# Properties

 Label 74.3.d.b.31.1 Level $74$ Weight $3$ Character 74.31 Analytic conductor $2.016$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$74 = 2 \cdot 37$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 74.d (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.01635395627$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 31.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 74.31 Dual form 74.3.d.b.43.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.00000i) q^{2} +4.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(-4.00000 + 4.00000i) q^{6} -4.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -7.00000 q^{9} +O(q^{10})$$ $$q+(1.00000 + 1.00000i) q^{2} +4.00000i q^{3} +2.00000i q^{4} +(3.00000 - 3.00000i) q^{5} +(-4.00000 + 4.00000i) q^{6} -4.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -7.00000 q^{9} +6.00000 q^{10} +4.00000i q^{11} -8.00000 q^{12} +(3.00000 - 3.00000i) q^{13} +(-4.00000 - 4.00000i) q^{14} +(12.0000 + 12.0000i) q^{15} -4.00000 q^{16} +(23.0000 - 23.0000i) q^{17} +(-7.00000 - 7.00000i) q^{18} +(10.0000 - 10.0000i) q^{19} +(6.00000 + 6.00000i) q^{20} -16.0000i q^{21} +(-4.00000 + 4.00000i) q^{22} +(-10.0000 + 10.0000i) q^{23} +(-8.00000 - 8.00000i) q^{24} +7.00000i q^{25} +6.00000 q^{26} +8.00000i q^{27} -8.00000i q^{28} +(-19.0000 - 19.0000i) q^{29} +24.0000i q^{30} +(-18.0000 - 18.0000i) q^{31} +(-4.00000 - 4.00000i) q^{32} -16.0000 q^{33} +46.0000 q^{34} +(-12.0000 + 12.0000i) q^{35} -14.0000i q^{36} -37.0000i q^{37} +20.0000 q^{38} +(12.0000 + 12.0000i) q^{39} +12.0000i q^{40} +74.0000i q^{41} +(16.0000 - 16.0000i) q^{42} +(42.0000 - 42.0000i) q^{43} -8.00000 q^{44} +(-21.0000 + 21.0000i) q^{45} -20.0000 q^{46} -44.0000 q^{47} -16.0000i q^{48} -33.0000 q^{49} +(-7.00000 + 7.00000i) q^{50} +(92.0000 + 92.0000i) q^{51} +(6.00000 + 6.00000i) q^{52} -80.0000 q^{53} +(-8.00000 + 8.00000i) q^{54} +(12.0000 + 12.0000i) q^{55} +(8.00000 - 8.00000i) q^{56} +(40.0000 + 40.0000i) q^{57} -38.0000i q^{58} +(-54.0000 + 54.0000i) q^{59} +(-24.0000 + 24.0000i) q^{60} +(-3.00000 - 3.00000i) q^{61} -36.0000i q^{62} +28.0000 q^{63} -8.00000i q^{64} -18.0000i q^{65} +(-16.0000 - 16.0000i) q^{66} -12.0000i q^{67} +(46.0000 + 46.0000i) q^{68} +(-40.0000 - 40.0000i) q^{69} -24.0000 q^{70} +124.000 q^{71} +(14.0000 - 14.0000i) q^{72} -10.0000i q^{73} +(37.0000 - 37.0000i) q^{74} -28.0000 q^{75} +(20.0000 + 20.0000i) q^{76} -16.0000i q^{77} +24.0000i q^{78} +(14.0000 - 14.0000i) q^{79} +(-12.0000 + 12.0000i) q^{80} -95.0000 q^{81} +(-74.0000 + 74.0000i) q^{82} -64.0000 q^{83} +32.0000 q^{84} -138.000i q^{85} +84.0000 q^{86} +(76.0000 - 76.0000i) q^{87} +(-8.00000 - 8.00000i) q^{88} +(17.0000 + 17.0000i) q^{89} -42.0000 q^{90} +(-12.0000 + 12.0000i) q^{91} +(-20.0000 - 20.0000i) q^{92} +(72.0000 - 72.0000i) q^{93} +(-44.0000 - 44.0000i) q^{94} -60.0000i q^{95} +(16.0000 - 16.0000i) q^{96} +(129.000 - 129.000i) q^{97} +(-33.0000 - 33.0000i) q^{98} -28.0000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 6 q^{5} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 14 q^{9} + O(q^{10})$$ $$2 q + 2 q^{2} + 6 q^{5} - 8 q^{6} - 8 q^{7} - 4 q^{8} - 14 q^{9} + 12 q^{10} - 16 q^{12} + 6 q^{13} - 8 q^{14} + 24 q^{15} - 8 q^{16} + 46 q^{17} - 14 q^{18} + 20 q^{19} + 12 q^{20} - 8 q^{22} - 20 q^{23} - 16 q^{24} + 12 q^{26} - 38 q^{29} - 36 q^{31} - 8 q^{32} - 32 q^{33} + 92 q^{34} - 24 q^{35} + 40 q^{38} + 24 q^{39} + 32 q^{42} + 84 q^{43} - 16 q^{44} - 42 q^{45} - 40 q^{46} - 88 q^{47} - 66 q^{49} - 14 q^{50} + 184 q^{51} + 12 q^{52} - 160 q^{53} - 16 q^{54} + 24 q^{55} + 16 q^{56} + 80 q^{57} - 108 q^{59} - 48 q^{60} - 6 q^{61} + 56 q^{63} - 32 q^{66} + 92 q^{68} - 80 q^{69} - 48 q^{70} + 248 q^{71} + 28 q^{72} + 74 q^{74} - 56 q^{75} + 40 q^{76} + 28 q^{79} - 24 q^{80} - 190 q^{81} - 148 q^{82} - 128 q^{83} + 64 q^{84} + 168 q^{86} + 152 q^{87} - 16 q^{88} + 34 q^{89} - 84 q^{90} - 24 q^{91} - 40 q^{92} + 144 q^{93} - 88 q^{94} + 32 q^{96} + 258 q^{97} - 66 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$$.

 $$n$$ $$39$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 + 1.00000i 0.500000 + 0.500000i
$$3$$ 4.00000i 1.33333i 0.745356 + 0.666667i $$0.232280\pi$$
−0.745356 + 0.666667i $$0.767720\pi$$
$$4$$ 2.00000i 0.500000i
$$5$$ 3.00000 3.00000i 0.600000 0.600000i −0.340312 0.940312i $$-0.610533\pi$$
0.940312 + 0.340312i $$0.110533\pi$$
$$6$$ −4.00000 + 4.00000i −0.666667 + 0.666667i
$$7$$ −4.00000 −0.571429 −0.285714 0.958315i $$-0.592231\pi$$
−0.285714 + 0.958315i $$0.592231\pi$$
$$8$$ −2.00000 + 2.00000i −0.250000 + 0.250000i
$$9$$ −7.00000 −0.777778
$$10$$ 6.00000 0.600000
$$11$$ 4.00000i 0.363636i 0.983332 + 0.181818i $$0.0581982\pi$$
−0.983332 + 0.181818i $$0.941802\pi$$
$$12$$ −8.00000 −0.666667
$$13$$ 3.00000 3.00000i 0.230769 0.230769i −0.582245 0.813014i $$-0.697825\pi$$
0.813014 + 0.582245i $$0.197825\pi$$
$$14$$ −4.00000 4.00000i −0.285714 0.285714i
$$15$$ 12.0000 + 12.0000i 0.800000 + 0.800000i
$$16$$ −4.00000 −0.250000
$$17$$ 23.0000 23.0000i 1.35294 1.35294i 0.470588 0.882353i $$-0.344042\pi$$
0.882353 0.470588i $$-0.155958\pi$$
$$18$$ −7.00000 7.00000i −0.388889 0.388889i
$$19$$ 10.0000 10.0000i 0.526316 0.526316i −0.393156 0.919472i $$-0.628617\pi$$
0.919472 + 0.393156i $$0.128617\pi$$
$$20$$ 6.00000 + 6.00000i 0.300000 + 0.300000i
