# Properties

 Label 1134.2.t.c.593.1 Level $1134$ Weight $2$ Character 1134.593 Analytic conductor $9.055$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.t (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.05503558921$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 378) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 593.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.593 Dual form 1134.2.t.c.1025.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +(1.50000 - 0.866025i) q^{10} +(-1.73205 - 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 3.00000i) q^{17} +(6.00000 + 3.46410i) q^{19} +(-0.866025 + 1.50000i) q^{20} +6.00000i q^{23} -2.00000 q^{25} +(2.50000 + 0.866025i) q^{28} +(-7.79423 - 4.50000i) q^{29} +(-3.00000 - 1.73205i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.00000 + 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-2.00000 + 3.46410i) q^{37} -6.92820 q^{38} -1.73205i q^{40} +(1.73205 + 3.00000i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-3.00000 - 5.19615i) q^{46} +(-1.73205 - 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{50} +(-2.59808 + 1.50000i) q^{53} +(-2.59808 + 0.500000i) q^{56} +9.00000 q^{58} +(-6.06218 + 10.5000i) q^{59} +(-3.00000 + 1.73205i) q^{61} +3.46410 q^{62} -1.00000 q^{64} +(-7.00000 + 12.1244i) q^{67} -3.46410 q^{68} +(3.00000 + 3.46410i) q^{70} -6.00000i q^{71} +(-10.5000 + 6.06218i) q^{73} -4.00000i q^{74} +(6.00000 - 3.46410i) q^{76} +(-5.50000 - 9.52628i) q^{79} +(0.866025 + 1.50000i) q^{80} +(-3.00000 - 1.73205i) q^{82} +(-8.66025 + 15.0000i) q^{83} +(3.00000 + 5.19615i) q^{85} +8.00000i q^{86} +(-5.19615 + 9.00000i) q^{89} +(5.19615 + 3.00000i) q^{92} +(3.00000 + 1.73205i) q^{94} +(-10.3923 - 6.00000i) q^{95} +(6.00000 + 3.46410i) q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} + 2q^{7} + O(q^{10})$$ $$4q + 2q^{4} + 2q^{7} + 6q^{10} - 2q^{16} + 24q^{19} - 8q^{25} + 10q^{28} - 12q^{31} + 12q^{34} - 8q^{37} + 16q^{43} - 12q^{46} - 26q^{49} + 36q^{58} - 12q^{61} - 4q^{64} - 28q^{67} + 12q^{70} - 42q^{73} + 24q^{76} - 22q^{79} - 12q^{82} + 12q^{85} + 12q^{94} + 24q^{97} + O(q^{100})$$

## Character values

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

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ 0 0
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ −1.73205 −0.774597 −0.387298 0.921954i $$-0.626592\pi$$
−0.387298 + 0.921954i $$0.626592\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 2.59808i 0.188982 + 0.981981i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 1.50000 0.866025i 0.474342 0.273861i
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$14$$ −1.73205 2.00000i −0.462910 0.534522i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.73205 3.00000i −0.420084 0.727607i 0.575863 0.817546i $$-0.304666\pi$$
−0.995947 + 0.0899392i $$0.971333\pi$$
$$18$$ 0 0
$$19$$ 6.00000 + 3.46410i 1.37649 + 0.794719i 0.991736 0.128298i $$-0.0409513\pi$$
0.384759 + 0.923017i $$0.374285\pi$$
$$20$$ −0.866025 + 1.50000i −0.193649 + 0.335410i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 6.00000i 1.25109i 0.780189 + 0.625543i $$0.215123\pi$$
−0.780189 + 0.625543i $$0.784877\pi$$
$$24$$ 0 0
$$25$$ −2.00000 −0.400000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 2.50000 + 0.866025i 0.472456 + 0.163663i
$$29$$ −7.79423 4.50000i −1.44735 0.835629i −0.449029 0.893517i $$-0.648230\pi$$
−0.998323 + 0.0578882i $$0.981563\pi$$
$$30$$ 0 0
$$31$$ −3.00000 1.73205i −0.538816 0.311086i 0.205783 0.978598i $$-0.434026\pi$$
−0.744599 + 0.667512i $$0.767359\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ 3.00000 + 1.73205i 0.514496 + 0.297044i
$$35$$ −0.866025 4.50000i −0.146385 0.760639i
$$36$$ 0 0
$$37$$ −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i $$-0.939977\pi$$
0.653476 + 0.756948i $$0.273310\pi$$
$$38$$ −6.92820 −1.12390
$$39$$ 0 0
$$40$$ 1.73205i 0.273861i
$$41$$ 1.73205 + 3.00000i 0.270501 + 0.468521i 0.968990 0.247099i $$-0.0794774\pi$$
−0.698489 + 0.715621i $$0.746144\pi$$
$$42$$ 0 0
$$43$$ 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i $$-0.624505\pi$$
0.991241 0.132068i $$-0.0421616\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −3.00000 5.19615i −0.442326 0.766131i
$$47$$ −1.73205 3.00000i −0.252646 0.437595i 0.711608 0.702577i $$-0.247967\pi$$
−0.964253 + 0.264982i $$0.914634\pi$$
$$48$$ 0 0
