# Properties

 Label 1078.2.e.m.67.1 Level $1078$ Weight $2$ Character 1078.67 Analytic conductor $8.608$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1078.e (of order $$3$$, degree $$2$$, not 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: $$8.60787333789$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.1 Root $$-0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1078.67 Dual form 1078.2.e.m.177.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-1.20711 + 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.292893 - 0.507306i) q^{5} +2.41421 q^{6} +1.00000 q^{8} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-1.20711 + 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.292893 - 0.507306i) q^{5} +2.41421 q^{6} +1.00000 q^{8} +(-1.41421 - 2.44949i) q^{9} +(-0.292893 + 0.507306i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.20711 - 2.09077i) q^{12} +3.82843 q^{13} +1.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.82843 - 3.16693i) q^{17} +(-1.41421 + 2.44949i) q^{18} +(-0.292893 - 0.507306i) q^{19} +0.585786 q^{20} +1.00000 q^{22} +(3.12132 + 5.40629i) q^{23} +(-1.20711 + 2.09077i) q^{24} +(2.32843 - 4.03295i) q^{25} +(-1.91421 - 3.31552i) q^{26} -0.414214 q^{27} +2.65685 q^{29} +(-0.707107 - 1.22474i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.20711 - 2.09077i) q^{33} -3.65685 q^{34} +2.82843 q^{36} +(4.70711 + 8.15295i) q^{37} +(-0.292893 + 0.507306i) q^{38} +(-4.62132 + 8.00436i) q^{39} +(-0.292893 - 0.507306i) q^{40} +5.41421 q^{41} -5.65685 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-0.828427 + 1.43488i) q^{45} +(3.12132 - 5.40629i) q^{46} +(-5.24264 - 9.08052i) q^{47} +2.41421 q^{48} -4.65685 q^{50} +(4.41421 + 7.64564i) q^{51} +(-1.91421 + 3.31552i) q^{52} +(-3.94975 + 6.84116i) q^{53} +(0.207107 + 0.358719i) q^{54} +0.585786 q^{55} +1.41421 q^{57} +(-1.32843 - 2.30090i) q^{58} +(-2.79289 + 4.83743i) q^{59} +(-0.707107 + 1.22474i) q^{60} +(5.91421 + 10.2437i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-1.12132 - 1.94218i) q^{65} +(-1.20711 + 2.09077i) q^{66} +(-1.37868 + 2.38794i) q^{67} +(1.82843 + 3.16693i) q^{68} -15.0711 q^{69} -11.0711 q^{71} +(-1.41421 - 2.44949i) q^{72} +(-4.70711 + 8.15295i) q^{73} +(4.70711 - 8.15295i) q^{74} +(5.62132 + 9.73641i) q^{75} +0.585786 q^{76} +9.24264 q^{78} +(6.62132 + 11.4685i) q^{79} +(-0.292893 + 0.507306i) q^{80} +(4.74264 - 8.21449i) q^{81} +(-2.70711 - 4.68885i) q^{82} +12.1421 q^{83} -2.14214 q^{85} +(2.82843 + 4.89898i) q^{86} +(-3.20711 + 5.55487i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(6.24264 + 10.8126i) q^{89} +1.65685 q^{90} -6.24264 q^{92} +(-4.82843 - 8.36308i) q^{93} +(-5.24264 + 9.08052i) q^{94} +(-0.171573 + 0.297173i) q^{95} +(-1.20711 - 2.09077i) q^{96} +3.82843 q^{97} +2.82843 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8}+O(q^{10})$$ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 $$4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} - 4 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 4 q^{19} + 8 q^{20} + 4 q^{22} + 4 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 4 q^{27} - 12 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{33} + 8 q^{34} + 16 q^{37} - 4 q^{38} - 10 q^{39} - 4 q^{40} + 16 q^{41} - 2 q^{44} + 8 q^{45} + 4 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} + 12 q^{51} - 2 q^{52} + 4 q^{53} - 2 q^{54} + 8 q^{55} + 6 q^{58} - 14 q^{59} + 18 q^{61} + 16 q^{62} + 4 q^{64} + 4 q^{65} - 2 q^{66} - 14 q^{67} - 4 q^{68} - 32 q^{69} - 16 q^{71} - 16 q^{73} + 16 q^{74} + 14 q^{75} + 8 q^{76} + 20 q^{78} + 18 q^{79} - 4 q^{80} + 2 q^{81} - 8 q^{82} - 8 q^{83} + 48 q^{85} - 10 q^{87} - 2 q^{88} + 8 q^{89} - 16 q^{90} - 8 q^{92} - 8 q^{93} - 4 q^{94} - 12 q^{95} - 2 q^{96} + 4 q^{97}+O(q^{100})$$ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 - 4 * q^10 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 4 * q^19 + 8 * q^20 + 4 * q^22 + 4 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 4 * q^27 - 12 * q^29 - 8 * q^31 - 2 * q^32 - 2 * q^33 + 8 * q^34 + 16 * q^37 - 4 * q^38 - 10 * q^39 - 4 * q^40 + 16 * q^41 - 2 * q^44 + 8 * q^45 + 4 * q^46 - 4 * q^47 + 4 * q^48 + 4 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 2 * q^54 + 8 * q^55 + 6 * q^58 - 14 * q^59 + 18 * q^61 + 16 * q^62 + 4 * q^64 + 4 * q^65 - 2 * q^66 - 14 * q^67 - 4 * q^68 - 32 * q^69 - 16 * q^71 - 16 * q^73 + 16 * q^74 + 14 * q^75 + 8 * q^76 + 20 * q^78 + 18 * q^79 - 4 * q^80 + 2 * q^81 - 8 * q^82 - 8 * q^83 + 48 * q^85 - 10 * q^87 - 2 * q^88 + 8 * q^89 - 16 * q^90 - 8 * q^92 - 8 * q^93 - 4 * q^94 - 12 * q^95 - 2 * q^96 + 4 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$981$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ −1.20711 + 2.09077i −0.696923 + 1.20711i 0.272605 + 0.962126i $$0.412115\pi$$
−0.969528 + 0.244981i $$0.921218\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −0.292893 0.507306i −0.130986 0.226874i 0.793071 0.609129i $$-0.208481\pi$$
−0.924057 + 0.382255i $$0.875148\pi$$
$$6$$ 2.41421 0.985599
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ −1.41421 2.44949i −0.471405 0.816497i
$$10$$ −0.292893 + 0.507306i −0.0926210 + 0.160424i
$$11$$ −0.500000 + 0.866025i −0.150756 + 0.261116i
$$12$$ −1.20711 2.09077i −0.348462 0.603553i
$$13$$ 3.82843 1.06181 0.530907 0.847430i $$-0.321851\pi$$