$$21$$ 16.0000i 0.761905i
$$22$$ −4.00000 + 4.00000i −0.181818 + 0.181818i
$$23$$ −10.0000 + 10.0000i −0.434783 + 0.434783i −0.890252 0.455469i $$-0.849472\pi$$
0.455469 + 0.890252i $$0.349472\pi$$
$$24$$ −8.00000 8.00000i −0.333333 0.333333i
$$25$$ 7.00000i 0.280000i
$$26$$ 6.00000 0.230769
$$27$$ 8.00000i 0.296296i
$$28$$ 8.00000i 0.285714i
$$29$$ −19.0000 19.0000i −0.655172 0.655172i 0.299061 0.954234i $$-0.403326\pi$$
−0.954234 + 0.299061i $$0.903326\pi$$
$$30$$ 24.0000i 0.800000i
$$31$$ −18.0000 18.0000i −0.580645 0.580645i 0.354435 0.935081i $$-0.384673\pi$$
−0.935081 + 0.354435i $$0.884673\pi$$
$$32$$ −4.00000 4.00000i −0.125000 0.125000i
$$33$$ −16.0000 −0.484848
$$34$$ 46.0000 1.35294
$$35$$ −12.0000 + 12.0000i −0.342857 + 0.342857i
$$36$$ 14.0000i 0.388889i
$$37$$ 37.0000i 1.00000i
$$38$$ 20.0000 0.526316
$$39$$ 12.0000 + 12.0000i 0.307692 + 0.307692i
$$40$$ 12.0000i 0.300000i
$$41$$ 74.0000i 1.80488i 0.430818 + 0.902439i $$0.358225\pi$$
−0.430818 + 0.902439i $$0.641775\pi$$
$$42$$ 16.0000 16.0000i 0.380952 0.380952i
$$43$$ 42.0000 42.0000i 0.976744 0.976744i −0.0229915 0.999736i $$-0.507319\pi$$
0.999736 + 0.0229915i $$0.00731906\pi$$
$$44$$ −8.00000 −0.181818
$$45$$ −21.0000 + 21.0000i −0.466667 + 0.466667i
$$46$$ −20.0000 −0.434783
$$47$$ −44.0000 −0.936170 −0.468085 0.883683i $$-0.655056\pi$$
−0.468085 + 0.883683i $$0.655056\pi$$
$$48$$ 16.0000i 0.333333i
$$49$$ −33.0000 −0.673469
$$50$$ −7.00000 + 7.00000i −0.140000 + 0.140000i
$$51$$ 92.0000 + 92.0000i 1.80392 + 1.80392i
$$52$$ 6.00000 + 6.00000i 0.115385 + 0.115385i
$$53$$ −80.0000 −1.50943 −0.754717 0.656051i $$-0.772226\pi$$
−0.754717 + 0.656051i $$0.772226\pi$$
$$54$$ −8.00000 + 8.00000i −0.148148 + 0.148148i
$$55$$ 12.0000 + 12.0000i 0.218182 + 0.218182i
$$56$$ 8.00000 8.00000i 0.142857 0.142857i
$$57$$ 40.0000 + 40.0000i 0.701754 + 0.701754i
$$58$$ 38.0000i 0.655172i
$$59$$ −54.0000 + 54.0000i −0.915254 + 0.915254i −0.996679 0.0814252i $$-0.974053\pi$$
0.0814252 + 0.996679i $$0.474053\pi$$
$$60$$ −24.0000 + 24.0000i −0.400000 + 0.400000i
$$61$$ −3.00000 3.00000i −0.0491803 0.0491803i 0.682089 0.731269i $$-0.261072\pi$$
−0.731269 + 0.682089i $$0.761072\pi$$
$$62$$ 36.0000i 0.580645i
$$63$$ 28.0000 0.444444
$$64$$ 8.00000i 0.125000i
$$65$$ 18.0000i 0.276923i
$$66$$ −16.0000 16.0000i −0.242424 0.242424i
$$67$$ 12.0000i 0.179104i −0.995982 0.0895522i $$-0.971456\pi$$
0.995982 0.0895522i $$-0.0285436\pi$$
$$68$$ 46.0000 + 46.0000i 0.676471 + 0.676471i
$$69$$ −40.0000 40.0000i −0.579710 0.579710i
$$70$$ −24.0000 −0.342857
$$71$$ 124.000 1.74648 0.873239 0.487291i $$-0.162015\pi$$
0.873239 + 0.487291i $$0.162015\pi$$
$$72$$ 14.0000 14.0000i 0.194444 0.194444i
$$73$$ 10.0000i 0.136986i −0.997652 0.0684932i $$-0.978181\pi$$
0.997652 0.0684932i $$-0.0218191\pi$$
$$74$$ 37.0000 37.0000i 0.500000 0.500000i
$$75$$ −28.0000 −0.373333
$$76$$ 20.0000 + 20.0000i 0.263158 + 0.263158i
$$77$$ 16.0000i 0.207792i
$$78$$ 24.0000i 0.307692i
$$79$$ 14.0000 14.0000i 0.177215 0.177215i −0.612926 0.790141i $$-0.710007\pi$$
0.790141 + 0.612926i $$0.210007\pi$$
$$80$$ −12.0000 + 12.0000i −0.150000 + 0.150000i
$$81$$ −95.0000 −1.17284
$$82$$ −74.0000 + 74.0000i −0.902439 + 0.902439i
$$83$$ −64.0000 −0.771084 −0.385542 0.922690i $$-0.625986\pi$$
−0.385542 + 0.922690i $$0.625986\pi$$
$$84$$ 32.0000 0.380952
$$85$$ 138.000i 1.62353i
$$86$$ 84.0000 0.976744
$$87$$ 76.0000 76.0000i 0.873563 0.873563i
$$88$$ −8.00000 8.00000i −0.0909091 0.0909091i
$$89$$ 17.0000 + 17.0000i 0.191011 + 0.191011i 0.796133 0.605122i $$-0.206876\pi$$
−0.605122 + 0.796133i $$0.706876\pi$$
$$90$$ −42.0000 −0.466667
$$91$$ −12.0000 + 12.0000i −0.131868 + 0.131868i
$$92$$ −20.0000 20.0000i −0.217391 0.217391i
$$93$$ 72.0000 72.0000i 0.774194 0.774194i
$$94$$ −44.0000 44.0000i −0.468085 0.468085i
$$95$$ 60.0000i 0.631579i
$$96$$ 16.0000 16.0000i 0.166667 0.166667i
$$97$$ 129.000 129.000i 1.32990 1.32990i 0.424442 0.905455i $$-0.360470\pi$$
0.905455 0.424442i $$-0.139530\pi$$
$$98$$ −33.0000 33.0000i −0.336735 0.336735i
$$99$$ 28.0000i 0.282828i
$$100$$ −14.0000 −0.140000
$$101$$ 118.000i 1.16832i 0.811640 + 0.584158i $$0.198575\pi$$
−0.811640 + 0.584158i $$0.801425\pi$$
$$102$$ 184.000i 1.80392i
$$103$$ −42.0000 42.0000i −0.407767 0.407767i 0.473192 0.880959i $$-0.343102\pi$$
−0.880959 + 0.473192i $$0.843102\pi$$
$$104$$ 12.0000i 0.115385i
$$105$$ −48.0000 48.0000i −0.457143 0.457143i
$$106$$ −80.0000 80.0000i −0.754717 0.754717i
$$107$$ −24.0000 −0.224299 −0.112150 0.993691i $$-0.535774\pi$$
−0.112150 + 0.993691i $$0.535774\pi$$
$$108$$ −16.0000 −0.148148
$$109$$ −91.0000 + 91.0000i −0.834862 + 0.834862i −0.988177 0.153315i $$-0.951005\pi$$
0.153315 + 0.988177i $$0.451005\pi$$
$$110$$ 24.0000i 0.218182i
$$111$$ 148.000 1.33333
$$112$$ 16.0000 0.142857
$$113$$ 7.00000 + 7.00000i 0.0619469 + 0.0619469i 0.737402 0.675455i $$-0.236053\pi$$
−0.675455 + 0.737402i $$0.736053\pi$$
$$114$$ 80.0000i 0.701754i
$$115$$ 60.0000i 0.521739i
$$116$$ 38.0000 38.0000i 0.327586 0.327586i
$$117$$ −21.0000 + 21.0000i −0.179487 + 0.179487i
$$118$$ −108.000 −0.915254
$$119$$ −92.0000 + 92.0000i −0.773109 + 0.773109i
$$120$$ −48.0000 −0.400000
$$121$$ 105.000 0.867769
$$122$$ 6.00000i 0.0491803i
$$123$$ −296.000 −2.40650
$$124$$ 36.0000 36.0000i 0.290323 0.290323i
$$125$$ 96.0000 + 96.0000i 0.768000 + 0.768000i
