.0000 −0.624229 −0.312115 0.950044i $$-0.601037\pi$$
−0.312115 + 0.950044i $$0.601037\pi$$
$$504$$ 0 0
$$505$$ −12.0000 −0.533993
$$506$$ 0 0
$$507$$ −2.00000 + 3.46410i −0.0888231 + 0.153846i
$$508$$ 0 0
$$509$$ −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i $$-0.209119\pi$$
−0.924821 + 0.380402i $$0.875786\pi$$
$$510$$ 0 0
$$511$$ 22.0000 19.0526i 0.973223 0.842836i
$$512$$ 0 0
$$513$$ −2.50000 4.33013i −0.110378 0.191180i
$$514$$ 0 0
$$515$$ 9.00000 15.5885i 0.396587 0.686909i
$$516$$ 0 0
$$517$$ −12.0000 −0.527759
$$518$$ 0 0
$$519$$ −20.0000 −0.877903
$$520$$ 0 0
$$521$$ 6.00000 10.3923i 0.262865 0.455295i −0.704137 0.710064i $$-0.748666\pi$$
0.967002 + 0.254769i $$0.0819994\pi$$
$$522$$ 0 0
$$523$$ −14.5000 25.1147i −0.634041 1.09819i −0.986718 0.162446i $$-0.948062\pi$$
0.352677 0.935745i $$-0.385272\pi$$
$$524$$ 0 0
$$525$$ −0.500000 2.59808i −0.0218218 0.113389i
$$526$$ 0 0
$$527$$ −14.0000 24.2487i −0.609850 1.05629i
$$528$$ 0 0
$$529$$ 3.50000 6.06218i 0.152174 0.263573i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 6.00000 0.259889
$$534$$ 0 0
$$535$$ 12.0000 20.7846i 0.518805 0.898597i
$$536$$ 0 0
$$537$$ 13.0000 + 22.5167i 0.560991 + 0.971666i
$$538$$ 0 0
$$539$$ 39.0000 15.5885i 1.67985 0.671442i
$$540$$ 0 0
$$541$$ −0.500000 0.866025i −0.0214967 0.0372333i 0.855077 0.518501i $$-0.173510\pi$$
−0.876574 + 0.481268i $$0.840176\pi$$
$$542$$ 0 0
$$543$$ −3.50000 + 6.06218i −0.150199 + 0.260153i
$$544$$ 0 0
$$545$$ −22.0000 −0.942376
$$546$$ 0 0
$$547$$ 4.00000 0.171028 0.0855138 0.996337i $$-0.472747\pi$$
0.0855138 + 0.996337i $$0.472747\pi$$
$$548$$ 0 0
$$549$$ −5.00000 + 8.66025i −0.213395 + 0.369611i
$$550$$ 0 0
$$551$$ −10.0000 17.3205i −0.426014 0.737878i
$$552$$ 0 0
$$553$$ −0.500000 2.59808i −0.0212622 0.110481i
$$554$$ 0 0
$$555$$ −9.00000 15.5885i −0.382029 0.661693i
$$556$$ 0 0
$$557$$ 1.00000 1.73205i 0.0423714 0.0733893i −0.844062 0.536246i $$-0.819842\pi$$
0.886433 + 0.462856i $$0.153175\pi$$
$$558$$ 0 0
$$559$$ 3.00000 0.126886
$$560$$ 0 0
$$561$$ 24.0000 1.01328
$$562$$ 0 0
$$563$$ 1.00000 1.73205i 0.0421450 0.0729972i −0.844183 0.536054i $$-0.819914\pi$$
0.886328 + 0.463057i $$0.153248\pi$$
$$564$$ 0 0
$$565$$ −6.00000 10.3923i −0.252422 0.437208i
$$566$$ 0 0
$$567$$ −2.00000 + 1.73205i −0.0839921 + 0.0727393i
$$568$$ 0 0
$$569$$ 9.00000 + 15.5885i 0.377300 + 0.653502i 0.990668 0.136295i $$-0.0435194\pi$$
−0.613369 + 0.789797i $$0.710186\pi$$
$$570$$ 0 0
$$571$$ −11.5000 + 19.9186i −0.481260 + 0.833567i −0.999769 0.0215055i $$-0.993154\pi$$
0.518509 + 0.855072i $$0.326487\pi$$
$$572$$ 0 0
$$573$$ −10.0000 −0.417756
$$574$$ 0 0
$$575$$ 4.00000 0.166812
$$576$$ 0 0