0.530907 + 0.847430i $$0.321851\pi$$
$$14$$ 0 0
$$15$$ 1.41421 0.365148
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 1.82843 3.16693i 0.443459 0.768093i −0.554485 0.832194i $$-0.687085\pi$$
0.997943 + 0.0641009i $$0.0204179\pi$$
$$18$$ −1.41421 + 2.44949i −0.333333 + 0.577350i
$$19$$ −0.292893 0.507306i −0.0671943 0.116384i 0.830471 0.557062i $$-0.188071\pi$$
−0.897665 + 0.440678i $$0.854738\pi$$
$$20$$ 0.585786 0.130986
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ 3.12132 + 5.40629i 0.650840 + 1.12729i 0.982919 + 0.184037i $$0.0589166\pi$$
−0.332079 + 0.943252i $$0.607750\pi$$
$$24$$ −1.20711 + 2.09077i −0.246400 + 0.426777i
$$25$$ 2.32843 4.03295i 0.465685 0.806591i
$$26$$ −1.91421 3.31552i −0.375408 0.650226i
$$27$$ −0.414214 −0.0797154
$$28$$ 0 0
$$29$$ 2.65685 0.493365 0.246683 0.969096i $$-0.420659\pi$$
0.246683 + 0.969096i $$0.420659\pi$$
$$30$$ −0.707107 1.22474i −0.129099 0.223607i
$$31$$ −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i $$-0.950287\pi$$
0.628619 + 0.777714i $$0.283621\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ −1.20711 2.09077i −0.210130 0.363956i
$$34$$ −3.65685 −0.627145
$$35$$ 0 0
$$36$$ 2.82843 0.471405
$$37$$ 4.70711 + 8.15295i 0.773844 + 1.34034i 0.935442 + 0.353480i $$0.115002\pi$$
−0.161599 + 0.986857i $$0.551665\pi$$
$$38$$ −0.292893 + 0.507306i −0.0475136 + 0.0822959i
$$39$$ −4.62132 + 8.00436i −0.740003 + 1.28172i
$$40$$ −0.292893 0.507306i −0.0463105 0.0802121i
$$41$$ 5.41421 0.845558 0.422779 0.906233i $$-0.361055\pi$$
0.422779 + 0.906233i $$0.361055\pi$$
$$42$$ 0 0
$$43$$ −5.65685 −0.862662 −0.431331 0.902194i $$-0.641956\pi$$
−0.431331 + 0.902194i $$0.641956\pi$$
$$44$$ −0.500000 0.866025i −0.0753778 0.130558i
$$45$$ −0.828427 + 1.43488i −0.123495 + 0.213899i
$$46$$ 3.12132 5.40629i 0.460214 0.797113i
$$47$$ −5.24264 9.08052i −0.764718 1.32453i −0.940396 0.340082i $$-0.889545\pi$$
0.175678 0.984448i $$-0.443788\pi$$
$$48$$ 2.41421 0.348462
$$49$$ 0 0
$$50$$ −4.65685 −0.658579
$$51$$ 4.41421 + 7.64564i 0.618114 + 1.07060i
$$52$$ −1.91421 + 3.31552i −0.265454 + 0.459779i
$$53$$ −3.94975 + 6.84116i −0.542540 + 0.939706i 0.456218 + 0.889868i $$0.349204\pi$$
−0.998757 + 0.0498379i $$0.984130\pi$$
$$54$$ 0.207107 + 0.358719i 0.0281837 + 0.0488155i
$$55$$ 0.585786 0.0789874
$$56$$ 0 0
$$57$$ 1.41421 0.187317
$$58$$ −1.32843 2.30090i −0.174431 0.302123i
$$59$$ −2.79289 + 4.83743i −0.363604 + 0.629780i −0.988551 0.150887i $$-0.951787\pi$$
0.624947 + 0.780667i $$0.285120\pi$$
$$60$$ −0.707107 + 1.22474i −0.0912871 + 0.158114i
$$61$$ 5.91421 + 10.2437i 0.757237 + 1.31157i 0.944254 + 0.329217i $$0.106785\pi$$
−0.187017 + 0.982357i $$0.559882\pi$$
$$62$$ 4.00000 0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −1.12132 1.94218i −0.139083 0.240898i
$$66$$ −1.20711 + 2.09077i −0.148585 + 0.257356i
$$67$$ −1.37868 + 2.38794i −0.168433 + 0.291734i −0.937869 0.346990i $$-0.887204\pi$$
0.769436 + 0.638723i $$0.220537\pi$$
$$68$$ 1.82843 + 3.16693i 0.221729 + 0.384047i
$$69$$ −15.0711 −1.81434
$$70$$ 0 0
$$71$$ −11.0711 −1.31389 −0.656947 0.753937i $$-0.728152\pi$$
−0.656947 + 0.753937i $$0.728152\pi$$
$$72$$ −1.41421 2.44949i −0.166667 0.288675i
$$73$$ −4.70711 + 8.15295i −0.550925 + 0.954230i 0.447283 + 0.894393i $$0.352392\pi$$
−0.998208 + 0.0598379i $$0.980942\pi$$
$$74$$ 4.70711 8.15295i 0.547190 0.947761i
$$75$$ 5.62132 + 9.73641i 0.649094 + 1.12426i
$$76$$ 0.585786 0.0671943
$$77$$ 0 0
$$78$$ 9.24264 1.04652
$$79$$ 6.62132 + 11.4685i 0.744957 + 1.29030i 0.950215 + 0.311595i $$0.100863\pi$$
−0.205258 + 0.978708i $$0.565803\pi$$
$$80$$ −0.292893 + 0.507306i −0.0327465 + 0.0567185i
$$81$$ 4.74264 8.21449i 0.526960 0.912722i
$$82$$ −2.70711 4.68885i −0.298950 0.517796i
$$83$$ 12.1421 1.33277 0.666386 0.745607i $$-0.267840\pi$$
0.666386 + 0.745607i $$0.267840\pi$$
$$84$$ 0 0
$$85$$ −2.14214 −0.232347
$$86$$ 2.82843 + 4.89898i 0.304997 + 0.528271i
$$87$$ −3.20711 + 5.55487i −0.343838 + 0.595545i
$$88$$ −0.500000 + 0.866025i −0.0533002 + 0.0923186i
$$89$$ 6.24264 + 10.8126i 0.661719 + 1.14613i 0.980164 + 0.198189i $$0.0635060\pi$$
−0.318445 + 0.947941i $$0.603161\pi$$
$$90$$ 1.65685 0.174648
$$91$$ 0 0
$$92$$ −6.24264 −0.650840
$$93$$ −4.82843 8.36308i −0.500685 0.867211i
$$94$$ −5.24264 + 9.08052i −0.540737 + 0.936584i
$$95$$ −0.171573 + 0.297173i −0.0176030 + 0.0304893i
$$96$$ −1.20711 2.09077i −0.123200 0.213388i
$$97$$ 3.82843 0.388718 0.194359 0.980930i $$-0.437737\pi$$
0.194359 + 0.980930i $$0.437737\pi$$
$$98$$ 0 0
$$99$$ 2.82843 0.284268
$$100$$ 2.32843 + 4.03295i 0.232843 + 0.403295i
$$101$$ 3.08579 5.34474i 0.307047 0.531821i −0.670668 0.741758i $$-0.733992\pi$$
0.977715 + 0.209936i $$0.0673257\pi$$
$$102$$ 4.41421 7.64564i 0.437072 0.757031i
$$103$$ 6.70711 + 11.6170i 0.660871 + 1.14466i 0.980387 + 0.197081i $$0.0631462\pi$$
−0.319516 + 0.947581i $$0.603520\pi$$
$$104$$ 3.82843 0.375408
$$105$$ 0 0
$$106$$ 7.89949 0.767267
$$107$$ 1.53553 + 2.65962i 0.148446 + 0.257115i 0.930653 0.365903i $$-0.119240\pi$$
−0.782207 + 0.623018i $$0.785906\pi$$
$$108$$ 0.207107 0.358719i 0.0199289 0.0345178i
$$109$$ −8.24264 + 14.2767i −0.789502 + 1.36746i 0.136771 + 0.990603i $$0.456328\pi$$
−0.926272 + 0.376854i $$0.877006\pi$$
$$110$$ −0.292893 0.507306i −0.0279263 0.0483697i
$$111$$ −22.7279 −2.15724
$$112$$ 0 0
$$113$$ −8.17157 −0.768717 −0.384358 0.923184i $$-0.625577\pi$$