$$126$$ 28.0000 + 28.0000i 0.222222 + 0.222222i
$$127$$ 76.0000 0.598425 0.299213 0.954186i $$-0.403276\pi$$
0.299213 + 0.954186i $$0.403276\pi$$
$$128$$ 8.00000 8.00000i 0.0625000 0.0625000i
$$129$$ 168.000 + 168.000i 1.30233 + 1.30233i
$$130$$ 18.0000 18.0000i 0.138462 0.138462i
$$131$$ 70.0000 + 70.0000i 0.534351 + 0.534351i 0.921864 0.387513i $$-0.126666\pi$$
−0.387513 + 0.921864i $$0.626666\pi$$
$$132$$ 32.0000i 0.242424i
$$133$$ −40.0000 + 40.0000i −0.300752 + 0.300752i
$$134$$ 12.0000 12.0000i 0.0895522 0.0895522i
$$135$$ 24.0000 + 24.0000i 0.177778 + 0.177778i
$$136$$ 92.0000i 0.676471i
$$137$$ 216.000 1.57664 0.788321 0.615264i $$-0.210951\pi$$
0.788321 + 0.615264i $$0.210951\pi$$
$$138$$ 80.0000i 0.579710i
$$139$$ 180.000i 1.29496i 0.762081 + 0.647482i $$0.224178\pi$$
−0.762081 + 0.647482i $$0.775822\pi$$
$$140$$ −24.0000 24.0000i −0.171429 0.171429i
$$141$$ 176.000i 1.24823i
$$142$$ 124.000 + 124.000i 0.873239 + 0.873239i
$$143$$ 12.0000 + 12.0000i 0.0839161 + 0.0839161i
$$144$$ 28.0000 0.194444
$$145$$ −114.000 −0.786207
$$146$$ 10.0000 10.0000i 0.0684932 0.0684932i
$$147$$ 132.000i 0.897959i
$$148$$ 74.0000 0.500000
$$149$$ −34.0000 −0.228188 −0.114094 0.993470i $$-0.536396\pi$$
−0.114094 + 0.993470i $$0.536396\pi$$
$$150$$ −28.0000 28.0000i −0.186667 0.186667i
$$151$$ 72.0000i 0.476821i −0.971164 0.238411i $$-0.923374\pi$$
0.971164 0.238411i $$-0.0766264\pi$$
$$152$$ 40.0000i 0.263158i
$$153$$ −161.000 + 161.000i −1.05229 + 1.05229i
$$154$$ 16.0000 16.0000i 0.103896 0.103896i
$$155$$ −108.000 −0.696774
$$156$$ −24.0000 + 24.0000i −0.153846 + 0.153846i
$$157$$ −14.0000 −0.0891720 −0.0445860 0.999006i $$-0.514197\pi$$
−0.0445860 + 0.999006i $$0.514197\pi$$
$$158$$ 28.0000 0.177215
$$159$$ 320.000i 2.01258i
$$160$$ −24.0000 −0.150000
$$161$$ 40.0000 40.0000i 0.248447 0.248447i
$$162$$ −95.0000 95.0000i −0.586420 0.586420i
$$163$$ −66.0000 66.0000i −0.404908 0.404908i 0.475051 0.879959i $$-0.342430\pi$$
−0.879959 + 0.475051i $$0.842430\pi$$
$$164$$ −148.000 −0.902439
$$165$$ −48.0000 + 48.0000i −0.290909 + 0.290909i
$$166$$ −64.0000 64.0000i −0.385542 0.385542i
$$167$$ −230.000 + 230.000i −1.37725 + 1.37725i −0.528003 + 0.849242i $$0.677059\pi$$
−0.849242 + 0.528003i $$0.822941\pi$$
$$168$$ 32.0000 + 32.0000i 0.190476 + 0.190476i
$$169$$ 151.000i 0.893491i
$$170$$ 138.000 138.000i 0.811765 0.811765i
$$171$$ −70.0000 + 70.0000i −0.409357 + 0.409357i
$$172$$ 84.0000 + 84.0000i 0.488372 + 0.488372i
$$173$$ 88.0000i 0.508671i −0.967116 0.254335i $$-0.918143\pi$$
0.967116 0.254335i $$-0.0818567\pi$$
$$174$$ 152.000 0.873563
$$175$$ 28.0000i 0.160000i
$$176$$ 16.0000i 0.0909091i
$$177$$ −216.000 216.000i −1.22034 1.22034i
$$178$$ 34.0000i 0.191011i
$$179$$ −166.000 166.000i −0.927374 0.927374i 0.0701614 0.997536i $$-0.477649\pi$$
−0.997536 + 0.0701614i $$0.977649\pi$$
$$180$$ −42.0000 42.0000i −0.233333 0.233333i
$$181$$ 304.000 1.67956 0.839779 0.542928i $$-0.182684\pi$$
0.839779 + 0.542928i $$0.182684\pi$$
$$182$$ −24.0000 −0.131868
$$183$$ 12.0000 12.0000i 0.0655738 0.0655738i
$$184$$ 40.0000i 0.217391i
$$185$$ −111.000 111.000i −0.600000 0.600000i
$$186$$ 144.000 0.774194
$$187$$ 92.0000 + 92.0000i 0.491979 + 0.491979i
$$188$$ 88.0000i 0.468085i
$$189$$ 32.0000i 0.169312i
$$190$$ 60.0000 60.0000i 0.315789 0.315789i
$$191$$ 186.000 186.000i 0.973822 0.973822i −0.0258440 0.999666i $$-0.508227\pi$$
0.999666 + 0.0258440i $$0.00822732\pi$$
$$192$$ 32.0000 0.166667
$$193$$ −9.00000 + 9.00000i −0.0466321 + 0.0466321i −0.730038 0.683406i $$-0.760498\pi$$
0.683406 + 0.730038i $$0.260498\pi$$
$$194$$ 258.000 1.32990
$$195$$ 72.0000 0.369231
$$196$$ 66.0000i 0.336735i
$$197$$ 34.0000 0.172589 0.0862944 0.996270i $$-0.472497\pi$$
0.0862944 + 0.996270i $$0.472497\pi$$
$$198$$ 28.0000 28.0000i 0.141414 0.141414i
$$199$$ 46.0000 + 46.0000i 0.231156 + 0.231156i 0.813175 0.582019i $$-0.197737\pi$$
−0.582019 + 0.813175i $$0.697737\pi$$
$$200$$ −14.0000 14.0000i −0.0700000 0.0700000i
$$201$$ 48.0000 0.238806
$$202$$ −118.000 + 118.000i −0.584158 + 0.584158i
$$203$$ 76.0000 + 76.0000i 0.374384 + 0.374384i
$$204$$ −184.000 + 184.000i −0.901961 + 0.901961i
$$205$$ 222.000 + 222.000i 1.08293 + 1.08293i
$$206$$ 84.0000i 0.407767i
$$207$$ 70.0000 70.0000i 0.338164 0.338164i
$$208$$ −12.0000 + 12.0000i −0.0576923 + 0.0576923i
$$209$$ 40.0000 + 40.0000i 0.191388 + 0.191388i
$$210$$ 96.0000i 0.457143i
$$211$$ −208.000 −0.985782 −0.492891 0.870091i $$-0.664060\pi$$
−0.492891 + 0.870091i $$0.664060\pi$$
$$212$$ 160.000i 0.754717i
$$213$$ 496.000i 2.32864i
$$214$$ −24.0000 24.0000i −0.112150 0.112150i
$$215$$ 252.000i 1.17209i
$$216$$ −16.0000 16.0000i −0.0740741 0.0740741i
$$217$$ 72.0000 + 72.0000i 0.331797 + 0.331797i
$$218$$ −182.000 −0.834862
$$219$$ 40.0000 0.182648
$$220$$ −24.0000 + 24.0000i −0.109091 + 0.109091i
$$221$$ 138.000i 0.624434i
$$222$$ 148.000 + 148.000i 0.666667 + 0.666667i
$$223$$ −124.000 −0.556054 −0.278027 0.960573i $$-0.589680\pi$$
−0.278027 + 0.960573i $$0.589680\pi$$
$$224$$ 16.0000 + 16.0000i 0.0714286 + 0.0714286i
$$225$$ 49.0000i 0.217778i
$$226$$ 14.0000i 0.0619469i
$$227$$ −90.0000 + 90.0000i −0.396476 + 0.396476i −0.876988 0.480512i $$-0.840451\pi$$
0.480512 + 0.876988i $$0.340451\pi$$
$$228$$ −80.0000 + 80.0000i −0.350877 + 0.350877i
$$229$$ −2.00000 −0.00873362 −0.00436681 0.999990i $$-0.501390\pi$$