$$577$$ −19.5000 + 33.7750i −0.811796 + 1.40607i 0.0998105 + 0.995006i $$0.468176\pi$$
−0.911606 + 0.411065i $$0.865157\pi$$
$$578$$ 0 0
$$579$$ 1.50000 + 2.59808i 0.0623379 + 0.107972i
$$580$$ 0 0
$$581$$ 15.0000 + 5.19615i 0.622305 + 0.215573i
$$582$$ 0 0
$$583$$ 24.0000 + 41.5692i 0.993978 + 1.72162i
$$584$$ 0 0
$$585$$ 3.00000 5.19615i 0.124035 0.214834i
$$586$$ 0 0
$$587$$ 16.0000 0.660391 0.330195 0.943913i $$-0.392885\pi$$
0.330195 + 0.943913i $$0.392885\pi$$
$$588$$ 0 0
$$589$$ −35.0000 −1.44215
$$590$$ 0 0
$$591$$ −6.00000 + 10.3923i −0.246807 + 0.427482i
$$592$$ 0 0
$$593$$ 15.0000 + 25.9808i 0.615976 + 1.06690i 0.990212 + 0.139569i $$0.0445716\pi$$
−0.374236 + 0.927333i $$0.622095\pi$$
$$594$$ 0 0
$$595$$ 20.0000 + 6.92820i 0.819920 + 0.284029i
$$596$$ 0 0
$$597$$ −8.00000 13.8564i −0.327418 0.567105i
$$598$$ 0 0
$$599$$ −2.00000 + 3.46410i −0.0817178 + 0.141539i −0.903988 0.427558i $$-0.859374\pi$$
0.822270 + 0.569097i $$0.192707\pi$$
$$600$$ 0 0
$$601$$ 31.0000 1.26452 0.632258 0.774758i $$-0.282128\pi$$
0.632258 + 0.774758i $$0.282128\pi$$
$$602$$ 0 0
$$603$$ −15.0000 −0.610847
$$604$$ 0 0
$$605$$ −25.0000 + 43.3013i −1.01639 + 1.76045i
$$606$$ 0 0
$$607$$ −0.500000 0.866025i −0.0202944 0.0351509i 0.855700 0.517472i $$-0.173127\pi$$
−0.875994 + 0.482322i $$0.839794\pi$$
$$608$$ 0 0
$$609$$ −8.00000 + 6.92820i −0.324176 + 0.280745i
$$610$$ 0 0
$$611$$ 3.00000 + 5.19615i 0.121367 + 0.210214i
$$612$$ 0 0
$$613$$ 19.0000 32.9090i 0.767403 1.32918i −0.171564 0.985173i $$-0.554882\pi$$
0.938967 0.344008i $$-0.111785\pi$$
$$614$$ 0 0
$$615$$ 4.00000 0.161296
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 0 0
$$619$$ −4.50000 + 7.79423i −0.180870 + 0.313276i −0.942177 0.335115i $$-0.891225\pi$$
0.761307 + 0.648392i $$0.224558\pi$$
$$620$$ 0 0
$$621$$ −2.00000 3.46410i −0.0802572 0.139010i
$$622$$ 0 0
$$623$$ 4.00000 + 20.7846i 0.160257 + 0.832718i
$$624$$ 0 0
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 0 0
$$627$$ 15.0000 25.9808i 0.599042 1.03757i
$$628$$ 0 0
$$629$$ −36.0000 −1.43541
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ 0 0
$$633$$ −2.00000 + 3.46410i −0.0794929 + 0.137686i
$$634$$ 0 0
$$635$$ 1.00000 + 1.73205i 0.0396838 + 0.0687343i
$$636$$ 0 0
$$637$$ −16.5000 12.9904i −0.653754 0.514698i
$$638$$ 0 0
$$639$$ 3.00000 + 5.19615i 0.118678 + 0.205557i
$$640$$ 0 0
$$641$$ 10.0000 17.3205i 0.394976 0.684119i −0.598122 0.801405i $$-0.704086\pi$$
0.993098 + 0.117286i $$0.0374195\pi$$
$$642$$ 0 0
$$643$$ −17.0000 −0.670415 −0.335207 0.942144i $$-0.608806\pi$$
−0.335207 + 0.942144i $$0.608806\pi$$
$$644$$ 0 0
$$645$$ 2.00000 0.0787499
$$646$$ 0 0
$$647$$ 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i $$-0.718214\pi$$
