# Properties

 Label 475.2.j.a.49.1 Level $475$ Weight $2$ Character 475.49 Analytic conductor $3.793$ Analytic rank $0$ Dimension $4$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 475.j (of order $$6$$, 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: $$3.79289409601$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 95) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 49.1 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 475.49 Dual form 475.2.j.a.349.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.73205 - 1.00000i) q^{3} +(-1.00000 - 1.73205i) q^{4} -4.00000i q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-1.73205 - 1.00000i) q^{3} +(-1.00000 - 1.73205i) q^{4} -4.00000i q^{7} +(0.500000 + 0.866025i) q^{9} +3.00000 q^{11} +4.00000i q^{12} +(-1.73205 + 1.00000i) q^{13} +(-2.00000 + 3.46410i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(3.50000 + 2.59808i) q^{19} +(-4.00000 + 6.92820i) q^{21} +4.00000i q^{27} +(-6.92820 + 4.00000i) q^{28} +(-1.50000 - 2.59808i) q^{29} -7.00000 q^{31} +(-5.19615 - 3.00000i) q^{33} +(1.00000 - 1.73205i) q^{36} +8.00000i q^{37} +4.00000 q^{39} +(3.00000 - 5.19615i) q^{41} +(-3.46410 - 2.00000i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(5.19615 - 3.00000i) q^{47} +(6.92820 - 4.00000i) q^{48} -9.00000 q^{49} +(6.00000 + 10.3923i) q^{51} +(3.46410 + 2.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-3.46410 - 8.00000i) q^{57} +(-7.50000 + 12.9904i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(3.46410 - 2.00000i) q^{63} +8.00000 q^{64} +(1.73205 - 1.00000i) q^{67} +12.0000i q^{68} +(1.50000 - 2.59808i) q^{71} +(6.92820 + 4.00000i) q^{73} +(1.00000 - 8.66025i) q^{76} -12.0000i q^{77} +(2.50000 - 4.33013i) q^{79} +(5.50000 - 9.52628i) q^{81} -12.0000i q^{83} +16.0000 q^{84} +6.00000i q^{87} +(-7.50000 - 12.9904i) q^{89} +(4.00000 + 6.92820i) q^{91} +(12.1244 + 7.00000i) q^{93} +(-6.92820 - 4.00000i) q^{97} +(1.50000 + 2.59808i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{4} + 2 q^{9}+O(q^{10})$$ 4 * q - 4 * q^4 + 2 * q^9 $$4 q - 4 q^{4} + 2 q^{9} + 12 q^{11} - 8 q^{16} + 14 q^{19} - 16 q^{21} - 6 q^{29} - 28 q^{31} + 4 q^{36} + 16 q^{39} + 12 q^{41} - 12 q^{44} - 36 q^{49} + 24 q^{51} - 30 q^{59} - 10 q^{61} + 32 q^{64} + 6 q^{71} + 4 q^{76} + 10 q^{79} + 22 q^{81} + 64 q^{84} - 30 q^{89} + 16 q^{91} + 6 q^{99}+O(q^{100})$$ 4 * q - 4 * q^4 + 2 * q^9 + 12 * q^11 - 8 * q^16 + 14 * q^19 - 16 * q^21 - 6 * q^29 - 28 * q^31 + 4 * q^36 + 16 * q^39 + 12 * q^41 - 12 * q^44 - 36 * q^49 + 24 * q^51 - 30 * q^59 - 10 * q^61 + 32 * q^64 + 6 * q^71 + 4 * q^76 + 10 * q^79 + 22 * q^81 + 64 * q^84 - 30 * q^89 + 16 * q^91 + 6 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$3$$ −1.73205 1.00000i −1.00000 0.577350i −0.0917517 0.995782i $$-0.529247\pi$$
−0.908248 + 0.418432i $$0.862580\pi$$
$$4$$ −1.00000 1.73205i −0.500000 0.866025i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 4.00000i 1.51186i −0.654654 0.755929i $$-0.727186\pi$$
0.654654 0.755929i $$-0.272814\pi$$
$$8$$ 0 0
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 4.00000i 1.15470i
$$13$$ −1.73205 + 1.00000i −0.480384 + 0.277350i −0.720577 0.693375i $$-0.756123\pi$$
0.240192 + 0.970725i $$0.422790\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −2.00000 + 3.46410i −0.500000 + 0.866025i
$$17$$ −5.19615 3.00000i −1.26025 0.727607i −0.287129 0.957892i $$-0.592701\pi$$
−0.973123 + 0.230285i $$0.926034\pi$$
$$18$$ 0 0
$$19$$ 3.50000 + 2.59808i 0.802955 + 0.596040i
$$20$$ 0 0
$$21$$ −4.00000 + 6.92820i −0.872872 + 1.51186i
$$22$$ 0 0
$$23$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 4.00000i 0.769800i
$$28$$ −6.92820 + 4.00000i −1.30931 + 0.755929i
$$29$$ −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i $$-0.256518\pi$$
−0.971023 + 0.238987i $$0.923185\pi$$
$$30$$ 0 0