−0.384358 + 0.923184i $$0.625577\pi$$
$$114$$ −0.707107 1.22474i −0.0662266 0.114708i
$$115$$ 1.82843 3.16693i 0.170502 0.295318i
$$116$$ −1.32843 + 2.30090i −0.123341 + 0.213634i
$$117$$ −5.41421 9.37769i −0.500544 0.866968i
$$118$$ 5.58579 0.514213
$$119$$ 0 0
$$120$$ 1.41421 0.129099
$$121$$ −0.500000 0.866025i −0.0454545 0.0787296i
$$122$$ 5.91421 10.2437i 0.535448 0.927423i
$$123$$ −6.53553 + 11.3199i −0.589289 + 1.02068i
$$124$$ −2.00000 3.46410i −0.179605 0.311086i
$$125$$ −5.65685 −0.505964
$$126$$ 0 0
$$127$$ 15.7279 1.39563 0.697814 0.716279i $$-0.254156\pi$$
0.697814 + 0.716279i $$0.254156\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 6.82843 11.8272i 0.601209 1.04133i
$$130$$ −1.12132 + 1.94218i −0.0983463 + 0.170341i
$$131$$ −0.292893 0.507306i −0.0255902 0.0443235i 0.852947 0.521998i $$-0.174813\pi$$
−0.878537 + 0.477674i $$0.841480\pi$$
$$132$$ 2.41421 0.210130
$$133$$ 0 0
$$134$$ 2.75736 0.238200
$$135$$ 0.121320 + 0.210133i 0.0104416 + 0.0180854i
$$136$$ 1.82843 3.16693i 0.156786 0.271562i
$$137$$ 8.32843 14.4253i 0.711546 1.23243i −0.252731 0.967537i $$-0.581329\pi$$
0.964277 0.264897i $$-0.0853378\pi$$
$$138$$ 7.53553 + 13.0519i 0.641467 + 1.11105i
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 25.3137 2.13180
$$142$$ 5.53553 + 9.58783i 0.464532 + 0.804592i
$$143$$ −1.91421 + 3.31552i −0.160075 + 0.277257i
$$144$$ −1.41421 + 2.44949i −0.117851 + 0.204124i
$$145$$ −0.778175 1.34784i −0.0646239 0.111932i
$$146$$ 9.41421 0.779126
$$147$$ 0 0
$$148$$ −9.41421 −0.773844
$$149$$ −8.82843 15.2913i −0.723253 1.25271i −0.959689 0.281064i $$-0.909313\pi$$
0.236436 0.971647i $$-0.424021\pi$$
$$150$$ 5.62132 9.73641i 0.458979 0.794975i
$$151$$ 7.86396 13.6208i 0.639960 1.10844i −0.345481 0.938426i $$-0.612284\pi$$
0.985441 0.170018i $$-0.0543825\pi$$
$$152$$ −0.292893 0.507306i −0.0237568 0.0411479i
$$153$$ −10.3431 −0.836194
$$154$$ 0 0
$$155$$ 2.34315 0.188206
$$156$$ −4.62132 8.00436i −0.370002 0.640862i
$$157$$ 8.82843 15.2913i 0.704585 1.22038i −0.262256 0.964998i $$-0.584466\pi$$
0.966841 0.255379i $$-0.0822002\pi$$
$$158$$ 6.62132 11.4685i 0.526764 0.912382i
$$159$$ −9.53553 16.5160i −0.756217 1.30981i
$$160$$ 0.585786 0.0463105
$$161$$ 0 0
$$162$$ −9.48528 −0.745234
$$163$$ −4.86396 8.42463i −0.380975 0.659868i 0.610227 0.792227i $$-0.291078\pi$$
−0.991202 + 0.132359i $$0.957745\pi$$
$$164$$ −2.70711 + 4.68885i −0.211390 + 0.366137i
$$165$$ −0.707107 + 1.22474i −0.0550482 + 0.0953463i
$$166$$ −6.07107 10.5154i −0.471206 0.816153i
$$167$$ −13.7279 −1.06230 −0.531149 0.847278i $$-0.678240\pi$$
−0.531149 + 0.847278i $$0.678240\pi$$
$$168$$ 0 0
$$169$$ 1.65685 0.127450
$$170$$ 1.07107 + 1.85514i 0.0821472 + 0.142283i
$$171$$ −0.828427 + 1.43488i −0.0633514 + 0.109728i
$$172$$ 2.82843 4.89898i 0.215666 0.373544i
$$173$$ −4.91421 8.51167i −0.373621 0.647130i 0.616499 0.787356i $$-0.288551\pi$$
−0.990120 + 0.140226i $$0.955217\pi$$
$$174$$ 6.41421 0.486260
$$175$$ 0 0
$$176$$ 1.00000 0.0753778
$$177$$ −6.74264 11.6786i −0.506808 0.877817i
$$178$$ 6.24264 10.8126i 0.467906 0.810436i
$$179$$ −0.449747 + 0.778985i −0.0336157 + 0.0582241i −0.882344 0.470605i $$-0.844036\pi$$
0.848728 + 0.528829i $$0.177369\pi$$
$$180$$ −0.828427 1.43488i −0.0617473 0.106949i
$$181$$ 7.65685 0.569129 0.284565 0.958657i $$-0.408151\pi$$
0.284565 + 0.958657i $$0.408151\pi$$
$$182$$ 0 0
$$183$$ −28.5563 −2.11095
$$184$$ 3.12132 + 5.40629i 0.230107 + 0.398557i
$$185$$ 2.75736 4.77589i 0.202725 0.351130i
$$186$$ −4.82843 + 8.36308i −0.354037 + 0.613211i
$$187$$ 1.82843 + 3.16693i 0.133708 + 0.231589i
$$188$$ 10.4853 0.764718
$$189$$ 0 0
$$190$$ 0.343146 0.0248944
$$191$$ 3.58579 + 6.21076i 0.259458 + 0.449395i 0.966097 0.258180i $$-0.0831226\pi$$
−0.706639 + 0.707575i $$0.749789\pi$$
$$192$$ −1.20711 + 2.09077i −0.0871154 + 0.150888i
$$193$$ −10.9497 + 18.9655i −0.788180 + 1.36517i 0.138901 + 0.990306i $$0.455643\pi$$
−0.927081 + 0.374862i $$0.877690\pi$$
$$194$$ −1.91421 3.31552i −0.137433 0.238040i
$$195$$ 5.41421 0.387720
$$196$$ 0 0
$$197$$ −0.514719 −0.0366722 −0.0183361 0.999832i $$-0.505837\pi$$
−0.0183361 + 0.999832i $$0.505837\pi$$
$$198$$ −1.41421 2.44949i −0.100504 0.174078i
$$199$$ 0.0502525 0.0870399i 0.00356231 0.00617010i −0.864239 0.503082i $$-0.832199\pi$$
0.867801 + 0.496912i $$0.165533\pi$$
$$200$$ 2.32843 4.03295i 0.164645 0.285173i
$$201$$ −3.32843 5.76500i −0.234769 0.406632i
$$202$$ −6.17157 −0.434230
$$203$$ 0 0
$$204$$ −8.82843 −0.618114
$$205$$ −1.58579 2.74666i −0.110756 0.191835i
$$206$$ 6.70711 11.6170i 0.467306 0.809398i
$$207$$ 8.82843 15.2913i 0.613618 1.06282i
$$208$$ −1.91421 3.31552i −0.132727 0.229890i
$$209$$ 0.585786 0.0405197
$$210$$ 0 0
$$211$$ 7.41421 0.510416 0.255208 0.966886i $$-0.417856\pi$$
0.255208 + 0.966886i $$0.417856\pi$$
$$212$$ −3.94975 6.84116i −0.271270 0.469853i
$$213$$ 13.3640 23.1471i 0.915684 1.58601i
$$214$$ 1.53553 2.65962i 0.104967 0.181808i
$$215$$ 1.65685 + 2.86976i 0.112997 + 0.195716i
$$216$$ −0.414214 −0.0281837
$$217$$ 0 0
$$218$$ 16.4853 1.11652
$$219$$ −11.3640 19.6830i −0.767905 1.33005i
$$220$$ −0.292893 + 0.507306i −0.0197469 + 0.0342026i
$$221$$ 7.00000 12.1244i 0.470871 0.815572i
$$222$$ 11.3640 + 19.6830i 0.762699 + 1.32103i
$$223$$ −8.58579 −0.574947 −0.287473 0.957789i $$-0.592815\pi$$
−0.287473 + 0.957789i $$0.592815\pi$$
$$224$$ 0 0
