# Properties

 Label 90.2.c.a.19.1 Level $90$ Weight $2$ Character 90.19 Analytic conductor $0.719$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$90 = 2 \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 90.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.718653618192$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 30) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 19.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 90.19 Dual form 90.2.c.a.19.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -2.00000i q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -2.00000i q^{7} +1.00000i q^{8} +(-1.00000 - 2.00000i) q^{10} -2.00000 q^{11} +6.00000i q^{13} -2.00000 q^{14} +1.00000 q^{16} +2.00000i q^{17} +(-2.00000 + 1.00000i) q^{20} +2.00000i q^{22} +4.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +6.00000 q^{26} +2.00000i q^{28} -8.00000 q^{31} -1.00000i q^{32} +2.00000 q^{34} +(-2.00000 - 4.00000i) q^{35} -2.00000i q^{37} +(1.00000 + 2.00000i) q^{40} -2.00000 q^{41} -4.00000i q^{43} +2.00000 q^{44} +4.00000 q^{46} -8.00000i q^{47} +3.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -6.00000i q^{52} -6.00000i q^{53} +(-4.00000 + 2.00000i) q^{55} +2.00000 q^{56} +10.0000 q^{59} +2.00000 q^{61} +8.00000i q^{62} -1.00000 q^{64} +(6.00000 + 12.0000i) q^{65} +8.00000i q^{67} -2.00000i q^{68} +(-4.00000 + 2.00000i) q^{70} -12.0000 q^{71} -4.00000i q^{73} -2.00000 q^{74} +4.00000i q^{77} +(2.00000 - 1.00000i) q^{80} +2.00000i q^{82} +4.00000i q^{83} +(2.00000 + 4.00000i) q^{85} -4.00000 q^{86} -2.00000i q^{88} -10.0000 q^{89} +12.0000 q^{91} -4.00000i q^{92} -8.00000 q^{94} +8.00000i q^{97} -3.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{4} + 4q^{5} + O(q^{10})$$ $$2q - 2q^{4} + 4q^{5} - 2q^{10} - 4q^{11} - 4q^{14} + 2q^{16} - 4q^{20} + 6q^{25} + 12q^{26} - 16q^{31} + 4q^{34} - 4q^{35} + 2q^{40} - 4q^{41} + 4q^{44} + 8q^{46} + 6q^{49} - 8q^{50} - 8q^{55} + 4q^{56} + 20q^{59} + 4q^{61} - 2q^{64} + 12q^{65} - 8q^{70} - 24q^{71} - 4q^{74} + 4q^{80} + 4q^{85} - 8q^{86} - 20q^{89} + 24q^{91} - 16q^{94} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$$.

 $$n$$ $$11$$ $$37$$ $$\chi(n)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ 2.00000 1.00000i 0.894427 0.447214i
$$6$$ 0 0
$$7$$ 2.00000i 0.755929i −0.925820 0.377964i $$-0.876624\pi$$
0.925820 0.377964i $$-0.123376\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ −1.00000 2.00000i −0.316228 0.632456i
$$11$$ −2.00000 −0.603023 −0.301511 0.953463i $$-0.597491\pi$$
−0.301511 + 0.953463i $$0.597491\pi$$
$$12$$ 0 0
$$13$$ 6.00000i 1.66410i 0.554700 + 0.832050i $$0.312833\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ −2.00000 −0.534522
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 2.00000i 0.485071i 0.970143 + 0.242536i $$0.0779791\pi$$
−0.970143 + 0.242536i $$0.922021\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ −2.00000 + 1.00000i −0.447214 + 0.223607i
$$21$$ 0 0
$$22$$ 2.00000i 0.426401i
$$23$$ 4.00000i 0.834058i 0.908893 + 0.417029i $$0.136929\pi$$
−0.908893 + 0.417029i $$0.863071\pi$$
$$24$$ 0 0
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ 6.00000 1.17670
$$27$$ 0 0
$$28$$ 2.00000i 0.377964i
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −8.00000 −1.43684 −0.718421 0.695608i $$-0.755135\pi$$
−0.718421 + 0.695608i $$0.755135\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 2.00000 0.342997
$$35$$ −2.00000 4.00000i −0.338062 0.676123i
$$36$$ 0 0
$$37$$ 2.00000i 0.328798i −0.986394 0.164399i $$-0.947432\pi$$
0.986394 0.164399i $$-0.0525685\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 1.00000 + 2.00000i 0.158114 + 0.316228i
