# Properties

 Label 342.2.g.c.163.1 Level $342$ Weight $2$ Character 342.163 Analytic conductor $2.731$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$342 = 2 \cdot 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 342.g (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.73088374913$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 114) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 163.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 342.163 Dual form 342.2.g.c.235.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{7} +1.00000 q^{8} +2.00000 q^{11} +(1.50000 + 2.59808i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-1.00000 + 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} +(2.50000 + 4.33013i) q^{25} -3.00000 q^{26} +(-0.500000 - 0.866025i) q^{28} -3.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{34} -5.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(2.00000 - 3.46410i) q^{41} +(4.50000 - 7.79423i) q^{43} +(-1.00000 - 1.73205i) q^{44} -4.00000 q^{46} +(5.00000 + 8.66025i) q^{47} -6.00000 q^{49} -5.00000 q^{50} +(1.50000 - 2.59808i) q^{52} +(-2.00000 - 3.46410i) q^{53} +1.00000 q^{56} +(-7.00000 + 12.1244i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(1.50000 - 2.59808i) q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{67} -4.00000 q^{68} +(7.00000 - 12.1244i) q^{71} +(5.50000 - 9.52628i) q^{73} +(2.50000 - 4.33013i) q^{74} +(-0.500000 - 4.33013i) q^{76} +2.00000 q^{77} +(-0.500000 + 0.866025i) q^{79} +(2.00000 + 3.46410i) q^{82} -8.00000 q^{83} +(4.50000 + 7.79423i) q^{86} +2.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(1.50000 + 2.59808i) q^{91} +(2.00000 - 3.46410i) q^{92} -10.0000 q^{94} +(-1.00000 + 1.73205i) q^{97} +(3.00000 - 5.19615i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} - q^{4} + 2 q^{7} + 2 q^{8}+O(q^{10})$$ 2 * q - q^2 - q^4 + 2 * q^7 + 2 * q^8 $$2 q - q^{2} - q^{4} + 2 q^{7} + 2 q^{8} + 4 q^{11} + 3 q^{13} - q^{14} - q^{16} + 4 q^{17} + 8 q^{19} - 2 q^{22} + 4 q^{23} + 5 q^{25} - 6 q^{26} - q^{28} - 6 q^{31} - q^{32} + 4 q^{34} - 10 q^{37} - 7 q^{38} + 4 q^{41} + 9 q^{43} - 2 q^{44} - 8 q^{46} + 10 q^{47} - 12 q^{49} - 10 q^{50} + 3 q^{52} - 4 q^{53} + 2 q^{56} - 14 q^{59} - 11 q^{61} + 3 q^{62} + 2 q^{64} - 3 q^{67} - 8 q^{68} + 14 q^{71} + 11 q^{73} + 5 q^{74} - q^{76} + 4 q^{77} - q^{79} + 4 q^{82} - 16 q^{83} + 9 q^{86} + 4 q^{88} - 14 q^{89} + 3 q^{91} + 4 q^{92} - 20 q^{94} - 2 q^{97} + 6 q^{98}+O(q^{100})$$ 2 * q - q^2 - q^4 + 2 * q^7 + 2 * q^8 + 4 * q^11 + 3 * q^13 - q^14 - q^16 + 4 * q^17 + 8 * q^19 - 2 * q^22 + 4 * q^23 + 5 * q^25 - 6 * q^26 - q^28 - 6 * q^31 - q^32 + 4 * q^34 - 10 * q^37 - 7 * q^38 + 4 * q^41 + 9 * q^43 - 2 * q^44 - 8 * q^46 + 10 * q^47 - 12 * q^49 - 10 * q^50 + 3 * q^52 - 4 * q^53 + 2 * q^56 - 14 * q^59 - 11 * q^61 + 3 * q^62 + 2 * q^64 - 3 * q^67 - 8 * q^68 + 14 * q^71 + 11 * q^73 + 5 * q^74 - q^76 + 4 * q^77 - q^79 + 4 * q^82 - 16 * q^83 + 9 * q^86 + 4 * q^88 - 14 * q^89 + 3 * q^91 + 4 * q^92 - 20 * q^94 - 2 * q^97 + 6 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$325$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$5$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964 0.188982 0.981981i $$-0.439481\pi$$
0.188982 + 0.981981i $$0.439481\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ 1.50000 + 2.59808i 0.416025 + 0.720577i 0.995535 0.0943882i $$-0.0300895\pi$$
−0.579510 + 0.814965i $$0.696756\pi$$
$$14$$ −0.500000 + 0.866025i −0.133631 + 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i $$-0.672127\pi$$
0.999853 + 0.0171533i $$0.00546033\pi$$
$$18$$ 0 0
$$19$$ 4.00000 + 1.73205i 0.917663 + 0.397360i
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −1.00000 + 1.73205i −0.213201 + 0.369274i
$$23$$ 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
$$25$$ 2.50000 + 4.33013i 0.500000 + 0.866025i
$$26$$ −3.00000 −0.588348
$$27$$ 0 0
$$28$$ −0.500000 0.866025i −0.0944911 0.163663i
$$29$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$30$$ 0 0
$$31$$ −3.00000 −0.538816 −0.269408 0.963026i $$-0.586828\pi$$
−0.269408 + 0.963026i $$0.586828\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 2.00000 + 3.46410i 0.342997 + 0.594089i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −5.00000 −0.821995 −0.410997 0.911636i $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ −3.50000 + 2.59808i −0.567775 + 0.421464i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 2.00000 3.46410i 0.312348 0.541002i −0.666523 0.745485i $$-0.732218\pi$$