$$31$$ −7.00000 −1.25724 −0.628619 0.777714i $$-0.716379\pi$$
−0.628619 + 0.777714i $$0.716379\pi$$
$$32$$ 0 0
$$33$$ −5.19615 3.00000i −0.904534 0.522233i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 1.73205i 0.166667 0.288675i
$$37$$ 8.00000i 1.31519i 0.753371 + 0.657596i $$0.228427\pi$$
−0.753371 + 0.657596i $$0.771573\pi$$
$$38$$ 0 0
$$39$$ 4.00000 0.640513
$$40$$ 0 0
$$41$$ 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i $$-0.678120\pi$$
0.999353 + 0.0359748i $$0.0114536\pi$$
$$42$$ 0 0
$$43$$ −3.46410 2.00000i −0.528271 0.304997i 0.212041 0.977261i $$-0.431989\pi$$
−0.740312 + 0.672264i $$0.765322\pi$$
$$44$$ −3.00000 5.19615i −0.452267 0.783349i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 5.19615 3.00000i 0.757937 0.437595i −0.0706177 0.997503i $$-0.522497\pi$$
0.828554 + 0.559908i $$0.189164\pi$$
$$48$$ 6.92820 4.00000i 1.00000 0.577350i
$$49$$ −9.00000 −1.28571
$$50$$ 0 0
$$51$$ 6.00000 + 10.3923i 0.840168 + 1.45521i
$$52$$ 3.46410 + 2.00000i 0.480384 + 0.277350i
$$53$$ 5.19615 3.00000i 0.713746 0.412082i −0.0987002 0.995117i $$-0.531468\pi$$
0.812447 + 0.583036i $$0.198135\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −3.46410 8.00000i −0.458831 1.05963i
$$58$$ 0 0
$$59$$ −7.50000 + 12.9904i −0.976417 + 1.69120i −0.301239 + 0.953549i $$0.597400\pi$$
−0.675178 + 0.737655i $$0.735933\pi$$
$$60$$ 0 0
$$61$$ −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i $$-0.270381\pi$$
−0.980507 + 0.196485i $$0.937047\pi$$
$$62$$ 0 0
$$63$$ 3.46410 2.00000i 0.436436 0.251976i
$$64$$ 8.00000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.73205 1.00000i 0.211604 0.122169i −0.390453 0.920623i $$-0.627682\pi$$
0.602056 + 0.798454i $$0.294348\pi$$
$$68$$ 12.0000i 1.45521i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.50000 2.59808i 0.178017 0.308335i −0.763184 0.646181i $$-0.776365\pi$$
0.941201 + 0.337846i $$0.109698\pi$$
$$72$$ 0 0
$$73$$ 6.92820 + 4.00000i 0.810885 + 0.468165i 0.847263 0.531174i $$-0.178249\pi$$
−0.0363782 + 0.999338i $$0.511582\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 1.00000 8.66025i 0.114708 0.993399i
$$77$$ 12.0000i 1.36753i
$$78$$ 0 0
$$79$$ 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i $$-0.742577\pi$$
0.971698 + 0.236225i $$0.0759104\pi$$
$$80$$ 0 0
$$81$$ 5.50000 9.52628i 0.611111 1.05848i
$$82$$ 0 0
$$83$$ 12.0000i 1.31717i −0.752506 0.658586i $$-0.771155\pi$$
0.752506 0.658586i $$-0.228845\pi$$
$$84$$ 16.0000 1.74574
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 6.00000i 0.643268i
$$88$$ 0 0
$$89$$ −7.50000 12.9904i −0.794998 1.37698i −0.922840 0.385183i $$-0.874138\pi$$
0.127842 0.991795i $$-0.459195\pi$$
$$90$$ 0 0
$$91$$ 4.00000 + 6.92820i 0.419314 + 0.726273i
$$92$$ 0 0
$$93$$ 12.1244 + 7.00000i 1.25724 + 0.725866i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −6.92820 4.00000i −0.703452 0.406138i 0.105180 0.994453i $$-0.466458\pi$$
−0.808632 + 0.588315i $$0.799792\pi$$
$$98$$ 0 0
$$99$$ 1.50000 + 2.59808i 0.150756 + 0.261116i
$$100$$ 0 0
$$101$$ −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i $$-0.898506\pi$$
0.203317 0.979113i $$-0.434828\pi$$
$$102$$ 0 0
$$103$$ 16.0000i 1.57653i 0.615338 + 0.788263i $$0.289020\pi$$
−0.615338 + 0.788263i $$0.710980\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 6.92820 4.00000i 0.666667 0.384900i
$$109$$ 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i $$-0.656723\pi$$
0.999512 0.0312328i $$-0.00994332\pi$$
$$110$$ 0 0
$$111$$ 8.00000 13.8564i 0.759326 1.31519i
$$112$$ 13.8564 + 8.00000i 1.30931 + 0.755929i
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −3.00000 + 5.19615i −0.278543 + 0.482451i
$$117$$ −1.73205 1.00000i −0.160128 0.0924500i
$$118$$ 0 0
$$119$$ −12.0000 + 20.7846i −1.10004 + 1.90532i
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ −10.3923 + 6.00000i −0.937043 + 0.541002i
