# Properties

 Label 50.3.c.c.43.1 Level $50$ Weight $3$ Character 50.43 Analytic conductor $1.362$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,3,Mod(7,50)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("50.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$50 = 2 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 50.c (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$1.36240132180$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 10) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 43.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 50.43 Dual form 50.3.c.c.7.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.00000i) q^{2} +(2.00000 + 2.00000i) q^{3} -2.00000i q^{4} +4.00000 q^{6} +(-2.00000 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -1.00000i q^{9} +O(q^{10})$$ $$q+(1.00000 - 1.00000i) q^{2} +(2.00000 + 2.00000i) q^{3} -2.00000i q^{4} +4.00000 q^{6} +(-2.00000 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -1.00000i q^{9} -8.00000 q^{11} +(4.00000 - 4.00000i) q^{12} +(-3.00000 - 3.00000i) q^{13} +4.00000i q^{14} -4.00000 q^{16} +(-7.00000 + 7.00000i) q^{17} +(-1.00000 - 1.00000i) q^{18} +20.0000i q^{19} -8.00000 q^{21} +(-8.00000 + 8.00000i) q^{22} +(2.00000 + 2.00000i) q^{23} -8.00000i q^{24} -6.00000 q^{26} +(20.0000 - 20.0000i) q^{27} +(4.00000 + 4.00000i) q^{28} -40.0000i q^{29} +52.0000 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-16.0000 - 16.0000i) q^{33} +14.0000i q^{34} -2.00000 q^{36} +(3.00000 - 3.00000i) q^{37} +(20.0000 + 20.0000i) q^{38} -12.0000i q^{39} -8.00000 q^{41} +(-8.00000 + 8.00000i) q^{42} +(42.0000 + 42.0000i) q^{43} +16.0000i q^{44} +4.00000 q^{46} +(18.0000 - 18.0000i) q^{47} +(-8.00000 - 8.00000i) q^{48} +41.0000i q^{49} -28.0000 q^{51} +(-6.00000 + 6.00000i) q^{52} +(-53.0000 - 53.0000i) q^{53} -40.0000i q^{54} +8.00000 q^{56} +(-40.0000 + 40.0000i) q^{57} +(-40.0000 - 40.0000i) q^{58} +20.0000i q^{59} -48.0000 q^{61} +(52.0000 - 52.0000i) q^{62} +(2.00000 + 2.00000i) q^{63} +8.00000i q^{64} -32.0000 q^{66} +(-62.0000 + 62.0000i) q^{67} +(14.0000 + 14.0000i) q^{68} +8.00000i q^{69} -28.0000 q^{71} +(-2.00000 + 2.00000i) q^{72} +(47.0000 + 47.0000i) q^{73} -6.00000i q^{74} +40.0000 q^{76} +(16.0000 - 16.0000i) q^{77} +(-12.0000 - 12.0000i) q^{78} +71.0000 q^{81} +(-8.00000 + 8.00000i) q^{82} +(-18.0000 - 18.0000i) q^{83} +16.0000i q^{84} +84.0000 q^{86} +(80.0000 - 80.0000i) q^{87} +(16.0000 + 16.0000i) q^{88} -80.0000i q^{89} +12.0000 q^{91} +(4.00000 - 4.00000i) q^{92} +(104.000 + 104.000i) q^{93} -36.0000i q^{94} -16.0000 q^{96} +(63.0000 - 63.0000i) q^{97} +(41.0000 + 41.0000i) q^{98} +8.00000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 4 q^{3} + 8 q^{6} - 4 q^{7} - 4 q^{8}+O(q^{10})$$ 2 * q + 2 * q^2 + 4 * q^3 + 8 * q^6 - 4 * q^7 - 4 * q^8 $$2 q + 2 q^{2} + 4 q^{3} + 8 q^{6} - 4 q^{7} - 4 q^{8} - 16 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} - 14 q^{17} - 2 q^{18} - 16 q^{21} - 16 q^{22} + 4 q^{23} - 12 q^{26} + 40 q^{27} + 8 q^{28} + 104 q^{31} - 8 q^{32} - 32 q^{33} - 4 q^{36} + 6 q^{37} + 40 q^{38} - 16 q^{41} - 16 q^{42} + 84 q^{43} + 8 q^{46} + 36 q^{47} - 16 q^{48} - 56 q^{51} - 12 q^{52} - 106 q^{53} + 16 q^{56} - 80 q^{57} - 80 q^{58} - 96 q^{61} + 104 q^{62} + 4 q^{63} - 64 q^{66} - 124 q^{67} + 28 q^{68} - 56 q^{71} - 4 q^{72} + 94 q^{73} + 80 q^{76} + 32 q^{77} - 24 q^{78} + 142 q^{81} - 16 q^{82} - 36 q^{83} + 168 q^{86} + 160 q^{87} + 32 q^{88} + 24 q^{91} + 8 q^{92} + 208 q^{93} - 32 q^{96} + 126 q^{97} + 82 q^{98}+O(q^{100})$$ 2 * q + 2 * q^2 + 4 * q^3 + 8 * q^6 - 4 * q^7 - 4 * q^8 - 16 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 - 14 * q^17 - 2 * q^18 - 16 * q^21 - 16 * q^22 + 4 * q^23 - 12 * q^26 + 40 * q^27 + 8 * q^28 + 104 * q^31 - 8 * q^32 - 32 * q^33 - 4 * q^36 + 6 * q^37 + 40 * q^38 - 16 * q^41 - 16 * q^42 + 84 * q^43 + 8 * q^46 + 36 * q^47 - 16 * q^48 - 56 * q^51 - 12 * q^52 - 106 * q^53 + 16 * q^56 - 80 * q^57 - 80 * q^58 - 96 * q^61 + 104 * q^62 + 4 * q^63 - 64 * q^66 - 124 * q^67 + 28 * q^68 - 56 * q^71 - 4 * q^72 + 94 * q^73 + 80 * q^76 + 32 * q^77 - 24 * q^78 + 142 * q^81 - 16 * q^82 - 36 * q^83 + 168 * q^86 + 160 * q^87 + 32 * q^88 + 24 * q^91 + 8 * q^92 + 208 * q^93 - 32 * q^96 + 126 * q^97 + 82 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$$.