0.978870 + 0.204483i $$0.0655513\pi$$
$$42$$ 0 0
$$43$$ 4.50000 7.79423i 0.686244 1.18861i −0.286801 0.957990i $$-0.592592\pi$$
0.973044 0.230618i $$-0.0740749\pi$$
$$44$$ −1.00000 1.73205i −0.150756 0.261116i
$$45$$ 0 0
$$46$$ −4.00000 −0.589768
$$47$$ 5.00000 + 8.66025i 0.729325 + 1.26323i 0.957169 + 0.289530i $$0.0934991\pi$$
−0.227844 + 0.973698i $$0.573168\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ −5.00000 −0.707107
$$51$$ 0 0
$$52$$ 1.50000 2.59808i 0.208013 0.360288i
$$53$$ −2.00000 3.46410i −0.274721 0.475831i 0.695344 0.718677i $$-0.255252\pi$$
−0.970065 + 0.242846i $$0.921919\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −7.00000 + 12.1244i −0.911322 + 1.57846i −0.0991242 + 0.995075i $$0.531604\pi$$
−0.812198 + 0.583382i $$0.801729\pi$$
$$60$$ 0 0
$$61$$ −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i $$-0.917971\pi$$
0.262776 0.964857i $$-0.415362\pi$$
$$62$$ 1.50000 2.59808i 0.190500 0.329956i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i $$-0.225330\pi$$
−0.942987 + 0.332830i $$0.891996\pi$$
$$68$$ −4.00000 −0.485071
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 7.00000 12.1244i 0.830747 1.43890i −0.0666994 0.997773i $$-0.521247\pi$$
0.897447 0.441123i $$-0.145420\pi$$
$$72$$ 0 0
$$73$$ 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i $$-0.610721\pi$$
0.984594 0.174855i $$-0.0559458\pi$$
$$74$$ 2.50000 4.33013i 0.290619 0.503367i
$$75$$ 0 0
$$76$$ −0.500000 4.33013i −0.0573539 0.496700i
$$77$$ 2.00000 0.227921
$$78$$ 0 0
$$79$$ −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i $$-0.851249\pi$$
0.836527 + 0.547926i $$0.184582\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 2.00000 + 3.46410i 0.220863 + 0.382546i
$$83$$ −8.00000 −0.878114 −0.439057 0.898459i $$-0.644687\pi$$
−0.439057 + 0.898459i $$0.644687\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 4.50000 + 7.79423i 0.485247 + 0.840473i
$$87$$ 0 0
$$88$$ 2.00000 0.213201
$$89$$ −7.00000 12.1244i −0.741999 1.28518i −0.951584 0.307389i $$-0.900545\pi$$
0.209585 0.977790i $$-0.432789\pi$$
$$90$$ 0 0
$$91$$ 1.50000 + 2.59808i 0.157243 + 0.272352i
$$92$$ 2.00000 3.46410i 0.208514 0.361158i
$$93$$ 0 0
$$94$$ −10.0000 −1.03142
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i $$-0.865709\pi$$
0.810782 + 0.585348i $$0.199042\pi$$
$$98$$ 3.00000 5.19615i 0.303046 0.524891i
$$99$$ 0 0
$$100$$ 2.50000 4.33013i 0.250000 0.433013i
$$101$$ −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
$$103$$ −3.00000 −0.295599 −0.147799 0.989017i $$-0.547219\pi$$
−0.147799 + 0.989017i $$0.547219\pi$$
$$104$$ 1.50000 + 2.59808i 0.147087 + 0.254762i
$$105$$ 0 0
$$106$$ 4.00000 0.388514
$$107$$ 10.0000 0.966736 0.483368 0.875417i $$-0.339413\pi$$
0.483368 + 0.875417i $$0.339413\pi$$
$$108$$ 0 0
$$109$$ −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i $$0.400578\pi$$
−0.977769 + 0.209687i $$0.932756\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −0.500000 + 0.866025i −0.0472456 + 0.0818317i
$$113$$ −10.0000 −0.940721 −0.470360 0.882474i $$-0.655876\pi$$
−0.470360 + 0.882474i $$0.655876\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −7.00000 12.1244i −0.644402 1.11614i
$$119$$ 2.00000 3.46410i 0.183340 0.317554i
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 11.0000 0.995893
$$123$$ 0 0
$$124$$ 1.50000 + 2.59808i 0.134704 + 0.233314i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i $$-0.0511671\pi$$
−0.632166 + 0.774833i $$0.717834\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i $$-0.917752\pi$$
0.704692 + 0.709514i $$0.251085\pi$$
$$132$$ 0 0
$$133$$ 4.00000 + 1.73205i 0.346844 + 0.150188i
$$134$$ 3.00000 0.259161
$$135$$ 0 0
$$136$$ 2.00000 3.46410i 0.171499 0.297044i
$$137$$ −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i $$-0.249173\pi$$
−0.965250 + 0.261329i $$0.915839\pi$$
$$138$$ 0 0
$$139$$ 9.50000 + 16.4545i 0.805779 + 1.39565i 0.915764 + 0.401718i $$0.131587\pi$$
−0.109984 + 0.993933i $$0.535080\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 7.00000 + 12.1244i 0.587427 + 1.01745i
$$143$$ 3.00000 + 5.19615i 0.250873 + 0.434524i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 5.50000 + 9.52628i 0.455183 + 0.788400i
$$147$$ 0 0
$$148$$ 2.50000 + 4.33013i 0.205499 + 0.355934i