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ 1.73205 1.00000i 0.244949 0.141421i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −2.59808 + 1.50000i −0.356873 + 0.206041i −0.667708 0.744423i $$-0.732725\pi$$
0.310835 + 0.950464i $$0.399391\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −2.59808 + 0.500000i −0.347183 + 0.0668153i
$$57$$ 0 0
$$58$$ 9.00000 1.18176
$$59$$ −6.06218 + 10.5000i −0.789228 + 1.36698i 0.137212 + 0.990542i $$0.456186\pi$$
−0.926440 + 0.376442i $$0.877147\pi$$
$$60$$ 0 0
$$61$$ −3.00000 + 1.73205i −0.384111 + 0.221766i −0.679605 0.733578i $$-0.737849\pi$$
0.295495 + 0.955344i $$0.404516\pi$$
$$62$$ 3.46410 0.439941
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −7.00000 + 12.1244i −0.855186 + 1.48123i 0.0212861 + 0.999773i $$0.493224\pi$$
−0.876472 + 0.481452i $$0.840109\pi$$
$$68$$ −3.46410 −0.420084
$$69$$ 0 0
$$70$$ 3.00000 + 3.46410i 0.358569 + 0.414039i
$$71$$ 6.00000i 0.712069i −0.934473 0.356034i $$-0.884129\pi$$
0.934473 0.356034i $$-0.115871\pi$$
$$72$$ 0 0
$$73$$ −10.5000 + 6.06218i −1.22893 + 0.709524i −0.966807 0.255510i $$-0.917757\pi$$
−0.262126 + 0.965034i $$0.584423\pi$$
$$74$$ 4.00000i 0.464991i
$$75$$ 0 0
$$76$$ 6.00000 3.46410i 0.688247 0.397360i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −5.50000 9.52628i −0.618798 1.07179i −0.989705 0.143120i $$-0.954286\pi$$
0.370907 0.928670i $$-0.379047\pi$$
$$80$$ 0.866025 + 1.50000i 0.0968246 + 0.167705i
$$81$$ 0 0
$$82$$ −3.00000 1.73205i −0.331295 0.191273i
$$83$$ −8.66025 + 15.0000i −0.950586 + 1.64646i −0.206427 + 0.978462i $$0.566184\pi$$
−0.744160 + 0.668002i $$0.767150\pi$$
$$84$$ 0 0
$$85$$ 3.00000 + 5.19615i 0.325396 + 0.563602i
$$86$$ 8.00000i 0.862662i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −5.19615 + 9.00000i −0.550791 + 0.953998i 0.447427 + 0.894321i $$0.352341\pi$$
−0.998218 + 0.0596775i $$0.980993\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 5.19615 + 3.00000i 0.541736 + 0.312772i
$$93$$ 0 0
$$94$$ 3.00000 + 1.73205i 0.309426 + 0.178647i
$$95$$ −10.3923 6.00000i −1.06623 0.615587i
$$96$$ 0 0
$$97$$ 6.00000 + 3.46410i 0.609208 + 0.351726i 0.772655 0.634826i $$-0.218928\pi$$
−0.163448 + 0.986552i $$0.552261\pi$$
$$98$$ 4.33013 5.50000i 0.437409 0.555584i
$$99$$ 0 0
$$100$$ −1.00000 + 1.73205i −0.100000 + 0.173205i
$$101$$ −5.19615 −0.517036 −0.258518 0.966006i $$-0.583234\pi$$
−0.258518 + 0.966006i $$0.583234\pi$$
$$102$$ 0 0
$$103$$ 10.3923i 1.02398i −0.858990 0.511992i $$-0.828908\pi$$
0.858990 0.511992i $$-0.171092\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 1.50000 2.59808i 0.145693 0.252347i
$$107$$ 2.59808 + 1.50000i 0.251166 + 0.145010i 0.620298 0.784366i $$-0.287012\pi$$
−0.369132 + 0.929377i $$0.620345\pi$$
$$108$$ 0 0
$$109$$ −8.00000 13.8564i −0.766261 1.32720i −0.939577 0.342337i $$-0.888782\pi$$
0.173316 0.984866i $$-0.444552\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 2.00000 1.73205i 0.188982 0.163663i
$$113$$ 15.5885 9.00000i 1.46644 0.846649i 0.467143 0.884182i $$-0.345283\pi$$
0.999295 + 0.0375328i $$0.0119499\pi$$
$$114$$ 0 0
$$115$$ 10.3923i 0.969087i
$$116$$ −7.79423 + 4.50000i −0.723676 + 0.417815i
$$117$$ 0 0
$$118$$ 12.1244i 1.11614i
$$119$$ 6.92820 6.00000i 0.635107 0.550019i
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ 1.73205 3.00000i 0.156813 0.271607i
$$123$$ 0 0
$$124$$ −3.00000 + 1.73205i −0.269408 + 0.155543i
$$125$$ 12.1244 1.08444
$$126$$ 0 0
$$127$$ −7.00000 −0.621150 −0.310575 0.950549i $$-0.600522\pi$$
−0.310575 + 0.950549i $$0.600522\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −10.3923 −0.907980 −0.453990 0.891007i $$-0.650000\pi$$
−0.453990 + 0.891007i $$0.650000\pi$$
$$132$$ 0 0
$$133$$ −6.00000 + 17.3205i −0.520266 + 1.50188i
$$134$$ 14.0000i 1.20942i
$$135$$ 0 0
$$136$$ 3.00000 1.73205i 0.257248 0.148522i
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ −9.00000 + 5.19615i −0.763370 + 0.440732i −0.830504 0.557012i $$-0.811948\pi$$
0.0671344 + 0.997744i $$0.478614\pi$$
$$140$$ −4.33013 1.50000i −0.365963 0.126773i
$$141$$ 0 0
$$142$$ 3.00000 + 5.19615i 0.251754 + 0.436051i
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 13.5000 + 7.79423i 1.12111 + 0.647275i
$$146$$ 6.06218 10.5000i 0.501709 0.868986i
$$147$$ 0 0
$$148$$ 2.00000 + 3.46410i 0.164399 + 0.284747i
$$149$$ 15.0000i 1.22885i −0.788976 0.614424i $$-0.789388\pi$$
0.788976 0.614424i $$-0.210612\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ −3.46410 + 6.00000i −0.280976 + 0.486664i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 5.19615 + 3.00000i 0.417365 + 0.240966i