 $$n$$ $$27$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$3$$ 2.00000 + 2.00000i 0.666667 + 0.666667i 0.956943 0.290276i $$-0.0937472\pi$$
−0.290276 + 0.956943i $$0.593747\pi$$
$$4$$ 2.00000i 0.500000i
$$5$$ 0 0
$$6$$ 4.00000 0.666667
$$7$$ −2.00000 + 2.00000i −0.285714 + 0.285714i −0.835383 0.549669i $$-0.814754\pi$$
0.549669 + 0.835383i $$0.314754\pi$$
$$8$$ −2.00000 2.00000i −0.250000 0.250000i
$$9$$ 1.00000i 0.111111i
$$10$$ 0 0
$$11$$ −8.00000 −0.727273 −0.363636 0.931541i $$-0.618465\pi$$
−0.363636 + 0.931541i $$0.618465\pi$$
$$12$$ 4.00000 4.00000i 0.333333 0.333333i
$$13$$ −3.00000 3.00000i −0.230769 0.230769i 0.582245 0.813014i $$-0.302175\pi$$
−0.813014 + 0.582245i $$0.802175\pi$$
$$14$$ 4.00000i 0.285714i
$$15$$ 0 0
$$16$$ −4.00000 −0.250000
$$17$$ −7.00000 + 7.00000i −0.411765 + 0.411765i −0.882353 0.470588i $$-0.844042\pi$$
0.470588 + 0.882353i $$0.344042\pi$$
$$18$$ −1.00000 1.00000i −0.0555556 0.0555556i
$$19$$ 20.0000i 1.05263i 0.850289 + 0.526316i $$0.176427\pi$$
−0.850289 + 0.526316i $$0.823573\pi$$
$$20$$ 0 0
$$21$$ −8.00000 −0.380952
$$22$$ −8.00000 + 8.00000i −0.363636 + 0.363636i
$$23$$ 2.00000 + 2.00000i 0.0869565 + 0.0869565i 0.749247 0.662291i $$-0.230416\pi$$
−0.662291 + 0.749247i $$0.730416\pi$$
$$24$$ 8.00000i 0.333333i
$$25$$ 0 0
$$26$$ −6.00000 −0.230769
$$27$$ 20.0000 20.0000i 0.740741 0.740741i
$$28$$ 4.00000 + 4.00000i 0.142857 + 0.142857i
$$29$$ 40.0000i 1.37931i −0.724138 0.689655i $$-0.757762\pi$$
0.724138 0.689655i $$-0.242238\pi$$
$$30$$ 0 0
$$31$$ 52.0000 1.67742 0.838710 0.544579i $$-0.183310\pi$$
0.838710 + 0.544579i $$0.183310\pi$$
$$32$$ −4.00000 + 4.00000i −0.125000 + 0.125000i
$$33$$ −16.0000 16.0000i −0.484848 0.484848i
$$34$$ 14.0000i 0.411765i
$$35$$ 0 0
$$36$$ −2.00000 −0.0555556
$$37$$ 3.00000 3.00000i 0.0810811 0.0810811i −0.665403 0.746484i $$-0.731740\pi$$
0.746484 + 0.665403i $$0.231740\pi$$
$$38$$ 20.0000 + 20.0000i 0.526316 + 0.526316i
$$39$$ 12.0000i 0.307692i
$$40$$ 0 0
$$41$$ −8.00000 −0.195122 −0.0975610 0.995230i $$-0.531104\pi$$
−0.0975610 + 0.995230i $$0.531104\pi$$
$$42$$ −8.00000 + 8.00000i −0.190476 + 0.190476i
$$43$$ 42.0000 + 42.0000i 0.976744 + 0.976744i 0.999736 0.0229915i $$-0.00731906\pi$$
−0.0229915 + 0.999736i $$0.507319\pi$$
$$44$$ 16.0000i 0.363636i
$$45$$ 0 0
$$46$$ 4.00000 0.0869565
$$47$$ 18.0000 18.0000i 0.382979 0.382979i −0.489195 0.872174i $$-0.662710\pi$$
0.872174 + 0.489195i $$0.162710\pi$$
$$48$$ −8.00000 8.00000i −0.166667 0.166667i
$$49$$ 41.0000i 0.836735i
$$50$$ 0 0
$$51$$ −28.0000 −0.549020
$$52$$ −6.00000 + 6.00000i −0.115385 + 0.115385i
$$53$$ −53.0000 53.0000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$54$$ 40.0000i 0.740741i
$$55$$ 0 0
$$56$$ 8.00000 0.142857
$$57$$ −40.0000 + 40.0000i −0.701754 + 0.701754i
$$58$$ −40.0000 40.0000i −0.689655 0.689655i
$$59$$ 20.0000i 0.338983i 0.985532 + 0.169492i $$0.0542125\pi$$
−0.985532 + 0.169492i $$0.945787\pi$$
$$60$$ 0 0
$$61$$ −48.0000 −0.786885 −0.393443 0.919349i $$-0.628716\pi$$
−0.393443 + 0.919349i $$0.628716\pi$$
$$62$$ 52.0000 52.0000i 0.838710 0.838710i
$$63$$ 2.00000 + 2.00000i 0.0317460 + 0.0317460i
$$64$$ 8.00000i 0.125000i
$$65$$ 0 0
$$66$$ −32.0000 −0.484848
$$67$$ −62.0000 + 62.0000i −0.925373 + 0.925373i −0.997403 0.0720294i $$-0.977052\pi$$
0.0720294 + 0.997403i $$0.477052\pi$$
$$68$$ 14.0000 + 14.0000i 0.205882 + 0.205882i
$$69$$ 8.00000i 0.115942i
$$70$$ 0 0
$$71$$ −28.0000 −0.394366 −0.197183 0.980367i $$-0.563179\pi$$
−0.197183 + 0.980367i $$0.563179\pi$$
$$72$$ −2.00000 + 2.00000i −0.0277778 + 0.0277778i
$$73$$ 47.0000 + 47.0000i 0.643836 + 0.643836i 0.951496 0.307661i $$-0.0995461\pi$$
−0.307661 + 0.951496i $$0.599546\pi$$
$$74$$ 6.00000i 0.0810811i
$$75$$ 0 0
$$76$$ 40.0000 0.526316
$$77$$ 16.0000 16.0000i 0.207792 0.207792i
$$78$$ −12.0000 12.0000i −0.153846 0.153846i
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 71.0000 0.876543
$$82$$ −8.00000 + 8.00000i −0.0975610 + 0.0975610i
$$83$$ −18.0000 18.0000i −0.216867 0.216867i 0.590310 0.807177i $$-0.299006\pi$$
−0.807177 + 0.590310i $$0.799006\pi$$
$$84$$ 16.0000i 0.190476i
$$85$$ 0 0
$$86$$ 84.0000 0.976744
$$87$$ 80.0000 80.0000i 0.919540 0.919540i
$$88$$ 16.0000 + 16.0000i 0.181818 + 0.181818i
$$89$$ 80.0000i 0.898876i −0.893311 0.449438i $$-0.851624\pi$$
0.893311 0.449438i $$-0.148376\pi$$
$$90$$ 0 0
$$91$$ 12.0000 0.131868
$$92$$ 4.00000 4.00000i 0.0434783 0.0434783i
$$93$$ 104.000 + 104.000i 1.11828 + 1.11828i
$$94$$ 36.0000i 0.382979i
$$95$$ 0 0
$$96$$ −16.0000 −0.166667
$$97$$ 63.0000 63.0000i 0.649485 0.649485i −0.303384 0.952868i $$-0.598116\pi$$
0.952868 + 0.303384i $$0.0981164\pi$$
$$98$$ 41.0000 + 41.0000i 0.418367 + 0.418367i
$$99$$ 8.00000i 0.0808081i
$$100$$ 0 0
$$101$$ 62.0000 0.613861 0.306931 0.951732i $$-0.400698\pi$$
0.306931 + 0.951732i $$0.400698\pi$$
$$102$$ −28.0000 + 28.0000i −0.274510 + 0.274510i
$$103$$ −118.000 118.000i −1.14563 1.14563i −0.987403 0.158229i $$-0.949422\pi$$
−0.158229 0.987403i $$-0.550578\pi$$