$$124$$ 7.00000 + 12.1244i 0.628619 + 1.08880i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1.73205 1.00000i 0.153695 0.0887357i −0.421180 0.906977i $$-0.638384\pi$$
0.574875 + 0.818241i $$0.305051\pi$$
$$128$$ 0 0
$$129$$ 4.00000 + 6.92820i 0.352180 + 0.609994i
$$130$$ 0 0
$$131$$ −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i $$0.342311\pi$$
−0.999602 + 0.0281993i $$0.991023\pi$$
$$132$$ 12.0000i 1.04447i
$$133$$ 10.3923 14.0000i 0.901127 1.21395i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −10.3923 + 6.00000i −0.887875 + 0.512615i −0.873247 0.487278i $$-0.837990\pi$$
−0.0146279 + 0.999893i $$0.504656\pi$$
$$138$$ 0 0
$$139$$ −8.00000 13.8564i −0.678551 1.17529i −0.975417 0.220366i $$-0.929275\pi$$
0.296866 0.954919i $$-0.404058\pi$$
$$140$$ 0 0
$$141$$ −12.0000 −1.01058
$$142$$ 0 0
$$143$$ −5.19615 + 3.00000i −0.434524 + 0.250873i
$$144$$ −4.00000 −0.333333
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 15.5885 + 9.00000i 1.28571 + 0.742307i
$$148$$ 13.8564 8.00000i 1.13899 0.657596i
$$149$$ 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i $$-0.794119\pi$$
0.920904 + 0.389789i $$0.127452\pi$$
$$150$$ 0 0
$$151$$ 17.0000 1.38344 0.691720 0.722166i $$-0.256853\pi$$
0.691720 + 0.722166i $$0.256853\pi$$
$$152$$ 0 0
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −4.00000 6.92820i −0.320256 0.554700i
$$157$$ −1.73205 1.00000i −0.138233 0.0798087i 0.429289 0.903167i $$-0.358764\pi$$
−0.567521 + 0.823359i $$0.692098\pi$$
$$158$$ 0 0
$$159$$ −12.0000 −0.951662
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 10.0000i 0.783260i 0.920123 + 0.391630i $$0.128089\pi$$
−0.920123 + 0.391630i $$0.871911\pi$$
$$164$$ −12.0000 −0.937043
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$168$$ 0 0
$$169$$ −4.50000 + 7.79423i −0.346154 + 0.599556i
$$170$$ 0 0
$$171$$ −0.500000 + 4.33013i −0.0382360 + 0.331133i
$$172$$ 8.00000i 0.609994i
$$173$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −6.00000 + 10.3923i −0.452267 + 0.783349i
$$177$$ 25.9808 15.0000i 1.95283 1.12747i
$$178$$ 0 0
$$179$$ 9.00000 0.672692 0.336346 0.941739i $$-0.390809\pi$$
0.336346 + 0.941739i $$0.390809\pi$$
$$180$$ 0 0
$$181$$ −1.00000 1.73205i −0.0743294 0.128742i 0.826465 0.562988i $$-0.190348\pi$$
−0.900794 + 0.434246i $$0.857015\pi$$
$$182$$ 0 0
$$183$$ 10.0000i 0.739221i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −15.5885 9.00000i −1.13994 0.658145i
$$188$$ −10.3923 6.00000i −0.757937 0.437595i
$$189$$ 16.0000 1.16383
$$190$$ 0 0
$$191$$ −15.0000 −1.08536 −0.542681 0.839939i $$-0.682591\pi$$
−0.542681 + 0.839939i $$0.682591\pi$$
$$192$$ −13.8564 8.00000i −1.00000 0.577350i
$$193$$ −13.8564 8.00000i −0.997406 0.575853i −0.0899262 0.995948i $$-0.528663\pi$$
−0.907480 + 0.420096i $$0.861996\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 9.00000 + 15.5885i 0.642857 + 1.11346i
$$197$$ 18.0000i 1.28245i −0.767354 0.641223i $$-0.778427\pi$$
0.767354 0.641223i $$-0.221573\pi$$
$$198$$ 0 0
$$199$$ −9.50000 16.4545i −0.673437 1.16643i −0.976923 0.213591i $$-0.931484\pi$$
0.303486 0.952836i $$-0.401849\pi$$
$$200$$ 0 0
$$201$$ −4.00000 −0.282138
$$202$$ 0 0
$$203$$ −10.3923 + 6.00000i −0.729397 + 0.421117i
$$204$$ 12.0000 20.7846i 0.840168 1.45521i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 8.00000i 0.554700i
$$209$$ 10.5000 + 7.79423i 0.726300 + 0.539138i
$$210$$ 0 0
$$211$$ 3.50000 6.06218i 0.240950 0.417338i −0.720035 0.693938i $$-0.755874\pi$$
0.960985 + 0.276600i $$0.0892077\pi$$
$$212$$ −10.3923 6.00000i −0.713746 0.412082i
$$213$$ −5.19615 + 3.00000i −0.356034 + 0.205557i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 28.0000i 1.90076i
$$218$$ 0 0
$$219$$ −8.00000 13.8564i −0.540590 0.936329i
$$220$$ 0 0
$$221$$ 12.0000 0.807207
$$222$$ 0 0
$$223$$ −3.46410 2.00000i −0.231973 0.133930i 0.379509 0.925188i $$-0.376093\pi$$