$$156$$ 0 0
$$157$$ −9.00000 5.19615i −0.718278 0.414698i 0.0958404 0.995397i $$-0.469446\pi$$
−0.814119 + 0.580699i $$0.802779\pi$$
$$158$$ 9.52628 + 5.50000i 0.757870 + 0.437557i
$$159$$ 0 0
$$160$$ −1.50000 0.866025i −0.118585 0.0684653i
$$161$$ −15.5885 + 3.00000i −1.22854 + 0.236433i
$$162$$ 0 0
$$163$$ −1.00000 + 1.73205i −0.0783260 + 0.135665i −0.902528 0.430632i $$-0.858291\pi$$
0.824202 + 0.566296i $$0.191624\pi$$
$$164$$ 3.46410 0.270501
$$165$$ 0 0
$$166$$ 17.3205i 1.34433i
$$167$$ 8.66025 + 15.0000i 0.670151 + 1.16073i 0.977861 + 0.209255i $$0.0671038\pi$$
−0.307711 + 0.951480i $$0.599563\pi$$
$$168$$ 0 0
$$169$$ −6.50000 + 11.2583i −0.500000 + 0.866025i
$$170$$ −5.19615 3.00000i −0.398527 0.230089i
$$171$$ 0 0
$$172$$ −4.00000 6.92820i −0.304997 0.528271i
$$173$$ −2.59808 4.50000i −0.197528 0.342129i 0.750198 0.661213i $$-0.229958\pi$$
−0.947726 + 0.319084i $$0.896625\pi$$
$$174$$ 0 0
$$175$$ −1.00000 5.19615i −0.0755929 0.392792i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 10.3923i 0.778936i
$$179$$ 12.9904 7.50000i 0.970947 0.560576i 0.0714220 0.997446i $$-0.477246\pi$$
0.899525 + 0.436870i $$0.143913\pi$$
$$180$$ 0 0
$$181$$ 17.3205i 1.28742i 0.765268 + 0.643712i $$0.222606\pi$$
−0.765268 + 0.643712i $$0.777394\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −6.00000 −0.442326
$$185$$ 3.46410 6.00000i 0.254686 0.441129i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −3.46410 −0.252646
$$189$$ 0 0
$$190$$ 12.0000 0.870572
$$191$$ 5.19615 3.00000i 0.375980 0.217072i −0.300088 0.953912i $$-0.597016\pi$$
0.676068 + 0.736839i $$0.263683\pi$$
$$192$$ 0 0
$$193$$ −5.00000 + 8.66025i −0.359908 + 0.623379i −0.987945 0.154805i $$-0.950525\pi$$
0.628037 + 0.778183i $$0.283859\pi$$
$$194$$ −6.92820 −0.497416
$$195$$ 0 0
$$196$$ −1.00000 + 6.92820i −0.0714286 + 0.494872i
$$197$$ 3.00000i 0.213741i 0.994273 + 0.106871i $$0.0340831\pi$$
−0.994273 + 0.106871i $$0.965917\pi$$
$$198$$ 0 0
$$199$$ 7.50000 4.33013i 0.531661 0.306955i −0.210032 0.977695i $$-0.567357\pi$$
0.741693 + 0.670740i $$0.234023\pi$$
$$200$$ 2.00000i 0.141421i
$$201$$ 0 0
$$202$$ 4.50000 2.59808i 0.316619 0.182800i
$$203$$ 7.79423 22.5000i 0.547048 1.57919i
$$204$$ 0 0
$$205$$ −3.00000 5.19615i −0.209529 0.362915i
$$206$$ 5.19615 + 9.00000i 0.362033 + 0.627060i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −8.00000 13.8564i −0.550743 0.953914i −0.998221 0.0596196i $$-0.981011\pi$$
0.447478 0.894295i $$-0.352322\pi$$
$$212$$ 3.00000i 0.206041i
$$213$$ 0 0
$$214$$ −3.00000 −0.205076
$$215$$ −6.92820 + 12.0000i −0.472500 + 0.818393i
$$216$$ 0 0
$$217$$ 3.00000 8.66025i 0.203653 0.587896i
$$218$$ 13.8564 + 8.00000i 0.938474 + 0.541828i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 13.5000 + 7.79423i 0.904027 + 0.521940i 0.878504 0.477734i $$-0.158542\pi$$
0.0255224 + 0.999674i $$0.491875\pi$$
$$224$$ −0.866025 + 2.50000i −0.0578638 + 0.167038i
$$225$$ 0 0
$$226$$ −9.00000 + 15.5885i −0.598671 + 1.03693i
$$227$$ 25.9808 1.72440 0.862202 0.506565i $$-0.169085\pi$$
0.862202 + 0.506565i $$0.169085\pi$$
$$228$$ 0 0
$$229$$ 3.46410i 0.228914i 0.993428 + 0.114457i $$0.0365129\pi$$
−0.993428 + 0.114457i $$0.963487\pi$$
$$230$$ 5.19615 + 9.00000i 0.342624 + 0.593442i
$$231$$ 0 0
$$232$$ 4.50000 7.79423i 0.295439 0.511716i
$$233$$ 25.9808 + 15.0000i 1.70206 + 0.982683i 0.943676 + 0.330870i $$0.107342\pi$$
0.758380 + 0.651813i $$0.225991\pi$$
$$234$$ 0 0
$$235$$ 3.00000 + 5.19615i 0.195698 + 0.338960i
$$236$$ 6.06218 + 10.5000i 0.394614 + 0.683492i
$$237$$ 0 0
$$238$$ −3.00000 + 8.66025i −0.194461 + 0.561361i
$$239$$ 20.7846 12.0000i 1.34444 0.776215i 0.356988 0.934109i $$-0.383804\pi$$
0.987456 + 0.157893i $$0.0504702\pi$$
$$240$$ 0 0
$$241$$ 1.73205i 0.111571i 0.998443 + 0.0557856i $$0.0177663\pi$$
−0.998443 + 0.0557856i $$0.982234\pi$$
$$242$$ −9.52628 + 5.50000i −0.612372 + 0.353553i
$$243$$ 0 0
$$244$$ 3.46410i 0.221766i
$$245$$ 11.2583 4.50000i 0.719268 0.287494i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 1.73205 3.00000i 0.109985 0.190500i
$$249$$ 0 0
$$250$$ −10.5000 + 6.06218i −0.664078 + 0.383406i
$$251$$ 8.66025 0.546630 0.273315 0.961925i $$-0.411880\pi$$
0.273315 + 0.961925i $$0.411880\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 6.06218 3.50000i 0.380375 0.219610i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −20.7846 −1.29651 −0.648254 0.761424i $$-0.724501\pi$$