−0.00436681 + 0.999990i $$0.501390\pi$$
$$230$$ −60.0000 + 60.0000i −0.260870 + 0.260870i
$$231$$ 64.0000 0.277056
$$232$$ 76.0000 0.327586
$$233$$ 42.0000i 0.180258i 0.995930 + 0.0901288i $$0.0287279\pi$$
−0.995930 + 0.0901288i $$0.971272\pi$$
$$234$$ −42.0000 −0.179487
$$235$$ −132.000 + 132.000i −0.561702 + 0.561702i
$$236$$ −108.000 108.000i −0.457627 0.457627i
$$237$$ 56.0000 + 56.0000i 0.236287 + 0.236287i
$$238$$ −184.000 −0.773109
$$239$$ 22.0000 22.0000i 0.0920502 0.0920502i −0.659582 0.751632i $$-0.729267\pi$$
0.751632 + 0.659582i $$0.229267\pi$$
$$240$$ −48.0000 48.0000i −0.200000 0.200000i
$$241$$ −175.000 + 175.000i −0.726141 + 0.726141i −0.969849 0.243708i $$-0.921636\pi$$
0.243708 + 0.969849i $$0.421636\pi$$
$$242$$ 105.000 + 105.000i 0.433884 + 0.433884i
$$243$$ 308.000i 1.26749i
$$244$$ 6.00000 6.00000i 0.0245902 0.0245902i
$$245$$ −99.0000 + 99.0000i −0.404082 + 0.404082i
$$246$$ −296.000 296.000i −1.20325 1.20325i
$$247$$ 60.0000i 0.242915i
$$248$$ 72.0000 0.290323
$$249$$ 256.000i 1.02811i
$$250$$ 192.000i 0.768000i
$$251$$ −198.000 198.000i −0.788845 0.788845i 0.192460 0.981305i $$-0.438353\pi$$
−0.981305 + 0.192460i $$0.938353\pi$$
$$252$$ 56.0000i 0.222222i
$$253$$ −40.0000 40.0000i −0.158103 0.158103i
$$254$$ 76.0000 + 76.0000i 0.299213 + 0.299213i
$$255$$ 552.000 2.16471
$$256$$ 16.0000 0.0625000
$$257$$ −159.000 + 159.000i −0.618677 + 0.618677i −0.945192 0.326515i $$-0.894126\pi$$
0.326515 + 0.945192i $$0.394126\pi$$
$$258$$ 336.000i 1.30233i
$$259$$ 148.000i 0.571429i
$$260$$ 36.0000 0.138462
$$261$$ 133.000 + 133.000i 0.509579 + 0.509579i
$$262$$ 140.000i 0.534351i
$$263$$ 88.0000i 0.334601i −0.985906 0.167300i $$-0.946495\pi$$
0.985906 0.167300i $$-0.0535050\pi$$
$$264$$ 32.0000 32.0000i 0.121212 0.121212i
$$265$$ −240.000 + 240.000i −0.905660 + 0.905660i
$$266$$ −80.0000 −0.300752
$$267$$ −68.0000 + 68.0000i −0.254682 + 0.254682i
$$268$$ 24.0000 0.0895522
$$269$$ 178.000 0.661710 0.330855 0.943682i $$-0.392663\pi$$
0.330855 + 0.943682i $$0.392663\pi$$
$$270$$ 48.0000i 0.177778i
$$271$$ 404.000 1.49077 0.745387 0.666631i $$-0.232265\pi$$
0.745387 + 0.666631i $$0.232265\pi$$
$$272$$ −92.0000 + 92.0000i −0.338235 + 0.338235i
$$273$$ −48.0000 48.0000i −0.175824 0.175824i
$$274$$ 216.000 + 216.000i 0.788321 + 0.788321i
$$275$$ −28.0000 −0.101818
$$276$$ 80.0000 80.0000i 0.289855 0.289855i
$$277$$ −147.000 147.000i −0.530686 0.530686i 0.390091 0.920776i $$-0.372444\pi$$
−0.920776 + 0.390091i $$0.872444\pi$$
$$278$$ −180.000 + 180.000i −0.647482 + 0.647482i
$$279$$ 126.000 + 126.000i 0.451613 + 0.451613i
$$280$$ 48.0000i 0.171429i
$$281$$ 135.000 135.000i 0.480427 0.480427i −0.424841 0.905268i $$-0.639670\pi$$
0.905268 + 0.424841i $$0.139670\pi$$
$$282$$ 176.000 176.000i 0.624113 0.624113i
$$283$$ −258.000 258.000i −0.911661 0.911661i 0.0847421 0.996403i $$-0.472993\pi$$
−0.996403 + 0.0847421i $$0.972993\pi$$
$$284$$ 248.000i 0.873239i
$$285$$ 240.000 0.842105
$$286$$ 24.0000i 0.0839161i
$$287$$ 296.000i 1.03136i
$$288$$ 28.0000 + 28.0000i 0.0972222 + 0.0972222i
$$289$$ 769.000i 2.66090i
$$290$$ −114.000 114.000i −0.393103 0.393103i
$$291$$ 516.000 + 516.000i 1.77320 + 1.77320i
$$292$$ 20.0000 0.0684932
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 132.000 132.000i 0.448980 0.448980i
$$295$$ 324.000i 1.09831i
$$296$$ 74.0000 + 74.0000i 0.250000 + 0.250000i
$$297$$ −32.0000 −0.107744
$$298$$ −34.0000 34.0000i −0.114094 0.114094i
$$299$$ 60.0000i 0.200669i
$$300$$ 56.0000i 0.186667i
$$301$$ −168.000 + 168.000i −0.558140 + 0.558140i
$$302$$ 72.0000 72.0000i 0.238411 0.238411i
$$303$$ −472.000 −1.55776
$$304$$ −40.0000 + 40.0000i −0.131579 + 0.131579i
$$305$$ −18.0000 −0.0590164
$$306$$ −322.000 −1.05229
$$307$$ 364.000i 1.18567i 0.805325 + 0.592834i $$0.201991\pi$$
−0.805325 + 0.592834i $$0.798009\pi$$
$$308$$ 32.0000 0.103896
$$309$$ 168.000 168.000i 0.543689 0.543689i
$$310$$ −108.000 108.000i −0.348387 0.348387i
$$311$$ −238.000 238.000i −0.765273 0.765273i 0.211997 0.977270i $$-0.432003\pi$$
−0.977270 + 0.211997i $$0.932003\pi$$
$$312$$ −48.0000 −0.153846
$$313$$ 87.0000 87.0000i 0.277955 0.277955i −0.554337 0.832292i $$-0.687028\pi$$
0.832292 + 0.554337i $$0.187028\pi$$
$$314$$ −14.0000 14.0000i −0.0445860 0.0445860i
$$315$$ 84.0000 84.0000i 0.266667 0.266667i
$$316$$ 28.0000 + 28.0000i 0.0886076 + 0.0886076i
$$317$$ 264.000i 0.832808i 0.909180 + 0.416404i $$0.136710\pi$$
−0.909180 + 0.416404i $$0.863290\pi$$
$$318$$ 320.000 320.000i 1.00629 1.00629i
$$319$$ 76.0000 76.0000i 0.238245 0.238245i
$$320$$ −24.0000 24.0000i −0.0750000 0.0750000i
$$321$$ 96.0000i 0.299065i
$$322$$ 80.0000 0.248447
$$323$$ 460.000i 1.42415i
$$324$$ 190.000i 0.586420i
$$325$$ 21.0000 + 21.0000i 0.0646154 + 0.0646154i
$$326$$ 132.000i 0.404908i
$$327$$ −364.000 364.000i −1.11315 1.11315i
$$328$$ −148.000 148.000i −0.451220 0.451220i
$$329$$ 176.000 0.534954
$$330$$ −96.0000 −0.290909
$$331$$ −326.000 + 326.000i −0.984894 + 0.984894i −0.999888 0.0149933i $$-0.995227\pi$$
0.0149933 + 0.999888i $$0.495227\pi$$
$$332$$ 128.000i 0.385542i
$$333$$ 259.000i 0.777778i
$$334$$ −460.000 −1.37725
$$335$$ −36.0000 36.0000i −0.107463 0.107463i
$$336$$ 64.0000i 0.190476i
$$337$$ 230.000i 0.682493i −0.939974 0.341246i $$-0.889151\pi$$
0.939974 0.341246i $$-0.110849\pi$$
$$338$$ −151.000 + 151.000i −0.446746 + 0.446746i