$$225$$ −13.1716 −0.878105
$$226$$ 4.08579 + 7.07679i 0.271782 + 0.470741i
$$227$$ −14.4142 + 24.9662i −0.956705 + 1.65706i −0.226288 + 0.974061i $$0.572659\pi$$
−0.730417 + 0.683001i $$0.760674\pi$$
$$228$$ −0.707107 + 1.22474i −0.0468293 + 0.0811107i
$$229$$ 11.6569 + 20.1903i 0.770307 + 1.33421i 0.937395 + 0.348268i $$0.113230\pi$$
−0.167088 + 0.985942i $$0.553436\pi$$
$$230$$ −3.65685 −0.241126
$$231$$ 0 0
$$232$$ 2.65685 0.174431
$$233$$ −0.707107 1.22474i −0.0463241 0.0802357i 0.841934 0.539581i $$-0.181417\pi$$
−0.888258 + 0.459345i $$0.848084\pi$$
$$234$$ −5.41421 + 9.37769i −0.353938 + 0.613039i
$$235$$ −3.07107 + 5.31925i −0.200334 + 0.346989i
$$236$$ −2.79289 4.83743i −0.181802 0.314890i
$$237$$ −31.9706 −2.07671
$$238$$ 0 0
$$239$$ 20.2132 1.30748 0.653742 0.756718i $$-0.273198\pi$$
0.653742 + 0.756718i $$0.273198\pi$$
$$240$$ −0.707107 1.22474i −0.0456435 0.0790569i
$$241$$ 6.12132 10.6024i 0.394309 0.682963i −0.598704 0.800971i $$-0.704317\pi$$
0.993013 + 0.118007i $$0.0376507\pi$$
$$242$$ −0.500000 + 0.866025i −0.0321412 + 0.0556702i
$$243$$ 10.8284 + 18.7554i 0.694644 + 1.20316i
$$244$$ −11.8284 −0.757237
$$245$$ 0 0
$$246$$ 13.0711 0.833381
$$247$$ −1.12132 1.94218i −0.0713479 0.123578i
$$248$$ −2.00000 + 3.46410i −0.127000 + 0.219971i
$$249$$ −14.6569 + 25.3864i −0.928840 + 1.60880i
$$250$$ 2.82843 + 4.89898i 0.178885 + 0.309839i
$$251$$ 26.1421 1.65008 0.825038 0.565077i $$-0.191153\pi$$
0.825038 + 0.565077i $$0.191153\pi$$
$$252$$ 0 0
$$253$$ −6.24264 −0.392471
$$254$$ −7.86396 13.6208i −0.493429 0.854644i
$$255$$ 2.58579 4.47871i 0.161928 0.280468i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −12.5711 21.7737i −0.784162 1.35821i −0.929499 0.368826i $$-0.879760\pi$$
0.145337 0.989382i $$-0.453573\pi$$
$$258$$ −13.6569 −0.850239
$$259$$ 0 0
$$260$$ 2.24264 0.139083
$$261$$ −3.75736 6.50794i −0.232575 0.402831i
$$262$$ −0.292893 + 0.507306i −0.0180950 + 0.0313415i
$$263$$ 8.52082 14.7585i 0.525416 0.910047i −0.474146 0.880446i $$-0.657243\pi$$
0.999562 0.0296008i $$-0.00942362\pi$$
$$264$$ −1.20711 2.09077i −0.0742923 0.128678i
$$265$$ 4.62742 0.284260
$$266$$ 0 0
$$267$$ −30.1421 −1.84467
$$268$$ −1.37868 2.38794i −0.0842163 0.145867i
$$269$$ 1.17157 2.02922i 0.0714321 0.123724i −0.828097 0.560585i $$-0.810576\pi$$
0.899529 + 0.436861i $$0.143910\pi$$
$$270$$ 0.121320 0.210133i 0.00738332 0.0127883i
$$271$$ 2.27817 + 3.94591i 0.138389 + 0.239697i 0.926887 0.375340i $$-0.122474\pi$$
−0.788498 + 0.615038i $$0.789141\pi$$
$$272$$ −3.65685 −0.221729
$$273$$ 0 0
$$274$$ −16.6569 −1.00628
$$275$$ 2.32843 + 4.03295i 0.140409 + 0.243196i
$$276$$ 7.53553 13.0519i 0.453586 0.785634i
$$277$$ −0.914214 + 1.58346i −0.0549298 + 0.0951412i −0.892183 0.451675i $$-0.850827\pi$$
0.837253 + 0.546816i $$0.184160\pi$$
$$278$$ 0 0
$$279$$ 11.3137 0.677334
$$280$$ 0 0
$$281$$ 8.72792 0.520664 0.260332 0.965519i $$-0.416168\pi$$
0.260332 + 0.965519i $$0.416168\pi$$
$$282$$ −12.6569 21.9223i −0.753705 1.30545i
$$283$$ −11.7071 + 20.2773i −0.695915 + 1.20536i 0.273956 + 0.961742i $$0.411668\pi$$
−0.969871 + 0.243618i $$0.921666\pi$$
$$284$$ 5.53553 9.58783i 0.328474 0.568933i
$$285$$ −0.414214 0.717439i −0.0245359 0.0424974i
$$286$$ 3.82843 0.226380
$$287$$ 0 0
$$288$$ 2.82843 0.166667
$$289$$ 1.81371 + 3.14144i 0.106689 + 0.184790i
$$290$$ −0.778175 + 1.34784i −0.0456960 + 0.0791478i
$$291$$ −4.62132 + 8.00436i −0.270907 + 0.469224i
$$292$$ −4.70711 8.15295i −0.275463 0.477115i
$$293$$ 10.8284 0.632603 0.316302 0.948659i $$-0.397559\pi$$
0.316302 + 0.948659i $$0.397559\pi$$
$$294$$ 0 0
$$295$$ 3.27208 0.190508
$$296$$ 4.70711 + 8.15295i 0.273595 + 0.473880i
$$297$$ 0.207107 0.358719i 0.0120176 0.0208150i
$$298$$ −8.82843 + 15.2913i −0.511417 + 0.885800i
$$299$$ 11.9497 + 20.6976i 0.691072 + 1.19697i
$$300$$ −11.2426 −0.649094
$$301$$ 0 0
$$302$$ −15.7279 −0.905040
$$303$$ 7.44975 + 12.9033i 0.427977 + 0.741278i
$$304$$ −0.292893 + 0.507306i −0.0167986 + 0.0290960i
$$305$$ 3.46447 6.00063i 0.198375 0.343595i
$$306$$ 5.17157 + 8.95743i 0.295639 + 0.512062i
$$307$$ −9.89949 −0.564994 −0.282497 0.959268i $$-0.591163\pi$$
−0.282497 + 0.959268i $$0.591163\pi$$
$$308$$ 0 0
$$309$$ −32.3848 −1.84231
$$310$$ −1.17157 2.02922i −0.0665409 0.115252i
$$311$$ 8.36396 14.4868i 0.474277 0.821471i −0.525289 0.850924i $$-0.676043\pi$$
0.999566 + 0.0294522i $$0.00937629\pi$$
$$312$$ −4.62132 + 8.00436i −0.261631 + 0.453158i
$$313$$ −10.3284 17.8894i −0.583797 1.01117i −0.995024 0.0996335i $$-0.968233\pi$$
0.411227 0.911533i $$-0.365100\pi$$
$$314$$ −17.6569 −0.996434
$$315$$ 0 0
$$316$$ −13.2426 −0.744957
$$317$$ −4.34315 7.52255i −0.243935 0.422508i 0.717896 0.696150i $$-0.245105\pi$$
−0.961832 + 0.273642i $$0.911772\pi$$
$$318$$ −9.53553 + 16.5160i −0.534726 + 0.926173i
$$319$$ −1.32843 + 2.30090i −0.0743776 + 0.128826i
$$320$$ −0.292893 0.507306i −0.0163732 0.0283593i
$$321$$ −7.41421 −0.413821
$$322$$ 0 0
$$323$$ −2.14214 −0.119192
$$324$$ 4.74264 + 8.21449i 0.263480 + 0.456361i
$$325$$ 8.91421 15.4399i 0.494472 0.856450i
$$326$$ −4.86396 + 8.42463i −0.269390 + 0.466597i
$$327$$ −19.8995 34.4669i −1.10044 1.90603i
$$328$$ 5.41421 0.298950
$$329$$ 0 0
$$330$$ 1.41421 0.0778499
$$331$$ 12.0355 + 20.8462i 0.661533 + 1.14581i 0.980213 + 0.197946i $$0.0634271\pi$$
−0.318680 + 0.947862i $$0.603240\pi$$
$$332$$ −6.07107 + 10.5154i −0.333193 + 0.577107i