−0.648254 + 0.761424i $$0.724501\pi$$
$$258$$ 0 0
$$259$$ −10.0000 3.46410i −0.621370 0.215249i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 9.00000 5.19615i 0.556022 0.321019i
$$263$$ 18.0000i 1.10993i 0.831875 + 0.554964i $$0.187268\pi$$
−0.831875 + 0.554964i $$0.812732\pi$$
$$264$$ 0 0
$$265$$ 4.50000 2.59808i 0.276433 0.159599i
$$266$$ −3.46410 18.0000i −0.212398 1.10365i
$$267$$ 0 0
$$268$$ 7.00000 + 12.1244i 0.427593 + 0.740613i
$$269$$ −0.866025 1.50000i −0.0528025 0.0914566i 0.838416 0.545031i $$-0.183482\pi$$
−0.891219 + 0.453574i $$0.850149\pi$$
$$270$$ 0 0
$$271$$ 10.5000 + 6.06218i 0.637830 + 0.368251i 0.783778 0.621041i $$-0.213290\pi$$
−0.145948 + 0.989292i $$0.546623\pi$$
$$272$$ −1.73205 + 3.00000i −0.105021 + 0.181902i
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ 5.19615 9.00000i 0.311645 0.539784i
$$279$$ 0 0
$$280$$ 4.50000 0.866025i 0.268926 0.0517549i
$$281$$ 15.5885 + 9.00000i 0.929929 + 0.536895i 0.886789 0.462174i $$-0.152930\pi$$
0.0431402 + 0.999069i $$0.486264\pi$$
$$282$$ 0 0
$$283$$ −6.00000 3.46410i −0.356663 0.205919i 0.310953 0.950425i $$-0.399352\pi$$
−0.667616 + 0.744506i $$0.732685\pi$$
$$284$$ −5.19615 3.00000i −0.308335 0.178017i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −6.92820 + 6.00000i −0.408959 + 0.354169i
$$288$$ 0 0
$$289$$ 2.50000 4.33013i 0.147059 0.254713i
$$290$$ −15.5885 −0.915386
$$291$$ 0 0
$$292$$ 12.1244i 0.709524i
$$293$$ 14.7224 + 25.5000i 0.860094 + 1.48973i 0.871838 + 0.489795i $$0.162928\pi$$
−0.0117441 + 0.999931i $$0.503738\pi$$
$$294$$ 0 0
$$295$$ 10.5000 18.1865i 0.611334 1.05886i
$$296$$ −3.46410 2.00000i −0.201347 0.116248i
$$297$$ 0 0
$$298$$ 7.50000 + 12.9904i 0.434463 + 0.752513i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 20.0000 + 6.92820i 1.15278 + 0.399335i
$$302$$ 6.92820 4.00000i 0.398673 0.230174i
$$303$$ 0 0
$$304$$ 6.92820i 0.397360i
$$305$$ 5.19615 3.00000i 0.297531 0.171780i
$$306$$ 0 0
$$307$$ 6.92820i 0.395413i −0.980261 0.197707i $$-0.936651\pi$$
0.980261 0.197707i $$-0.0633494\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −6.00000 −0.340777
$$311$$ −6.92820 + 12.0000i −0.392862 + 0.680458i −0.992826 0.119570i $$-0.961848\pi$$
0.599963 + 0.800027i $$0.295182\pi$$
$$312$$ 0 0
$$313$$ 19.5000 11.2583i 1.10221 0.636358i 0.165406 0.986226i $$-0.447107\pi$$
0.936799 + 0.349867i $$0.113773\pi$$
$$314$$ 10.3923 0.586472
$$315$$ 0 0
$$316$$ −11.0000 −0.618798
$$317$$ −5.19615 + 3.00000i −0.291845 + 0.168497i −0.638774 0.769395i $$-0.720558\pi$$
0.346929 + 0.937892i $$0.387225\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 1.73205 0.0968246
$$321$$ 0 0
$$322$$ 12.0000 10.3923i 0.668734 0.579141i
$$323$$ 24.0000i 1.33540i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 2.00000i 0.110770i
$$327$$ 0 0
$$328$$ −3.00000 + 1.73205i −0.165647 + 0.0956365i
$$329$$ 6.92820 6.00000i 0.381964 0.330791i
$$330$$ 0 0
$$331$$ −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i $$-0.255287\pi$$
−0.970091 + 0.242742i $$0.921953\pi$$
$$332$$ 8.66025 + 15.0000i 0.475293 + 0.823232i
$$333$$ 0 0
$$334$$ −15.0000 8.66025i −0.820763 0.473868i
$$335$$ 12.1244 21.0000i 0.662424 1.14735i
$$336$$ 0 0
$$337$$ 11.5000 + 19.9186i 0.626445 + 1.08503i 0.988260 + 0.152784i $$0.0488240\pi$$
−0.361815 + 0.932250i $$0.617843\pi$$
$$338$$ 13.0000i 0.707107i
$$339$$ 0 0
$$340$$ 6.00000 0.325396
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 6.92820 + 4.00000i 0.373544 + 0.215666i
$$345$$ 0 0
$$346$$ 4.50000 + 2.59808i 0.241921 + 0.139673i
$$347$$ −28.5788 16.5000i −1.53419 0.885766i −0.999162 0.0409337i $$-0.986967\pi$$
−0.535031 0.844833i $$-0.679700\pi$$
$$348$$ 0 0
$$349$$ 3.00000 + 1.73205i 0.160586 + 0.0927146i 0.578140 0.815938i $$-0.303779\pi$$
−0.417553 + 0.908652i $$0.637112\pi$$
$$350$$ 3.46410 + 4.00000i 0.185164 + 0.213809i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 3.46410 0.184376 0.0921878 0.995742i $$-0.470614\pi$$
0.0921878 + 0.995742i $$0.470614\pi$$
$$354$$ 0 0
$$355$$ 10.3923i 0.551566i
$$356$$ 5.19615 + 9.00000i 0.275396 + 0.476999i
$$357$$ 0 0
$$358$$ −7.50000 + 12.9904i −0.396387 + 0.686563i
$$359$$ −20.7846 12.0000i −1.09697 0.633336i −0.161546 0.986865i $$-0.551648\pi$$
−0.935423 + 0.353529i $$0.884981\pi$$
$$360$$ 0 0
$$361$$ 14.5000 + 25.1147i 0.763158 + 1.32183i
$$362$$ −8.66025 15.0000i −0.455173 0.788382i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 18.1865 10.5000i 0.951927 0.549595i
$$366$$ 0 0