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ 4.00000i 0.609994i −0.952353 0.304997i $$-0.901344\pi$$
0.952353 0.304997i $$-0.0986555\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0 0
$$46$$ 4.00000 0.589768
$$47$$ 8.00000i 1.16692i −0.812142 0.583460i $$-0.801699\pi$$
0.812142 0.583460i $$-0.198301\pi$$
$$48$$ 0 0
$$49$$ 3.00000 0.428571
$$50$$ −4.00000 3.00000i −0.565685 0.424264i
$$51$$ 0 0
$$52$$ 6.00000i 0.832050i
$$53$$ 6.00000i 0.824163i −0.911147 0.412082i $$-0.864802\pi$$
0.911147 0.412082i $$-0.135198\pi$$
$$54$$ 0 0
$$55$$ −4.00000 + 2.00000i −0.539360 + 0.269680i
$$56$$ 2.00000 0.267261
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 8.00000i 1.01600i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 6.00000 + 12.0000i 0.744208 + 1.48842i
$$66$$ 0 0
$$67$$ 8.00000i 0.977356i 0.872464 + 0.488678i $$0.162521\pi$$
−0.872464 + 0.488678i $$0.837479\pi$$
$$68$$ 2.00000i 0.242536i
$$69$$ 0 0
$$70$$ −4.00000 + 2.00000i −0.478091 + 0.239046i
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 0 0
$$73$$ 4.00000i 0.468165i −0.972217 0.234082i $$-0.924791\pi$$
0.972217 0.234082i $$-0.0752085\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4.00000i 0.455842i
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 2.00000 1.00000i 0.223607 0.111803i
$$81$$ 0 0
$$82$$ 2.00000i 0.220863i
$$83$$ 4.00000i 0.439057i 0.975606 + 0.219529i $$0.0704519\pi$$
−0.975606 + 0.219529i $$0.929548\pi$$
$$84$$ 0 0
$$85$$ 2.00000 + 4.00000i 0.216930 + 0.433861i
$$86$$ −4.00000 −0.431331
$$87$$ 0 0
$$88$$ 2.00000i 0.213201i
$$89$$ −10.0000 −1.06000 −0.529999 0.847998i $$-0.677808\pi$$
−0.529999 + 0.847998i $$0.677808\pi$$
$$90$$ 0 0
$$91$$ 12.0000 1.25794
$$92$$ 4.00000i 0.417029i
$$93$$ 0 0
$$94$$ −8.00000 −0.825137
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 8.00000i 0.812277i 0.913812 + 0.406138i $$0.133125\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ 3.00000i 0.303046i
$$99$$ 0 0
$$100$$ −3.00000 + 4.00000i −0.300000 + 0.400000i
$$101$$ 8.00000 0.796030 0.398015 0.917379i $$-0.369699\pi$$
0.398015 + 0.917379i $$0.369699\pi$$
$$102$$ 0 0
$$103$$ 14.0000i 1.37946i −0.724066 0.689730i $$-0.757729\pi$$
0.724066 0.689730i $$-0.242271\pi$$
$$104$$ −6.00000 −0.588348
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 12.0000i 1.16008i 0.814587 + 0.580042i $$0.196964\pi$$
−0.814587 + 0.580042i $$0.803036\pi$$
$$108$$ 0 0
$$109$$ −10.0000 −0.957826 −0.478913 0.877862i $$-0.658969\pi$$
−0.478913 + 0.877862i $$0.658969\pi$$
$$110$$ 2.00000 + 4.00000i 0.190693 + 0.381385i
$$111$$ 0 0
$$112$$ 2.00000i 0.188982i
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 0 0
$$115$$ 4.00000 + 8.00000i 0.373002 + 0.746004i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 10.0000i 0.920575i
$$119$$ 4.00000 0.366679
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 2.00000i 0.181071i
$$123$$ 0 0
$$124$$ 8.00000 0.718421
$$125$$ 2.00000 11.0000i 0.178885 0.983870i
$$126$$ 0 0
$$127$$ 2.00000i 0.177471i −0.996055 0.0887357i $$-0.971717\pi$$
0.996055 0.0887357i $$-0.0282826\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ 12.0000 6.00000i 1.05247 0.526235i
$$131$$ 18.0000 1.57267 0.786334 0.617802i $$-0.211977\pi$$
0.786334 + 0.617802i $$0.211977\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 8.00000 0.691095
$$135$$ 0 0
$$136$$ −2.00000 −0.171499
$$137$$ 18.0000i 1.53784i −0.639343 0.768922i $$-0.720793\pi$$
0.639343 0.768922i $$-0.279207\pi$$
$$138$$ 0 0
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 2.00000 + 4.00000i 0.169031 + 0.338062i
$$141$$ 0 0
$$142$$ 12.0000i 1.00702i
$$143$$ 12.0000i 1.00349i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −4.00000 −0.331042
$$147$$ 0 0
$$148$$ 2.00000i 0.164399i