$$333$$ 13.3137 23.0600i 0.729587 1.26368i
$$334$$ 6.86396 + 11.8887i 0.375579 + 0.650522i
$$335$$ 1.61522 0.0882491
$$336$$ 0 0
$$337$$ −28.2426 −1.53847 −0.769237 0.638963i $$-0.779364\pi$$
−0.769237 + 0.638963i $$0.779364\pi$$
$$338$$ −0.828427 1.43488i −0.0450605 0.0780471i
$$339$$ 9.86396 17.0849i 0.535737 0.927923i
$$340$$ 1.07107 1.85514i 0.0580868 0.100609i
$$341$$ −2.00000 3.46410i −0.108306 0.187592i
$$342$$ 1.65685 0.0895924
$$343$$ 0 0
$$344$$ −5.65685 −0.304997
$$345$$ 4.41421 + 7.64564i 0.237653 + 0.411628i
$$346$$ −4.91421 + 8.51167i −0.264190 + 0.457590i
$$347$$ −8.70711 + 15.0812i −0.467422 + 0.809599i −0.999307 0.0372179i $$-0.988150\pi$$
0.531885 + 0.846816i $$0.321484\pi$$
$$348$$ −3.20711 5.55487i −0.171919 0.297772i
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0 0
$$351$$ −1.58579 −0.0846430
$$352$$ −0.500000 0.866025i −0.0266501 0.0461593i
$$353$$ −1.34315 + 2.32640i −0.0714884 + 0.123822i −0.899554 0.436810i $$-0.856108\pi$$
0.828065 + 0.560632i $$0.189442\pi$$
$$354$$ −6.74264 + 11.6786i −0.358367 + 0.620710i
$$355$$ 3.24264 + 5.61642i 0.172101 + 0.298089i
$$356$$ −12.4853 −0.661719
$$357$$ 0 0
$$358$$ 0.899495 0.0475398
$$359$$ −9.62132 16.6646i −0.507794 0.879525i −0.999959 0.00902308i $$-0.997128\pi$$
0.492165 0.870502i $$-0.336206\pi$$
$$360$$ −0.828427 + 1.43488i −0.0436619 + 0.0756247i
$$361$$ 9.32843 16.1573i 0.490970 0.850385i
$$362$$ −3.82843 6.63103i −0.201218 0.348519i
$$363$$ 2.41421 0.126713
$$364$$ 0 0
$$365$$ 5.51472 0.288654
$$366$$ 14.2782 + 24.7305i 0.746332 + 1.29269i
$$367$$ −5.36396 + 9.29065i −0.279996 + 0.484968i −0.971384 0.237516i $$-0.923667\pi$$
0.691387 + 0.722485i $$0.257000\pi$$
$$368$$ 3.12132 5.40629i 0.162710 0.281822i
$$369$$ −7.65685 13.2621i −0.398600 0.690395i
$$370$$ −5.51472 −0.286697
$$371$$ 0 0
$$372$$ 9.65685 0.500685
$$373$$ 9.98528 + 17.2950i 0.517018 + 0.895502i 0.999805 + 0.0197638i $$0.00629142\pi$$
−0.482786 + 0.875738i $$0.660375\pi$$
$$374$$ 1.82843 3.16693i 0.0945457 0.163758i
$$375$$ 6.82843 11.8272i 0.352618 0.610753i
$$376$$ −5.24264 9.08052i −0.270369 0.468292i
$$377$$ 10.1716 0.523863
$$378$$ 0 0
$$379$$ 27.8701 1.43159 0.715794 0.698311i $$-0.246065\pi$$
0.715794 + 0.698311i $$0.246065\pi$$
$$380$$ −0.171573 0.297173i −0.00880150 0.0152447i
$$381$$ −18.9853 + 32.8835i −0.972645 + 1.68467i
$$382$$ 3.58579 6.21076i 0.183465 0.317770i
$$383$$ −3.19239 5.52938i −0.163123 0.282538i 0.772864 0.634572i $$-0.218824\pi$$
−0.935987 + 0.352034i $$0.885490\pi$$
$$384$$ 2.41421 0.123200
$$385$$ 0 0
$$386$$ 21.8995 1.11465
$$387$$ 8.00000 + 13.8564i 0.406663 + 0.704361i
$$388$$ −1.91421 + 3.31552i −0.0971795 + 0.168320i
$$389$$ 11.3640 19.6830i 0.576176 0.997966i −0.419737 0.907646i $$-0.637878\pi$$
0.995913 0.0903199i $$-0.0287889\pi$$
$$390$$ −2.70711 4.68885i −0.137080 0.237429i
$$391$$ 22.8284 1.15448
$$392$$ 0 0
$$393$$ 1.41421 0.0713376
$$394$$ 0.257359 + 0.445759i 0.0129656 + 0.0224570i
$$395$$ 3.87868 6.71807i 0.195158 0.338023i
$$396$$ −1.41421 + 2.44949i −0.0710669 + 0.123091i
$$397$$ 11.0000 + 19.0526i 0.552074 + 0.956221i 0.998125 + 0.0612128i $$0.0194968\pi$$
−0.446051 + 0.895008i $$0.647170\pi$$
$$398$$ −0.100505 −0.00503786
$$399$$ 0 0
$$400$$ −4.65685 −0.232843
$$401$$ −9.15685 15.8601i −0.457271 0.792017i 0.541544 0.840672i $$-0.317840\pi$$
−0.998816 + 0.0486549i $$0.984507\pi$$
$$402$$ −3.32843 + 5.76500i −0.166007 + 0.287532i
$$403$$ −7.65685 + 13.2621i −0.381415 + 0.660630i
$$404$$ 3.08579 + 5.34474i 0.153524 + 0.265911i
$$405$$ −5.55635 −0.276097
$$406$$ 0 0
$$407$$ −9.41421 −0.466645
$$408$$ 4.41421 + 7.64564i 0.218536 + 0.378516i
$$409$$ 1.36396 2.36245i 0.0674435 0.116816i −0.830332 0.557269i $$-0.811849\pi$$
0.897775 + 0.440454i $$0.145182\pi$$
$$410$$ −1.58579 + 2.74666i −0.0783164 + 0.135648i
$$411$$ 20.1066 + 34.8257i 0.991786 + 1.71782i
$$412$$ −13.4142 −0.660871
$$413$$ 0 0
$$414$$ −17.6569 −0.867787
$$415$$ −3.55635 6.15978i −0.174574 0.302372i
$$416$$ −1.91421 + 3.31552i −0.0938520 + 0.162557i
$$417$$ 0 0
$$418$$ −0.292893 0.507306i −0.0143259 0.0248131i
$$419$$ 26.1421 1.27713 0.638563 0.769569i $$-0.279529\pi$$
0.638563 + 0.769569i $$0.279529\pi$$
$$420$$ 0 0
$$421$$ 0.686292 0.0334478 0.0167239 0.999860i $$-0.494676\pi$$
0.0167239 + 0.999860i $$0.494676\pi$$
$$422$$ −3.70711 6.42090i −0.180459 0.312564i
$$423$$ −14.8284 + 25.6836i −0.720983 + 1.24878i
$$424$$ −3.94975 + 6.84116i −0.191817 + 0.332236i
$$425$$ −8.51472 14.7479i −0.413025 0.715379i
$$426$$ −26.7279 −1.29497
$$427$$ 0 0
$$428$$ −3.07107 −0.148446
$$429$$ −4.62132 8.00436i −0.223119 0.386454i
$$430$$ 1.65685 2.86976i 0.0799006 0.138392i
$$431$$ 8.79289 15.2297i 0.423539 0.733591i −0.572744 0.819734i $$-0.694121\pi$$
0.996283 + 0.0861437i $$0.0274544\pi$$
$$432$$ 0.207107 + 0.358719i 0.00996443 + 0.0172589i
$$433$$ −26.1421 −1.25631 −0.628155 0.778088i $$-0.716190\pi$$
−0.628155 + 0.778088i $$0.716190\pi$$
$$434$$ 0 0
$$435$$ 3.75736 0.180152
$$436$$ −8.24264 14.2767i −0.394751 0.683729i
$$437$$ 1.82843 3.16693i 0.0874655 0.151495i
$$438$$ −11.3640 + 19.6830i −0.542991 + 0.940488i
$$439$$ −13.6924 23.7159i −0.653502 1.13190i −0.982267 0.187487i $$-0.939966\pi$$
0.328765 0.944412i $$-0.393368\pi$$
$$440$$ 0.585786 0.0279263
$$441$$ 0 0
$$442$$ −14.0000 −0.665912
$$443$$ −6.31371 10.9357i −0.299973 0.519569i 0.676156 0.736758i $$-0.263644\pi$$