$$367$$ 8.66025i 0.452062i −0.974120 0.226031i $$-0.927425\pi$$
0.974120 0.226031i $$-0.0725750\pi$$
$$368$$ 5.19615 3.00000i 0.270868 0.156386i
$$369$$ 0 0
$$370$$ 6.92820i 0.360180i
$$371$$ −5.19615 6.00000i −0.269771 0.311504i
$$372$$ 0 0
$$373$$ 14.0000 0.724893 0.362446 0.932005i $$-0.381942\pi$$
0.362446 + 0.932005i $$0.381942\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 3.00000 1.73205i 0.154713 0.0893237i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −14.0000 −0.719132 −0.359566 0.933120i $$-0.617075\pi$$
−0.359566 + 0.933120i $$0.617075\pi$$
$$380$$ −10.3923 + 6.00000i −0.533114 + 0.307794i
$$381$$ 0 0
$$382$$ −3.00000 + 5.19615i −0.153493 + 0.265858i
$$383$$ 17.3205 0.885037 0.442518 0.896759i $$-0.354085\pi$$
0.442518 + 0.896759i $$0.354085\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 10.0000i 0.508987i
$$387$$ 0 0
$$388$$ 6.00000 3.46410i 0.304604 0.175863i
$$389$$ 21.0000i 1.06474i −0.846511 0.532371i $$-0.821301\pi$$
0.846511 0.532371i $$-0.178699\pi$$
$$390$$ 0 0
$$391$$ 18.0000 10.3923i 0.910299 0.525561i
$$392$$ −2.59808 6.50000i −0.131223 0.328300i
$$393$$ 0 0
$$394$$ −1.50000 2.59808i −0.0755689 0.130889i
$$395$$ 9.52628 + 16.5000i 0.479319 + 0.830205i
$$396$$ 0 0
$$397$$ −24.0000 13.8564i −1.20453 0.695433i −0.242967 0.970034i $$-0.578121\pi$$
−0.961558 + 0.274601i $$0.911454\pi$$
$$398$$ −4.33013 + 7.50000i −0.217050 + 0.375941i
$$399$$ 0 0
$$400$$ 1.00000 + 1.73205i 0.0500000 + 0.0866025i
$$401$$ 6.00000i 0.299626i 0.988714 + 0.149813i $$0.0478671\pi$$
−0.988714 + 0.149813i $$0.952133\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −2.59808 + 4.50000i −0.129259 + 0.223883i
$$405$$ 0 0
$$406$$ 4.50000 + 23.3827i 0.223331 + 1.16046i
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 13.5000 + 7.79423i 0.667532 + 0.385400i 0.795141 0.606425i $$-0.207397\pi$$
−0.127609 + 0.991825i $$0.540730\pi$$
$$410$$ 5.19615 + 3.00000i 0.256620 + 0.148159i
$$411$$ 0 0
$$412$$ −9.00000 5.19615i −0.443398 0.255996i
$$413$$ −30.3109 10.5000i −1.49150 0.516671i
$$414$$ 0 0
$$415$$ 15.0000 25.9808i 0.736321 1.27535i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −1.73205 3.00000i −0.0846162 0.146560i 0.820611 0.571487i $$-0.193633\pi$$
−0.905228 + 0.424927i $$0.860300\pi$$
$$420$$ 0 0
$$421$$ −16.0000 + 27.7128i −0.779792 + 1.35064i 0.152269 + 0.988339i $$0.451342\pi$$
−0.932061 + 0.362301i $$0.881991\pi$$
$$422$$ 13.8564 + 8.00000i 0.674519 + 0.389434i
$$423$$ 0 0
$$424$$ −1.50000 2.59808i −0.0728464 0.126174i
$$425$$ 3.46410 + 6.00000i 0.168034 + 0.291043i
$$426$$ 0 0
$$427$$ −6.00000 6.92820i −0.290360 0.335279i
$$428$$ 2.59808 1.50000i 0.125583 0.0725052i
$$429$$ 0 0
$$430$$ 13.8564i 0.668215i
$$431$$ −31.1769 + 18.0000i −1.50174 + 0.867029i −0.501741 + 0.865018i $$0.667307\pi$$
−0.999998 + 0.00201168i $$0.999360\pi$$
$$432$$ 0 0
$$433$$ 1.73205i 0.0832370i 0.999134 + 0.0416185i $$0.0132514\pi$$
−0.999134 + 0.0416185i $$0.986749\pi$$
$$434$$ 1.73205 + 9.00000i 0.0831411 + 0.432014i
$$435$$ 0 0
$$436$$ −16.0000 −0.766261
$$437$$ −20.7846 + 36.0000i −0.994263 + 1.72211i
$$438$$ 0 0
$$439$$ 27.0000 15.5885i 1.28864 0.743996i 0.310228 0.950662i $$-0.399595\pi$$
0.978412 + 0.206666i $$0.0662612\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −7.79423 + 4.50000i −0.370315 + 0.213801i −0.673596 0.739100i $$-0.735251\pi$$
0.303281 + 0.952901i $$0.401918\pi$$
$$444$$ 0 0
$$445$$ 9.00000 15.5885i 0.426641 0.738964i
$$446$$ −15.5885 −0.738135
$$447$$ 0 0
$$448$$ −0.500000 2.59808i −0.0236228 0.122748i
$$449$$ 6.00000i 0.283158i −0.989927 0.141579i $$-0.954782\pi$$
0.989927 0.141579i $$-0.0452178\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 18.0000i 0.846649i
$$453$$ 0 0
$$454$$ −22.5000 + 12.9904i −1.05598 + 0.609669i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 20.5000 + 35.5070i 0.958950 + 1.66095i 0.725059 + 0.688686i $$0.241812\pi$$
0.233890 + 0.972263i $$0.424854\pi$$
$$458$$ −1.73205 3.00000i −0.0809334 0.140181i
$$459$$ 0 0
$$460$$ −9.00000 5.19615i −0.419627 0.242272i
$$461$$ −11.2583 + 19.5000i −0.524353 + 0.908206i 0.475245 + 0.879853i $$0.342359\pi$$
−0.999598 + 0.0283522i $$0.990974\pi$$
$$462$$ 0 0
$$463$$ −11.5000 19.9186i −0.534450 0.925695i −0.999190 0.0402476i $$-0.987185\pi$$
0.464739 0.885448i $$-0.346148\pi$$
$$464$$ 9.00000i 0.417815i
$$465$$ 0 0
$$466$$ −30.0000 −1.38972
$$467$$ −2.59808 + 4.50000i −0.120225 + 0.208235i −0.919856 0.392256i $$-0.871695\pi$$
0.799632 + 0.600491i $$0.205028\pi$$