−0.611482 + 0.791258i $$0.709426\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 24.0000i 1.59294i −0.604681 0.796468i $$-0.706699\pi$$
0.604681 0.796468i $$-0.293301\pi$$
$$228$$ −10.3923 + 14.0000i −0.688247 + 0.927173i
$$229$$ 7.00000 0.462573 0.231287 0.972886i $$-0.425707\pi$$
0.231287 + 0.972886i $$0.425707\pi$$
$$230$$ 0 0
$$231$$ −12.0000 + 20.7846i −0.789542 + 1.36753i
$$232$$ 0 0
$$233$$ 5.19615 + 3.00000i 0.340411 + 0.196537i 0.660454 0.750867i $$-0.270364\pi$$
−0.320043 + 0.947403i $$0.603697\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 30.0000 1.95283
$$237$$ −8.66025 + 5.00000i −0.562544 + 0.324785i
$$238$$ 0 0
$$239$$ 3.00000 0.194054 0.0970269 0.995282i $$-0.469067\pi$$
0.0970269 + 0.995282i $$0.469067\pi$$
$$240$$ 0 0
$$241$$ −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i $$-0.218151\pi$$
−0.935242 + 0.354010i $$0.884818\pi$$
$$242$$ 0 0
$$243$$ −8.66025 + 5.00000i −0.555556 + 0.320750i
$$244$$ −5.00000 + 8.66025i −0.320092 + 0.554416i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −8.66025 1.00000i −0.551039 0.0636285i
$$248$$ 0 0
$$249$$ −12.0000 + 20.7846i −0.760469 + 1.31717i
$$250$$ 0 0
$$251$$ 7.50000 + 12.9904i 0.473396 + 0.819946i 0.999536 0.0304521i $$-0.00969471\pi$$
−0.526140 + 0.850398i $$0.676361\pi$$
$$252$$ −6.92820 4.00000i −0.436436 0.251976i
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ −15.5885 + 9.00000i −0.972381 + 0.561405i −0.899961 0.435970i $$-0.856405\pi$$
−0.0724199 + 0.997374i $$0.523072\pi$$
$$258$$ 0 0
$$259$$ 32.0000 1.98838
$$260$$ 0 0
$$261$$ 1.50000 2.59808i 0.0928477 0.160817i
$$262$$ 0 0
$$263$$ −15.5885 9.00000i −0.961225 0.554964i −0.0646755 0.997906i $$-0.520601\pi$$
−0.896550 + 0.442943i $$0.853935\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 30.0000i 1.83597i
$$268$$ −3.46410 2.00000i −0.211604 0.122169i
$$269$$ −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i $$0.387814\pi$$
−0.985389 + 0.170321i $$0.945520\pi$$
$$270$$ 0 0
$$271$$ −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i $$-0.941766\pi$$
0.649211 + 0.760609i $$0.275099\pi$$
$$272$$ 20.7846 12.0000i 1.26025 0.727607i
$$273$$ 16.0000i 0.968364i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 8.00000i 0.480673i 0.970690 + 0.240337i $$0.0772579\pi$$
−0.970690 + 0.240337i $$0.922742\pi$$
$$278$$ 0 0
$$279$$ −3.50000 6.06218i −0.209540 0.362933i
$$280$$ 0 0
$$281$$ −3.00000 5.19615i −0.178965 0.309976i 0.762561 0.646916i $$-0.223942\pi$$
−0.941526 + 0.336939i $$0.890608\pi$$
$$282$$ 0 0
$$283$$ 12.1244 + 7.00000i 0.720718 + 0.416107i 0.815017 0.579437i $$-0.196728\pi$$
−0.0942988 + 0.995544i $$0.530061\pi$$
$$284$$ −6.00000 −0.356034
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −20.7846 12.0000i −1.22688 0.708338i
$$288$$ 0 0
$$289$$ 9.50000 + 16.4545i 0.558824 + 0.967911i
$$290$$ 0 0
$$291$$ 8.00000 + 13.8564i 0.468968 + 0.812277i
$$292$$ 16.0000i 0.936329i
$$293$$ 24.0000i 1.40209i −0.713115 0.701047i $$-0.752716\pi$$
0.713115 0.701047i $$-0.247284\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 12.0000i 0.696311i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −8.00000 + 13.8564i −0.461112 + 0.798670i
$$302$$ 0 0
$$303$$ 30.0000i 1.72345i
$$304$$ −16.0000 + 6.92820i −0.917663 + 0.397360i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 29.4449 + 17.0000i 1.68051 + 0.970241i 0.961324 + 0.275421i $$0.0888172\pi$$
0.719183 + 0.694820i $$0.244516\pi$$
$$308$$ −20.7846 + 12.0000i −1.18431 + 0.683763i
$$309$$ 16.0000 27.7128i 0.910208 1.57653i
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 0 0
$$313$$ 8.66025 5.00000i 0.489506 0.282617i −0.234863 0.972028i $$-0.575464\pi$$
0.724370 + 0.689412i $$0.242131\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ 20.7846 12.0000i 1.16738 0.673987i 0.214318 0.976764i $$-0.431247\pi$$
0.953062 + 0.302777i $$0.0979136\pi$$