$$149$$ −11.0000 + 19.0526i −0.901155 + 1.56085i −0.0751583 + 0.997172i $$0.523946\pi$$
−0.825997 + 0.563675i $$0.809387\pi$$
$$150$$ 0 0
$$151$$ −20.0000 −1.62758 −0.813788 0.581161i $$-0.802599\pi$$
−0.813788 + 0.581161i $$0.802599\pi$$
$$152$$ 4.00000 + 1.73205i 0.324443 + 0.140488i
$$153$$ 0 0
$$154$$ −1.00000 + 1.73205i −0.0805823 + 0.139573i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 10.5000 18.1865i 0.837991 1.45144i −0.0535803 0.998564i $$-0.517063\pi$$
0.891572 0.452880i $$-0.149603\pi$$
$$158$$ −0.500000 0.866025i −0.0397779 0.0688973i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 2.00000 + 3.46410i 0.157622 + 0.273009i
$$162$$ 0 0
$$163$$ 11.0000 0.861586 0.430793 0.902451i $$-0.358234\pi$$
0.430793 + 0.902451i $$0.358234\pi$$
$$164$$ −4.00000 −0.312348
$$165$$ 0 0
$$166$$ 4.00000 6.92820i 0.310460 0.537733i
$$167$$ 3.00000 + 5.19615i 0.232147 + 0.402090i 0.958440 0.285295i $$-0.0920916\pi$$
−0.726293 + 0.687386i $$0.758758\pi$$
$$168$$ 0 0
$$169$$ 2.00000 3.46410i 0.153846 0.266469i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −9.00000 −0.686244
$$173$$ −12.0000 + 20.7846i −0.912343 + 1.58022i −0.101598 + 0.994826i $$0.532395\pi$$
−0.810745 + 0.585399i $$0.800938\pi$$
$$174$$ 0 0
$$175$$ 2.50000 + 4.33013i 0.188982 + 0.327327i
$$176$$ −1.00000 + 1.73205i −0.0753778 + 0.130558i
$$177$$ 0 0
$$178$$ 14.0000 1.04934
$$179$$ −4.00000 −0.298974 −0.149487 0.988764i $$-0.547762\pi$$
−0.149487 + 0.988764i $$0.547762\pi$$
$$180$$ 0 0
$$181$$ 9.00000 + 15.5885i 0.668965 + 1.15868i 0.978194 + 0.207693i $$0.0665956\pi$$
−0.309229 + 0.950988i $$0.600071\pi$$
$$182$$ −3.00000 −0.222375
$$183$$ 0 0
$$184$$ 2.00000 + 3.46410i 0.147442 + 0.255377i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 4.00000 6.92820i 0.292509 0.506640i
$$188$$ 5.00000 8.66025i 0.364662 0.631614i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 8.00000 0.578860 0.289430 0.957199i $$-0.406534\pi$$
0.289430 + 0.957199i $$0.406534\pi$$
$$192$$ 0 0
$$193$$ 6.50000 11.2583i 0.467880 0.810392i −0.531446 0.847092i $$-0.678351\pi$$
0.999326 + 0.0366998i $$0.0116845\pi$$
$$194$$ −1.00000 1.73205i −0.0717958 0.124354i
$$195$$ 0 0
$$196$$ 3.00000 + 5.19615i 0.214286 + 0.371154i
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ 0 0
$$199$$ −2.50000 4.33013i −0.177220 0.306955i 0.763707 0.645563i $$-0.223377\pi$$
−0.940927 + 0.338608i $$0.890044\pi$$
$$200$$ 2.50000 + 4.33013i 0.176777 + 0.306186i
$$201$$ 0 0
$$202$$ 10.0000 0.703598
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 1.50000 2.59808i 0.104510 0.181017i
$$207$$ 0 0
$$208$$ −3.00000 −0.208013
$$209$$ 8.00000 + 3.46410i 0.553372 + 0.239617i
$$210$$ 0 0
$$211$$ −12.5000 + 21.6506i −0.860535 + 1.49049i 0.0108774 + 0.999941i $$0.496538\pi$$
−0.871413 + 0.490550i $$0.836796\pi$$
$$212$$ −2.00000 + 3.46410i −0.137361 + 0.237915i
$$213$$ 0 0
$$214$$ −5.00000 + 8.66025i −0.341793 + 0.592003i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −3.00000 −0.203653
$$218$$ −7.00000 12.1244i −0.474100 0.821165i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ −4.50000 + 7.79423i −0.301342 + 0.521940i −0.976440 0.215788i $$-0.930768\pi$$
0.675098 + 0.737728i $$0.264101\pi$$
$$224$$ −0.500000 0.866025i −0.0334077 0.0578638i
$$225$$ 0 0
$$226$$ 5.00000 8.66025i 0.332595 0.576072i
$$227$$ −8.00000 −0.530979 −0.265489 0.964114i $$-0.585534\pi$$
−0.265489 + 0.964114i $$0.585534\pi$$
$$228$$ 0 0
$$229$$ −11.0000 −0.726900 −0.363450 0.931614i $$-0.618401\pi$$
−0.363450 + 0.931614i $$0.618401\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 9.00000 15.5885i 0.589610 1.02123i −0.404674 0.914461i $$-0.632615\pi$$
0.994283 0.106773i $$-0.0340517\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 14.0000 0.911322
$$237$$ 0 0
$$238$$ 2.00000 + 3.46410i 0.129641 + 0.224544i
$$239$$ 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 $$-0.868727\pi$$
0.110963 0.993825i $$-0.464606\pi$$
$$242$$ 3.50000 6.06218i 0.224989 0.389692i
$$243$$ 0 0
$$244$$ −5.50000 + 9.52628i −0.352101 + 0.609858i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.50000 + 12.9904i 0.0954427 + 0.826558i
$$248$$ −3.00000 −0.190500
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −9.00000 15.5885i −0.568075 0.983935i −0.996756 0.0804789i $$-0.974355\pi$$
0.428681 0.903456i $$-0.358978\pi$$
$$252$$ 0 0
$$253$$ 4.00000 + 6.92820i 0.251478 + 0.435572i
$$254$$ −8.00000 −0.501965