$$104$$ 12.0000i 0.115385i
$$105$$ 0 0
$$106$$ −106.000 −1.00000
$$107$$ −142.000 + 142.000i −1.32710 + 1.32710i −0.419217 + 0.907886i $$0.637695\pi$$
−0.907886 + 0.419217i $$0.862305\pi$$
$$108$$ −40.0000 40.0000i −0.370370 0.370370i
$$109$$ 10.0000i 0.0917431i 0.998947 + 0.0458716i $$0.0146065\pi$$
−0.998947 + 0.0458716i $$0.985394\pi$$
$$110$$ 0 0
$$111$$ 12.0000 0.108108
$$112$$ 8.00000 8.00000i 0.0714286 0.0714286i
$$113$$ −23.0000 23.0000i −0.203540 0.203540i 0.597975 0.801515i $$-0.295972\pi$$
−0.801515 + 0.597975i $$0.795972\pi$$
$$114$$ 80.0000i 0.701754i
$$115$$ 0 0
$$116$$ −80.0000 −0.689655
$$117$$ −3.00000 + 3.00000i −0.0256410 + 0.0256410i
$$118$$ 20.0000 + 20.0000i 0.169492 + 0.169492i
$$119$$ 28.0000i 0.235294i
$$120$$ 0 0
$$121$$ −57.0000 −0.471074
$$122$$ −48.0000 + 48.0000i −0.393443 + 0.393443i
$$123$$ −16.0000 16.0000i −0.130081 0.130081i
$$124$$ 104.000i 0.838710i
$$125$$ 0 0
$$126$$ 4.00000 0.0317460
$$127$$ 118.000 118.000i 0.929134 0.929134i −0.0685161 0.997650i $$-0.521826\pi$$
0.997650 + 0.0685161i $$0.0218265\pi$$
$$128$$ 8.00000 + 8.00000i 0.0625000 + 0.0625000i
$$129$$ 168.000i 1.30233i
$$130$$ 0 0
$$131$$ −128.000 −0.977099 −0.488550 0.872536i $$-0.662474\pi$$
−0.488550 + 0.872536i $$0.662474\pi$$
$$132$$ −32.0000 + 32.0000i −0.242424 + 0.242424i
$$133$$ −40.0000 40.0000i −0.300752 0.300752i
$$134$$ 124.000i 0.925373i
$$135$$ 0 0
$$136$$ 28.0000 0.205882
$$137$$ 63.0000 63.0000i 0.459854 0.459854i −0.438753 0.898607i $$-0.644580\pi$$
0.898607 + 0.438753i $$0.144580\pi$$
$$138$$ 8.00000 + 8.00000i 0.0579710 + 0.0579710i
$$139$$ 140.000i 1.00719i −0.863939 0.503597i $$-0.832010\pi$$
0.863939 0.503597i $$-0.167990\pi$$
$$140$$ 0 0
$$141$$ 72.0000 0.510638
$$142$$ −28.0000 + 28.0000i −0.197183 + 0.197183i
$$143$$ 24.0000 + 24.0000i 0.167832 + 0.167832i
$$144$$ 4.00000i 0.0277778i
$$145$$ 0 0
$$146$$ 94.0000 0.643836
$$147$$ −82.0000 + 82.0000i −0.557823 + 0.557823i
$$148$$ −6.00000 6.00000i −0.0405405 0.0405405i
$$149$$ 150.000i 1.00671i 0.864079 + 0.503356i $$0.167901\pi$$
−0.864079 + 0.503356i $$0.832099\pi$$
$$150$$ 0 0
$$151$$ 52.0000 0.344371 0.172185 0.985065i $$-0.444917\pi$$
0.172185 + 0.985065i $$0.444917\pi$$
$$152$$ 40.0000 40.0000i 0.263158 0.263158i
$$153$$ 7.00000 + 7.00000i 0.0457516 + 0.0457516i
$$154$$ 32.0000i 0.207792i
$$155$$ 0 0
$$156$$ −24.0000 −0.153846
$$157$$ −27.0000 + 27.0000i −0.171975 + 0.171975i −0.787846 0.615872i $$-0.788804\pi$$
0.615872 + 0.787846i $$0.288804\pi$$
$$158$$ 0 0
$$159$$ 212.000i 1.33333i
$$160$$ 0 0
$$161$$ −8.00000 −0.0496894
$$162$$ 71.0000 71.0000i 0.438272 0.438272i
$$163$$ 82.0000 + 82.0000i 0.503067 + 0.503067i 0.912390 0.409322i $$-0.134235\pi$$
−0.409322 + 0.912390i $$0.634235\pi$$
$$164$$ 16.0000i 0.0975610i
$$165$$ 0 0
$$166$$ −36.0000 −0.216867
$$167$$ −62.0000 + 62.0000i −0.371257 + 0.371257i −0.867935 0.496678i $$-0.834553\pi$$
0.496678 + 0.867935i $$0.334553\pi$$
$$168$$ 16.0000 + 16.0000i 0.0952381 + 0.0952381i
$$169$$ 151.000i 0.893491i
$$170$$ 0 0
$$171$$ 20.0000 0.116959
$$172$$ 84.0000 84.0000i 0.488372 0.488372i
$$173$$ 107.000 + 107.000i 0.618497 + 0.618497i 0.945146 0.326649i $$-0.105919\pi$$
−0.326649 + 0.945146i $$0.605919\pi$$
$$174$$ 160.000i 0.919540i
$$175$$ 0 0
$$176$$ 32.0000 0.181818
$$177$$ −40.0000 + 40.0000i −0.225989 + 0.225989i
$$178$$ −80.0000 80.0000i −0.449438 0.449438i
$$179$$ 220.000i 1.22905i 0.788897 + 0.614525i $$0.210652\pi$$
−0.788897 + 0.614525i $$0.789348\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.0110497 0.00552486 0.999985i $$-0.498241\pi$$
0.00552486 + 0.999985i $$0.498241\pi$$
$$182$$ 12.0000 12.0000i 0.0659341 0.0659341i
$$183$$ −96.0000 96.0000i −0.524590 0.524590i
$$184$$ 8.00000i 0.0434783i
$$185$$ 0 0
$$186$$ 208.000 1.11828
$$187$$ 56.0000 56.0000i 0.299465 0.299465i
$$188$$ −36.0000 36.0000i −0.191489 0.191489i
$$189$$ 80.0000i 0.423280i
$$190$$ 0 0
$$191$$ 212.000 1.10995 0.554974 0.831868i $$-0.312728\pi$$
0.554974 + 0.831868i $$0.312728\pi$$
$$192$$ −16.0000 + 16.0000i −0.0833333 + 0.0833333i
$$193$$ 57.0000 + 57.0000i 0.295337 + 0.295337i 0.839184 0.543847i $$-0.183033\pi$$
−0.543847 + 0.839184i $$0.683033\pi$$
$$194$$ 126.000i 0.649485i
$$195$$ 0 0
$$196$$ 82.0000 0.418367
$$197$$ 3.00000 3.00000i 0.0152284 0.0152284i −0.699452 0.714680i $$-0.746572\pi$$
0.714680 + 0.699452i $$0.246572\pi$$
$$198$$ 8.00000 + 8.00000i 0.0404040 + 0.0404040i
$$199$$ 120.000i 0.603015i 0.953464 + 0.301508i $$0.0974898\pi$$
−0.953464 + 0.301508i $$0.902510\pi$$
$$200$$ 0 0
$$201$$ −248.000 −1.23383
$$202$$ 62.0000 62.0000i 0.306931 0.306931i
$$203$$ 80.0000 + 80.0000i 0.394089 + 0.394089i
$$204$$ 56.0000i 0.274510i
$$205$$ 0 0
$$206$$ −236.000 −1.14563
$$207$$ 2.00000 2.00000i 0.00966184 0.00966184i
$$208$$ 12.0000 + 12.0000i 0.0576923 + 0.0576923i
$$209$$ 160.000i 0.765550i
$$210$$ 0 0
$$211$$ −328.000 −1.55450 −0.777251 0.629190i $$-0.783387\pi$$
−0.777251 + 0.629190i $$0.783387\pi$$
$$212$$ −106.000 + 106.000i −0.500000 + 0.500000i