$$318$$ 0 0
$$319$$ −4.50000 7.79423i −0.251952 0.436393i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −10.3923 24.0000i −0.578243 1.33540i
$$324$$ −22.0000 −1.22222
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −19.0526 + 11.0000i −1.05361 + 0.608301i
$$328$$ 0 0
$$329$$ −12.0000 20.7846i −0.661581 1.14589i
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ −20.7846 + 12.0000i −1.14070 + 0.658586i
$$333$$ −6.92820 + 4.00000i −0.379663 + 0.219199i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ −16.0000 27.7128i −0.872872 1.51186i
$$337$$ 13.8564 + 8.00000i 0.754807 + 0.435788i 0.827428 0.561572i $$-0.189803\pi$$
−0.0726214 + 0.997360i $$0.523136\pi$$
$$338$$ 0 0
$$339$$ −6.00000 + 10.3923i −0.325875 + 0.564433i
$$340$$ 0 0
$$341$$ −21.0000 −1.13721
$$342$$ 0 0
$$343$$ 8.00000i 0.431959i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −10.3923 6.00000i −0.557888 0.322097i 0.194409 0.980921i $$-0.437721\pi$$
−0.752297 + 0.658824i $$0.771054\pi$$
$$348$$ 10.3923 6.00000i 0.557086 0.321634i
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ −4.00000 6.92820i −0.213504 0.369800i
$$352$$ 0 0
$$353$$ 12.0000i 0.638696i −0.947638 0.319348i $$-0.896536\pi$$
0.947638 0.319348i $$-0.103464\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −15.0000 + 25.9808i −0.794998 + 1.37698i
$$357$$ 41.5692 24.0000i 2.20008 1.27021i
$$358$$ 0 0
$$359$$ 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i $$-0.615019\pi$$
0.986865 0.161546i $$-0.0516481\pi$$
$$360$$ 0 0
$$361$$ 5.50000 + 18.1865i 0.289474 + 0.957186i
$$362$$ 0 0
$$363$$ 3.46410 + 2.00000i 0.181818 + 0.104973i
$$364$$ 8.00000 13.8564i 0.419314 0.726273i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −3.46410 + 2.00000i −0.180825 + 0.104399i −0.587680 0.809093i $$-0.699959\pi$$
0.406855 + 0.913493i $$0.366625\pi$$
$$368$$ 0 0
$$369$$ 6.00000 0.312348
$$370$$ 0 0
$$371$$ −12.0000 20.7846i −0.623009 1.07908i
$$372$$ 28.0000i 1.45173i
$$373$$ 4.00000i 0.207112i 0.994624 + 0.103556i $$0.0330221\pi$$
−0.994624 + 0.103556i $$0.966978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 5.19615 + 3.00000i 0.267615 + 0.154508i
$$378$$ 0 0
$$379$$ 37.0000 1.90056 0.950281 0.311393i $$-0.100796\pi$$
0.950281 + 0.311393i $$0.100796\pi$$
$$380$$ 0 0
$$381$$ −4.00000 −0.204926
$$382$$ 0 0
$$383$$ 25.9808 + 15.0000i 1.32755 + 0.766464i 0.984921 0.173005i $$-0.0553476\pi$$
0.342634 + 0.939469i $$0.388681\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 4.00000i 0.203331i
$$388$$ 16.0000i 0.812277i
$$389$$ 7.50000 + 12.9904i 0.380265 + 0.658638i 0.991100 0.133120i $$-0.0424994\pi$$
−0.610835 + 0.791758i $$0.709166\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 20.7846 12.0000i 1.04844 0.605320i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 3.00000 5.19615i 0.150756 0.261116i
$$397$$ −6.92820 4.00000i −0.347717 0.200754i 0.315963 0.948772i $$-0.397673\pi$$
−0.663679 + 0.748017i $$0.731006\pi$$
$$398$$ 0 0
$$399$$ −32.0000 + 13.8564i −1.60200 + 0.693688i
$$400$$ 0 0
$$401$$ 16.5000 28.5788i 0.823971 1.42716i −0.0787327 0.996896i $$-0.525087\pi$$
0.902703 0.430263i $$-0.141579\pi$$
$$402$$ 0 0
$$403$$ 12.1244 7.00000i 0.603957 0.348695i
$$404$$ −15.0000 + 25.9808i −0.746278 + 1.29259i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 24.0000i 1.18964i
$$408$$ 0 0
$$409$$ 11.5000 + 19.9186i 0.568638 + 0.984911i 0.996701 + 0.0811615i $$0.0258630\pi$$
−0.428063 + 0.903749i $$0.640804\pi$$
$$410$$ 0 0
$$411$$ 24.0000 1.18383
$$412$$ 27.7128 16.0000i 1.36531 0.788263i
$$413$$ 51.9615 + 30.0000i 2.55686 + 1.47620i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 32.0000i 1.56705i
$$418$$ 0 0
$$419$$ 3.00000 0.146560 0.0732798 0.997311i $$-0.476653\pi$$
0.0732798 + 0.997311i $$0.476653\pi$$
$$420$$ 0 0
$$421$$ 9.50000 16.4545i 0.463002 0.801942i −0.536107 0.844150i $$-0.680106\pi$$