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −6.00000 10.3923i −0.374270 0.648254i 0.615948 0.787787i $$-0.288773\pi$$
−0.990217 + 0.139533i $$0.955440\pi$$
$$258$$ 0 0
$$259$$ −5.00000 −0.310685
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −3.00000 5.19615i −0.185341 0.321019i
$$263$$ 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i $$-0.646065\pi$$
0.997906 0.0646755i $$-0.0206012\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −3.50000 + 2.59808i −0.214599 + 0.159298i
$$267$$ 0 0
$$268$$ −1.50000 + 2.59808i −0.0916271 + 0.158703i
$$269$$ 1.00000 1.73205i 0.0609711 0.105605i −0.833929 0.551872i $$-0.813914\pi$$
0.894900 + 0.446267i $$0.147247\pi$$
$$270$$ 0 0
$$271$$ 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i $$-0.671801\pi$$
0.999870 + 0.0161307i $$0.00513477\pi$$
$$272$$ 2.00000 + 3.46410i 0.121268 + 0.210042i
$$273$$ 0 0
$$274$$ 6.00000 0.362473
$$275$$ 5.00000 + 8.66025i 0.301511 + 0.522233i
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ −19.0000 −1.13954
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −4.00000 6.92820i −0.238620 0.413302i 0.721699 0.692207i $$-0.243362\pi$$
−0.960319 + 0.278906i $$0.910028\pi$$
$$282$$ 0 0
$$283$$ 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i $$-0.630708\pi$$
0.993626 0.112728i $$-0.0359589\pi$$
$$284$$ −14.0000 −0.830747
$$285$$ 0 0
$$286$$ −6.00000 −0.354787
$$287$$ 2.00000 3.46410i 0.118056 0.204479i
$$288$$ 0 0
$$289$$ 0.500000 + 0.866025i 0.0294118 + 0.0509427i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −11.0000 −0.643726
$$293$$ −14.0000 −0.817889 −0.408944 0.912559i $$-0.634103\pi$$
−0.408944 + 0.912559i $$0.634103\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −5.00000 −0.290619
$$297$$ 0 0
$$298$$ −11.0000 19.0526i −0.637213 1.10369i
$$299$$ −6.00000 + 10.3923i −0.346989 + 0.601003i
$$300$$ 0 0
$$301$$ 4.50000 7.79423i 0.259376 0.449252i
$$302$$ 10.0000 17.3205i 0.575435 0.996683i
$$303$$ 0 0
$$304$$ −3.50000 + 2.59808i −0.200739 + 0.149010i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 6.00000 10.3923i 0.342438 0.593120i −0.642447 0.766330i $$-0.722081\pi$$
0.984885 + 0.173210i $$0.0554140\pi$$
$$308$$ −1.00000 1.73205i −0.0569803 0.0986928i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −10.0000 −0.567048 −0.283524 0.958965i $$-0.591504\pi$$
−0.283524 + 0.958965i $$0.591504\pi$$
$$312$$ 0 0
$$313$$ −3.00000 5.19615i −0.169570 0.293704i 0.768699 0.639611i $$-0.220905\pi$$
−0.938269 + 0.345907i $$0.887571\pi$$
$$314$$ 10.5000 + 18.1865i 0.592549 + 1.02633i
$$315$$ 0 0
$$316$$ 1.00000 0.0562544
$$317$$ 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i $$-0.0572566\pi$$
−0.646872 + 0.762598i $$0.723923\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −4.00000 −0.222911
$$323$$ 14.0000 10.3923i 0.778981 0.578243i
$$324$$ 0 0
$$325$$ −7.50000 + 12.9904i −0.416025 + 0.720577i
$$326$$ −5.50000 + 9.52628i −0.304617 + 0.527612i
$$327$$ 0 0
$$328$$ 2.00000 3.46410i 0.110432 0.191273i
$$329$$ 5.00000 + 8.66025i 0.275659 + 0.477455i
$$330$$ 0 0
$$331$$ 15.0000 0.824475 0.412237 0.911077i $$-0.364747\pi$$
0.412237 + 0.911077i $$0.364747\pi$$
$$332$$ 4.00000 + 6.92820i 0.219529 + 0.380235i
$$333$$ 0 0
$$334$$ −6.00000 −0.328305
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 9.50000 16.4545i 0.517498 0.896333i −0.482295 0.876009i $$-0.660197\pi$$
0.999793 0.0203242i $$-0.00646983\pi$$
$$338$$ 2.00000 + 3.46410i 0.108786 + 0.188422i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −6.00000 −0.324918
$$342$$ 0 0
$$343$$ −13.0000 −0.701934
$$344$$ 4.50000 7.79423i 0.242624 0.420237i
$$345$$ 0 0
$$346$$ −12.0000 20.7846i −0.645124 1.11739i
$$347$$ 8.00000 13.8564i 0.429463 0.743851i −0.567363 0.823468i $$-0.692036\pi$$
0.996826 + 0.0796169i $$0.0253697\pi$$
$$348$$ 0 0
$$349$$ −29.0000 −1.55233 −0.776167 0.630527i $$-0.782839\pi$$
−0.776167 + 0.630527i $$0.782839\pi$$
$$350$$ −5.00000 −0.267261
$$351$$ 0 0
$$352$$ −1.00000 1.73205i −0.0533002 0.0923186i
$$353$$ 12.0000 0.638696 0.319348 0.947638i $$-0.396536\pi$$
0.319348 + 0.947638i $$0.396536\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −7.00000 + 12.1244i −0.370999 + 0.642590i
$$357$$ 0 0
$$358$$ 2.00000 3.46410i 0.105703 0.183083i
$$359$$ −18.0000 + 31.1769i −0.950004 + 1.64545i −0.204595 + 0.978847i $$0.565588\pi$$
−0.745409 + 0.666608i $$0.767746\pi$$
$$360$$ 0 0