$$213$$ −56.0000 56.0000i −0.262911 0.262911i
$$214$$ 284.000i 1.32710i
$$215$$ 0 0
$$216$$ −80.0000 −0.370370
$$217$$ −104.000 + 104.000i −0.479263 + 0.479263i
$$218$$ 10.0000 + 10.0000i 0.0458716 + 0.0458716i
$$219$$ 188.000i 0.858447i
$$220$$ 0 0
$$221$$ 42.0000 0.190045
$$222$$ 12.0000 12.0000i 0.0540541 0.0540541i
$$223$$ −138.000 138.000i −0.618834 0.618834i 0.326398 0.945232i $$-0.394165\pi$$
−0.945232 + 0.326398i $$0.894165\pi$$
$$224$$ 16.0000i 0.0714286i
$$225$$ 0 0
$$226$$ −46.0000 −0.203540
$$227$$ −2.00000 + 2.00000i −0.00881057 + 0.00881057i −0.711498 0.702688i $$-0.751983\pi$$
0.702688 + 0.711498i $$0.251983\pi$$
$$228$$ 80.0000 + 80.0000i 0.350877 + 0.350877i
$$229$$ 120.000i 0.524017i −0.965066 0.262009i $$-0.915615\pi$$
0.965066 0.262009i $$-0.0843849\pi$$
$$230$$ 0 0
$$231$$ 64.0000 0.277056
$$232$$ −80.0000 + 80.0000i −0.344828 + 0.344828i
$$233$$ −183.000 183.000i −0.785408 0.785408i 0.195330 0.980738i $$-0.437422\pi$$
−0.980738 + 0.195330i $$0.937422\pi$$
$$234$$ 6.00000i 0.0256410i
$$235$$ 0 0
$$236$$ 40.0000 0.169492
$$237$$ 0 0
$$238$$ −28.0000 28.0000i −0.117647 0.117647i
$$239$$ 120.000i 0.502092i −0.967975 0.251046i $$-0.919225\pi$$
0.967975 0.251046i $$-0.0807746\pi$$
$$240$$ 0 0
$$241$$ 232.000 0.962656 0.481328 0.876541i $$-0.340155\pi$$
0.481328 + 0.876541i $$0.340155\pi$$
$$242$$ −57.0000 + 57.0000i −0.235537 + 0.235537i
$$243$$ −38.0000 38.0000i −0.156379 0.156379i
$$244$$ 96.0000i 0.393443i
$$245$$ 0 0
$$246$$ −32.0000 −0.130081
$$247$$ 60.0000 60.0000i 0.242915 0.242915i
$$248$$ −104.000 104.000i −0.419355 0.419355i
$$249$$ 72.0000i 0.289157i
$$250$$ 0 0
$$251$$ −48.0000 −0.191235 −0.0956175 0.995418i $$-0.530483\pi$$
−0.0956175 + 0.995418i $$0.530483\pi$$
$$252$$ 4.00000 4.00000i 0.0158730 0.0158730i
$$253$$ −16.0000 16.0000i −0.0632411 0.0632411i
$$254$$ 236.000i 0.929134i
$$255$$ 0 0
$$256$$ 16.0000 0.0625000
$$257$$ 313.000 313.000i 1.21790 1.21790i 0.249532 0.968366i $$-0.419723\pi$$
0.968366 0.249532i $$-0.0802769\pi$$
$$258$$ 168.000 + 168.000i 0.651163 + 0.651163i
$$259$$ 12.0000i 0.0463320i
$$260$$ 0 0
$$261$$ −40.0000 −0.153257
$$262$$ −128.000 + 128.000i −0.488550 + 0.488550i
$$263$$ 262.000 + 262.000i 0.996198 + 0.996198i 0.999993 0.00379508i $$-0.00120801\pi$$
−0.00379508 + 0.999993i $$0.501208\pi$$
$$264$$ 64.0000i 0.242424i
$$265$$ 0 0
$$266$$ −80.0000 −0.300752
$$267$$ 160.000 160.000i 0.599251 0.599251i
$$268$$ 124.000 + 124.000i 0.462687 + 0.462687i
$$269$$ 10.0000i 0.0371747i −0.999827 0.0185874i $$-0.994083\pi$$
0.999827 0.0185874i $$-0.00591688\pi$$
$$270$$ 0 0
$$271$$ 252.000 0.929889 0.464945 0.885340i $$-0.346074\pi$$
0.464945 + 0.885340i $$0.346074\pi$$
$$272$$ 28.0000 28.0000i 0.102941 0.102941i
$$273$$ 24.0000 + 24.0000i 0.0879121 + 0.0879121i
$$274$$ 126.000i 0.459854i
$$275$$ 0 0
$$276$$ 16.0000 0.0579710
$$277$$ −267.000 + 267.000i −0.963899 + 0.963899i −0.999371 0.0354718i $$-0.988707\pi$$
0.0354718 + 0.999371i $$0.488707\pi$$
$$278$$ −140.000 140.000i −0.503597 0.503597i
$$279$$ 52.0000i 0.186380i
$$280$$ 0 0
$$281$$ 312.000 1.11032 0.555160 0.831743i $$-0.312657\pi$$
0.555160 + 0.831743i $$0.312657\pi$$
$$282$$ 72.0000 72.0000i 0.255319 0.255319i
$$283$$ 262.000 + 262.000i 0.925795 + 0.925795i 0.997431 0.0716358i $$-0.0228219\pi$$
−0.0716358 + 0.997431i $$0.522822\pi$$
$$284$$ 56.0000i 0.197183i
$$285$$ 0 0
$$286$$ 48.0000 0.167832
$$287$$ 16.0000 16.0000i 0.0557491 0.0557491i
$$288$$ 4.00000 + 4.00000i 0.0138889 + 0.0138889i
$$289$$ 191.000i 0.660900i
$$290$$ 0 0
$$291$$ 252.000 0.865979
$$292$$ 94.0000 94.0000i 0.321918 0.321918i
$$293$$ −243.000 243.000i −0.829352 0.829352i 0.158075 0.987427i $$-0.449471\pi$$
−0.987427 + 0.158075i $$0.949471\pi$$
$$294$$ 164.000i 0.557823i
$$295$$ 0 0
$$296$$ −12.0000 −0.0405405
$$297$$ −160.000 + 160.000i −0.538721 + 0.538721i
$$298$$ 150.000 + 150.000i 0.503356 + 0.503356i
$$299$$ 12.0000i 0.0401338i
$$300$$ 0 0
$$301$$ −168.000 −0.558140
$$302$$ 52.0000 52.0000i 0.172185 0.172185i
$$303$$ 124.000 + 124.000i 0.409241 + 0.409241i
$$304$$ 80.0000i 0.263158i
$$305$$ 0 0
$$306$$ 14.0000 0.0457516
$$307$$ 18.0000 18.0000i 0.0586319 0.0586319i −0.677183 0.735815i $$-0.736799\pi$$
0.735815 + 0.677183i $$0.236799\pi$$
$$308$$ −32.0000 32.0000i −0.103896 0.103896i
$$309$$ 472.000i 1.52751i
$$310$$ 0 0
$$311$$ −388.000 −1.24759 −0.623794 0.781589i $$-0.714410\pi$$
−0.623794 + 0.781589i $$0.714410\pi$$
$$312$$ −24.0000 + 24.0000i −0.0769231 + 0.0769231i
$$313$$ −183.000 183.000i −0.584665 0.584665i 0.351517 0.936182i $$-0.385666\pi$$
−0.936182 + 0.351517i $$0.885666\pi$$
$$314$$ 54.0000i 0.171975i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 213.000 213.000i 0.671924 0.671924i −0.286235 0.958159i $$-0.592404\pi$$
0.958159 + 0.286235i $$0.0924038\pi$$
$$318$$ −212.000 212.000i −0.666667 0.666667i
$$319$$ 320.000i 1.00313i
$$320$$ 0 0
$$321$$ −568.000 −1.76947
$$322$$ −8.00000 + 8.00000i −0.0248447 + 0.0248447i
$$323$$ −140.000 140.000i −0.433437 0.433437i