$$339$$ −28.0000 + 28.0000i −0.0825959 + 0.0825959i
$$340$$ 276.000 0.811765
$$341$$ 72.0000 72.0000i 0.211144 0.211144i
$$342$$ −140.000 −0.409357
$$343$$ 328.000 0.956268
$$344$$ 168.000i 0.488372i
$$345$$ −240.000 −0.695652
$$346$$ 88.0000 88.0000i 0.254335 0.254335i
$$347$$ 362.000 + 362.000i 1.04323 + 1.04323i 0.999022 + 0.0442052i $$0.0140755\pi$$
0.0442052 + 0.999022i $$0.485924\pi$$
$$348$$ 152.000 + 152.000i 0.436782 + 0.436782i
$$349$$ −48.0000 −0.137536 −0.0687679 0.997633i $$-0.521907\pi$$
−0.0687679 + 0.997633i $$0.521907\pi$$
$$350$$ 28.0000 28.0000i 0.0800000 0.0800000i
$$351$$ 24.0000 + 24.0000i 0.0683761 + 0.0683761i
$$352$$ 16.0000 16.0000i 0.0454545 0.0454545i
$$353$$ 343.000 + 343.000i 0.971671 + 0.971671i 0.999610 0.0279383i $$-0.00889418\pi$$
−0.0279383 + 0.999610i $$0.508894\pi$$
$$354$$ 432.000i 1.22034i
$$355$$ 372.000 372.000i 1.04789 1.04789i
$$356$$ −34.0000 + 34.0000i −0.0955056 + 0.0955056i
$$357$$ −368.000 368.000i −1.03081 1.03081i
$$358$$ 332.000i 0.927374i
$$359$$ −404.000 −1.12535 −0.562674 0.826679i $$-0.690227\pi$$
−0.562674 + 0.826679i $$0.690227\pi$$
$$360$$ 84.0000i 0.233333i
$$361$$ 161.000i 0.445983i
$$362$$ 304.000 + 304.000i 0.839779 + 0.839779i
$$363$$ 420.000i 1.15702i
$$364$$ −24.0000 24.0000i −0.0659341 0.0659341i
$$365$$ −30.0000 30.0000i −0.0821918 0.0821918i
$$366$$ 24.0000 0.0655738
$$367$$ 492.000 1.34060 0.670300 0.742090i $$-0.266166\pi$$
0.670300 + 0.742090i $$0.266166\pi$$
$$368$$ 40.0000 40.0000i 0.108696 0.108696i
$$369$$ 518.000i 1.40379i
$$370$$ 222.000i 0.600000i
$$371$$ 320.000 0.862534
$$372$$ 144.000 + 144.000i 0.387097 + 0.387097i
$$373$$ 488.000i 1.30831i −0.756360 0.654155i $$-0.773024\pi$$
0.756360 0.654155i $$-0.226976\pi$$
$$374$$ 184.000i 0.491979i
$$375$$ −384.000 + 384.000i −1.02400 + 1.02400i
$$376$$ 88.0000 88.0000i 0.234043 0.234043i
$$377$$ −114.000 −0.302387
$$378$$ 32.0000 32.0000i 0.0846561 0.0846561i
$$379$$ −440.000 −1.16095 −0.580475 0.814278i $$-0.697133\pi$$
−0.580475 + 0.814278i $$0.697133\pi$$
$$380$$ 120.000 0.315789
$$381$$ 304.000i 0.797900i
$$382$$ 372.000 0.973822
$$383$$ −450.000 + 450.000i −1.17493 + 1.17493i −0.193917 + 0.981018i $$0.562119\pi$$
−0.981018 + 0.193917i $$0.937881\pi$$
$$384$$ 32.0000 + 32.0000i 0.0833333 + 0.0833333i
$$385$$ −48.0000 48.0000i −0.124675 0.124675i
$$386$$ −18.0000 −0.0466321
$$387$$ −294.000 + 294.000i −0.759690 + 0.759690i
$$388$$ 258.000 + 258.000i 0.664948 + 0.664948i
$$389$$ 21.0000 21.0000i 0.0539846 0.0539846i −0.679599 0.733584i $$-0.737846\pi$$
0.733584 + 0.679599i $$0.237846\pi$$
$$390$$ 72.0000 + 72.0000i 0.184615 + 0.184615i
$$391$$ 460.000i 1.17647i
$$392$$ 66.0000 66.0000i 0.168367 0.168367i
$$393$$ −280.000 + 280.000i −0.712468 + 0.712468i
$$394$$ 34.0000 + 34.0000i 0.0862944 + 0.0862944i
$$395$$ 84.0000i 0.212658i
$$396$$ 56.0000 0.141414
$$397$$ 646.000i 1.62720i −0.581422 0.813602i $$-0.697504\pi$$
0.581422 0.813602i $$-0.302496\pi$$
$$398$$ 92.0000i 0.231156i
$$399$$ −160.000 160.000i −0.401003 0.401003i
$$400$$ 28.0000i 0.0700000i
$$401$$ 273.000 + 273.000i 0.680798 + 0.680798i 0.960180 0.279382i $$-0.0901296\pi$$
−0.279382 + 0.960180i $$0.590130\pi$$
$$402$$ 48.0000 + 48.0000i 0.119403 + 0.119403i
$$403$$ −108.000 −0.267990
$$404$$ −236.000 −0.584158
$$405$$ −285.000 + 285.000i −0.703704 + 0.703704i
$$406$$ 152.000i 0.374384i
$$407$$ 148.000 0.363636
$$408$$ −368.000 −0.901961
$$409$$ 39.0000 + 39.0000i 0.0953545 + 0.0953545i 0.753175 0.657820i $$-0.228521\pi$$
−0.657820 + 0.753175i $$0.728521\pi$$
$$410$$ 444.000i 1.08293i
$$411$$ 864.000i 2.10219i
$$412$$ 84.0000 84.0000i 0.203883 0.203883i
$$413$$ 216.000 216.000i 0.523002 0.523002i
$$414$$ 140.000 0.338164
$$415$$ −192.000 + 192.000i −0.462651 + 0.462651i
$$416$$ −24.0000 −0.0576923
$$417$$ −720.000 −1.72662
$$418$$ 80.0000i 0.191388i
$$419$$ 464.000 1.10740 0.553699 0.832717i $$-0.313216\pi$$
0.553699 + 0.832717i $$0.313216\pi$$
$$420$$ 96.0000 96.0000i 0.228571 0.228571i
$$421$$ −469.000 469.000i −1.11401 1.11401i −0.992602 0.121412i $$-0.961258\pi$$
−0.121412 0.992602i $$-0.538742\pi$$
$$422$$ −208.000 208.000i −0.492891 0.492891i
$$423$$ 308.000 0.728132
$$424$$ 160.000 160.000i 0.377358 0.377358i
$$425$$ 161.000 + 161.000i 0.378824 + 0.378824i
$$426$$ −496.000 + 496.000i −1.16432 + 1.16432i
$$427$$ 12.0000 + 12.0000i 0.0281030 + 0.0281030i
$$428$$ 48.0000i 0.112150i
$$429$$ −48.0000 + 48.0000i −0.111888 + 0.111888i
$$430$$ 252.000 252.000i 0.586047 0.586047i
$$431$$ 450.000 + 450.000i 1.04408 + 1.04408i 0.998982 + 0.0451011i $$0.0143610\pi$$
0.0451011 + 0.998982i $$0.485639\pi$$
$$432$$ 32.0000i 0.0740741i
$$433$$ 200.000 0.461894 0.230947 0.972966i $$-0.425818\pi$$
0.230947 + 0.972966i $$0.425818\pi$$
$$434$$ 144.000i 0.331797i
$$435$$ 456.000i 1.04828i
$$436$$ −182.000 182.000i −0.417431 0.417431i
$$437$$ 200.000i 0.457666i
$$438$$ 40.0000 + 40.0000i 0.0913242 + 0.0913242i
$$439$$ 246.000 + 246.000i 0.560364 + 0.560364i 0.929411 0.369046i $$-0.120316\pi$$
−0.369046 + 0.929411i $$0.620316\pi$$
$$440$$ −48.0000 −0.109091
$$441$$ 231.000 0.523810
$$442$$ 138.000 138.000i 0.312217 0.312217i
$$443$$ 668.000i 1.50790i −0.656931 0.753950i $$-0.728146\pi$$
0.656931 0.753950i $$-0.271854\pi$$
$$444$$ 296.000i 0.666667i
$$445$$ 102.000 0.229213
$$446$$ −124.000 124.000i −0.278027 0.278027i
$$447$$ 136.000i 0.304251i