−0.976130 + 0.217189i $$0.930311\pi$$
$$444$$ 11.3640 19.6830i 0.539310 0.934112i
$$445$$ 3.65685 6.33386i 0.173352 0.300254i
$$446$$ 4.29289 + 7.43551i 0.203274 + 0.352082i
$$447$$ 42.6274 2.01621
$$448$$ 0 0
$$449$$ 22.3431 1.05444 0.527219 0.849729i $$-0.323235\pi$$
0.527219 + 0.849729i $$0.323235\pi$$
$$450$$ 6.58579 + 11.4069i 0.310457 + 0.537727i
$$451$$ −2.70711 + 4.68885i −0.127473 + 0.220789i
$$452$$ 4.08579 7.07679i 0.192179 0.332864i
$$453$$ 18.9853 + 32.8835i 0.892006 + 1.54500i
$$454$$ 28.8284 1.35299
$$455$$ 0 0
$$456$$ 1.41421 0.0662266
$$457$$ 5.82843 + 10.0951i 0.272642 + 0.472230i 0.969538 0.244943i $$-0.0787691\pi$$
−0.696895 + 0.717173i $$0.745436\pi$$
$$458$$ 11.6569 20.1903i 0.544689 0.943429i
$$459$$ −0.757359 + 1.31178i −0.0353505 + 0.0612289i
$$460$$ 1.82843 + 3.16693i 0.0852509 + 0.147659i
$$461$$ 8.31371 0.387208 0.193604 0.981080i $$-0.437982\pi$$
0.193604 + 0.981080i $$0.437982\pi$$
$$462$$ 0 0
$$463$$ 12.8284 0.596188 0.298094 0.954537i $$-0.403649\pi$$
0.298094 + 0.954537i $$0.403649\pi$$
$$464$$ −1.32843 2.30090i −0.0616707 0.106817i
$$465$$ −2.82843 + 4.89898i −0.131165 + 0.227185i
$$466$$ −0.707107 + 1.22474i −0.0327561 + 0.0567352i
$$467$$ −17.0000 29.4449i −0.786666 1.36255i −0.927999 0.372584i $$-0.878472\pi$$
0.141332 0.989962i $$-0.454861\pi$$
$$468$$ 10.8284 0.500544
$$469$$ 0 0
$$470$$ 6.14214 0.283316
$$471$$ 21.3137 + 36.9164i 0.982084 + 1.70102i
$$472$$ −2.79289 + 4.83743i −0.128553 + 0.222661i
$$473$$ 2.82843 4.89898i 0.130051 0.225255i
$$474$$ 15.9853 + 27.6873i 0.734228 + 1.27172i
$$475$$ −2.72792 −0.125166
$$476$$ 0 0
$$477$$ 22.3431 1.02302
$$478$$ −10.1066 17.5051i −0.462265 0.800667i
$$479$$ −5.96447 + 10.3308i −0.272523 + 0.472024i −0.969507 0.245062i $$-0.921192\pi$$
0.696984 + 0.717087i $$0.254525\pi$$
$$480$$ −0.707107 + 1.22474i −0.0322749 + 0.0559017i
$$481$$ 18.0208 + 31.2130i 0.821678 + 1.42319i
$$482$$ −12.2426 −0.557637
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ −1.12132 1.94218i −0.0509165 0.0881900i
$$486$$ 10.8284 18.7554i 0.491187 0.850762i
$$487$$ 4.82843 8.36308i 0.218797 0.378967i −0.735644 0.677369i $$-0.763120\pi$$
0.954440 + 0.298402i $$0.0964534\pi$$
$$488$$ 5.91421 + 10.2437i 0.267724 + 0.463711i
$$489$$ 23.4853 1.06204
$$490$$ 0 0
$$491$$ 19.1716 0.865201 0.432600 0.901586i $$-0.357596\pi$$
0.432600 + 0.901586i $$0.357596\pi$$
$$492$$ −6.53553 11.3199i −0.294645 0.510339i
$$493$$ 4.85786 8.41407i 0.218787 0.378951i
$$494$$ −1.12132 + 1.94218i −0.0504506 + 0.0873830i
$$495$$ −0.828427 1.43488i −0.0372350 0.0644930i
$$496$$ 4.00000 0.179605
$$497$$ 0 0
$$498$$ 29.3137 1.31358
$$499$$ −11.0711 19.1757i −0.495609 0.858420i 0.504378 0.863483i $$-0.331722\pi$$
−0.999987 + 0.00506282i $$0.998388\pi$$
$$500$$ 2.82843 4.89898i 0.126491 0.219089i
$$501$$ 16.5711 28.7019i 0.740341 1.28231i
$$502$$ −13.0711 22.6398i −0.583390 1.01046i
$$503$$ −4.21320 −0.187857 −0.0939287 0.995579i $$-0.529943\pi$$
−0.0939287 + 0.995579i $$0.529943\pi$$
$$504$$ 0 0
$$505$$ −3.61522 −0.160875
$$506$$ 3.12132 + 5.40629i 0.138760 + 0.240339i
$$507$$ −2.00000 + 3.46410i −0.0888231 + 0.153846i
$$508$$ −7.86396 + 13.6208i −0.348907 + 0.604324i
$$509$$ 4.65685 + 8.06591i 0.206411 + 0.357515i 0.950582 0.310475i $$-0.100488\pi$$
−0.744170 + 0.667990i $$0.767155\pi$$
$$510$$ −5.17157 −0.229001
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0.121320 + 0.210133i 0.00535642 + 0.00927760i
$$514$$ −12.5711 + 21.7737i −0.554486 + 0.960398i
$$515$$ 3.92893 6.80511i 0.173129 0.299869i
$$516$$ 6.82843 + 11.8272i 0.300605 + 0.520663i
$$517$$ 10.4853 0.461142
$$518$$ 0 0
$$519$$ 23.7279 1.04154
$$520$$ −1.12132 1.94218i −0.0491731 0.0851704i
$$521$$ −14.1421 + 24.4949i −0.619578 + 1.07314i 0.369984 + 0.929038i $$0.379363\pi$$
−0.989563 + 0.144103i $$0.953970\pi$$
$$522$$ −3.75736 + 6.50794i −0.164455 + 0.284845i
$$523$$ −6.36396 11.0227i −0.278277 0.481989i 0.692680 0.721245i $$-0.256430\pi$$
−0.970957 + 0.239256i $$0.923097\pi$$
$$524$$ 0.585786 0.0255902
$$525$$ 0 0
$$526$$ −17.0416 −0.743050
$$527$$ 7.31371 + 12.6677i 0.318590 + 0.551814i
$$528$$ −1.20711 + 2.09077i −0.0525326 + 0.0909891i
$$529$$ −7.98528 + 13.8309i −0.347186 + 0.601344i
$$530$$ −2.31371 4.00746i −0.100501 0.174073i
$$531$$ 15.7990 0.685618
$$532$$ 0 0
$$533$$ 20.7279 0.897826
$$534$$ 15.0711 + 26.1039i 0.652189 + 1.12962i
$$535$$ 0.899495 1.55797i 0.0388886 0.0673570i
$$536$$ −1.37868 + 2.38794i −0.0595499 + 0.103143i
$$537$$ −1.08579 1.88064i −0.0468551 0.0811555i
$$538$$ −2.34315 −0.101020
$$539$$ 0 0
$$540$$ −0.242641 −0.0104416
$$541$$ 6.42893 + 11.1352i 0.276401 + 0.478741i 0.970488 0.241151i $$-0.0775248\pi$$
−0.694086 + 0.719892i $$0.744191\pi$$
$$542$$ 2.27817 3.94591i 0.0978560 0.169492i
$$543$$ −9.24264 + 16.0087i −0.396640 + 0.687000i
$$544$$ 1.82843 + 3.16693i 0.0783932 + 0.135781i
$$545$$ 9.65685 0.413654
$$546$$ 0 0
$$547$$ 34.8701 1.49094 0.745468 0.666541i $$-0.232226\pi$$
0.745468 + 0.666541i $$0.232226\pi$$
$$548$$ 8.32843 + 14.4253i 0.355773 + 0.616217i
$$549$$ 16.7279 28.9736i 0.713930 1.23656i
$$550$$ 2.32843 4.03295i 0.0992845 0.171966i
$$551$$ −0.778175 1.34784i −0.0331514 0.0574198i
$$552$$ −15.0711 −0.641467
$$553$$ 0 0
$$554$$ 1.82843 0.0776824
$$555$$ 6.65685 + 11.5300i 0.282568 + 0.489422i
$$556$$ 0 0
$$557$$ −3.75736 + 6.50794i −0.159204 + 0.275750i −0.934582 0.355748i $$-0.884226\pi$$