$$324$$ 142.000i 0.438272i
$$325$$ 0 0
$$326$$ 164.000 0.503067
$$327$$ −20.0000 + 20.0000i −0.0611621 + 0.0611621i
$$328$$ 16.0000 + 16.0000i 0.0487805 + 0.0487805i
$$329$$ 72.0000i 0.218845i
$$330$$ 0 0
$$331$$ 232.000 0.700906 0.350453 0.936580i $$-0.386028\pi$$
0.350453 + 0.936580i $$0.386028\pi$$
$$332$$ −36.0000 + 36.0000i −0.108434 + 0.108434i
$$333$$ −3.00000 3.00000i −0.00900901 0.00900901i
$$334$$ 124.000i 0.371257i
$$335$$ 0 0
$$336$$ 32.0000 0.0952381
$$337$$ −417.000 + 417.000i −1.23739 + 1.23739i −0.276324 + 0.961064i $$0.589116\pi$$
−0.961064 + 0.276324i $$0.910884\pi$$
$$338$$ −151.000 151.000i −0.446746 0.446746i
$$339$$ 92.0000i 0.271386i
$$340$$ 0 0
$$341$$ −416.000 −1.21994
$$342$$ 20.0000 20.0000i 0.0584795 0.0584795i
$$343$$ −180.000 180.000i −0.524781 0.524781i
$$344$$ 168.000i 0.488372i
$$345$$ 0 0
$$346$$ 214.000 0.618497
$$347$$ −202.000 + 202.000i −0.582133 + 0.582133i −0.935489 0.353356i $$-0.885040\pi$$
0.353356 + 0.935489i $$0.385040\pi$$
$$348$$ −160.000 160.000i −0.459770 0.459770i
$$349$$ 440.000i 1.26074i 0.776293 + 0.630372i $$0.217098\pi$$
−0.776293 + 0.630372i $$0.782902\pi$$
$$350$$ 0 0
$$351$$ −120.000 −0.341880
$$352$$ 32.0000 32.0000i 0.0909091 0.0909091i
$$353$$ 447.000 + 447.000i 1.26629 + 1.26629i 0.947991 + 0.318298i $$0.103111\pi$$
0.318298 + 0.947991i $$0.396889\pi$$
$$354$$ 80.0000i 0.225989i
$$355$$ 0 0
$$356$$ −160.000 −0.449438
$$357$$ 56.0000 56.0000i 0.156863 0.156863i
$$358$$ 220.000 + 220.000i 0.614525 + 0.614525i
$$359$$ 400.000i 1.11421i 0.830443 + 0.557103i $$0.188087\pi$$
−0.830443 + 0.557103i $$0.811913\pi$$
$$360$$ 0 0
$$361$$ −39.0000 −0.108033
$$362$$ 2.00000 2.00000i 0.00552486 0.00552486i
$$363$$ −114.000 114.000i −0.314050 0.314050i
$$364$$ 24.0000i 0.0659341i
$$365$$ 0 0
$$366$$ −192.000 −0.524590
$$367$$ 118.000 118.000i 0.321526 0.321526i −0.527826 0.849352i $$-0.676993\pi$$
0.849352 + 0.527826i $$0.176993\pi$$
$$368$$ −8.00000 8.00000i −0.0217391 0.0217391i
$$369$$ 8.00000i 0.0216802i
$$370$$ 0 0
$$371$$ 212.000 0.571429
$$372$$ 208.000 208.000i 0.559140 0.559140i
$$373$$ 107.000 + 107.000i 0.286863 + 0.286863i 0.835839 0.548975i $$-0.184982\pi$$
−0.548975 + 0.835839i $$0.684982\pi$$
$$374$$ 112.000i 0.299465i
$$375$$ 0 0
$$376$$ −72.0000 −0.191489
$$377$$ −120.000 + 120.000i −0.318302 + 0.318302i
$$378$$ 80.0000 + 80.0000i 0.211640 + 0.211640i
$$379$$ 340.000i 0.897098i −0.893758 0.448549i $$-0.851941\pi$$
0.893758 0.448549i $$-0.148059\pi$$
$$380$$ 0 0
$$381$$ 472.000 1.23885
$$382$$ 212.000 212.000i 0.554974 0.554974i
$$383$$ 342.000 + 342.000i 0.892950 + 0.892950i 0.994800 0.101849i $$-0.0324760\pi$$
−0.101849 + 0.994800i $$0.532476\pi$$
$$384$$ 32.0000i 0.0833333i
$$385$$ 0 0
$$386$$ 114.000 0.295337
$$387$$ 42.0000 42.0000i 0.108527 0.108527i
$$388$$ −126.000 126.000i −0.324742 0.324742i
$$389$$ 390.000i 1.00257i −0.865282 0.501285i $$-0.832861\pi$$
0.865282 0.501285i $$-0.167139\pi$$
$$390$$ 0 0
$$391$$ −28.0000 −0.0716113
$$392$$ 82.0000 82.0000i 0.209184 0.209184i
$$393$$ −256.000 256.000i −0.651399 0.651399i
$$394$$ 6.00000i 0.0152284i
$$395$$ 0 0
$$396$$ 16.0000 0.0404040
$$397$$ 323.000 323.000i 0.813602 0.813602i −0.171570 0.985172i $$-0.554884\pi$$
0.985172 + 0.171570i $$0.0548839\pi$$
$$398$$ 120.000 + 120.000i 0.301508 + 0.301508i
$$399$$ 160.000i 0.401003i
$$400$$ 0 0
$$401$$ 642.000 1.60100 0.800499 0.599334i $$-0.204568\pi$$
0.800499 + 0.599334i $$0.204568\pi$$
$$402$$ −248.000 + 248.000i −0.616915 + 0.616915i
$$403$$ −156.000 156.000i −0.387097 0.387097i
$$404$$ 124.000i 0.306931i
$$405$$ 0 0
$$406$$ 160.000 0.394089
$$407$$ −24.0000 + 24.0000i −0.0589681 + 0.0589681i
$$408$$ 56.0000 + 56.0000i 0.137255 + 0.137255i
$$409$$ 150.000i 0.366748i 0.983043 + 0.183374i $$0.0587020\pi$$
−0.983043 + 0.183374i $$0.941298\pi$$
$$410$$ 0 0
$$411$$ 252.000 0.613139
$$412$$ −236.000 + 236.000i −0.572816 + 0.572816i
$$413$$ −40.0000 40.0000i −0.0968523 0.0968523i
$$414$$ 4.00000i 0.00966184i
$$415$$ 0 0
$$416$$ 24.0000 0.0576923
$$417$$ 280.000 280.000i 0.671463 0.671463i
$$418$$ −160.000 160.000i −0.382775 0.382775i
$$419$$ 300.000i 0.715990i −0.933723 0.357995i $$-0.883460\pi$$
0.933723 0.357995i $$-0.116540\pi$$
$$420$$ 0 0
$$421$$ −208.000 −0.494062 −0.247031 0.969008i $$-0.579455\pi$$
−0.247031 + 0.969008i $$0.579455\pi$$
$$422$$ −328.000 + 328.000i −0.777251 + 0.777251i
$$423$$ −18.0000 18.0000i −0.0425532 0.0425532i
$$424$$ 212.000i 0.500000i
$$425$$ 0 0
$$426$$ −112.000 −0.262911
$$427$$ 96.0000 96.0000i 0.224824 0.224824i
$$428$$ 284.000 + 284.000i 0.663551 + 0.663551i
$$429$$ 96.0000i 0.223776i
$$430$$ 0 0
$$431$$ −788.000 −1.82831 −0.914153 0.405369i $$-0.867143\pi$$
−0.914153 + 0.405369i $$0.867143\pi$$
$$432$$ −80.0000 + 80.0000i −0.185185 + 0.185185i
$$433$$ 367.000 + 367.000i 0.847575 + 0.847575i 0.989830 0.142255i $$-0.0454353\pi$$
−0.142255 + 0.989830i $$0.545435\pi$$
$$434$$ 208.000i 0.479263i
$$435$$ 0 0
$$436$$ 20.0000 0.0458716