0.999109 + 0.0422075i $$0.0134391\pi$$
$$422$$ 0 0
$$423$$ 5.19615 + 3.00000i 0.252646 + 0.145865i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −17.3205 + 10.0000i −0.838198 + 0.483934i
$$428$$ 0 0
$$429$$ 12.0000 0.579365
$$430$$ 0 0
$$431$$ 7.50000 + 12.9904i 0.361262 + 0.625725i 0.988169 0.153370i $$-0.0490126\pi$$
−0.626907 + 0.779094i $$0.715679\pi$$
$$432$$ −13.8564 8.00000i −0.666667 0.384900i
$$433$$ −6.92820 + 4.00000i −0.332948 + 0.192228i −0.657149 0.753760i $$-0.728238\pi$$
0.324201 + 0.945988i $$0.394905\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −22.0000 −1.05361
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −6.50000 + 11.2583i −0.310228 + 0.537331i −0.978412 0.206666i $$-0.933739\pi$$
0.668184 + 0.743996i $$0.267072\pi$$
$$440$$ 0 0
$$441$$ −4.50000 7.79423i −0.214286 0.371154i
$$442$$ 0 0
$$443$$ 10.3923 6.00000i 0.493753 0.285069i −0.232377 0.972626i $$-0.574650\pi$$
0.726130 + 0.687557i $$0.241317\pi$$
$$444$$ −32.0000 −1.51865
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −5.19615 + 3.00000i −0.245770 + 0.141895i
$$448$$ 32.0000i 1.51186i
$$449$$ 9.00000 0.424736 0.212368 0.977190i $$-0.431882\pi$$
0.212368 + 0.977190i $$0.431882\pi$$
$$450$$ 0 0
$$451$$ 9.00000 15.5885i 0.423793 0.734032i
$$452$$ −10.3923 + 6.00000i −0.488813 + 0.282216i
$$453$$ −29.4449 17.0000i −1.38344 0.798730i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 22.0000i 1.02912i −0.857455 0.514558i $$-0.827956\pi$$
0.857455 0.514558i $$-0.172044\pi$$
$$458$$ 0 0
$$459$$ 12.0000 20.7846i 0.560112 0.970143i
$$460$$ 0 0
$$461$$ 4.50000 7.79423i 0.209586 0.363013i −0.741998 0.670402i $$-0.766122\pi$$
0.951584 + 0.307388i $$0.0994551\pi$$
$$462$$ 0 0
$$463$$ 16.0000i 0.743583i 0.928316 + 0.371792i $$0.121256\pi$$
−0.928316 + 0.371792i $$0.878744\pi$$
$$464$$ 12.0000 0.557086
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 4.00000i 0.184900i
$$469$$ −4.00000 6.92820i −0.184703 0.319915i
$$470$$ 0 0
$$471$$ 2.00000 + 3.46410i 0.0921551 + 0.159617i
$$472$$ 0 0
$$473$$ −10.3923 6.00000i −0.477839 0.275880i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 48.0000 2.20008
$$477$$ 5.19615 + 3.00000i 0.237915 + 0.137361i
$$478$$ 0 0
$$479$$ 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i $$-0.0553307\pi$$
−0.642246 + 0.766498i $$0.721997\pi$$
$$480$$ 0 0
$$481$$ −8.00000 13.8564i −0.364769 0.631798i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 2.00000 + 3.46410i 0.0909091 + 0.157459i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 2.00000i 0.0906287i 0.998973 + 0.0453143i $$0.0144289\pi$$
−0.998973 + 0.0453143i $$0.985571\pi$$
$$488$$ 0 0
$$489$$ 10.0000 17.3205i 0.452216 0.783260i
$$490$$ 0 0
$$491$$ 7.50000 12.9904i 0.338470 0.586248i −0.645675 0.763612i $$-0.723424\pi$$
0.984145 + 0.177365i $$0.0567572\pi$$
$$492$$ 20.7846 + 12.0000i 0.937043 + 0.541002i
$$493$$ 18.0000i 0.810679i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 14.0000 24.2487i 0.628619 1.08880i
$$497$$ −10.3923 6.00000i −0.466159 0.269137i
$$498$$ 0 0
$$499$$ 10.0000 17.3205i 0.447661 0.775372i −0.550572 0.834788i $$-0.685590\pi$$
0.998233 + 0.0594153i $$0.0189236\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 36.3731 21.0000i 1.62179 0.936344i 0.635355 0.772220i $$-0.280854\pi$$
0.986440 0.164124i $$-0.0524796\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 15.5885 9.00000i 0.692308 0.399704i
$$508$$ −3.46410 2.00000i −0.153695 0.0887357i
$$509$$ −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i $$-0.297281\pi$$
−0.993593 + 0.113020i $$0.963948\pi$$
$$510$$ 0 0
$$511$$ 16.0000 27.7128i 0.707798 1.22594i
$$512$$ 0 0
$$513$$ −10.3923 + 14.0000i −0.458831 + 0.618115i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 8.00000 13.8564i 0.352180 0.609994i