$$149$$ −20.0000 −1.63846 −0.819232 0.573462i $$-0.805600\pi$$
−0.819232 + 0.573462i $$0.805600\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 4.00000 0.322329
$$155$$ −16.0000 + 8.00000i −1.28515 + 0.642575i
$$156$$ 0 0
$$157$$ 22.0000i 1.75579i −0.478852 0.877896i $$-0.658947\pi$$
0.478852 0.877896i $$-0.341053\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −1.00000 2.00000i −0.0790569 0.158114i
$$161$$ 8.00000 0.630488
$$162$$ 0 0
$$163$$ 16.0000i 1.25322i 0.779334 + 0.626608i $$0.215557\pi$$
−0.779334 + 0.626608i $$0.784443\pi$$
$$164$$ 2.00000 0.156174
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ 12.0000i 0.928588i 0.885681 + 0.464294i $$0.153692\pi$$
−0.885681 + 0.464294i $$0.846308\pi$$
$$168$$ 0 0
$$169$$ −23.0000 −1.76923
$$170$$ 4.00000 2.00000i 0.306786 0.153393i
$$171$$ 0 0
$$172$$ 4.00000i 0.304997i
$$173$$ 14.0000i 1.06440i 0.846619 + 0.532200i $$0.178635\pi$$
−0.846619 + 0.532200i $$0.821365\pi$$
$$174$$ 0 0
$$175$$ −8.00000 6.00000i −0.604743 0.453557i
$$176$$ −2.00000 −0.150756
$$177$$ 0 0
$$178$$ 10.0000i 0.749532i
$$179$$ 10.0000 0.747435 0.373718 0.927543i $$-0.378083\pi$$
0.373718 + 0.927543i $$0.378083\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 12.0000i 0.889499i
$$183$$ 0 0
$$184$$ −4.00000 −0.294884
$$185$$ −2.00000 4.00000i −0.147043 0.294086i
$$186$$ 0 0
$$187$$ 4.00000i 0.292509i
$$188$$ 8.00000i 0.583460i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −12.0000 −0.868290 −0.434145 0.900843i $$-0.642949\pi$$
−0.434145 + 0.900843i $$0.642949\pi$$
$$192$$ 0 0
$$193$$ 4.00000i 0.287926i −0.989583 0.143963i $$-0.954015\pi$$
0.989583 0.143963i $$-0.0459847\pi$$
$$194$$ 8.00000 0.574367
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ 22.0000i 1.56744i 0.621117 + 0.783718i $$0.286679\pi$$
−0.621117 + 0.783718i $$0.713321\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 4.00000 + 3.00000i 0.282843 + 0.212132i
$$201$$ 0 0
$$202$$ 8.00000i 0.562878i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −4.00000 + 2.00000i −0.279372 + 0.139686i
$$206$$ −14.0000 −0.975426
$$207$$ 0 0
$$208$$ 6.00000i 0.416025i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 6.00000i 0.412082i
$$213$$ 0 0
$$214$$ 12.0000 0.820303
$$215$$ −4.00000 8.00000i −0.272798 0.545595i
$$216$$ 0 0
$$217$$ 16.0000i 1.08615i
$$218$$ 10.0000i 0.677285i
$$219$$ 0 0
$$220$$ 4.00000 2.00000i 0.269680 0.134840i
$$221$$ −12.0000 −0.807207
$$222$$ 0 0
$$223$$ 26.0000i 1.74109i 0.492090 + 0.870544i $$0.336233\pi$$
−0.492090 + 0.870544i $$0.663767\pi$$
$$224$$ −2.00000 −0.133631
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ 28.0000i 1.85843i −0.369546 0.929213i $$-0.620487\pi$$
0.369546 0.929213i $$-0.379513\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ 8.00000 4.00000i 0.527504 0.263752i
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 14.0000i 0.917170i 0.888650 + 0.458585i $$0.151644\pi$$
−0.888650 + 0.458585i $$0.848356\pi$$
$$234$$ 0 0
$$235$$ −8.00000 16.0000i −0.521862 1.04372i
$$236$$ −10.0000 −0.650945
$$237$$ 0 0
$$238$$ 4.00000i 0.259281i
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 0 0
$$241$$ 22.0000 1.41714 0.708572 0.705638i $$-0.249340\pi$$
0.708572 + 0.705638i $$0.249340\pi$$
$$242$$ 7.00000i 0.449977i
$$243$$ 0 0
$$244$$ −2.00000 −0.128037
$$245$$ 6.00000 3.00000i 0.383326 0.191663i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 8.00000i 0.508001i
$$249$$ 0 0
$$250$$ −11.0000 2.00000i −0.695701 0.126491i
$$251$$ 18.0000 1.13615 0.568075 0.822977i $$-0.307688\pi$$
0.568075 + 0.822977i $$0.307688\pi$$
$$252$$ 0 0
$$253$$ 8.00000i 0.502956i
$$254$$ −2.00000 −0.125491
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000i 1.12281i −0.827541 0.561405i $$-0.810261\pi$$