$$437$$ −40.0000 + 40.0000i −0.0915332 + 0.0915332i
$$438$$ 188.000 + 188.000i 0.429224 + 0.429224i
$$439$$ 560.000i 1.27563i −0.770191 0.637813i $$-0.779839\pi$$
0.770191 0.637813i $$-0.220161\pi$$
$$440$$ 0 0
$$441$$ 41.0000 0.0929705
$$442$$ 42.0000 42.0000i 0.0950226 0.0950226i
$$443$$ −378.000 378.000i −0.853273 0.853273i 0.137262 0.990535i $$-0.456170\pi$$
−0.990535 + 0.137262i $$0.956170\pi$$
$$444$$ 24.0000i 0.0540541i
$$445$$ 0 0
$$446$$ −276.000 −0.618834
$$447$$ −300.000 + 300.000i −0.671141 + 0.671141i
$$448$$ −16.0000 16.0000i −0.0357143 0.0357143i
$$449$$ 410.000i 0.913140i 0.889687 + 0.456570i $$0.150922\pi$$
−0.889687 + 0.456570i $$0.849078\pi$$
$$450$$ 0 0
$$451$$ 64.0000 0.141907
$$452$$ −46.0000 + 46.0000i −0.101770 + 0.101770i
$$453$$ 104.000 + 104.000i 0.229581 + 0.229581i
$$454$$ 4.00000i 0.00881057i
$$455$$ 0 0
$$456$$ 160.000 0.350877
$$457$$ 393.000 393.000i 0.859956 0.859956i −0.131376 0.991333i $$-0.541940\pi$$
0.991333 + 0.131376i $$0.0419396\pi$$
$$458$$ −120.000 120.000i −0.262009 0.262009i
$$459$$ 280.000i 0.610022i
$$460$$ 0 0
$$461$$ 622.000 1.34924 0.674620 0.738165i $$-0.264307\pi$$
0.674620 + 0.738165i $$0.264307\pi$$
$$462$$ 64.0000 64.0000i 0.138528 0.138528i
$$463$$ −278.000 278.000i −0.600432 0.600432i 0.339995 0.940427i $$-0.389575\pi$$
−0.940427 + 0.339995i $$0.889575\pi$$
$$464$$ 160.000i 0.344828i
$$465$$ 0 0
$$466$$ −366.000 −0.785408
$$467$$ 38.0000 38.0000i 0.0813704 0.0813704i −0.665250 0.746621i $$-0.731675\pi$$
0.746621 + 0.665250i $$0.231675\pi$$
$$468$$ 6.00000 + 6.00000i 0.0128205 + 0.0128205i
$$469$$ 248.000i 0.528785i
$$470$$ 0 0
$$471$$ −108.000 −0.229299
$$472$$ 40.0000 40.0000i 0.0847458 0.0847458i
$$473$$ −336.000 336.000i −0.710359 0.710359i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −56.0000 −0.117647
$$477$$ −53.0000 + 53.0000i −0.111111 + 0.111111i
$$478$$ −120.000 120.000i −0.251046 0.251046i
$$479$$ 440.000i 0.918580i 0.888286 + 0.459290i $$0.151896\pi$$
−0.888286 + 0.459290i $$0.848104\pi$$
$$480$$ 0 0
$$481$$ −18.0000 −0.0374220
$$482$$ 232.000 232.000i 0.481328 0.481328i
$$483$$ −16.0000 16.0000i −0.0331263 0.0331263i
$$484$$ 114.000i 0.235537i
$$485$$ 0 0
$$486$$ −76.0000 −0.156379
$$487$$ −522.000 + 522.000i −1.07187 + 1.07187i −0.0746595 + 0.997209i $$0.523787\pi$$
−0.997209 + 0.0746595i $$0.976213\pi$$
$$488$$ 96.0000 + 96.0000i 0.196721 + 0.196721i
$$489$$ 328.000i 0.670757i
$$490$$ 0 0
$$491$$ −328.000 −0.668024 −0.334012 0.942569i $$-0.608403\pi$$
−0.334012 + 0.942569i $$0.608403\pi$$
$$492$$ −32.0000 + 32.0000i −0.0650407 + 0.0650407i
$$493$$ 280.000 + 280.000i 0.567951 + 0.567951i
$$494$$ 120.000i 0.242915i
$$495$$ 0 0
$$496$$ −208.000 −0.419355
$$497$$ 56.0000 56.0000i 0.112676 0.112676i
$$498$$ −72.0000 72.0000i −0.144578 0.144578i
$$499$$ 380.000i 0.761523i −0.924673 0.380762i $$-0.875662\pi$$
0.924673 0.380762i $$-0.124338\pi$$
$$500$$ 0 0
$$501$$ −248.000 −0.495010
$$502$$ −48.0000 + 48.0000i −0.0956175 + 0.0956175i
$$503$$ 42.0000 + 42.0000i 0.0834990 + 0.0834990i 0.747623 0.664124i $$-0.231195\pi$$
−0.664124 + 0.747623i $$0.731195\pi$$
$$504$$ 8.00000i 0.0158730i
$$505$$ 0 0
$$506$$ −32.0000 −0.0632411
$$507$$ 302.000 302.000i 0.595661 0.595661i
$$508$$ −236.000 236.000i −0.464567 0.464567i
$$509$$ 440.000i 0.864440i 0.901768 + 0.432220i $$0.142270\pi$$
−0.901768 + 0.432220i $$0.857730\pi$$
$$510$$ 0 0
$$511$$ −188.000 −0.367906
$$512$$ 16.0000 16.0000i 0.0312500 0.0312500i
$$513$$ 400.000 + 400.000i 0.779727 + 0.779727i
$$514$$ 626.000i 1.21790i
$$515$$ 0 0
$$516$$ 336.000 0.651163
$$517$$ −144.000 + 144.000i −0.278530 + 0.278530i
$$518$$ 12.0000 + 12.0000i 0.0231660 + 0.0231660i
$$519$$ 428.000i 0.824663i
$$520$$ 0 0
$$521$$ −258.000 −0.495202 −0.247601 0.968862i $$-0.579642\pi$$
−0.247601 + 0.968862i $$0.579642\pi$$
$$522$$ −40.0000 + 40.0000i −0.0766284 + 0.0766284i
$$523$$ −258.000 258.000i −0.493308 0.493308i 0.416039 0.909347i $$-0.363418\pi$$
−0.909347 + 0.416039i $$0.863418\pi$$
$$524$$ 256.000i 0.488550i
$$525$$ 0 0
$$526$$ 524.000 0.996198
$$527$$ −364.000 + 364.000i −0.690702 + 0.690702i
$$528$$ 64.0000 + 64.0000i 0.121212 + 0.121212i
$$529$$ 521.000i 0.984877i
$$530$$ 0 0
$$531$$ 20.0000 0.0376648
$$532$$ −80.0000 + 80.0000i −0.150376 + 0.150376i
$$533$$ 24.0000 + 24.0000i 0.0450281 + 0.0450281i
$$534$$ 320.000i 0.599251i
$$535$$ 0 0
$$536$$ 248.000 0.462687
$$537$$ −440.000 + 440.000i −0.819367 + 0.819367i
$$538$$ −10.0000 10.0000i −0.0185874 0.0185874i
$$539$$ 328.000i 0.608534i
$$540$$ 0 0
$$541$$ −338.000 −0.624769 −0.312384 0.949956i $$-0.601128\pi$$
−0.312384 + 0.949956i $$0.601128\pi$$
$$542$$ 252.000 252.000i 0.464945 0.464945i
$$543$$ 4.00000 + 4.00000i 0.00736648 + 0.00736648i
$$544$$ 56.0000i 0.102941i
$$545$$ 0 0
$$546$$ 48.0000 0.0879121
$$547$$ 558.000 558.000i 1.02011 1.02011i 0.0203161 0.999794i $$-0.493533\pi$$
0.999794 0.0203161i $$-0.00646725\pi$$
$$548$$ −126.000 126.000i −0.229927 0.229927i
$$549$$ 48.0000i 0.0874317i
$$550$$ 0 0
$$551$$ 800.000 1.45191