$$448$$ 32.0000i 0.0714286i
$$449$$ 199.000 199.000i 0.443207 0.443207i −0.449881 0.893088i $$-0.648534\pi$$
0.893088 + 0.449881i $$0.148534\pi$$
$$450$$ 49.0000 49.0000i 0.108889 0.108889i
$$451$$ −296.000 −0.656319
$$452$$ −14.0000 + 14.0000i −0.0309735 + 0.0309735i
$$453$$ 288.000 0.635762
$$454$$ −180.000 −0.396476
$$455$$ 72.0000i 0.158242i
$$456$$ −160.000 −0.350877
$$457$$ −255.000 + 255.000i −0.557987 + 0.557987i −0.928734 0.370747i $$-0.879102\pi$$
0.370747 + 0.928734i $$0.379102\pi$$
$$458$$ −2.00000 2.00000i −0.00436681 0.00436681i
$$459$$ 184.000 + 184.000i 0.400871 + 0.400871i
$$460$$ −120.000 −0.260870
$$461$$ −555.000 + 555.000i −1.20390 + 1.20390i −0.230935 + 0.972969i $$0.574179\pi$$
−0.972969 + 0.230935i $$0.925821\pi$$
$$462$$ 64.0000 + 64.0000i 0.138528 + 0.138528i
$$463$$ 554.000 554.000i 1.19654 1.19654i 0.221350 0.975194i $$-0.428954\pi$$
0.975194 0.221350i $$-0.0710463\pi$$
$$464$$ 76.0000 + 76.0000i 0.163793 + 0.163793i
$$465$$ 432.000i 0.929032i
$$466$$ −42.0000 + 42.0000i −0.0901288 + 0.0901288i
$$467$$ 158.000 158.000i 0.338330 0.338330i −0.517409 0.855738i $$-0.673103\pi$$
0.855738 + 0.517409i $$0.173103\pi$$
$$468$$ −42.0000 42.0000i −0.0897436 0.0897436i
$$469$$ 48.0000i 0.102345i
$$470$$ −264.000 −0.561702
$$471$$ 56.0000i 0.118896i
$$472$$ 216.000i 0.457627i
$$473$$ 168.000 + 168.000i 0.355180 + 0.355180i
$$474$$ 112.000i 0.236287i
$$475$$ 70.0000 + 70.0000i 0.147368 + 0.147368i
$$476$$ −184.000 184.000i −0.386555 0.386555i
$$477$$ 560.000 1.17400
$$478$$ 44.0000 0.0920502
$$479$$ 290.000 290.000i 0.605428 0.605428i −0.336320 0.941748i $$-0.609182\pi$$
0.941748 + 0.336320i $$0.109182\pi$$
$$480$$ 96.0000i 0.200000i
$$481$$ −111.000 111.000i −0.230769 0.230769i
$$482$$ −350.000 −0.726141
$$483$$ 160.000 + 160.000i 0.331263 + 0.331263i
$$484$$ 210.000i 0.433884i
$$485$$ 774.000i 1.59588i
$$486$$ 308.000 308.000i 0.633745 0.633745i
$$487$$ 266.000 266.000i 0.546201 0.546201i −0.379139 0.925340i $$-0.623780\pi$$
0.925340 + 0.379139i $$0.123780\pi$$
$$488$$ 12.0000 0.0245902
$$489$$ 264.000 264.000i 0.539877 0.539877i
$$490$$ −198.000 −0.404082
$$491$$ 312.000 0.635438 0.317719 0.948185i $$-0.397083\pi$$
0.317719 + 0.948185i $$0.397083\pi$$
$$492$$ 592.000i 1.20325i
$$493$$ −874.000 −1.77282
$$494$$ 60.0000 60.0000i 0.121457 0.121457i
$$495$$ −84.0000 84.0000i −0.169697 0.169697i
$$496$$ 72.0000 + 72.0000i 0.145161 + 0.145161i
$$497$$ −496.000 −0.997988
$$498$$ 256.000 256.000i 0.514056 0.514056i
$$499$$ −210.000 210.000i −0.420842 0.420842i 0.464652 0.885493i $$-0.346180\pi$$
−0.885493 + 0.464652i $$0.846180\pi$$
$$500$$ −192.000 + 192.000i −0.384000 + 0.384000i
$$501$$ −920.000 920.000i −1.83633 1.83633i
$$502$$ 396.000i 0.788845i
$$503$$ 298.000 298.000i 0.592445 0.592445i −0.345846 0.938291i $$-0.612408\pi$$
0.938291 + 0.345846i $$0.112408\pi$$
$$504$$ −56.0000 + 56.0000i −0.111111 + 0.111111i
$$505$$ 354.000 + 354.000i 0.700990 + 0.700990i
$$506$$ 80.0000i 0.158103i
$$507$$ −604.000 −1.19132
$$508$$ 152.000i 0.299213i
$$509$$ 808.000i 1.58743i 0.608292 + 0.793713i $$0.291855\pi$$
−0.608292 + 0.793713i $$0.708145\pi$$
$$510$$ 552.000 + 552.000i 1.08235 + 1.08235i
$$511$$ 40.0000i 0.0782779i
$$512$$ 16.0000 + 16.0000i 0.0312500 + 0.0312500i
$$513$$ 80.0000 + 80.0000i 0.155945 + 0.155945i
$$514$$ −318.000 −0.618677
$$515$$ −252.000 −0.489320
$$516$$ −336.000 + 336.000i −0.651163 + 0.651163i
$$517$$ 176.000i 0.340426i
$$518$$ −148.000 + 148.000i −0.285714 + 0.285714i
$$519$$ 352.000 0.678227
$$520$$ 36.0000 + 36.0000i 0.0692308 + 0.0692308i
$$521$$ 170.000i 0.326296i −0.986602 0.163148i $$-0.947835\pi$$
0.986602 0.163148i $$-0.0521647\pi$$
$$522$$ 266.000i 0.509579i
$$523$$ 654.000 654.000i 1.25048 1.25048i 0.294972 0.955506i $$-0.404690\pi$$
0.955506 0.294972i $$-0.0953104\pi$$
$$524$$ −140.000 + 140.000i −0.267176 + 0.267176i
$$525$$ 112.000 0.213333
$$526$$ 88.0000 88.0000i 0.167300 0.167300i
$$527$$ −828.000 −1.57116
$$528$$ 64.0000 0.121212
$$529$$ 329.000i 0.621928i
$$530$$ −480.000 −0.905660
$$531$$ 378.000 378.000i 0.711864 0.711864i
$$532$$ −80.0000 80.0000i −0.150376 0.150376i
$$533$$ 222.000 + 222.000i 0.416510 + 0.416510i
$$534$$ −136.000 −0.254682
$$535$$ −72.0000 + 72.0000i −0.134579 + 0.134579i
$$536$$ 24.0000 + 24.0000i 0.0447761 + 0.0447761i
$$537$$ 664.000 664.000i 1.23650 1.23650i
$$538$$ 178.000 + 178.000i 0.330855 + 0.330855i
$$539$$ 132.000i 0.244898i
$$540$$ −48.0000 + 48.0000i −0.0888889 + 0.0888889i
$$541$$ 147.000 147.000i 0.271719 0.271719i −0.558073 0.829792i $$-0.688459\pi$$
0.829792 + 0.558073i $$0.188459\pi$$
$$542$$ 404.000 + 404.000i 0.745387 + 0.745387i
$$543$$ 1216.00i 2.23941i
$$544$$ −184.000 −0.338235
$$545$$ 546.000i 1.00183i
$$546$$ 96.0000i 0.175824i
$$547$$ −294.000 294.000i −0.537477 0.537477i 0.385310 0.922787i $$-0.374095\pi$$
−0.922787 + 0.385310i $$0.874095\pi$$
$$548$$ 432.000i 0.788321i
$$549$$ 21.0000 + 21.0000i 0.0382514 + 0.0382514i
$$550$$ −28.0000 28.0000i −0.0509091 0.0509091i
$$551$$ −380.000 −0.689655
$$552$$ 160.000 0.289855
$$553$$ −56.0000 + 56.0000i −0.101266 + 0.101266i
$$554$$ 294.000i 0.530686i
$$555$$ 444.000 444.000i 0.800000 0.800000i
$$556$$ −360.000 −0.647482
$$557$$ −179.000 179.000i −0.321364 0.321364i 0.527926 0.849290i $$-0.322970\pi$$
−0.849290 + 0.527926i $$0.822970\pi$$
$$558$$ 252.000i 0.451613i