0.827541 0.561405i $$-0.189739\pi$$
$$258$$ 0 0
$$259$$ −4.00000 −0.248548
$$260$$ −6.00000 12.0000i −0.372104 0.744208i
$$261$$ 0 0
$$262$$ 18.0000i 1.11204i
$$263$$ 4.00000i 0.246651i 0.992366 + 0.123325i $$0.0393559\pi$$
−0.992366 + 0.123325i $$0.960644\pi$$
$$264$$ 0 0
$$265$$ −6.00000 12.0000i −0.368577 0.737154i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 8.00000i 0.488678i
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 0 0
$$274$$ −18.0000 −1.08742
$$275$$ −6.00000 + 8.00000i −0.361814 + 0.482418i
$$276$$ 0 0
$$277$$ 2.00000i 0.120168i −0.998193 0.0600842i $$-0.980863\pi$$
0.998193 0.0600842i $$-0.0191369\pi$$
$$278$$ 20.0000i 1.19952i
$$279$$ 0 0
$$280$$ 4.00000 2.00000i 0.239046 0.119523i
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 0 0
$$283$$ 16.0000i 0.951101i 0.879688 + 0.475551i $$0.157751\pi$$
−0.879688 + 0.475551i $$0.842249\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 0 0
$$286$$ −12.0000 −0.709575
$$287$$ 4.00000i 0.236113i
$$288$$ 0 0
$$289$$ 13.0000 0.764706
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 4.00000i 0.234082i
$$293$$ 6.00000i 0.350524i −0.984522 0.175262i $$-0.943923\pi$$
0.984522 0.175262i $$-0.0560772\pi$$
$$294$$ 0 0
$$295$$ 20.0000 10.0000i 1.16445 0.582223i
$$296$$ 2.00000 0.116248
$$297$$ 0 0
$$298$$ 20.0000i 1.15857i
$$299$$ −24.0000 −1.38796
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 8.00000i 0.460348i
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 4.00000 2.00000i 0.229039 0.114520i
$$306$$ 0 0
$$307$$ 12.0000i 0.684876i −0.939540 0.342438i $$-0.888747\pi$$
0.939540 0.342438i $$-0.111253\pi$$
$$308$$ 4.00000i 0.227921i
$$309$$ 0 0
$$310$$ 8.00000 + 16.0000i 0.454369 + 0.908739i
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ 4.00000i 0.226093i −0.993590 0.113047i $$-0.963939\pi$$
0.993590 0.113047i $$-0.0360610\pi$$
$$314$$ −22.0000 −1.24153
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2.00000i 0.112331i 0.998421 + 0.0561656i $$0.0178875\pi$$
−0.998421 + 0.0561656i $$0.982113\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −2.00000 + 1.00000i −0.111803 + 0.0559017i
$$321$$ 0 0
$$322$$ 8.00000i 0.445823i
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 24.0000 + 18.0000i 1.33128 + 0.998460i
$$326$$ 16.0000 0.886158
$$327$$ 0 0
$$328$$ 2.00000i 0.110432i
$$329$$ −16.0000 −0.882109
$$330$$ 0 0
$$331$$ −8.00000 −0.439720 −0.219860 0.975531i $$-0.570560\pi$$
−0.219860 + 0.975531i $$0.570560\pi$$
$$332$$ 4.00000i 0.219529i
$$333$$ 0 0
$$334$$ 12.0000 0.656611
$$335$$ 8.00000 + 16.0000i 0.437087 + 0.874173i
$$336$$ 0 0
$$337$$ 28.0000i 1.52526i 0.646837 + 0.762629i $$0.276092\pi$$
−0.646837 + 0.762629i $$0.723908\pi$$
$$338$$ 23.0000i 1.25104i
$$339$$ 0 0
$$340$$ −2.00000 4.00000i −0.108465 0.216930i
$$341$$ 16.0000 0.866449
$$342$$ 0 0
$$343$$ 20.0000i 1.07990i
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ 14.0000 0.752645
$$347$$ 12.0000i 0.644194i 0.946707 + 0.322097i $$0.104388\pi$$
−0.946707 + 0.322097i $$0.895612\pi$$
$$348$$ 0 0
$$349$$ −10.0000 −0.535288 −0.267644 0.963518i $$-0.586245\pi$$
−0.267644 + 0.963518i $$0.586245\pi$$
$$350$$ −6.00000 + 8.00000i −0.320713 + 0.427618i
$$351$$ 0 0
$$352$$ 2.00000i 0.106600i
$$353$$ 14.0000i 0.745145i 0.928003 + 0.372572i $$0.121524\pi$$
−0.928003 + 0.372572i $$0.878476\pi$$
$$354$$ 0 0
$$355$$ −24.0000 + 12.0000i −1.27379 + 0.636894i
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ 10.0000i 0.528516i
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 2.00000i 0.105118i
$$363$$ 0 0
$$364$$ −12.0000 −0.628971
$$365$$ −4.00000 8.00000i −0.209370 0.418739i
$$366$$ 0 0
$$367$$ 2.00000i 0.104399i −0.998637 0.0521996i $$-0.983377\pi$$