$$552$$ 16.0000 16.0000i 0.0289855 0.0289855i
$$553$$ 0 0
$$554$$ 534.000i 0.963899i
$$555$$ 0 0
$$556$$ −280.000 −0.503597
$$557$$ 3.00000 3.00000i 0.00538600 0.00538600i −0.704409 0.709795i $$-0.748788\pi$$
0.709795 + 0.704409i $$0.248788\pi$$
$$558$$ −52.0000 52.0000i −0.0931900 0.0931900i
$$559$$ 252.000i 0.450805i
$$560$$ 0 0
$$561$$ 224.000 0.399287
$$562$$ 312.000 312.000i 0.555160 0.555160i
$$563$$ 42.0000 + 42.0000i 0.0746004 + 0.0746004i 0.743422 0.668822i $$-0.233201\pi$$
−0.668822 + 0.743422i $$0.733201\pi$$
$$564$$ 144.000i 0.255319i
$$565$$ 0 0
$$566$$ 524.000 0.925795
$$567$$ −142.000 + 142.000i −0.250441 + 0.250441i
$$568$$ 56.0000 + 56.0000i 0.0985915 + 0.0985915i
$$569$$ 950.000i 1.66960i −0.550557 0.834798i $$-0.685584\pi$$
0.550557 0.834798i $$-0.314416\pi$$
$$570$$ 0 0
$$571$$ 392.000 0.686515 0.343257 0.939241i $$-0.388470\pi$$
0.343257 + 0.939241i $$0.388470\pi$$
$$572$$ 48.0000 48.0000i 0.0839161 0.0839161i
$$573$$ 424.000 + 424.000i 0.739965 + 0.739965i
$$574$$ 32.0000i 0.0557491i
$$575$$ 0 0
$$576$$ 8.00000 0.0138889
$$577$$ 473.000 473.000i 0.819757 0.819757i −0.166315 0.986073i $$-0.553187\pi$$
0.986073 + 0.166315i $$0.0531869\pi$$
$$578$$ 191.000 + 191.000i 0.330450 + 0.330450i
$$579$$ 228.000i 0.393782i
$$580$$ 0 0
$$581$$ 72.0000 0.123924
$$582$$ 252.000 252.000i 0.432990 0.432990i
$$583$$ 424.000 + 424.000i 0.727273 + 0.727273i
$$584$$ 188.000i 0.321918i
$$585$$ 0 0
$$586$$ −486.000 −0.829352
$$587$$ 198.000 198.000i 0.337308 0.337308i −0.518045 0.855353i $$-0.673340\pi$$
0.855353 + 0.518045i $$0.173340\pi$$
$$588$$ 164.000 + 164.000i 0.278912 + 0.278912i
$$589$$ 1040.00i 1.76570i
$$590$$ 0 0
$$591$$ 12.0000 0.0203046
$$592$$ −12.0000 + 12.0000i −0.0202703 + 0.0202703i
$$593$$ 47.0000 + 47.0000i 0.0792580 + 0.0792580i 0.745624 0.666366i $$-0.232151\pi$$
−0.666366 + 0.745624i $$0.732151\pi$$
$$594$$ 320.000i 0.538721i
$$595$$ 0 0
$$596$$ 300.000 0.503356
$$597$$ −240.000 + 240.000i −0.402010 + 0.402010i
$$598$$ −12.0000 12.0000i −0.0200669 0.0200669i
$$599$$ 520.000i 0.868114i −0.900886 0.434057i $$-0.857082\pi$$
0.900886 0.434057i $$-0.142918\pi$$
$$600$$ 0 0
$$601$$ −328.000 −0.545757 −0.272879 0.962048i $$-0.587976\pi$$
−0.272879 + 0.962048i $$0.587976\pi$$
$$602$$ −168.000 + 168.000i −0.279070 + 0.279070i
$$603$$ 62.0000 + 62.0000i 0.102819 + 0.102819i
$$604$$ 104.000i 0.172185i
$$605$$ 0 0
$$606$$ 248.000 0.409241
$$607$$ −462.000 + 462.000i −0.761120 + 0.761120i −0.976525 0.215405i $$-0.930893\pi$$
0.215405 + 0.976525i $$0.430893\pi$$
$$608$$ −80.0000 80.0000i −0.131579 0.131579i
$$609$$ 320.000i 0.525452i
$$610$$ 0 0
$$611$$ −108.000 −0.176759
$$612$$ 14.0000 14.0000i 0.0228758 0.0228758i
$$613$$ −723.000 723.000i −1.17945 1.17945i −0.979886 0.199560i $$-0.936049\pi$$
−0.199560 0.979886i $$-0.563951\pi$$
$$614$$ 36.0000i 0.0586319i
$$615$$ 0 0
$$616$$ −64.0000 −0.103896
$$617$$ −327.000 + 327.000i −0.529984 + 0.529984i −0.920567 0.390584i $$-0.872273\pi$$
0.390584 + 0.920567i $$0.372273\pi$$
$$618$$ −472.000 472.000i −0.763754 0.763754i
$$619$$ 660.000i 1.06624i 0.846041 + 0.533118i $$0.178980\pi$$
−0.846041 + 0.533118i $$0.821020\pi$$
$$620$$ 0 0
$$621$$ 80.0000 0.128824
$$622$$ −388.000 + 388.000i −0.623794 + 0.623794i
$$623$$ 160.000 + 160.000i 0.256822 + 0.256822i
$$624$$ 48.0000i 0.0769231i
$$625$$ 0 0
$$626$$ −366.000 −0.584665
$$627$$ 320.000 320.000i 0.510367 0.510367i
$$628$$ 54.0000 + 54.0000i 0.0859873 + 0.0859873i
$$629$$ 42.0000i 0.0667727i
$$630$$ 0 0
$$631$$ −548.000 −0.868463 −0.434231 0.900801i $$-0.642980\pi$$
−0.434231 + 0.900801i $$0.642980\pi$$
$$632$$ 0 0
$$633$$ −656.000 656.000i −1.03633 1.03633i
$$634$$ 426.000i 0.671924i
$$635$$ 0 0
$$636$$ −424.000 −0.666667
$$637$$ 123.000 123.000i 0.193093 0.193093i
$$638$$ 320.000 + 320.000i 0.501567 + 0.501567i
$$639$$ 28.0000i 0.0438185i
$$640$$ 0 0
$$641$$ −568.000 −0.886115 −0.443058 0.896493i $$-0.646106\pi$$
−0.443058 + 0.896493i $$0.646106\pi$$
$$642$$ −568.000 + 568.000i −0.884735 + 0.884735i
$$643$$ 342.000 + 342.000i 0.531882 + 0.531882i 0.921132 0.389250i $$-0.127266\pi$$
−0.389250 + 0.921132i $$0.627266\pi$$
$$644$$ 16.0000i 0.0248447i
$$645$$ 0 0
$$646$$ −280.000 −0.433437
$$647$$ 118.000 118.000i 0.182380 0.182380i −0.610012 0.792392i $$-0.708835\pi$$
0.792392 + 0.610012i $$0.208835\pi$$
$$648$$ −142.000 142.000i −0.219136 0.219136i
$$649$$ 160.000i 0.246533i
$$650$$ 0 0
$$651$$ −416.000 −0.639017
$$652$$ 164.000 164.000i 0.251534 0.251534i
$$653$$ −453.000 453.000i −0.693721 0.693721i 0.269327 0.963049i $$-0.413199\pi$$
−0.963049 + 0.269327i $$0.913199\pi$$
$$654$$ 40.0000i 0.0611621i
$$655$$ 0 0
$$656$$ 32.0000 0.0487805
$$657$$ 47.0000 47.0000i 0.0715373 0.0715373i
$$658$$ 72.0000 + 72.0000i 0.109422 + 0.109422i
$$659$$ 140.000i 0.212443i −0.994342 0.106222i $$-0.966125\pi$$
0.994342 0.106222i $$-0.0338753\pi$$
$$660$$ 0 0
$$661$$ 512.000 0.774584 0.387292 0.921957i $$-0.373411\pi$$
0.387292 + 0.921957i $$0.373411\pi$$
$$662$$ 232.000 232.000i 0.350453 0.350453i