$$361$$ 13.0000 + 13.8564i 0.684211 + 0.729285i
$$362$$ −18.0000 −0.946059
$$363$$ 0 0
$$364$$ 1.50000 2.59808i 0.0786214 0.136176i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −11.5000 19.9186i −0.600295 1.03974i −0.992776 0.119982i $$-0.961716\pi$$
0.392481 0.919760i $$-0.371617\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −2.00000 3.46410i −0.103835 0.179847i
$$372$$ 0 0
$$373$$ 26.0000 1.34623 0.673114 0.739538i $$-0.264956\pi$$
0.673114 + 0.739538i $$0.264956\pi$$
$$374$$ 4.00000 + 6.92820i 0.206835 + 0.358249i
$$375$$ 0 0
$$376$$ 5.00000 + 8.66025i 0.257855 + 0.446619i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −13.0000 −0.667765 −0.333883 0.942615i $$-0.608359\pi$$
−0.333883 + 0.942615i $$0.608359\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −4.00000 + 6.92820i −0.204658 + 0.354478i
$$383$$ 7.00000 12.1244i 0.357683 0.619526i −0.629890 0.776684i $$-0.716900\pi$$
0.987573 + 0.157159i $$0.0502334\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 6.50000 + 11.2583i 0.330841 + 0.573034i
$$387$$ 0 0
$$388$$ 2.00000 0.101535
$$389$$ −8.00000 13.8564i −0.405616 0.702548i 0.588777 0.808296i $$-0.299610\pi$$
−0.994393 + 0.105748i $$0.966276\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ −6.00000 −0.303046
$$393$$ 0 0
$$394$$ −1.00000 + 1.73205i −0.0503793 + 0.0872595i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i $$-0.956176\pi$$
0.614123 + 0.789210i $$0.289510\pi$$
$$398$$ 5.00000 0.250627
$$399$$ 0 0
$$400$$ −5.00000 −0.250000
$$401$$ 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i $$-0.684957\pi$$
0.998350 + 0.0574304i $$0.0182907\pi$$
$$402$$ 0 0
$$403$$ −4.50000 7.79423i −0.224161 0.388258i
$$404$$ −5.00000 + 8.66025i −0.248759 + 0.430864i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −10.0000 −0.495682
$$408$$ 0 0
$$409$$ 15.0000 + 25.9808i 0.741702 + 1.28467i 0.951720 + 0.306968i $$0.0993146\pi$$
−0.210017 + 0.977698i $$0.567352\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 1.50000 + 2.59808i 0.0738997 + 0.127998i
$$413$$ −7.00000 + 12.1244i −0.344447 + 0.596601i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.50000 2.59808i 0.0735436 0.127381i
$$417$$ 0 0
$$418$$ −7.00000 + 5.19615i −0.342381 + 0.254152i
$$419$$ −18.0000 −0.879358 −0.439679 0.898155i $$-0.644908\pi$$
−0.439679 + 0.898155i $$0.644908\pi$$
$$420$$ 0 0
$$421$$ −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i $$-0.911690\pi$$
0.718076 + 0.695965i $$0.245023\pi$$
$$422$$ −12.5000 21.6506i −0.608490 1.05394i
$$423$$ 0 0
$$424$$ −2.00000 3.46410i −0.0971286 0.168232i
$$425$$ 20.0000 0.970143
$$426$$ 0 0
$$427$$ −5.50000 9.52628i −0.266164 0.461009i
$$428$$ −5.00000 8.66025i −0.241684 0.418609i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −5.00000 8.66025i −0.240842 0.417150i 0.720113 0.693857i $$-0.244090\pi$$
−0.960954 + 0.276707i $$0.910757\pi$$
$$432$$ 0 0
$$433$$ 4.50000 + 7.79423i 0.216256 + 0.374567i 0.953660 0.300885i $$-0.0972820\pi$$
−0.737404 + 0.675452i $$0.763949\pi$$
$$434$$ 1.50000 2.59808i 0.0720023 0.124712i
$$435$$ 0 0
$$436$$ 14.0000 0.670478
$$437$$ 2.00000 + 17.3205i 0.0956730 + 0.828552i
$$438$$ 0 0
$$439$$ −9.50000 + 16.4545i −0.453410 + 0.785330i −0.998595 0.0529862i $$-0.983126\pi$$
0.545185 + 0.838316i $$0.316459\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −6.00000 + 10.3923i −0.285391 + 0.494312i
$$443$$ 12.0000 + 20.7846i 0.570137 + 0.987507i 0.996551 + 0.0829786i $$0.0264433\pi$$
−0.426414 + 0.904528i $$0.640223\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −4.50000 7.79423i −0.213081 0.369067i
$$447$$ 0 0
$$448$$ 1.00000 0.0472456
$$449$$ 36.0000 1.69895 0.849473 0.527633i $$-0.176920\pi$$
0.849473 + 0.527633i $$0.176920\pi$$
$$450$$ 0 0
$$451$$ 4.00000 6.92820i 0.188353 0.326236i
$$452$$ 5.00000 + 8.66025i 0.235180 + 0.407344i
$$453$$ 0 0
$$454$$ 4.00000 6.92820i 0.187729 0.325157i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 5.00000 0.233890 0.116945 0.993138i $$-0.462690\pi$$
0.116945 + 0.993138i $$0.462690\pi$$
$$458$$ 5.50000 9.52628i 0.256998 0.445134i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 3.00000 5.19615i 0.139724 0.242009i −0.787668 0.616100i $$-0.788712\pi$$
0.927392 + 0.374091i $$0.122045\pi$$
$$462$$ 0 0
$$463$$ −9.00000 −0.418265 −0.209133 0.977887i $$-0.567064\pi$$
−0.209133 + 0.977887i $$0.567064\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 9.00000 + 15.5885i 0.416917 + 0.722121i