0.998637 0.0521996i $$-0.0166232\pi$$
$$368$$ 4.00000i 0.208514i
$$369$$ 0 0
$$370$$ −4.00000 + 2.00000i −0.207950 + 0.103975i
$$371$$ −12.0000 −0.623009
$$372$$ 0 0
$$373$$ 6.00000i 0.310668i 0.987862 + 0.155334i $$0.0496454\pi$$
−0.987862 + 0.155334i $$0.950355\pi$$
$$374$$ −4.00000 −0.206835
$$375$$ 0 0
$$376$$ 8.00000 0.412568
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 12.0000i 0.613973i
$$383$$ 16.0000i 0.817562i −0.912633 0.408781i $$-0.865954\pi$$
0.912633 0.408781i $$-0.134046\pi$$
$$384$$ 0 0
$$385$$ 4.00000 + 8.00000i 0.203859 + 0.407718i
$$386$$ −4.00000 −0.203595
$$387$$ 0 0
$$388$$ 8.00000i 0.406138i
$$389$$ 20.0000 1.01404 0.507020 0.861934i $$-0.330747\pi$$
0.507020 + 0.861934i $$0.330747\pi$$
$$390$$ 0 0
$$391$$ −8.00000 −0.404577
$$392$$ 3.00000i 0.151523i
$$393$$ 0 0
$$394$$ 22.0000 1.10834
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 2.00000i 0.100377i −0.998740 0.0501886i $$-0.984018\pi$$
0.998740 0.0501886i $$-0.0159822\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 3.00000 4.00000i 0.150000 0.200000i
$$401$$ −22.0000 −1.09863 −0.549314 0.835616i $$-0.685111\pi$$
−0.549314 + 0.835616i $$0.685111\pi$$
$$402$$ 0 0
$$403$$ 48.0000i 2.39105i
$$404$$ −8.00000 −0.398015
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 4.00000i 0.198273i
$$408$$ 0 0
$$409$$ 10.0000 0.494468 0.247234 0.968956i $$-0.420478\pi$$
0.247234 + 0.968956i $$0.420478\pi$$
$$410$$ 2.00000 + 4.00000i 0.0987730 + 0.197546i
$$411$$ 0 0
$$412$$ 14.0000i 0.689730i
$$413$$ 20.0000i 0.984136i
$$414$$ 0 0
$$415$$ 4.00000 + 8.00000i 0.196352 + 0.392705i
$$416$$ 6.00000 0.294174
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −10.0000 −0.488532 −0.244266 0.969708i $$-0.578547\pi$$
−0.244266 + 0.969708i $$0.578547\pi$$
$$420$$ 0 0
$$421$$ 22.0000 1.07221 0.536107 0.844150i $$-0.319894\pi$$
0.536107 + 0.844150i $$0.319894\pi$$
$$422$$ 12.0000i 0.584151i
$$423$$ 0 0
$$424$$ 6.00000 0.291386
$$425$$ 8.00000 + 6.00000i 0.388057 + 0.291043i
$$426$$ 0 0
$$427$$ 4.00000i 0.193574i
$$428$$ 12.0000i 0.580042i
$$429$$ 0 0
$$430$$ −8.00000 + 4.00000i −0.385794 + 0.192897i
$$431$$ −32.0000 −1.54139 −0.770693 0.637207i $$-0.780090\pi$$
−0.770693 + 0.637207i $$0.780090\pi$$
$$432$$ 0 0
$$433$$ 4.00000i 0.192228i −0.995370 0.0961139i $$-0.969359\pi$$
0.995370 0.0961139i $$-0.0306413\pi$$
$$434$$ 16.0000 0.768025
$$435$$ 0 0
$$436$$ 10.0000 0.478913
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ −2.00000 4.00000i −0.0953463 0.190693i
$$441$$ 0 0
$$442$$ 12.0000i 0.570782i
$$443$$ 36.0000i 1.71041i −0.518289 0.855206i $$-0.673431\pi$$
0.518289 0.855206i $$-0.326569\pi$$
$$444$$ 0 0
$$445$$ −20.0000 + 10.0000i −0.948091 + 0.474045i
$$446$$ 26.0000 1.23114
$$447$$ 0 0
$$448$$ 2.00000i 0.0944911i
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 4.00000 0.188353
$$452$$ 6.00000i 0.282216i
$$453$$ 0 0
$$454$$ −28.0000 −1.31411
$$455$$ 24.0000 12.0000i 1.12514 0.562569i
$$456$$ 0 0
$$457$$ 32.0000i 1.49690i −0.663193 0.748448i $$-0.730799\pi$$
0.663193 0.748448i $$-0.269201\pi$$
$$458$$ 10.0000i 0.467269i
$$459$$ 0 0
$$460$$ −4.00000 8.00000i −0.186501 0.373002i
$$461$$ −12.0000 −0.558896 −0.279448 0.960161i $$-0.590151\pi$$
−0.279448 + 0.960161i $$0.590151\pi$$
$$462$$ 0 0
$$463$$ 6.00000i 0.278844i 0.990233 + 0.139422i $$0.0445244\pi$$
−0.990233 + 0.139422i $$0.955476\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 14.0000 0.648537
$$467$$ 12.0000i 0.555294i 0.960683 + 0.277647i $$0.0895545\pi$$
−0.960683 + 0.277647i $$0.910445\pi$$
$$468$$ 0 0
$$469$$ 16.0000 0.738811
$$470$$ −16.0000 + 8.00000i −0.738025 + 0.369012i
$$471$$ 0 0
$$472$$ 10.0000i 0.460287i
$$473$$ 8.00000i 0.367840i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −4.00000 −0.183340