$$517$$ 15.5885 9.00000i 0.685580 0.395820i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −45.0000 −1.97149 −0.985743 0.168259i $$-0.946186\pi$$
−0.985743 + 0.168259i $$0.946186\pi$$
$$522$$ 0 0
$$523$$ −22.5167 + 13.0000i −0.984585 + 0.568450i −0.903651 0.428269i $$-0.859124\pi$$
−0.0809336 + 0.996719i $$0.525790\pi$$
$$524$$ 24.0000 1.04844
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 36.3731 + 21.0000i 1.58444 + 0.914774i
$$528$$ 20.7846 12.0000i 0.904534 0.522233i
$$529$$ −11.5000 + 19.9186i −0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ −15.0000 −0.650945
$$532$$ −34.6410 4.00000i −1.50188 0.173422i
$$533$$ 12.0000i 0.519778i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −15.5885 9.00000i −0.672692 0.388379i
$$538$$ 0 0
$$539$$ −27.0000 −1.16297
$$540$$ 0 0
$$541$$ 18.5000 + 32.0429i 0.795377 + 1.37763i 0.922599 + 0.385759i $$0.126061\pi$$
−0.127222 + 0.991874i $$0.540606\pi$$
$$542$$ 0 0
$$543$$ 4.00000i 0.171656i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −3.46410 + 2.00000i −0.148114 + 0.0855138i −0.572226 0.820096i $$-0.693920\pi$$
0.424111 + 0.905610i $$0.360587\pi$$
$$548$$ 20.7846 + 12.0000i 0.887875 + 0.512615i
$$549$$ 2.50000 4.33013i 0.106697 0.184805i
$$550$$ 0 0
$$551$$ 1.50000 12.9904i 0.0639021 0.553409i
$$552$$ 0 0
$$553$$ −17.3205 10.0000i −0.736543 0.425243i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −16.0000 + 27.7128i −0.678551 + 1.17529i
$$557$$ 10.3923 6.00000i 0.440336 0.254228i −0.263404 0.964686i $$-0.584845\pi$$
0.703740 + 0.710457i $$0.251512\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ 18.0000 + 31.1769i 0.759961 + 1.31629i
$$562$$ 0 0
$$563$$ 6.00000i 0.252870i −0.991975 0.126435i $$-0.959647\pi$$
0.991975 0.126435i $$-0.0403535\pi$$
$$564$$ 12.0000 + 20.7846i 0.505291 + 0.875190i
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −38.1051 22.0000i −1.60026 0.923913i
$$568$$ 0 0
$$569$$ −39.0000 −1.63497 −0.817483 0.575953i $$-0.804631\pi$$
−0.817483 + 0.575953i $$0.804631\pi$$
$$570$$ 0 0
$$571$$ −7.00000 −0.292941 −0.146470 0.989215i $$-0.546791\pi$$
−0.146470 + 0.989215i $$0.546791\pi$$
$$572$$ 10.3923 + 6.00000i 0.434524 + 0.250873i
$$573$$ 25.9808 + 15.0000i 1.08536 + 0.626634i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 4.00000 + 6.92820i 0.166667 + 0.288675i
$$577$$ 16.0000i 0.666089i −0.942911 0.333044i $$-0.891924\pi$$
0.942911 0.333044i $$-0.108076\pi$$
$$578$$ 0 0
$$579$$ 16.0000 + 27.7128i 0.664937 + 1.15171i
$$580$$ 0 0
$$581$$ −48.0000 −1.99138
$$582$$ 0 0
$$583$$ 15.5885 9.00000i 0.645608 0.372742i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 31.1769 + 18.0000i 1.28681 + 0.742940i 0.978084 0.208212i $$-0.0667643\pi$$
0.308725 + 0.951151i $$0.400098\pi$$
$$588$$ 36.0000i 1.48461i
$$589$$ −24.5000 18.1865i −1.00950 0.749363i
$$590$$ 0 0
$$591$$ −18.0000 + 31.1769i −0.740421 + 1.28245i
$$592$$ −27.7128 16.0000i −1.13899 0.657596i
$$593$$ −10.3923 + 6.00000i −0.426761 + 0.246390i −0.697966 0.716131i $$-0.745911\pi$$
0.271205 + 0.962522i $$0.412578\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ 38.0000i 1.55524i
$$598$$ 0 0
$$599$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$600$$ 0 0
$$601$$ −31.0000 −1.26452 −0.632258 0.774758i $$-0.717872\pi$$
−0.632258 + 0.774758i $$0.717872\pi$$
$$602$$ 0 0
$$603$$ 1.73205 + 1.00000i 0.0705346 + 0.0407231i
$$604$$ −17.0000 29.4449i −0.691720 1.19809i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 2.00000i 0.0811775i 0.999176 + 0.0405887i $$0.0129233\pi$$
−0.999176 + 0.0405887i $$0.987077\pi$$
$$608$$ 0 0
$$609$$ 24.0000 0.972529
$$610$$ 0 0
$$611$$ −6.00000 + 10.3923i −0.242734 + 0.420428i
$$612$$ −10.3923 + 6.00000i −0.420084 + 0.242536i
$$613$$ 1.73205 + 1.00000i 0.0699569 + 0.0403896i 0.534570 0.845124i $$-0.320473\pi$$
−0.464614 + 0.885514i $$0.653807\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 31.1769 18.0000i 1.25514 0.724653i 0.283011 0.959117i $$-0.408667\pi$$