$$467$$ −8.00000 −0.370196 −0.185098 0.982720i $$-0.559260\pi$$
−0.185098 + 0.982720i $$0.559260\pi$$
$$468$$ 0 0
$$469$$ −1.50000 2.59808i −0.0692636 0.119968i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −7.00000 + 12.1244i −0.322201 + 0.558069i
$$473$$ 9.00000 15.5885i 0.413820 0.716758i
$$474$$ 0 0
$$475$$ 2.50000 + 21.6506i 0.114708 + 0.993399i
$$476$$ −4.00000 −0.183340
$$477$$ 0 0
$$478$$ −6.00000 + 10.3923i −0.274434 + 0.475333i
$$479$$ 3.00000 + 5.19615i 0.137073 + 0.237418i 0.926388 0.376571i $$-0.122897\pi$$
−0.789314 + 0.613990i $$0.789564\pi$$
$$480$$ 0 0
$$481$$ −7.50000 12.9904i −0.341971 0.592310i
$$482$$ 25.0000 1.13872
$$483$$ 0 0
$$484$$ 3.50000 + 6.06218i 0.159091 + 0.275554i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 32.0000 1.45006 0.725029 0.688718i $$-0.241826\pi$$
0.725029 + 0.688718i $$0.241826\pi$$
$$488$$ −5.50000 9.52628i −0.248973 0.431234i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 15.0000 25.9808i 0.676941 1.17250i −0.298957 0.954267i $$-0.596639\pi$$
0.975898 0.218229i $$-0.0700279\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −12.0000 5.19615i −0.539906 0.233786i
$$495$$ 0 0
$$496$$ 1.50000 2.59808i 0.0673520 0.116657i
$$497$$ 7.00000 12.1244i 0.313993 0.543852i
$$498$$ 0 0
$$499$$ −2.50000 + 4.33013i −0.111915 + 0.193843i −0.916542 0.399937i $$-0.869032\pi$$
0.804627 + 0.593780i $$0.202365\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 18.0000 0.803379
$$503$$ 8.00000 + 13.8564i 0.356702 + 0.617827i 0.987408 0.158196i $$-0.0505677\pi$$
−0.630705 + 0.776022i $$0.717234\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −8.00000 −0.355643
$$507$$ 0 0
$$508$$ 4.00000 6.92820i 0.177471 0.307389i
$$509$$ 13.0000 + 22.5167i 0.576215 + 0.998033i 0.995908 + 0.0903676i $$0.0288042\pi$$
−0.419694 + 0.907666i $$0.637862\pi$$
$$510$$ 0 0
$$511$$ 5.50000 9.52628i 0.243306 0.421418i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 12.0000 0.529297
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 10.0000 + 17.3205i 0.439799 + 0.761755i
$$518$$ 2.50000 4.33013i 0.109844 0.190255i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −34.0000 −1.48957 −0.744784 0.667306i $$-0.767447\pi$$
−0.744784 + 0.667306i $$0.767447\pi$$
$$522$$ 0 0
$$523$$ −18.5000 32.0429i −0.808949 1.40114i −0.913593 0.406630i $$-0.866704\pi$$
0.104644 0.994510i $$-0.466630\pi$$
$$524$$ 6.00000 0.262111
$$525$$ 0 0
$$526$$ 9.00000 + 15.5885i 0.392419 + 0.679689i
$$527$$ −6.00000 + 10.3923i −0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ 3.50000 6.06218i 0.152174 0.263573i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −0.500000 4.33013i −0.0216777 0.187735i
$$533$$ 12.0000 0.519778
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −1.50000 2.59808i −0.0647901 0.112220i
$$537$$ 0 0
$$538$$ 1.00000 + 1.73205i 0.0431131 + 0.0746740i
$$539$$ −12.0000 −0.516877
$$540$$ 0 0
$$541$$ 15.5000 + 26.8468i 0.666397 + 1.15423i 0.978905 + 0.204318i $$0.0654977\pi$$
−0.312507 + 0.949915i $$0.601169\pi$$
$$542$$ 8.00000 + 13.8564i 0.343629 + 0.595184i
$$543$$ 0 0
$$544$$ −4.00000 −0.171499
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −5.50000 9.52628i −0.235163 0.407314i 0.724157 0.689635i $$-0.242229\pi$$
−0.959320 + 0.282321i $$0.908896\pi$$
$$548$$ −3.00000 + 5.19615i −0.128154 + 0.221969i
$$549$$ 0 0
$$550$$ −10.0000 −0.426401
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −0.500000 + 0.866025i −0.0212622 + 0.0368271i
$$554$$ 1.00000 1.73205i 0.0424859 0.0735878i
$$555$$ 0 0
$$556$$ 9.50000 16.4545i 0.402890 0.697826i
$$557$$ 17.0000 + 29.4449i 0.720313 + 1.24762i 0.960874 + 0.276985i $$0.0893352\pi$$
−0.240561 + 0.970634i $$0.577331\pi$$
$$558$$ 0 0
$$559$$ 27.0000 1.14198
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 8.00000 0.337460
$$563$$ 6.00000 0.252870 0.126435 0.991975i $$-0.459647\pi$$
0.126435 + 0.991975i $$0.459647\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 10.0000 + 17.3205i 0.420331 + 0.728035i
$$567$$ 0 0
$$568$$ 7.00000 12.1244i 0.293713 0.508727i
$$569$$ −24.0000 −1.00613 −0.503066 0.864248i $$-0.667795\pi$$
−0.503066 + 0.864248i $$0.667795\pi$$
$$570$$ 0 0
$$571$$ −7.00000 −0.292941 −0.146470 0.989215i $$-0.546791\pi$$
−0.146470 + 0.989215i $$0.546791\pi$$
$$572$$ 3.00000 5.19615i 0.125436 0.217262i
$$573$$ 0 0
$$574$$ 2.00000 + 3.46410i 0.0834784 + 0.144589i