$$468$$ 0 0
$$469$$ −35.0000 12.1244i −1.61615 0.559851i
$$470$$ −5.19615 3.00000i −0.239681 0.138380i
$$471$$ 0 0
$$472$$ −10.5000 6.06218i −0.483302 0.279034i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −12.0000 6.92820i −0.550598 0.317888i
$$476$$ −1.73205 9.00000i −0.0793884 0.412514i
$$477$$ 0 0
$$478$$ −12.0000 + 20.7846i −0.548867 + 0.950666i
$$479$$ −13.8564 −0.633115 −0.316558 0.948573i $$-0.602527\pi$$
−0.316558 + 0.948573i $$0.602527\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −0.866025 1.50000i −0.0394464 0.0683231i
$$483$$ 0 0
$$484$$ 5.50000 9.52628i 0.250000 0.433013i
$$485$$ −10.3923 6.00000i −0.471890 0.272446i
$$486$$ 0 0
$$487$$ −0.500000 0.866025i −0.0226572 0.0392434i 0.854475 0.519493i $$-0.173879\pi$$
−0.877132 + 0.480250i $$0.840546\pi$$
$$488$$ −1.73205 3.00000i −0.0784063 0.135804i
$$489$$ 0 0
$$490$$ −7.50000 + 9.52628i −0.338815 + 0.430353i
$$491$$ −2.59808 + 1.50000i −0.117250 + 0.0676941i −0.557478 0.830192i $$-0.688231\pi$$
0.440228 + 0.897886i $$0.354898\pi$$
$$492$$ 0 0
$$493$$ 31.1769i 1.40414i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 3.46410i 0.155543i
$$497$$ 15.5885 3.00000i 0.699238 0.134568i
$$498$$ 0 0
$$499$$ −14.0000 −0.626726 −0.313363 0.949633i $$-0.601456\pi$$
−0.313363 + 0.949633i $$0.601456\pi$$
$$500$$ 6.06218 10.5000i 0.271109 0.469574i
$$501$$ 0 0
$$502$$ −7.50000 + 4.33013i −0.334741 + 0.193263i
$$503$$ 27.7128 1.23565 0.617827 0.786314i $$-0.288013\pi$$
0.617827 + 0.786314i $$0.288013\pi$$
$$504$$ 0 0
$$505$$ 9.00000 0.400495
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −3.50000 + 6.06218i −0.155287 + 0.268966i
$$509$$ −34.6410 −1.53544 −0.767718 0.640788i $$-0.778608\pi$$
−0.767718 + 0.640788i $$0.778608\pi$$
$$510$$ 0 0
$$511$$ −21.0000 24.2487i −0.928985 1.07270i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 18.0000 10.3923i 0.793946 0.458385i
$$515$$ 18.0000i 0.793175i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 10.3923 2.00000i 0.456612 0.0878750i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.73205 + 3.00000i 0.0758825 + 0.131432i 0.901470 0.432842i $$-0.142489\pi$$
−0.825587 + 0.564275i $$0.809156\pi$$
$$522$$ 0 0
$$523$$ 18.0000 + 10.3923i 0.787085 + 0.454424i 0.838935 0.544231i $$-0.183179\pi$$
−0.0518503 + 0.998655i $$0.516512\pi$$
$$524$$ −5.19615 + 9.00000i −0.226995 + 0.393167i
$$525$$ 0 0
$$526$$ −9.00000 15.5885i −0.392419 0.679689i
$$527$$ 12.0000i 0.522728i
$$528$$ 0 0
$$529$$ −13.0000 −0.565217
$$530$$ −2.59808 + 4.50000i −0.112853 + 0.195468i
$$531$$ 0 0
$$532$$ 12.0000 + 13.8564i 0.520266 + 0.600751i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −4.50000 2.59808i −0.194552 0.112325i
$$536$$ −12.1244 7.00000i −0.523692 0.302354i
$$537$$ 0 0
$$538$$ 1.50000 + 0.866025i 0.0646696 + 0.0373370i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 17.0000 29.4449i 0.730887 1.26593i −0.225617 0.974216i $$-0.572440\pi$$
0.956504 0.291718i $$-0.0942267\pi$$
$$542$$ −12.1244 −0.520786
$$543$$ 0 0
$$544$$ 3.46410i 0.148522i
$$545$$ 13.8564 + 24.0000i 0.593543 + 1.02805i
$$546$$ 0 0
$$547$$ −4.00000 + 6.92820i −0.171028 + 0.296229i −0.938779 0.344519i $$-0.888042\pi$$
0.767752 + 0.640747i $$0.221375\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −31.1769 54.0000i −1.32818 2.30048i
$$552$$ 0 0
$$553$$ 22.0000 19.0526i 0.935535 0.810197i
$$554$$ −6.92820 + 4.00000i −0.294351 + 0.169944i
$$555$$ 0 0
$$556$$ 10.3923i 0.440732i
$$557$$ 15.5885 9.00000i 0.660504 0.381342i −0.131965 0.991254i $$-0.542129\pi$$
0.792469 + 0.609912i $$0.208795\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −3.46410 + 3.00000i −0.146385 + 0.126773i
$$561$$ 0 0
$$562$$ −18.0000 −0.759284
$$563$$ 2.59808 4.50000i 0.109496 0.189652i −0.806070 0.591820i $$-0.798410\pi$$
0.915566 + 0.402167i $$0.131743\pi$$
$$564$$ 0 0
$$565$$ −27.0000 + 15.5885i −1.13590 + 0.655811i
$$566$$ 6.92820 0.291214
$$567$$ 0 0
$$568$$ 6.00000 0.251754
$$569$$ −36.3731 + 21.0000i −1.52484 + 0.880366i −0.525271 + 0.850935i $$0.676036\pi$$
−0.999567 + 0.0294311i $$0.990630\pi$$
$$570$$ 0 0
$$571$$ 20.0000 34.6410i 0.836974 1.44968i −0.0554391 0.998462i $$-0.517656\pi$$
0.892413 0.451219i $$-0.149011\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 3.00000 8.66025i 0.125218 0.361472i
$$575$$ 12.0000i 0.500435i
$$576$$ 0 0
$$577$$ −13.5000 + 7.79423i −0.562012 + 0.324478i −0.753953 0.656929i $$-0.771855\pi$$
0.191940 + 0.981407i $$0.438522\pi$$