$$477$$ 0 0
$$478$$ 20.0000i 0.914779i
$$479$$ 20.0000 0.913823 0.456912 0.889512i $$-0.348956\pi$$
0.456912 + 0.889512i $$0.348956\pi$$
$$480$$ 0 0
$$481$$ 12.0000 0.547153
$$482$$ 22.0000i 1.00207i
$$483$$ 0 0
$$484$$ 7.00000 0.318182
$$485$$ 8.00000 + 16.0000i 0.363261 + 0.726523i
$$486$$ 0 0
$$487$$ 18.0000i 0.815658i 0.913058 + 0.407829i $$0.133714\pi$$
−0.913058 + 0.407829i $$0.866286\pi$$
$$488$$ 2.00000i 0.0905357i
$$489$$ 0 0
$$490$$ −3.00000 6.00000i −0.135526 0.271052i
$$491$$ 18.0000 0.812329 0.406164 0.913800i $$-0.366866\pi$$
0.406164 + 0.913800i $$0.366866\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −8.00000 −0.359211
$$497$$ 24.0000i 1.07655i
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ −2.00000 + 11.0000i −0.0894427 + 0.491935i
$$501$$ 0 0
$$502$$ 18.0000i 0.803379i
$$503$$ 24.0000i 1.07011i 0.844818 + 0.535054i $$0.179709\pi$$
−0.844818 + 0.535054i $$0.820291\pi$$
$$504$$ 0 0
$$505$$ 16.0000 8.00000i 0.711991 0.355995i
$$506$$ −8.00000 −0.355643
$$507$$ 0 0
$$508$$ 2.00000i 0.0887357i
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ −8.00000 −0.353899
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ −18.0000 −0.793946
$$515$$ −14.0000 28.0000i −0.616914 1.23383i
$$516$$ 0 0
$$517$$ 16.0000i 0.703679i
$$518$$ 4.00000i 0.175750i
$$519$$ 0 0
$$520$$ −12.0000 + 6.00000i −0.526235 + 0.263117i
$$521$$ −22.0000 −0.963837 −0.481919 0.876216i $$-0.660060\pi$$
−0.481919 + 0.876216i $$0.660060\pi$$
$$522$$ 0 0
$$523$$ 16.0000i 0.699631i 0.936819 + 0.349816i $$0.113756\pi$$
−0.936819 + 0.349816i $$0.886244\pi$$
$$524$$ −18.0000 −0.786334
$$525$$ 0 0
$$526$$ 4.00000 0.174408
$$527$$ 16.0000i 0.696971i
$$528$$ 0 0
$$529$$ 7.00000 0.304348
$$530$$ −12.0000 + 6.00000i −0.521247 + 0.260623i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 12.0000i 0.519778i
$$534$$ 0 0
$$535$$ 12.0000 + 24.0000i 0.518805 + 1.03761i
$$536$$ −8.00000 −0.345547
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ −38.0000 −1.63375 −0.816874 0.576816i $$-0.804295\pi$$
−0.816874 + 0.576816i $$0.804295\pi$$
$$542$$ 8.00000i 0.343629i
$$543$$ 0 0
$$544$$ 2.00000 0.0857493
$$545$$ −20.0000 + 10.0000i −0.856706 + 0.428353i
$$546$$ 0 0
$$547$$ 28.0000i 1.19719i 0.801050 + 0.598597i $$0.204275\pi$$
−0.801050 + 0.598597i $$0.795725\pi$$
$$548$$ 18.0000i 0.768922i
$$549$$ 0 0
$$550$$ 8.00000 + 6.00000i 0.341121 + 0.255841i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −2.00000 −0.0849719
$$555$$ 0 0
$$556$$ −20.0000 −0.848189
$$557$$ 18.0000i 0.762684i −0.924434 0.381342i $$-0.875462\pi$$
0.924434 0.381342i $$-0.124538\pi$$
$$558$$ 0 0
$$559$$ 24.0000 1.01509
$$560$$ −2.00000 4.00000i −0.0845154 0.169031i
$$561$$ 0 0
$$562$$ 18.0000i 0.759284i
$$563$$ 44.0000i 1.85438i 0.374593 + 0.927189i $$0.377783\pi$$
−0.374593 + 0.927189i $$0.622217\pi$$
$$564$$ 0 0
$$565$$ −6.00000 12.0000i −0.252422 0.504844i
$$566$$ 16.0000 0.672530
$$567$$ 0 0
$$568$$ 12.0000i 0.503509i
$$569$$ −10.0000 −0.419222 −0.209611 0.977785i $$-0.567220\pi$$
−0.209611 + 0.977785i $$0.567220\pi$$
$$570$$ 0 0
$$571$$ −8.00000 −0.334790 −0.167395 0.985890i $$-0.553535\pi$$
−0.167395 + 0.985890i $$0.553535\pi$$
$$572$$ 12.0000i 0.501745i
$$573$$ 0 0
$$574$$ 4.00000 0.166957
$$575$$ 16.0000 + 12.0000i 0.667246 + 0.500435i
$$576$$ 0 0
$$577$$ 32.0000i 1.33218i −0.745873 0.666089i $$-0.767967\pi$$
0.745873 0.666089i $$-0.232033\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 8.00000 0.331896
$$582$$ 0 0
$$583$$ 12.0000i 0.496989i
$$584$$ 4.00000 0.165521
$$585$$ 0 0
$$586$$ −6.00000 −0.247858
$$587$$ 12.0000i 0.495293i 0.968850 + 0.247647i $$0.0796572\pi$$