0.775378 + 0.631498i $$0.217560\pi$$
$$558$$ −5.65685 9.79796i −0.239474 0.414781i
$$559$$ −21.6569 −0.915987
$$560$$ 0 0
$$561$$ −8.82843 −0.372736
$$562$$ −4.36396 7.55860i −0.184083 0.318840i
$$563$$ 4.53553 7.85578i 0.191150 0.331081i −0.754482 0.656321i $$-0.772112\pi$$
0.945632 + 0.325240i $$0.105445\pi$$
$$564$$ −12.6569 + 21.9223i −0.532950 + 0.923096i
$$565$$ 2.39340 + 4.14549i 0.100691 + 0.174402i
$$566$$ 23.4142 0.984173
$$567$$ 0 0
$$568$$ −11.0711 −0.464532
$$569$$ 2.00000 + 3.46410i 0.0838444 + 0.145223i 0.904898 0.425628i $$-0.139947\pi$$
−0.821054 + 0.570851i $$0.806613\pi$$
$$570$$ −0.414214 + 0.717439i −0.0173495 + 0.0300502i
$$571$$ −13.1924 + 22.8499i −0.552084 + 0.956238i 0.446040 + 0.895013i $$0.352834\pi$$
−0.998124 + 0.0612248i $$0.980499\pi$$
$$572$$ −1.91421 3.31552i −0.0800373 0.138629i
$$573$$ −17.3137 −0.723291
$$574$$ 0 0
$$575$$ 29.0711 1.21235
$$576$$ −1.41421 2.44949i −0.0589256 0.102062i
$$577$$ −4.84315 + 8.38857i −0.201623 + 0.349221i −0.949051 0.315121i $$-0.897955\pi$$
0.747429 + 0.664342i $$0.231288\pi$$
$$578$$ 1.81371 3.14144i 0.0754403 0.130666i
$$579$$ −26.4350 45.7868i −1.09860 1.90284i
$$580$$ 1.55635 0.0646239
$$581$$ 0 0
$$582$$ 9.24264 0.383120
$$583$$ −3.94975 6.84116i −0.163582 0.283332i
$$584$$ −4.70711 + 8.15295i −0.194781 + 0.337371i
$$585$$ −3.17157 + 5.49333i −0.131128 + 0.227121i
$$586$$ −5.41421 9.37769i −0.223659 0.387389i
$$587$$ 25.1005 1.03601 0.518004 0.855378i $$-0.326675\pi$$
0.518004 + 0.855378i $$0.326675\pi$$
$$588$$ 0 0
$$589$$ 2.34315 0.0965476
$$590$$ −1.63604 2.83370i −0.0673547 0.116662i
$$591$$ 0.621320 1.07616i 0.0255577 0.0442672i
$$592$$ 4.70711 8.15295i 0.193461 0.335084i
$$593$$ 11.8492 + 20.5235i 0.486590 + 0.842799i 0.999881 0.0154159i $$-0.00490721\pi$$
−0.513291 + 0.858215i $$0.671574\pi$$
$$594$$ −0.414214 −0.0169954
$$595$$ 0 0
$$596$$ 17.6569 0.723253
$$597$$ 0.121320 + 0.210133i 0.00496531 + 0.00860017i
$$598$$ 11.9497 20.6976i 0.488662 0.846387i
$$599$$ −21.3137 + 36.9164i −0.870855 + 1.50836i −0.00974040 + 0.999953i $$0.503101\pi$$
−0.861114 + 0.508412i $$0.830233\pi$$
$$600$$ 5.62132 + 9.73641i 0.229489 + 0.397487i
$$601$$ −31.9411 −1.30291 −0.651453 0.758689i $$-0.725840\pi$$
−0.651453 + 0.758689i $$0.725840\pi$$
$$602$$ 0 0
$$603$$ 7.79899 0.317599
$$604$$ 7.86396 + 13.6208i 0.319980 + 0.554222i
$$605$$ −0.292893 + 0.507306i −0.0119078 + 0.0206249i
$$606$$ 7.44975 12.9033i 0.302625 0.524162i
$$607$$ −21.4853 37.2136i −0.872061 1.51045i −0.859861 0.510528i $$-0.829450\pi$$
−0.0121994 0.999926i $$-0.503883\pi$$
$$608$$ 0.585786 0.0237568
$$609$$ 0 0
$$610$$ −6.92893 −0.280544
$$611$$ −20.0711 34.7641i −0.811988 1.40641i
$$612$$ 5.17157 8.95743i 0.209048 0.362083i
$$613$$ −14.3137 + 24.7921i −0.578125 + 1.00134i 0.417569 + 0.908645i $$0.362882\pi$$
−0.995694 + 0.0926971i $$0.970451\pi$$
$$614$$ 4.94975 + 8.57321i 0.199756 + 0.345987i
$$615$$ 7.65685 0.308754
$$616$$ 0 0
$$617$$ −41.9706 −1.68967 −0.844836 0.535026i $$-0.820302\pi$$
−0.844836 + 0.535026i $$0.820302\pi$$
$$618$$ 16.1924 + 28.0460i 0.651353 + 1.12818i
$$619$$ −10.9706 + 19.0016i −0.440944 + 0.763738i −0.997760 0.0668984i $$-0.978690\pi$$
0.556816 + 0.830636i $$0.312023\pi$$
$$620$$ −1.17157 + 2.02922i −0.0470515 + 0.0814956i
$$621$$ −1.29289 2.23936i −0.0518820 0.0898623i
$$622$$ −16.7279 −0.670729
$$623$$ 0 0
$$624$$ 9.24264 0.370002
$$625$$ −9.98528 17.2950i −0.399411 0.691801i
$$626$$ −10.3284 + 17.8894i −0.412807 + 0.715003i
$$627$$ −0.707107 + 1.22474i −0.0282391 + 0.0489116i
$$628$$ 8.82843 + 15.2913i 0.352293 + 0.610189i
$$629$$ 34.4264 1.37267
$$630$$ 0 0
$$631$$ 23.2721 0.926447 0.463223 0.886242i $$-0.346693\pi$$
0.463223 + 0.886242i $$0.346693\pi$$
$$632$$ 6.62132 + 11.4685i 0.263382 + 0.456191i
$$633$$ −8.94975 + 15.5014i −0.355721 + 0.616126i
$$634$$ −4.34315 + 7.52255i −0.172488 + 0.298759i
$$635$$ −4.60660 7.97887i −0.182807 0.316632i
$$636$$ 19.0711 0.756217
$$637$$ 0 0
$$638$$ 2.65685 0.105186
$$639$$ 15.6569 + 27.1185i 0.619376 + 1.07279i
$$640$$ −0.292893 + 0.507306i −0.0115776 + 0.0200530i
$$641$$ −7.64214 + 13.2366i −0.301846 + 0.522813i −0.976554 0.215272i $$-0.930936\pi$$
0.674708 + 0.738085i $$0.264270\pi$$
$$642$$ 3.70711 + 6.42090i 0.146308 + 0.253413i
$$643$$ −1.58579 −0.0625373 −0.0312687 0.999511i $$-0.509955\pi$$
−0.0312687 + 0.999511i $$0.509955\pi$$
$$644$$ 0 0
$$645$$ −8.00000 −0.315000
$$646$$ 1.07107 + 1.85514i 0.0421406 + 0.0729897i
$$647$$ 15.0919 26.1399i 0.593323 1.02767i −0.400458 0.916315i $$-0.631149\pi$$
0.993781 0.111351i $$-0.0355177\pi$$
$$648$$ 4.74264 8.21449i 0.186309 0.322696i
$$649$$ −2.79289 4.83743i −0.109631 0.189886i
$$650$$ −17.8284 −0.699288
$$651$$ 0 0
$$652$$ 9.72792 0.380975
$$653$$ 9.19239 + 15.9217i 0.359726 + 0.623064i 0.987915 0.154997i $$-0.0495369\pi$$
−0.628189 + 0.778061i $$0.716204\pi$$
$$654$$ −19.8995 + 34.4669i −0.778132 + 1.34776i
$$655$$ −0.171573 + 0.297173i −0.00670391 + 0.0116115i
$$656$$ −2.70711 4.68885i −0.105695 0.183069i
$$657$$ 26.6274 1.03883
$$658$$ 0 0
$$659$$ −12.0000 −0.467454 −0.233727 0.972302i $$-0.575092\pi$$
−0.233727 + 0.972302i $$0.575092\pi$$
$$660$$ −0.707107 1.22474i −0.0275241 0.0476731i
$$661$$ 9.48528 16.4290i 0.368935 0.639014i −0.620465 0.784234i $$-0.713056\pi$$
0.989399 + 0.145221i $$0.0463893\pi$$
$$662$$ 12.0355 20.8462i 0.467774 0.810209i