$$575$$ −10.0000 + 17.3205i −0.417029 + 0.722315i
$$576$$ 0 0
$$577$$ −14.0000 −0.582828 −0.291414 0.956597i $$-0.594126\pi$$
−0.291414 + 0.956597i $$0.594126\pi$$
$$578$$ −1.00000 −0.0415945
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −8.00000 −0.331896
$$582$$ 0 0
$$583$$ −4.00000 6.92820i −0.165663 0.286937i
$$584$$ 5.50000 9.52628i 0.227592 0.394200i
$$585$$ 0 0
$$586$$ 7.00000 12.1244i 0.289167 0.500853i
$$587$$ −1.00000 + 1.73205i −0.0412744 + 0.0714894i −0.885925 0.463829i $$-0.846475\pi$$
0.844650 + 0.535319i $$0.179808\pi$$
$$588$$ 0 0
$$589$$ −12.0000 5.19615i −0.494451 0.214104i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 2.50000 4.33013i 0.102749 0.177967i
$$593$$ 17.0000 + 29.4449i 0.698106 + 1.20916i 0.969122 + 0.246581i $$0.0793071\pi$$
−0.271016 + 0.962575i $$0.587360\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 22.0000 0.901155
$$597$$ 0 0
$$598$$ −6.00000 10.3923i −0.245358 0.424973i
$$599$$ −23.0000 39.8372i −0.939755 1.62770i −0.765928 0.642926i $$-0.777720\pi$$
−0.173826 0.984776i $$-0.555613\pi$$
$$600$$ 0 0
$$601$$ 27.0000 1.10135 0.550676 0.834719i $$-0.314370\pi$$
0.550676 + 0.834719i $$0.314370\pi$$
$$602$$ 4.50000 + 7.79423i 0.183406 + 0.317669i
$$603$$ 0 0
$$604$$ 10.0000 + 17.3205i 0.406894 + 0.704761i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 5.00000 0.202944 0.101472 0.994838i $$-0.467645\pi$$
0.101472 + 0.994838i $$0.467645\pi$$
$$608$$ −0.500000 4.33013i −0.0202777 0.175610i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −15.0000 + 25.9808i −0.606835 + 1.05107i
$$612$$ 0 0
$$613$$ −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i $$-0.846193\pi$$
0.845124 + 0.534570i $$0.179527\pi$$
$$614$$ 6.00000 + 10.3923i 0.242140 + 0.419399i
$$615$$ 0 0
$$616$$ 2.00000 0.0805823
$$617$$ −21.0000 36.3731i −0.845428 1.46432i −0.885249 0.465118i $$-0.846012\pi$$
0.0398207 0.999207i $$-0.487321\pi$$
$$618$$ 0 0
$$619$$ 1.00000 0.0401934 0.0200967 0.999798i $$-0.493603\pi$$
0.0200967 + 0.999798i $$0.493603\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 5.00000 8.66025i 0.200482 0.347245i
$$623$$ −7.00000 12.1244i −0.280449 0.485752i
$$624$$ 0 0
$$625$$ −12.5000 + 21.6506i −0.500000 + 0.866025i
$$626$$ 6.00000 0.239808
$$627$$ 0 0
$$628$$ −21.0000 −0.837991
$$629$$ −10.0000 + 17.3205i −0.398726 + 0.690614i
$$630$$ 0 0
$$631$$ −8.50000 14.7224i −0.338380 0.586091i 0.645748 0.763550i $$-0.276545\pi$$
−0.984128 + 0.177459i $$0.943212\pi$$
$$632$$ −0.500000 + 0.866025i −0.0198889 + 0.0344486i
$$633$$ 0 0
$$634$$ −12.0000 −0.476581
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −9.00000 15.5885i −0.356593 0.617637i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −7.00000 + 12.1244i −0.276483 + 0.478883i −0.970508 0.241068i $$-0.922502\pi$$
0.694025 + 0.719951i $$0.255836\pi$$
$$642$$ 0 0
$$643$$ −18.5000 + 32.0429i −0.729569 + 1.26365i 0.227497 + 0.973779i $$0.426946\pi$$
−0.957066 + 0.289871i $$0.906387\pi$$
$$644$$ 2.00000 3.46410i 0.0788110 0.136505i
$$645$$ 0 0
$$646$$ 2.00000 + 17.3205i 0.0786889 + 0.681466i
$$647$$ −48.0000 −1.88707 −0.943537 0.331266i $$-0.892524\pi$$
−0.943537 + 0.331266i $$0.892524\pi$$
$$648$$ 0 0
$$649$$ −14.0000 + 24.2487i −0.549548 + 0.951845i
$$650$$ −7.50000 12.9904i −0.294174 0.509525i
$$651$$ 0 0
$$652$$ −5.50000 9.52628i −0.215397 0.373078i
$$653$$ 42.0000 1.64359 0.821794 0.569785i $$-0.192974\pi$$
0.821794 + 0.569785i $$0.192974\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 2.00000 + 3.46410i 0.0780869 + 0.135250i
$$657$$ 0 0
$$658$$ −10.0000 −0.389841
$$659$$ −7.00000 12.1244i −0.272681 0.472298i 0.696866 0.717201i $$-0.254577\pi$$
−0.969548 + 0.244903i $$0.921244\pi$$
$$660$$ 0 0
$$661$$ −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i $$-0.228968\pi$$
−0.946729 + 0.322031i $$0.895634\pi$$
$$662$$ −7.50000 + 12.9904i −0.291496 + 0.504885i
$$663$$ 0 0
$$664$$ −8.00000 −0.310460
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 3.00000 5.19615i 0.116073 0.201045i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −11.0000 19.0526i −0.424650 0.735516i
$$672$$ 0 0
$$673$$ −1.00000 −0.0385472 −0.0192736 0.999814i $$-0.506135\pi$$
−0.0192736 + 0.999814i $$0.506135\pi$$
$$674$$ 9.50000 + 16.4545i 0.365926 + 0.633803i
$$675$$ 0 0
$$676$$ −4.00000 −0.153846
$$677$$ −18.0000 −0.691796 −0.345898 0.938272i $$-0.612426\pi$$
−0.345898 + 0.938272i $$0.612426\pi$$