0.986916 + 0.161233i $$0.0515470\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 3.50000 + 18.1865i 0.137176 + 0.712786i
$$652$$ 0 0
$$653$$ 11.0000 + 19.0526i 0.430463 + 0.745584i 0.996913 0.0785119i $$-0.0250169\pi$$
−0.566450 + 0.824096i $$0.691684\pi$$
$$654$$ 0 0
$$655$$ −14.0000 + 24.2487i −0.547025 + 0.947476i
$$656$$ 0 0
$$657$$ −11.0000 −0.429151
$$658$$ 0 0
$$659$$ −40.0000 −1.55818 −0.779089 0.626913i $$-0.784318\pi$$
−0.779089 + 0.626913i $$0.784318\pi$$
$$660$$ 0 0
$$661$$ −17.5000 + 30.3109i −0.680671 + 1.17896i 0.294105 + 0.955773i $$0.404978\pi$$
−0.974776 + 0.223184i $$0.928355\pi$$
$$662$$ 0 0
$$663$$ −6.00000 10.3923i −0.233021 0.403604i
$$664$$ 0 0
$$665$$ 20.0000 17.3205i 0.775567 0.671660i
$$666$$ 0 0
$$667$$ −8.00000 13.8564i −0.309761 0.536522i
$$668$$ 0 0
$$669$$ 12.0000 20.7846i 0.463947 0.803579i
$$670$$ 0 0
$$671$$ −60.0000 −2.31627
$$672$$ 0 0
$$673$$ 7.00000 0.269830 0.134915 0.990857i $$-0.456924\pi$$
0.134915 + 0.990857i $$0.456924\pi$$
$$674$$ 0 0
$$675$$ −0.500000 + 0.866025i −0.0192450 + 0.0333333i
$$676$$ 0 0
$$677$$ −6.00000 10.3923i −0.230599 0.399409i 0.727386 0.686229i $$-0.240735\pi$$
−0.957984 + 0.286820i $$0.907402\pi$$
$$678$$ 0 0
$$679$$ −35.0000 12.1244i −1.34318 0.465290i
$$680$$ 0 0
$$681$$ 7.00000 + 12.1244i 0.268241 + 0.464606i
$$682$$ 0 0
$$683$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$684$$ 0 0
$$685$$ 40.0000 1.52832
$$686$$ 0 0
$$687$$ 7.00000 0.267067
$$688$$ 0 0
$$689$$ 12.0000 20.7846i 0.457164 0.791831i
$$690$$ 0 0
$$691$$ 3.50000 + 6.06218i 0.133146 + 0.230616i 0.924888 0.380240i $$-0.124159\pi$$
−0.791742 + 0.610856i $$0.790825\pi$$
$$692$$ 0 0
$$693$$ −15.0000 5.19615i −0.569803 0.197386i
$$694$$ 0 0
$$695$$ 9.00000 + 15.5885i 0.341389 + 0.591304i
$$696$$ 0 0
$$697$$ 4.00000 6.92820i 0.151511 0.262424i
$$698$$ 0 0
$$699$$ −26.0000 −0.983410
$$700$$ 0 0
$$701$$ 28.0000 1.05755 0.528773 0.848763i $$-0.322652\pi$$
0.528773 + 0.848763i $$0.322652\pi$$
$$702$$ 0 0
$$703$$ −22.5000 + 38.9711i −0.848604 + 1.46982i
$$704$$ 0 0
$$705$$ 2.00000 + 3.46410i 0.0753244 + 0.130466i
$$706$$ 0 0
$$707$$ 12.0000 10.3923i 0.451306 0.390843i
$$708$$ 0 0
$$709$$ 25.0000 + 43.3013i 0.938895 + 1.62621i 0.767537 + 0.641004i $$0.221482\pi$$
0.171358 + 0.985209i $$0.445185\pi$$
$$710$$ 0 0
$$711$$ −0.500000 + 0.866025i −0.0187515 + 0.0324785i
$$712$$ 0 0
$$713$$ −28.0000 −1.04861
$$714$$ 0 0
$$715$$ 36.0000 1.34632
$$716$$ 0 0
$$717$$ 1.00000 1.73205i 0.0373457 0.0646846i
$$718$$ 0 0
$$719$$ 15.0000 + 25.9808i 0.559406 + 0.968919i 0.997546 + 0.0700124i $$0.0223039\pi$$
−0.438141 + 0.898906i $$0.644363\pi$$
$$720$$ 0 0
$$721$$ 4.50000 + 23.3827i 0.167589 + 0.870817i