−0.968850 + 0.247647i $$0.920343\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −10.0000 20.0000i −0.411693 0.823387i
$$591$$ 0 0
$$592$$ 2.00000i 0.0821995i
$$593$$ 6.00000i 0.246390i −0.992382 0.123195i $$-0.960686\pi$$
0.992382 0.123195i $$-0.0393141\pi$$
$$594$$ 0 0
$$595$$ 8.00000 4.00000i 0.327968 0.163984i
$$596$$ 20.0000 0.819232
$$597$$ 0 0
$$598$$ 24.0000i 0.981433i
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 2.00000 0.0815817 0.0407909 0.999168i $$-0.487012\pi$$
0.0407909 + 0.999168i $$0.487012\pi$$
$$602$$ 8.00000i 0.326056i
$$603$$ 0 0
$$604$$ 8.00000 0.325515
$$605$$ −14.0000 + 7.00000i −0.569181 + 0.284590i
$$606$$ 0 0
$$607$$ 22.0000i 0.892952i −0.894795 0.446476i $$-0.852679\pi$$
0.894795 0.446476i $$-0.147321\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −2.00000 4.00000i −0.0809776 0.161955i
$$611$$ 48.0000 1.94187
$$612$$ 0 0
$$613$$ 26.0000i 1.05013i 0.851062 + 0.525065i $$0.175959\pi$$
−0.851062 + 0.525065i $$0.824041\pi$$
$$614$$ −12.0000 −0.484281
$$615$$ 0 0
$$616$$ −4.00000 −0.161165
$$617$$ 2.00000i 0.0805170i 0.999189 + 0.0402585i $$0.0128181\pi$$
−0.999189 + 0.0402585i $$0.987182\pi$$
$$618$$ 0 0
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ 16.0000 8.00000i 0.642575 0.321288i
$$621$$ 0 0
$$622$$ 12.0000i 0.481156i
$$623$$ 20.0000i 0.801283i
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ −4.00000 −0.159872
$$627$$ 0 0
$$628$$ 22.0000i 0.877896i
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ 32.0000 1.27390 0.636950 0.770905i $$-0.280196\pi$$
0.636950 + 0.770905i $$0.280196\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 2.00000 0.0794301
$$635$$ −2.00000 4.00000i −0.0793676 0.158735i
$$636$$ 0 0
$$637$$ 18.0000i 0.713186i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 1.00000 + 2.00000i 0.0395285 + 0.0790569i
$$641$$ −2.00000 −0.0789953 −0.0394976 0.999220i $$-0.512576\pi$$
−0.0394976 + 0.999220i $$0.512576\pi$$
$$642$$ 0 0
$$643$$ 24.0000i 0.946468i −0.880937 0.473234i $$-0.843087\pi$$
0.880937 0.473234i $$-0.156913\pi$$
$$644$$ −8.00000 −0.315244
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 48.0000i 1.88707i −0.331266 0.943537i $$-0.607476\pi$$
0.331266 0.943537i $$-0.392524\pi$$
$$648$$ 0 0
$$649$$ −20.0000 −0.785069
$$650$$ 18.0000 24.0000i 0.706018 0.941357i
$$651$$ 0 0
$$652$$ 16.0000i 0.626608i
$$653$$ 26.0000i 1.01746i −0.860927 0.508729i $$-0.830115\pi$$
0.860927 0.508729i $$-0.169885\pi$$
$$654$$ 0 0
$$655$$ 36.0000 18.0000i 1.40664 0.703318i
$$656$$ −2.00000 −0.0780869
$$657$$ 0 0
$$658$$ 16.0000i 0.623745i
$$659$$ −50.0000 −1.94772 −0.973862 0.227142i $$-0.927062\pi$$
−0.973862 + 0.227142i $$0.927062\pi$$
$$660$$ 0 0
$$661$$ 2.00000 0.0777910 0.0388955 0.999243i $$-0.487616\pi$$
0.0388955 + 0.999243i $$0.487616\pi$$
$$662$$ 8.00000i 0.310929i
$$663$$ 0 0
$$664$$ −4.00000 −0.155230
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 12.0000i 0.464294i
$$669$$ 0 0
$$670$$ 16.0000 8.00000i 0.618134 0.309067i
$$671$$ −4.00000 −0.154418
$$672$$ 0 0
$$673$$ 36.0000i 1.38770i 0.720121 + 0.693849i $$0.244086\pi$$
−0.720121 + 0.693849i $$0.755914\pi$$
$$674$$ 28.0000 1.07852
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ 2.00000i 0.0768662i 0.999261 + 0.0384331i $$0.0122367\pi$$
−0.999261 + 0.0384331i $$0.987763\pi$$
$$678$$ 0 0
$$679$$ 16.0000 0.614024
$$680$$ −4.00000 + 2.00000i −0.153393 + 0.0766965i
$$681$$ 0 0
$$682$$ 16.0000i 0.612672i
$$683$$ 4.00000i 0.153056i 0.997067 + 0.0765279i $$0.0243834\pi$$
−0.997067 + 0.0765279i $$0.975617\pi$$
$$684$$ 0 0
$$685$$ −18.0000 36.0000i −0.687745 1.37549i
$$686$$ −20.0000 −0.763604
$$687$$ 0 0
$$688$$ 4.00000i 0.152499i
$$689$$ 36.0000 1.37149
$$690$$ 0 0
$$691$$ −8.00000 −0.304334 −0.152167 0.988355i $$-0.548625\pi$$