$$578$$ 5.00000i 0.207973i
$$579$$ 0 0
$$580$$ 13.5000 7.79423i 0.560557 0.323638i
$$581$$ −43.3013 15.0000i −1.79644 0.622305i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −6.06218 10.5000i −0.250855 0.434493i
$$585$$ 0 0
$$586$$ −25.5000 14.7224i −1.05340 0.608178i
$$587$$ −18.1865 + 31.5000i −0.750639 + 1.30014i 0.196875 + 0.980429i $$0.436921\pi$$
−0.947514 + 0.319716i $$0.896413\pi$$
$$588$$ 0 0
$$589$$ −12.0000 20.7846i −0.494451 0.856415i
$$590$$ 21.0000i 0.864556i
$$591$$ 0 0
$$592$$ 4.00000 0.164399
$$593$$ 12.1244 21.0000i 0.497888 0.862367i −0.502109 0.864804i $$-0.667443\pi$$
0.999997 + 0.00243746i $$0.000775869\pi$$
$$594$$ 0 0
$$595$$ −12.0000 + 10.3923i −0.491952 + 0.426043i
$$596$$ −12.9904 7.50000i −0.532107 0.307212i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 20.7846 + 12.0000i 0.849236 + 0.490307i 0.860393 0.509631i $$-0.170218\pi$$
−0.0111569 + 0.999938i $$0.503551\pi$$
$$600$$ 0 0
$$601$$ 1.50000 + 0.866025i 0.0611863 + 0.0353259i 0.530281 0.847822i $$-0.322086\pi$$
−0.469095 + 0.883148i $$0.655420\pi$$
$$602$$ −20.7846 + 4.00000i −0.847117 + 0.163028i
$$603$$ 0 0
$$604$$ −4.00000 + 6.92820i −0.162758 + 0.281905i
$$605$$ −19.0526 −0.774597
$$606$$ 0 0
$$607$$ 32.9090i 1.33573i 0.744281 + 0.667867i $$0.232792\pi$$
−0.744281 + 0.667867i $$0.767208\pi$$
$$608$$ 3.46410 + 6.00000i 0.140488 + 0.243332i
$$609$$ 0 0
$$610$$ −3.00000 + 5.19615i −0.121466 + 0.210386i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −4.00000 6.92820i −0.161558 0.279827i 0.773869 0.633345i $$-0.218319\pi$$
−0.935428 + 0.353518i $$0.884985\pi$$
$$614$$ 3.46410 + 6.00000i 0.139800 + 0.242140i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 5.19615 3.00000i 0.209189 0.120775i −0.391745 0.920074i $$-0.628129\pi$$
0.600935 + 0.799298i $$0.294795\pi$$
$$618$$ 0 0
$$619$$ 20.7846i 0.835404i 0.908584 + 0.417702i $$0.137164\pi$$
−0.908584 + 0.417702i $$0.862836\pi$$
$$620$$ 5.19615 3.00000i 0.208683 0.120483i
$$621$$ 0 0
$$622$$ 13.8564i 0.555591i
$$623$$ −25.9808 9.00000i −1.04090 0.360577i
$$624$$ 0 0
$$625$$ −11.0000 −0.440000
$$626$$ −11.2583 + 19.5000i −0.449973 + 0.779377i
$$627$$ 0 0
$$628$$ −9.00000 + 5.19615i −0.359139 + 0.207349i
$$629$$ 13.8564 0.552491
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ 9.52628 5.50000i 0.378935 0.218778i
$$633$$ 0 0
$$634$$ 3.00000 5.19615i 0.119145 0.206366i
$$635$$ 12.1244 0.481140
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1.50000 + 0.866025i −0.0592927 + 0.0342327i
$$641$$ 12.0000i 0.473972i −0.971513 0.236986i $$-0.923841\pi$$
0.971513 0.236986i $$-0.0761595\pi$$
$$642$$ 0 0
$$643$$ 24.0000 13.8564i 0.946468 0.546443i 0.0544858 0.998515i $$-0.482648\pi$$
0.891982 + 0.452071i $$0.149315\pi$$
$$644$$ −5.19615 + 15.0000i −0.204757 + 0.591083i
$$645$$ 0 0
$$646$$ 12.0000 + 20.7846i 0.472134 + 0.817760i
$$647$$ −5.19615 9.00000i −0.204282 0.353827i 0.745622 0.666369i $$-0.232153\pi$$
−0.949904 + 0.312543i $$0.898819\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 1.00000 + 1.73205i 0.0391630 + 0.0678323i
$$653$$ 15.0000i 0.586995i 0.955960 + 0.293498i $$0.0948193\pi$$
−0.955960 + 0.293498i $$0.905181\pi$$
$$654$$ 0 0
$$655$$ 18.0000 0.703318
$$656$$ 1.73205 3.00000i 0.0676252 0.117130i
$$657$$ 0 0
$$658$$ −3.00000 + 8.66025i −0.116952 + 0.337612i
$$659$$ −23.3827 13.5000i −0.910860 0.525885i −0.0301523 0.999545i $$-0.509599\pi$$
−0.880708 + 0.473660i $$0.842933\pi$$
$$660$$ 0 0
$$661$$ 12.0000 + 6.92820i 0.466746 + 0.269476i 0.714877 0.699251i $$-0.246483\pi$$
−0.248131 + 0.968727i $$0.579816\pi$$
$$662$$ 8.66025 + 5.00000i 0.336590 + 0.194331i
$$663$$ 0 0
$$664$$ −15.0000 8.66025i −0.582113 0.336083i
$$665$$ 10.3923 30.0000i 0.402996 1.16335i
$$666$$ 0 0
$$667$$ 27.0000 46.7654i 1.04544 1.81076i
$$668$$ 17.3205 0.670151
$$669$$ 0 0
$$670$$ 24.2487i 0.936809i
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 2.50000 4.33013i 0.0963679 0.166914i −0.813811 0.581130i $$-0.802611\pi$$
0.910179 + 0.414216i $$0.135944\pi$$
$$674$$ −19.9186 11.5000i −0.767235 0.442963i
$$675$$ 0 0
$$676$$ 6.50000 + 11.2583i 0.250000 + 0.433013i
$$677$$ 12.9904 + 22.5000i 0.499261 + 0.864745i 1.00000 0.000853228i $$-0.000271591\pi$$
−0.500739 + 0.865598i $$0.666938\pi$$
$$678$$ 0 0
$$679$$ −6.00000 + 17.3205i −0.230259 + 0.664700i
$$680$$ −5.19615 + 3.00000i −0.199263 + 0.115045i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 7.79423 4.50000i 0.298238 0.172188i −0.343413 0.939184i $$-0.611583\pi$$