$$678$$ 0 0
$$679$$ −1.00000 + 1.73205i −0.0383765 + 0.0664700i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 3.00000 5.19615i 0.114876 0.198971i
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 6.50000 11.2583i 0.248171 0.429845i
$$687$$ 0 0
$$688$$ 4.50000 + 7.79423i 0.171561 + 0.297152i
$$689$$ 6.00000 10.3923i 0.228582 0.395915i
$$690$$ 0 0
$$691$$ 4.00000 0.152167 0.0760836 0.997101i $$-0.475758\pi$$
0.0760836 + 0.997101i $$0.475758\pi$$
$$692$$ 24.0000 0.912343
$$693$$ 0 0
$$694$$ 8.00000 + 13.8564i 0.303676 + 0.525982i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −8.00000 13.8564i −0.303022 0.524849i
$$698$$ 14.5000 25.1147i 0.548833 0.950607i
$$699$$ 0 0
$$700$$ 2.50000 4.33013i 0.0944911 0.163663i
$$701$$ −22.0000 + 38.1051i −0.830929 + 1.43921i 0.0663742 + 0.997795i $$0.478857\pi$$
−0.897303 + 0.441416i $$0.854476\pi$$
$$702$$ 0 0
$$703$$ −20.0000 8.66025i −0.754314 0.326628i
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ −6.00000 + 10.3923i −0.225813 + 0.391120i
$$707$$ −5.00000 8.66025i −0.188044 0.325702i
$$708$$ 0 0
$$709$$ 15.5000 + 26.8468i 0.582115 + 1.00825i 0.995228 + 0.0975728i $$0.0311079\pi$$
−0.413114 + 0.910679i $$0.635559\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −7.00000 12.1244i −0.262336 0.454379i
$$713$$ −6.00000 10.3923i −0.224702 0.389195i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 2.00000 + 3.46410i 0.0747435 + 0.129460i
$$717$$ 0 0
$$718$$ −18.0000 31.1769i −0.671754 1.16351i
$$719$$ 20.0000 34.6410i 0.745874 1.29189i −0.203911 0.978989i $$-0.565365\pi$$
0.949785 0.312903i $$-0.101301\pi$$
$$720$$ 0 0
$$721$$ −3.00000 −0.111726
$$722$$ −18.5000 + 4.33013i −0.688499 + 0.161151i
$$723$$ 0 0
$$724$$ 9.00000 15.5885i 0.334482 0.579340i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −8.50000 + 14.7224i −0.315248 + 0.546025i −0.979490 0.201492i $$-0.935421\pi$$
0.664243 + 0.747517i $$0.268754\pi$$
$$728$$ 1.50000 + 2.59808i 0.0555937 + 0.0962911i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −18.0000 31.1769i −0.665754 1.15312i
$$732$$ 0 0
$$733$$ −2.00000 −0.0738717 −0.0369358 0.999318i $$-0.511760\pi$$
−0.0369358 + 0.999318i $$0.511760\pi$$
$$734$$ 23.0000 0.848945
$$735$$ 0 0
$$736$$ 2.00000 3.46410i 0.0737210 0.127688i
$$737$$ −3.00000 5.19615i −0.110506 0.191403i
$$738$$ 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
$$741$$ 0 0
$$742$$ 4.00000 0.146845
$$743$$ −9.00000 + 15.5885i −0.330178 + 0.571885i −0.982547 0.186017i $$-0.940442\pi$$
0.652369 + 0.757902i $$0.273775\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −13.0000 + 22.5167i −0.475964 + 0.824394i
$$747$$ 0 0
$$748$$ −8.00000 −0.292509
$$749$$ 10.0000 0.365392
$$750$$ 0 0
$$751$$ −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i $$-0.242893\pi$$
−0.959906 + 0.280321i $$0.909559\pi$$
$$752$$ −10.0000 −0.364662
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −2.50000 + 4.33013i −0.0908640 + 0.157381i −0.907875 0.419241i $$-0.862296\pi$$
0.817011 + 0.576622i $$0.195630\pi$$
$$758$$ 6.50000 11.2583i 0.236091 0.408921i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 34.0000 1.23250 0.616250 0.787551i $$-0.288651\pi$$
0.616250 + 0.787551i $$0.288651\pi$$
$$762$$ 0 0
$$763$$ −7.00000 + 12.1244i −0.253417 + 0.438931i
$$764$$ −4.00000 6.92820i −0.144715 0.250654i
$$765$$ 0 0
$$766$$ 7.00000 + 12.1244i 0.252920 + 0.438071i
$$767$$ −42.0000 −1.51653
$$768$$ 0 0
$$769$$ −13.5000 23.3827i −0.486822 0.843201i 0.513063 0.858351i $$-0.328511\pi$$
−0.999885 + 0.0151499i $$0.995177\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −13.0000 −0.467880
$$773$$ −9.00000 15.5885i −0.323708 0.560678i 0.657542 0.753418i $$-0.271596\pi$$
−0.981250 + 0.192740i $$0.938263\pi$$
$$774$$ 0 0
$$775$$ −7.50000 12.9904i −0.269408 0.466628i
$$776$$ −1.00000 + 1.73205i −0.0358979 + 0.0621770i
$$777$$ 0 0
$$778$$ 16.0000 0.573628
$$779$$ 14.0000 10.3923i 0.501602 0.372343i
$$780$$ 0 0
$$781$$ 14.0000 24.2487i 0.500959 0.867687i
$$782$$ −8.00000 + 13.8564i −0.286079 + 0.495504i
$$783$$ 0 0
$$784$$ 3.00000 5.19615i 0.107143 0.185577i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −47.0000 −1.67537 −0.837685 0.546154i $$-0.816091\pi$$
−0.837685 + 0.546154i $$0.816091\pi$$
$$788$$ −1.00000 1.73205i −0.0356235 0.0617018i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −10.0000 −0.355559
$$792$$ 0 0
$$793$$ 16.5000 28.5788i 0.585932 1.01486i