$$559$$ 252.000i 0.450805i
$$560$$ 48.0000 48.0000i 0.0857143 0.0857143i
$$561$$ −368.000 + 368.000i −0.655971 + 0.655971i
$$562$$ 270.000 0.480427
$$563$$ 282.000 282.000i 0.500888 0.500888i −0.410826 0.911714i $$-0.634760\pi$$
0.911714 + 0.410826i $$0.134760\pi$$
$$564$$ 352.000 0.624113
$$565$$ 42.0000 0.0743363
$$566$$ 516.000i 0.911661i
$$567$$ 380.000 0.670194
$$568$$ −248.000 + 248.000i −0.436620 + 0.436620i
$$569$$ 375.000 + 375.000i 0.659051 + 0.659051i 0.955156 0.296105i $$-0.0956877\pi$$
−0.296105 + 0.955156i $$0.595688\pi$$
$$570$$ 240.000 + 240.000i 0.421053 + 0.421053i
$$571$$ −184.000 −0.322242 −0.161121 0.986935i $$-0.551511\pi$$
−0.161121 + 0.986935i $$0.551511\pi$$
$$572$$ −24.0000 + 24.0000i −0.0419580 + 0.0419580i
$$573$$ 744.000 + 744.000i 1.29843 + 1.29843i
$$574$$ 296.000 296.000i 0.515679 0.515679i
$$575$$ −70.0000 70.0000i −0.121739 0.121739i
$$576$$ 56.0000i 0.0972222i
$$577$$ −623.000 + 623.000i −1.07972 + 1.07972i −0.0831889 + 0.996534i $$0.526510\pi$$
−0.996534 + 0.0831889i $$0.973490\pi$$
$$578$$ 769.000 769.000i 1.33045 1.33045i
$$579$$ −36.0000 36.0000i −0.0621762 0.0621762i
$$580$$ 228.000i 0.393103i
$$581$$ 256.000 0.440620
$$582$$ 1032.00i 1.77320i
$$583$$ 320.000i 0.548885i
$$584$$ 20.0000 + 20.0000i 0.0342466 + 0.0342466i
$$585$$ 126.000i 0.215385i
$$586$$ 0 0
$$587$$ −382.000 382.000i −0.650767 0.650767i 0.302411 0.953178i $$-0.402208\pi$$
−0.953178 + 0.302411i $$0.902208\pi$$
$$588$$ 264.000 0.448980
$$589$$ −360.000 −0.611205
$$590$$ −324.000 + 324.000i −0.549153 + 0.549153i
$$591$$ 136.000i 0.230118i
$$592$$ 148.000i 0.250000i
$$593$$ 734.000 1.23777 0.618887 0.785480i $$-0.287584\pi$$
0.618887 + 0.785480i $$0.287584\pi$$
$$594$$ −32.0000 32.0000i −0.0538721 0.0538721i
$$595$$ 552.000i 0.927731i
$$596$$ 68.0000i 0.114094i
$$597$$ −184.000 + 184.000i −0.308208 + 0.308208i
$$598$$ −60.0000 + 60.0000i −0.100334 + 0.100334i
$$599$$ −1004.00 −1.67613 −0.838063 0.545573i $$-0.816312\pi$$
−0.838063 + 0.545573i $$0.816312\pi$$
$$600$$ 56.0000 56.0000i 0.0933333 0.0933333i
$$601$$ 306.000 0.509151 0.254576 0.967053i $$-0.418064\pi$$
0.254576 + 0.967053i $$0.418064\pi$$
$$602$$ −336.000 −0.558140
$$603$$ 84.0000i 0.139303i
$$604$$ 144.000 0.238411
$$605$$ 315.000 315.000i 0.520661 0.520661i
$$606$$ −472.000 472.000i −0.778878 0.778878i
$$607$$ 298.000 + 298.000i 0.490939 + 0.490939i 0.908602 0.417663i $$-0.137151\pi$$
−0.417663 + 0.908602i $$0.637151\pi$$
$$608$$ −80.0000 −0.131579
$$609$$ −304.000 + 304.000i −0.499179 + 0.499179i
$$610$$ −18.0000 18.0000i −0.0295082 0.0295082i
$$611$$ −132.000 + 132.000i −0.216039 + 0.216039i
$$612$$ −322.000 322.000i −0.526144 0.526144i
$$613$$ 470.000i 0.766721i 0.923599 + 0.383361i $$0.125233\pi$$
−0.923599 + 0.383361i $$0.874767\pi$$
$$614$$ −364.000 + 364.000i −0.592834 + 0.592834i
$$615$$ −888.000 + 888.000i −1.44390 + 1.44390i
$$616$$ 32.0000 + 32.0000i 0.0519481 + 0.0519481i
$$617$$ 304.000i 0.492707i 0.969180 + 0.246353i $$0.0792324\pi$$
−0.969180 + 0.246353i $$0.920768\pi$$
$$618$$ 336.000 0.543689
$$619$$ 956.000i 1.54443i 0.635363 + 0.772213i $$0.280850\pi$$
−0.635363 + 0.772213i $$0.719150\pi$$
$$620$$ 216.000i 0.348387i
$$621$$ −80.0000 80.0000i −0.128824 0.128824i
$$622$$ 476.000i 0.765273i
$$623$$ −68.0000 68.0000i −0.109149 0.109149i
$$624$$ −48.0000 48.0000i −0.0769231 0.0769231i
$$625$$ 401.000 0.641600
$$626$$ 174.000 0.277955
$$627$$ −160.000 + 160.000i −0.255183 + 0.255183i
$$628$$ 28.0000i 0.0445860i
$$629$$ −851.000 851.000i −1.35294 1.35294i
$$630$$ 168.000 0.266667
$$631$$ −362.000 362.000i −0.573693 0.573693i 0.359466 0.933158i $$-0.382959\pi$$
−0.933158 + 0.359466i $$0.882959\pi$$
$$632$$ 56.0000i 0.0886076i
$$633$$ 832.000i 1.31438i
$$634$$ −264.000 + 264.000i −0.416404 + 0.416404i
$$635$$ 228.000 228.000i 0.359055 0.359055i
$$636$$ 640.000 1.00629
$$637$$ −99.0000 + 99.0000i −0.155416 + 0.155416i
$$638$$ 152.000 0.238245
$$639$$ −868.000 −1.35837
$$640$$ 48.0000i 0.0750000i
$$641$$ −398.000 −0.620905 −0.310452 0.950589i $$-0.600481\pi$$
−0.310452 + 0.950589i $$0.600481\pi$$
$$642$$ 96.0000 96.0000i 0.149533 0.149533i
$$643$$ 218.000 + 218.000i 0.339036 + 0.339036i 0.856004 0.516969i $$-0.172940\pi$$
−0.516969 + 0.856004i $$0.672940\pi$$
$$644$$ 80.0000 + 80.0000i 0.124224 + 0.124224i
$$645$$ 1008.00 1.56279
$$646$$ 460.000 460.000i 0.712074 0.712074i
$$647$$ −358.000 358.000i −0.553323 0.553323i 0.374075 0.927398i $$-0.377960\pi$$
−0.927398 + 0.374075i $$0.877960\pi$$
$$648$$ 190.000 190.000i 0.293210 0.293210i
$$649$$ −216.000 216.000i −0.332820 0.332820i
$$650$$ 42.0000i 0.0646154i
$$651$$ −288.000 + 288.000i −0.442396 + 0.442396i
$$652$$ 132.000 132.000i 0.202454 0.202454i
$$653$$ 555.000 + 555.000i 0.849923 + 0.849923i 0.990123 0.140200i $$-0.0447745\pi$$
−0.140200 + 0.990123i $$0.544774\pi$$
$$654$$ 728.000i 1.11315i
$$655$$ 420.000 0.641221
$$656$$ 296.000i 0.451220i
$$657$$ 70.0000i 0.106545i
$$658$$ 176.000 + 176.000i 0.267477 + 0.267477i
$$659$$ 788.000i 1.19575i 0.801589 + 0.597876i $$0.203988\pi$$
−0.801589 + 0.597876i $$0.796012\pi$$
$$660$$ −96.0000 96.0000i −0.145455 0.145455i
$$661$$ −661.000 661.000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$662$$ −652.000 −0.984894
$$663$$ 552.000 0.832579
$$664$$ 128.000 128.000i 0.192771 0.192771i
$$665$$ 240.000i 0.360902i
$$666$$ −259.000 + 259.000i −0.388889 + 0.388889i