−0.152167 + 0.988355i $$0.548625\pi$$
$$692$$ 14.0000i 0.532200i
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ 40.0000 20.0000i 1.51729 0.758643i
$$696$$ 0 0
$$697$$ 4.00000i 0.151511i
$$698$$ 10.0000i 0.378506i
$$699$$ 0 0
$$700$$ 8.00000 + 6.00000i 0.302372 + 0.226779i
$$701$$ −32.0000 −1.20862 −0.604312 0.796748i $$-0.706552\pi$$
−0.604312 + 0.796748i $$0.706552\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 2.00000 0.0753778
$$705$$ 0 0
$$706$$ 14.0000 0.526897
$$707$$ 16.0000i 0.601742i
$$708$$ 0 0
$$709$$ −30.0000 −1.12667 −0.563337 0.826227i $$-0.690483\pi$$
−0.563337 + 0.826227i $$0.690483\pi$$
$$710$$ 12.0000 + 24.0000i 0.450352 + 0.900704i
$$711$$ 0 0
$$712$$ 10.0000i 0.374766i
$$713$$ 32.0000i 1.19841i
$$714$$ 0 0
$$715$$ −12.0000 24.0000i −0.448775 0.897549i
$$716$$ −10.0000 −0.373718
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −40.0000 −1.49175 −0.745874 0.666087i $$-0.767968\pi$$
−0.745874 + 0.666087i $$0.767968\pi$$
$$720$$ 0 0
$$721$$ −28.0000 −1.04277
$$722$$ 19.0000i 0.707107i
$$723$$ 0 0
$$724$$ −2.00000 −0.0743294
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 18.0000i 0.667583i 0.942647 + 0.333792i $$0.108328\pi$$
−0.942647 + 0.333792i $$0.891672\pi$$
$$728$$ 12.0000i 0.444750i
$$729$$ 0 0
$$730$$ −8.00000 + 4.00000i −0.296093 + 0.148047i
$$731$$ 8.00000 0.295891
$$732$$ 0 0
$$733$$ 14.0000i 0.517102i −0.965998 0.258551i $$-0.916755\pi$$
0.965998 0.258551i $$-0.0832450\pi$$
$$734$$ −2.00000 −0.0738213
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 16.0000i 0.589368i
$$738$$ 0 0
$$739$$ −40.0000 −1.47142 −0.735712 0.677295i $$-0.763152\pi$$
−0.735712 + 0.677295i $$0.763152\pi$$
$$740$$ 2.00000 + 4.00000i 0.0735215 + 0.147043i
$$741$$ 0 0
$$742$$ 12.0000i 0.440534i
$$743$$ 24.0000i 0.880475i 0.897881 + 0.440237i $$0.145106\pi$$
−0.897881 + 0.440237i $$0.854894\pi$$
$$744$$ 0 0
$$745$$ −40.0000 + 20.0000i −1.46549 + 0.732743i
$$746$$ 6.00000 0.219676
$$747$$ 0 0
$$748$$ 4.00000i 0.146254i
$$749$$ 24.0000 0.876941
$$750$$ 0 0
$$751$$ 32.0000 1.16770 0.583848 0.811863i $$-0.301546\pi$$
0.583848 + 0.811863i $$0.301546\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −16.0000 + 8.00000i −0.582300 + 0.291150i
$$756$$ 0 0
$$757$$ 2.00000i 0.0726912i −0.999339 0.0363456i $$-0.988428\pi$$
0.999339 0.0363456i $$-0.0115717\pi$$
$$758$$ 20.0000i 0.726433i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 18.0000 0.652499 0.326250 0.945284i $$-0.394215\pi$$
0.326250 + 0.945284i $$0.394215\pi$$
$$762$$ 0 0
$$763$$ 20.0000i 0.724049i
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ −16.0000 −0.578103
$$767$$ 60.0000i 2.16647i
$$768$$ 0 0
$$769$$ 30.0000 1.08183 0.540914 0.841078i $$-0.318079\pi$$
0.540914 + 0.841078i $$0.318079\pi$$
$$770$$ 8.00000 4.00000i 0.288300 0.144150i
$$771$$ 0 0
$$772$$ 4.00000i 0.143963i
$$773$$ 54.0000i 1.94225i 0.238581 + 0.971123i $$0.423318\pi$$
−0.238581 + 0.971123i $$0.576682\pi$$
$$774$$ 0 0
$$775$$ −24.0000 + 32.0000i −0.862105 + 1.14947i
$$776$$ −8.00000 −0.287183
$$777$$ 0 0
$$778$$ 20.0000i 0.717035i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 24.0000 0.858788
$$782$$ 8.00000i 0.286079i
$$783$$ 0 0
$$784$$ 3.00000 0.107143
$$785$$ −22.0000 44.0000i −0.785214 1.57043i
$$786$$ 0 0
$$787$$ 32.0000i 1.14068i −0.821410 0.570338i $$-0.806812\pi$$
0.821410 0.570338i $$-0.193188\pi$$
$$788$$ 22.0000i 0.783718i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −12.0000 −0.426671
$$792$$ 0 0
$$793$$ 12.0000i 0.426132i
$$794$$ −2.00000 −0.0709773
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 2.00000i 0.0708436i 0.999372 + 0.0354218i $$0.0112775\pi$$
−0.999372 + 0.0354218i $$0.988723\pi$$
$$798$$ 0 0
$$799$$ 16.0000 0.566039