0.641651 + 0.766997i $$0.278250\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 16.4545 + 8.50000i 0.628235 + 0.324532i
$$687$$ 0 0
$$688$$ −8.00000 −0.304997
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 24.0000 13.8564i 0.913003 0.527123i 0.0316069 0.999500i $$-0.489938\pi$$
0.881396 + 0.472378i $$0.156604\pi$$
$$692$$ −5.19615 −0.197528
$$693$$ 0 0
$$694$$ 33.0000 1.25266
$$695$$ 15.5885 9.00000i 0.591304 0.341389i
$$696$$ 0 0
$$697$$ 6.00000 10.3923i 0.227266 0.393637i
$$698$$ −3.46410 −0.131118
$$699$$ 0 0
$$700$$ −5.00000 1.73205i −0.188982 0.0654654i
$$701$$ 27.0000i 1.01978i 0.860241 + 0.509888i $$0.170313\pi$$
−0.860241 + 0.509888i $$0.829687\pi$$
$$702$$ 0 0
$$703$$ −24.0000 + 13.8564i −0.905177 + 0.522604i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −3.00000 + 1.73205i −0.112906 + 0.0651866i
$$707$$ −2.59808 13.5000i −0.0977107 0.507720i
$$708$$ 0 0
$$709$$ −14.0000 24.2487i −0.525781 0.910679i −0.999549 0.0300298i $$-0.990440\pi$$
0.473768 0.880650i $$-0.342894\pi$$
$$710$$ −5.19615 9.00000i −0.195008 0.337764i
$$711$$ 0 0
$$712$$ −9.00000 5.19615i −0.337289 0.194734i
$$713$$ 10.3923 18.0000i 0.389195 0.674105i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 15.0000i 0.560576i
$$717$$ 0 0
$$718$$ 24.0000 0.895672
$$719$$ −24.2487 + 42.0000i −0.904324 + 1.56634i −0.0825027 + 0.996591i $$0.526291\pi$$
−0.821822 + 0.569745i $$0.807042\pi$$
$$720$$ 0 0
$$721$$ 27.0000 5.19615i 1.00553 0.193515i
$$722$$ −25.1147 14.5000i −0.934674 0.539634i
$$723$$ 0 0
$$724$$ 15.0000 + 8.66025i 0.557471 + 0.321856i
$$725$$ 15.5885 + 9.00000i 0.578941 + 0.334252i
$$726$$ 0 0
$$727$$ −10.5000 6.06218i −0.389423 0.224834i 0.292487 0.956270i $$-0.405517\pi$$
−0.681910 + 0.731436i $$0.738851\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −10.5000 + 18.1865i −0.388622 + 0.673114i
$$731$$ −27.7128 −1.02500
$$732$$ 0 0
$$733$$ 6.92820i 0.255899i 0.991781 + 0.127950i $$0.0408395\pi$$
−0.991781 + 0.127950i $$0.959160\pi$$
$$734$$ 4.33013 + 7.50000i 0.159828 + 0.276830i
$$735$$ 0 0
$$736$$ −3.00000 + 5.19615i −0.110581 + 0.191533i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 5.00000 + 8.66025i 0.183928 + 0.318573i 0.943215 0.332184i $$-0.107785\pi$$
−0.759287 + 0.650756i $$0.774452\pi$$
$$740$$ −3.46410 6.00000i −0.127343 0.220564i
$$741$$ 0 0
$$742$$ 7.50000 + 2.59808i 0.275334 + 0.0953784i
$$743$$ 31.1769 18.0000i 1.14377 0.660356i 0.196409 0.980522i $$-0.437072\pi$$
0.947361 + 0.320166i $$0.103739\pi$$
$$744$$ 0 0
$$745$$ 25.9808i 0.951861i
$$746$$ −12.1244 + 7.00000i −0.443904 + 0.256288i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −2.59808 + 7.50000i −0.0949316 + 0.274044i
$$750$$ 0 0
$$751$$ 7.00000 0.255434 0.127717 0.991811i $$-0.459235\pi$$
0.127717 + 0.991811i $$0.459235\pi$$
$$752$$ −1.73205 + 3.00000i −0.0631614 + 0.109399i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 13.8564 0.504286
$$756$$ 0 0
$$757$$ −38.0000 −1.38113 −0.690567 0.723269i $$-0.742639\pi$$
−0.690567 + 0.723269i $$0.742639\pi$$
$$758$$ 12.1244 7.00000i 0.440376 0.254251i
$$759$$ 0 0
$$760$$ 6.00000 10.3923i 0.217643 0.376969i
$$761$$ −34.6410 −1.25574 −0.627868 0.778320i $$-0.716072\pi$$
−0.627868 + 0.778320i $$0.716072\pi$$
$$762$$ 0 0
$$763$$ 32.0000 27.7128i 1.15848 1.00327i
$$764$$ 6.00000i 0.217072i
$$765$$ 0 0
$$766$$ −15.0000 + 8.66025i −0.541972 + 0.312908i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −42.0000 + 24.2487i −1.51456 + 0.874431i −0.514704 + 0.857368i $$0.672098\pi$$
−0.999854 + 0.0170631i $$0.994568\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 5.00000 + 8.66025i 0.179954 + 0.311689i
$$773$$ −6.92820 12.0000i −0.249190 0.431610i 0.714111 0.700032i $$-0.246831\pi$$
−0.963301 + 0.268422i $$0.913498\pi$$
$$774$$ 0 0
$$775$$ 6.00000 + 3.46410i 0.215526 + 0.124434i
$$776$$ −3.46410 + 6.00000i −0.124354 + 0.215387i
$$777$$ 0 0
$$778$$ 10.5000 + 18.1865i 0.376443 + 0.652019i
$$779$$ 24.0000i 0.859889i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −10.3923 + 18.0000i −0.371628 + 0.643679i
$$783$$ 0 0
$$784$$ 5.50000 + 4.33013i 0.196429 + 0.154647i
$$785$$ 15.5885 + 9.00000i 0.556376 + 0.321224i
$$786$$ 0 0
$$787$$ −3.00000 1.73205i −0.106938 0.0617409i 0.445577 0.895244i $$-0.352999\pi$$
−0.552515 + 0.833503i $$0.686332\pi$$
$$788$$ 2.59808 + 1.50000i 0.0925526 + 0.0534353i
$$789$$ 0 0
$$790$$ −16.5000 9.52628i −0.587044 0.338930i
$$791$$ 31.1769 + 36.0000i 1.10852 + 1.28001i
$$792$$ 0 0
$$793$$