$$667$$ 380.000 0.569715
$$668$$ −460.000 460.000i −0.688623 0.688623i
$$669$$ 496.000i 0.741405i
$$670$$ 72.0000i 0.107463i
$$671$$ 12.0000 12.0000i 0.0178838 0.0178838i
$$672$$ −64.0000 + 64.0000i −0.0952381 + 0.0952381i
$$673$$ 50.0000 0.0742942 0.0371471 0.999310i $$-0.488173\pi$$
0.0371471 + 0.999310i $$0.488173\pi$$
$$674$$ 230.000 230.000i 0.341246 0.341246i
$$675$$ −56.0000 −0.0829630
$$676$$ −302.000 −0.446746
$$677$$ 296.000i 0.437223i −0.975812 0.218612i $$-0.929847\pi$$
0.975812 0.218612i $$-0.0701527\pi$$
$$678$$ −56.0000 −0.0825959
$$679$$ −516.000 + 516.000i −0.759941 + 0.759941i
$$680$$ 276.000 + 276.000i 0.405882 + 0.405882i
$$681$$ −360.000 360.000i −0.528634 0.528634i
$$682$$ 144.000 0.211144
$$683$$ 6.00000 6.00000i 0.00878477 0.00878477i −0.702701 0.711486i $$-0.748023\pi$$
0.711486 + 0.702701i $$0.248023\pi$$
$$684$$ −140.000 140.000i −0.204678 0.204678i
$$685$$ 648.000 648.000i 0.945985 0.945985i
$$686$$ 328.000 + 328.000i 0.478134 + 0.478134i
$$687$$ 8.00000i 0.0116448i
$$688$$ −168.000 + 168.000i −0.244186 + 0.244186i
$$689$$ −240.000 + 240.000i −0.348331 + 0.348331i
$$690$$ −240.000 240.000i −0.347826 0.347826i
$$691$$ 708.000i 1.02460i −0.858806 0.512301i $$-0.828793\pi$$
0.858806 0.512301i $$-0.171207\pi$$
$$692$$ 176.000 0.254335
$$693$$ 112.000i 0.161616i
$$694$$ 724.000i 1.04323i
$$695$$ 540.000 + 540.000i 0.776978 + 0.776978i
$$696$$ 304.000i 0.436782i
$$697$$ 1702.00 + 1702.00i 2.44189 + 2.44189i
$$698$$ −48.0000 48.0000i −0.0687679 0.0687679i
$$699$$ −168.000 −0.240343
$$700$$ 56.0000 0.0800000
$$701$$ 291.000 291.000i 0.415121 0.415121i −0.468397 0.883518i $$-0.655168\pi$$
0.883518 + 0.468397i $$0.155168\pi$$
$$702$$ 48.0000i 0.0683761i
$$703$$ −370.000 370.000i −0.526316 0.526316i
$$704$$ 32.0000 0.0454545
$$705$$ −528.000 528.000i −0.748936 0.748936i
$$706$$ 686.000i 0.971671i
$$707$$ 472.000i 0.667610i
$$708$$ 432.000 432.000i 0.610169 0.610169i
$$709$$ −77.0000 + 77.0000i −0.108604 + 0.108604i −0.759320 0.650717i $$-0.774469\pi$$
0.650717 + 0.759320i $$0.274469\pi$$
$$710$$ 744.000 1.04789
$$711$$ −98.0000 + 98.0000i −0.137834 + 0.137834i
$$712$$ −68.0000 −0.0955056
$$713$$ 360.000 0.504909
$$714$$ 736.000i 1.03081i
$$715$$ 72.0000 0.100699
$$716$$ 332.000 332.000i 0.463687 0.463687i
$$717$$ 88.0000 + 88.0000i 0.122734 + 0.122734i
$$718$$ −404.000 404.000i −0.562674 0.562674i
$$719$$ −412.000 −0.573018 −0.286509 0.958078i $$-0.592495\pi$$
−0.286509 + 0.958078i $$0.592495\pi$$
$$720$$ 84.0000 84.0000i 0.116667 0.116667i
$$721$$ 168.000 + 168.000i 0.233010 + 0.233010i
$$722$$ −161.000 + 161.000i −0.222992 + 0.222992i
$$723$$ −700.000 700.000i −0.968188 0.968188i
$$724$$ 608.000i 0.839779i
$$725$$ 133.000 133.000i 0.183448 0.183448i
$$726$$ −420.000 + 420.000i −0.578512 + 0.578512i
$$727$$ −262.000 262.000i −0.360385 0.360385i 0.503570 0.863955i $$-0.332020\pi$$
−0.863955 + 0.503570i $$0.832020\pi$$
$$728$$ 48.0000i 0.0659341i
$$729$$ 377.000 0.517147
$$730$$ 60.0000i 0.0821918i
$$731$$ 1932.00i 2.64295i
$$732$$ 24.0000 + 24.0000i 0.0327869 + 0.0327869i
$$733$$ 682.000i 0.930423i 0.885200 + 0.465211i $$0.154022\pi$$
−0.885200 + 0.465211i $$0.845978\pi$$
$$734$$ 492.000 + 492.000i 0.670300 + 0.670300i
$$735$$ −396.000 396.000i −0.538776 0.538776i
$$736$$ 80.0000 0.108696
$$737$$ 48.0000 0.0651289
$$738$$ 518.000 518.000i 0.701897 0.701897i
$$739$$ 100.000i 0.135318i 0.997709 + 0.0676590i $$0.0215530\pi$$
−0.997709 + 0.0676590i $$0.978447\pi$$
$$740$$ 222.000 222.000i 0.300000 0.300000i
$$741$$ 240.000 0.323887
$$742$$ 320.000 + 320.000i 0.431267 + 0.431267i
$$743$$ 800.000i 1.07672i −0.842716 0.538358i $$-0.819045\pi$$
0.842716 0.538358i $$-0.180955\pi$$
$$744$$ 288.000i 0.387097i
$$745$$ −102.000 + 102.000i −0.136913 + 0.136913i
$$746$$ 488.000 488.000i 0.654155 0.654155i
$$747$$ 448.000 0.599732
$$748$$ −184.000 + 184.000i −0.245989 + 0.245989i
$$749$$ 96.0000 0.128171
$$750$$ −768.000 −1.02400
$$751$$ 536.000i 0.713715i 0.934159 + 0.356858i $$0.116152\pi$$
−0.934159 + 0.356858i $$0.883848\pi$$
$$752$$ 176.000 0.234043
$$753$$ 792.000 792.000i 1.05179 1.05179i
$$754$$ −114.000 114.000i −0.151194 0.151194i
$$755$$ −216.000 216.000i −0.286093 0.286093i
$$756$$ 64.0000 0.0846561
$$757$$ −157.000 + 157.000i −0.207398 + 0.207398i −0.803160 0.595763i $$-0.796850\pi$$
0.595763 + 0.803160i $$0.296850\pi$$
$$758$$ −440.000 440.000i −0.580475 0.580475i
$$759$$ 160.000 160.000i 0.210804 0.210804i
$$760$$ 120.000 + 120.000i 0.157895 + 0.157895i
$$761$$ 272.000i 0.357424i 0.983901 + 0.178712i $$0.0571931\pi$$
−0.983901 + 0.178712i $$0.942807\pi$$
$$762$$ −304.000 + 304.000i −0.398950 + 0.398950i
$$763$$ 364.000 364.000i 0.477064 0.477064i
$$764$$ 372.000 + 372.000i 0.486911 + 0.486911i
$$765$$ 966.000i 1.26275i
$$766$$ −900.000 −1.17493
$$767$$ 324.000i 0.422425i
$$768$$ 64.0000i 0.0833333i
$$769$$ −761.000 761.000i −0.989597 0.989597i 0.0103496 0.999946i $$-0.496706\pi$$
−0.999946 + 0.0103496i $$0.996706\pi$$
$$770$$ 96.0000i 0.124675i
$$771$$ −636.000 636.000i −0.824903 0.824903i
$$772$$ −18.0000 18.0000i −0.0233161 0.0233161i
$$773$$ −1282.00 −1.65847 −0.829237 0.558898i $$-0.811225\pi$$
−0.829237 + 0.558898i $$0.811225\pi$$
$$774$$ −588.000 −0.759690
$$775$$ 126.000 126.000i 0.162581 0.162581i
$$776$$ 516.000i 0.664948i
$$777$$ −592.000 −0.761905
$$778$$ 42.0000