$$663$$ 84.0000 + 84.0000i 0.126697 + 0.126697i
$$664$$ 72.0000i 0.108434i
$$665$$ 0 0
$$666$$ −6.00000 −0.00900901
$$667$$ 80.0000 80.0000i 0.119940 0.119940i
$$668$$ 124.000 + 124.000i 0.185629 + 0.185629i
$$669$$ 552.000i 0.825112i
$$670$$ 0 0
$$671$$ 384.000 0.572280
$$672$$ 32.0000 32.0000i 0.0476190 0.0476190i
$$673$$ −193.000 193.000i −0.286776 0.286776i 0.549028 0.835804i $$-0.314998\pi$$
−0.835804 + 0.549028i $$0.814998\pi$$
$$674$$ 834.000i 1.23739i
$$675$$ 0 0
$$676$$ −302.000 −0.446746
$$677$$ −157.000 + 157.000i −0.231905 + 0.231905i −0.813488 0.581582i $$-0.802434\pi$$
0.581582 + 0.813488i $$0.302434\pi$$
$$678$$ −92.0000 92.0000i −0.135693 0.135693i
$$679$$ 252.000i 0.371134i
$$680$$ 0 0
$$681$$ −8.00000 −0.0117474
$$682$$ −416.000 + 416.000i −0.609971 + 0.609971i
$$683$$ −438.000 438.000i −0.641288 0.641288i 0.309584 0.950872i $$-0.399810\pi$$
−0.950872 + 0.309584i $$0.899810\pi$$
$$684$$ 40.0000i 0.0584795i
$$685$$ 0 0
$$686$$ −360.000 −0.524781
$$687$$ 240.000 240.000i 0.349345 0.349345i
$$688$$ −168.000 168.000i −0.244186 0.244186i
$$689$$ 318.000i 0.461538i
$$690$$ 0 0
$$691$$ 1032.00 1.49349 0.746744 0.665112i $$-0.231616\pi$$
0.746744 + 0.665112i $$0.231616\pi$$
$$692$$ 214.000 214.000i 0.309249 0.309249i
$$693$$ −16.0000 16.0000i −0.0230880 0.0230880i
$$694$$ 404.000i 0.582133i
$$695$$ 0 0
$$696$$ −320.000 −0.459770
$$697$$ 56.0000 56.0000i 0.0803443 0.0803443i
$$698$$ 440.000 + 440.000i 0.630372 + 0.630372i
$$699$$ 732.000i 1.04721i
$$700$$ 0 0
$$701$$ −128.000 −0.182596 −0.0912981 0.995824i $$-0.529102\pi$$
−0.0912981 + 0.995824i $$0.529102\pi$$
$$702$$ −120.000 + 120.000i −0.170940 + 0.170940i
$$703$$ 60.0000 + 60.0000i 0.0853485 + 0.0853485i
$$704$$ 64.0000i 0.0909091i
$$705$$ 0 0
$$706$$ 894.000 1.26629
$$707$$ −124.000 + 124.000i −0.175389 + 0.175389i
$$708$$ 80.0000 + 80.0000i 0.112994 + 0.112994i
$$709$$ 760.000i 1.07193i −0.844239 0.535966i $$-0.819947\pi$$
0.844239 0.535966i $$-0.180053\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −160.000 + 160.000i −0.224719 + 0.224719i
$$713$$ 104.000 + 104.000i 0.145863 + 0.145863i
$$714$$ 112.000i 0.156863i
$$715$$ 0 0
$$716$$ 440.000 0.614525
$$717$$ 240.000 240.000i 0.334728 0.334728i
$$718$$ 400.000 + 400.000i 0.557103 + 0.557103i
$$719$$ 1160.00i 1.61335i 0.590994 + 0.806676i $$0.298736\pi$$
−0.590994 + 0.806676i $$0.701264\pi$$
$$720$$ 0 0
$$721$$ 472.000 0.654646
$$722$$ −39.0000 + 39.0000i −0.0540166 + 0.0540166i
$$723$$ 464.000 + 464.000i 0.641770 + 0.641770i
$$724$$ 4.00000i 0.00552486i
$$725$$ 0 0
$$726$$ −228.000 −0.314050
$$727$$ 558.000 558.000i 0.767538 0.767538i −0.210135 0.977672i $$-0.567390\pi$$
0.977672 + 0.210135i $$0.0673902\pi$$
$$728$$ −24.0000 24.0000i −0.0329670 0.0329670i
$$729$$ 791.000i 1.08505i
$$730$$ 0 0
$$731$$ −588.000 −0.804378
$$732$$ −192.000 + 192.000i −0.262295 + 0.262295i
$$733$$ 827.000 + 827.000i 1.12824 + 1.12824i 0.990463 + 0.137777i $$0.0439957\pi$$
0.137777 + 0.990463i $$0.456004\pi$$
$$734$$ 236.000i 0.321526i
$$735$$ 0 0
$$736$$ −16.0000 −0.0217391
$$737$$ 496.000 496.000i 0.672999 0.672999i
$$738$$ 8.00000 + 8.00000i 0.0108401 + 0.0108401i
$$739$$ 700.000i 0.947226i 0.880733 + 0.473613i $$0.157050\pi$$
−0.880733 + 0.473613i $$0.842950\pi$$
$$740$$ 0 0
$$741$$ 240.000 0.323887
$$742$$ 212.000 212.000i 0.285714 0.285714i
$$743$$ 382.000 + 382.000i 0.514132 + 0.514132i 0.915790 0.401658i $$-0.131566\pi$$
−0.401658 + 0.915790i $$0.631566\pi$$
$$744$$ 416.000i 0.559140i
$$745$$ 0 0
$$746$$ 214.000 0.286863
$$747$$ −18.0000 + 18.0000i −0.0240964 + 0.0240964i
$$748$$ −112.000 112.000i −0.149733 0.149733i
$$749$$ 568.000i 0.758344i
$$750$$ 0 0
$$751$$ −588.000 −0.782956 −0.391478 0.920187i $$-0.628036\pi$$
−0.391478 + 0.920187i $$0.628036\pi$$
$$752$$ −72.0000 + 72.0000i −0.0957447 + 0.0957447i
$$753$$ −96.0000 96.0000i −0.127490 0.127490i
$$754$$ 240.000i 0.318302i
$$755$$ 0 0
$$756$$ 160.000 0.211640
$$757$$ −987.000 + 987.000i −1.30383 + 1.30383i −0.378043 + 0.925788i $$0.623403\pi$$
−0.925788 + 0.378043i $$0.876597\pi$$
$$758$$ −340.000 340.000i −0.448549 0.448549i
$$759$$ 64.0000i 0.0843215i
$$760$$ 0 0
$$761$$ −158.000 −0.207622 −0.103811 0.994597i $$-0.533104\pi$$
−0.103811 + 0.994597i $$0.533104\pi$$
$$762$$ 472.000 472.000i 0.619423 0.619423i
$$763$$ −20.0000 20.0000i −0.0262123 0.0262123i
$$764$$ 424.000i 0.554974i
$$765$$ 0 0
$$766$$ 684.000 0.892950
$$767$$ 60.0000 60.0000i 0.0782269 0.0782269i
$$768$$ 32.0000 + 32.0000i 0.0416667 + 0.0416667i
$$769$$ 80.0000i 0.104031i −0.998646 0.0520156i $$-0.983435\pi$$
0.998646 0.0520156i $$-0.0165646\pi$$
$$770$$ 0 0
$$771$$ 1252.00 1.62387
$$772$$ 114.000 114.000i 0.147668 0.147668i
$$773$$ −243.000 243.000i −0.314360 0.314360i 0.532236 0.846596i $$-0.321352\pi$$
−0.846596 + 0.532236i $$0.821352\pi$$
$$774$$ 84.0000i 0.108527i
$$775$$ 0 0
$$776$$ −252.000 −0.324742
$$777$$ −24.0000 + 24.0000i −0.0308880 + 0.0308880i
$$778$$ −390.000 390.000i −0.501285 0.501285i
$$779$$ 160.000i