$$663$$ 16.8995 + 29.2708i 0.656322 + 1.13678i
$$664$$ 12.1421 0.471206
$$665$$ 0 0
$$666$$ −26.6274 −1.03179
$$667$$ 8.29289 + 14.3637i 0.321102 + 0.556165i
$$668$$ 6.86396 11.8887i 0.265575 0.459989i
$$669$$ 10.3640 17.9509i 0.400694 0.694022i
$$670$$ −0.807612 1.39882i −0.0312008 0.0540413i
$$671$$ −11.8284 −0.456631
$$672$$ 0 0
$$673$$ 5.55635 0.214182 0.107091 0.994249i $$-0.465846\pi$$
0.107091 + 0.994249i $$0.465846\pi$$
$$674$$ 14.1213 + 24.4588i 0.543933 + 0.942119i
$$675$$ −0.964466 + 1.67050i −0.0371223 + 0.0642977i
$$676$$ −0.828427 + 1.43488i −0.0318626 + 0.0551876i
$$677$$ −17.6569 30.5826i −0.678608 1.17538i −0.975400 0.220441i $$-0.929250\pi$$
0.296792 0.954942i $$-0.404083\pi$$
$$678$$ −19.7279 −0.757646
$$679$$ 0 0
$$680$$ −2.14214 −0.0821472
$$681$$ −34.7990 60.2736i −1.33350 2.30969i
$$682$$ −2.00000 + 3.46410i −0.0765840 + 0.132647i
$$683$$ −6.79289 + 11.7656i −0.259923 + 0.450200i −0.966221 0.257715i $$-0.917030\pi$$
0.706298 + 0.707914i $$0.250364\pi$$
$$684$$ −0.828427 1.43488i −0.0316757 0.0548639i
$$685$$ −9.75736 −0.372810
$$686$$ 0 0
$$687$$ −56.2843 −2.14738
$$688$$ 2.82843 + 4.89898i 0.107833 + 0.186772i
$$689$$ −15.1213 + 26.1909i −0.576076 + 0.997794i
$$690$$ 4.41421 7.64564i 0.168046 0.291065i
$$691$$ 14.0355 + 24.3103i 0.533937 + 0.924806i 0.999214 + 0.0396407i $$0.0126213\pi$$
−0.465277 + 0.885165i $$0.654045\pi$$
$$692$$ 9.82843 0.373621
$$693$$ 0 0
$$694$$ 17.4142 0.661035
$$695$$ 0 0
$$696$$ −3.20711 + 5.55487i −0.121565 + 0.210557i
$$697$$ 9.89949 17.1464i 0.374970 0.649467i
$$698$$ 0 0
$$699$$ 3.41421 0.129137
$$700$$ 0 0
$$701$$ −26.1127 −0.986263 −0.493132 0.869955i $$-0.664148\pi$$
−0.493132 + 0.869955i $$0.664148\pi$$
$$702$$ 0.792893 + 1.37333i 0.0299258 + 0.0518331i
$$703$$ 2.75736 4.77589i 0.103996 0.180126i
$$704$$ −0.500000 + 0.866025i −0.0188445 + 0.0326396i
$$705$$ −7.41421 12.8418i −0.279235 0.483650i
$$706$$ 2.68629 0.101100
$$707$$ 0 0
$$708$$ 13.4853 0.506808
$$709$$ 6.02082 + 10.4284i 0.226116 + 0.391645i 0.956654 0.291228i $$-0.0940637\pi$$
−0.730537 + 0.682873i $$0.760730\pi$$
$$710$$ 3.24264 5.61642i 0.121694 0.210780i
$$711$$ 18.7279 32.4377i 0.702352 1.21651i
$$712$$ 6.24264 + 10.8126i 0.233953 + 0.405218i
$$713$$ −24.9706 −0.935155
$$714$$ 0 0
$$715$$ 2.24264 0.0838700
$$716$$ −0.449747 0.778985i −0.0168079 0.0291121i
$$717$$ −24.3995 + 42.2612i −0.911216 + 1.57827i
$$718$$ −9.62132 + 16.6646i −0.359064 + 0.621918i
$$719$$ −0.757359 1.31178i −0.0282447 0.0489213i 0.851558 0.524261i $$-0.175658\pi$$
−0.879802 + 0.475340i $$0.842325\pi$$
$$720$$ 1.65685 0.0617473
$$721$$ 0 0
$$722$$ −18.6569 −0.694336
$$723$$ 14.7782 + 25.5965i 0.549606 + 0.951946i
$$724$$ −3.82843 + 6.63103i −0.142282 + 0.246440i
$$725$$ 6.18629 10.7150i 0.229753 0.397944i
$$726$$ −1.20711 2.09077i −0.0447999 0.0775958i
$$727$$ −36.4264 −1.35098 −0.675490 0.737369i $$-0.736068\pi$$
−0.675490 + 0.737369i $$0.736068\pi$$
$$728$$ 0 0
$$729$$ −23.8284 −0.882534
$$730$$ −2.75736 4.77589i −0.102054 0.176763i
$$731$$ −10.3431 + 17.9149i −0.382555 + 0.662605i
$$732$$ 14.2782 24.7305i 0.527737 0.914066i
$$733$$ −6.50000 11.2583i −0.240083 0.415836i 0.720655 0.693294i $$-0.243841\pi$$
−0.960738 + 0.277458i $$0.910508\pi$$
$$734$$ 10.7279 0.395975
$$735$$ 0 0
$$736$$ −6.24264 −0.230107
$$737$$ −1.37868 2.38794i −0.0507843 0.0879610i
$$738$$ −7.65685 + 13.2621i −0.281853 + 0.488183i
$$739$$ 26.2132 45.4026i 0.964268 1.67016i 0.252700 0.967545i $$-0.418681\pi$$
0.711568 0.702617i $$-0.247985\pi$$
$$740$$ 2.75736 + 4.77589i 0.101363 + 0.175565i
$$741$$ 5.41421 0.198896
$$742$$ 0 0
$$743$$ −13.3137 −0.488433 −0.244216 0.969721i $$-0.578531\pi$$
−0.244216 + 0.969721i $$0.578531\pi$$
$$744$$ −4.82843 8.36308i −0.177019 0.306605i
$$745$$ −5.17157 + 8.95743i −0.189472 + 0.328175i
$$746$$ 9.98528 17.2950i 0.365587 0.633215i
$$747$$ −17.1716 29.7420i −0.628275 1.08820i
$$748$$ −3.65685 −0.133708
$$749$$ 0 0
$$750$$ −13.6569 −0.498678
$$751$$ −22.8284 39.5400i −0.833021 1.44283i −0.895631 0.444797i $$-0.853276\pi$$
0.0626103 0.998038i $$-0.480057\pi$$
$$752$$ −5.24264 + 9.08052i −0.191179 + 0.331132i
$$753$$ −31.5563 + 54.6572i −1.14998 + 1.99182i
$$754$$ −5.08579 8.80884i −0.185213 0.320799i
$$755$$ −9.21320 −0.335303
$$756$$ 0 0
$$757$$ 8.34315 0.303237 0.151618 0.988439i $$-0.451552\pi$$
0.151618 + 0.988439i $$0.451552\pi$$
$$758$$ −13.9350 24.1362i −0.506143 0.876665i
$$759$$ 7.53553 13.0519i 0.273523 0.473755i
$$760$$ −0.171573 + 0.297173i −0.00622360 + 0.0107796i
$$761$$ 15.4853 + 26.8213i 0.561341 + 0.972271i 0.997380 + 0.0723433i $$0.0230477\pi$$
−0.436039 + 0.899928i $$0.643619\pi$$
$$762$$ 37.9706 1.37553
$$763$$ 0 0
$$764$$ −7.17157 −0.259458
$$765$$ 3.02944 + 5.24714i 0.109530 + 0.189711i
$$766$$ −3.19239 + 5.52938i −0.115346 + 0.199785i
$$767$$ −10.6924 + 18.5198i −0.386080 + 0.668710i
$$768$$ −1.20711 2.09077i −0.0435577 0.0754442i
$$769$$ −22.9706 −0.828340 −0.414170 0.910200i $$-0.635928\pi$$
−0.414170 + 0.910200i $$0.635928\pi$$
$$770$$ 0 0
$$771$$ 60.6985 2.18600
$$772$$ −10.9497 18.9655i −0.394090 0.682584i
$$773$$ −10.9706 + 19.0016i −0.394584 + 0.683439i −0.993048 0.117710i $$-0.962445\pi$$
0.598464 + 0.801150i $$0.295778\pi$$
$$774$$ 8.00000 13.8564i 0.287554 0.498058i
$$775$$ 9.31371 + 16.1318i 0.334558 + 0.579472i
$$776$$ 3.82843 0.137433
$$777$$ 0 0
$$778$$ &min