$$722$$ 0 0
$$723$$ −1.00000 1.73205i −0.0371904 0.0644157i
$$724$$ 0 0
$$725$$ −2.00000 + 3.46410i −0.0742781 + 0.128654i
$$726$$ 0 0
$$727$$ 5.00000 0.185440 0.0927199 0.995692i $$-0.470444\pi$$
0.0927199 + 0.995692i $$0.470444\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 2.00000 3.46410i 0.0739727 0.128124i
$$732$$ 0 0
$$733$$ 5.50000 + 9.52628i 0.203147 + 0.351861i 0.949541 0.313644i $$-0.101550\pi$$
−0.746394 + 0.665505i $$0.768216\pi$$
$$734$$ 0 0
$$735$$ −11.0000 8.66025i −0.405741 0.319438i
$$736$$ 0 0
$$737$$ −45.0000 77.9423i −1.65760 2.87104i
$$738$$ 0 0
$$739$$ 2.50000 4.33013i 0.0919640 0.159286i −0.816373 0.577524i $$-0.804019\pi$$
0.908337 + 0.418238i $$0.137352\pi$$
$$740$$ 0 0
$$741$$ −15.0000 −0.551039
$$742$$ 0 0
$$743$$ −34.0000 −1.24734 −0.623670 0.781688i $$-0.714359\pi$$
−0.623670 + 0.781688i $$0.714359\pi$$
$$744$$ 0 0
$$745$$ −4.00000 + 6.92820i −0.146549 + 0.253830i
$$746$$ 0 0
$$747$$ −3.00000 5.19615i −0.109764 0.190117i
$$748$$ 0 0
$$749$$ 6.00000 + 31.1769i 0.219235 + 1.13918i
$$750$$ 0 0
$$751$$ 18.5000 + 32.0429i 0.675075 + 1.16926i 0.976447 + 0.215757i $$0.0692219\pi$$
−0.301373 + 0.953506i $$0.597445\pi$$
$$752$$ 0 0
$$753$$ 2.00000 3.46410i 0.0728841 0.126239i
$$754$$ 0 0
$$755$$ −16.0000 −0.582300
$$756$$ 0 0
$$757$$ 10.0000 0.363456 0.181728 0.983349i $$-0.441831\pi$$
0.181728 + 0.983349i $$0.441831\pi$$
$$758$$ 0 0
$$759$$ 12.0000 20.7846i 0.435572 0.754434i
$$760$$ 0 0
$$761$$ 6.00000 + 10.3923i 0.217500 + 0.376721i 0.954043 0.299670i $$-0.0968765\pi$$
−0.736543 + 0.676391i $$0.763543\pi$$
$$762$$ 0 0
$$763$$ 22.0000 19.0526i 0.796453 0.689749i
$$764$$ 0 0
$$765$$ −4.00000 6.92820i −0.144620 0.250490i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 7.00000 0.252426 0.126213 0.992003i $$-0.459718\pi$$
0.126213 + 0.992003i $$0.459718\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 0 0
$$773$$ 25.0000 43.3013i 0.899188 1.55744i 0.0706526 0.997501i $$-0.477492\pi$$
0.828535 0.559937i $$-0.189175\pi$$
$$774$$ 0 0
$$775$$ 3.50000 + 6.06218i 0.125724 + 0.217760i
$$776$$ 0 0
$$777$$ 22.5000 + 7.79423i 0.807183 + 0.279616i
$$778$$ 0 0
$$779$$ −5.00000 8.66025i −0.179144 0.310286i
$$780$$ 0 0
$$781$$ −18.0000 + 31.1769i −0.644091 + 1.11560i
$$782$$ 0 0
$$783$$ 4.00000 0.142948
$$784$$ 0 0
$$785$$ 36.0000 1.28490
$$786$$ 0 0
$$787$$ 16.0000 27.7128i 0.570338 0.987855i −0.426193 0.904632i $$-0.640145\pi$$
0.996531 0.0832226i $$-0.0265213\pi$$
$$788$$ 0 0
$$789$$ −6.00000 10.3923i −0.213606 0.369976i
$$790$$ 0 0
$$791$$ 15.0000 + 5.19615i 0.533339 + 0.184754i
$$792$$ 0 0
$$793$$ 15.0000 + 25.9808i 0.532666 + 0.922604i
$$794$$ 0 0
$$795$$ 8.00000 13.8564i 0.283731