0.972125 + 0.234464i $$0.0753335\pi$$
$$618$$ 0 0
$$619$$ 4.00000 0.160774 0.0803868 0.996764i $$-0.474384\pi$$
0.0803868 + 0.996764i $$0.474384\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −51.9615 + 30.0000i −2.08179 + 1.20192i
$$624$$ −8.00000 + 13.8564i −0.320256 + 0.554700i
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −10.3923 24.0000i −0.415029 0.958468i
$$628$$ 4.00000i 0.159617i
$$629$$ 24.0000 41.5692i 0.956943 1.65747i
$$630$$ 0 0
$$631$$ 9.50000 + 16.4545i 0.378189 + 0.655043i 0.990799 0.135343i $$-0.0432136\pi$$
−0.612610 + 0.790386i $$0.709880\pi$$
$$632$$ 0 0
$$633$$ −12.1244 + 7.00000i −0.481900 + 0.278225i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 12.0000 + 20.7846i 0.475831 + 0.824163i
$$637$$ 15.5885 9.00000i 0.617637 0.356593i
$$638$$ 0 0
$$639$$ 3.00000 0.118678
$$640$$ 0 0
$$641$$ −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i $$-0.890212\pi$$
0.763367 + 0.645966i $$0.223545\pi$$
$$642$$ 0 0
$$643$$ −29.4449 17.0000i −1.16119 0.670415i −0.209603 0.977787i $$-0.567217\pi$$
−0.951589 + 0.307372i $$0.900550\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 18.0000i 0.707653i 0.935311 + 0.353827i $$0.115120\pi$$
−0.935311 + 0.353827i $$0.884880\pi$$
$$648$$ 0 0
$$649$$ −22.5000 + 38.9711i −0.883202 + 1.52975i
$$650$$ 0 0
$$651$$ 28.0000 48.4974i 1.09741 1.90076i
$$652$$ 17.3205 10.0000i 0.678323 0.391630i
$$653$$ 24.0000i 0.939193i −0.882881 0.469596i $$-0.844399\pi$$
0.882881 0.469596i $$-0.155601\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 12.0000 + 20.7846i 0.468521 + 0.811503i
$$657$$ 8.00000i 0.312110i
$$658$$ 0 0
$$659$$ −6.00000 10.3923i −0.233727 0.404827i 0.725175 0.688565i $$-0.241759\pi$$
−0.958902 + 0.283738i $$0.908425\pi$$
$$660$$ 0 0
$$661$$ −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i $$-0.197668\pi$$
−0.910541 + 0.413419i $$0.864334\pi$$
$$662$$ 0 0
$$663$$ −20.7846 12.0000i −0.807207 0.466041i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 4.00000 + 6.92820i 0.154649 + 0.267860i
$$670$$ 0 0
$$671$$ −7.50000 12.9904i −0.289534 0.501488i
$$672$$ 0 0
$$673$$ 4.00000i 0.154189i 0.997024 + 0.0770943i $$0.0245643\pi$$
−0.997024 + 0.0770943i $$0.975436\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 18.0000 0.692308
$$677$$ 48.0000i 1.84479i 0.386248 + 0.922395i $$0.373771\pi$$
−0.386248 + 0.922395i $$0.626229\pi$$
$$678$$ 0 0
$$679$$ −16.0000 + 27.7128i −0.614024 + 1.06352i
$$680$$ 0 0
$$681$$ −24.0000 + 41.5692i −0.919682 + 1.59294i
$$682$$ 0 0
$$683$$ 18.0000i 0.688751i 0.938832 + 0.344375i $$0.111909\pi$$
−0.938832 + 0.344375i $$0.888091\pi$$
$$684$$ 8.00000 3.46410i 0.305888 0.132453i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −12.1244 7.00000i −0.462573 0.267067i
$$688$$ 13.8564 8.00000i 0.528271 0.304997i
$$689$$ −6.00000 + 10.3923i −0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −37.0000 −1.40755 −0.703773 0.710425i $$-0.748503\pi$$
−0.703773 + 0.710425i $$0.748503\pi$$
$$692$$ 0 0
$$693$$ 10.3923 6.00000i 0.394771 0.227921i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −31.1769 + 18.0000i −1.18091 + 0.681799i
$$698$$ 0 0
$$699$$ −6.00000 10.3923i −0.226941 0.393073i
$$700$$ 0 0
$$701$$ −3.00000 + 5.19615i −0.113308 + 0.196256i −0.917102 0.398652i $$-0.869478\pi$$
0.803794 + 0.594908i $$0.202811\pi$$
$$702$$ 0 0
$$703$$ −20.7846 + 28.0000i −0.783906 + 1.05604i
$$704$$ 24.0000 0.904534
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −51.9615 + 30.0000i −1.95421 + 1.12827i
$$708$$ −51.9615 30.0000i −1.95283 1.12747i
$$709$$ −15.5000 26.8468i −0.582115 1.00825i −0.995228 0.0975728i $$-0.968892\pi$$
0.413114 0.910679i $$-0.364441\pi$$
$$710$$ 0 0
$$711$$ 5.00000 0.187515
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −9.00000 15.5885i −0.336346 0.582568i
$$717$$ −5.19615 3.00000i −0.194054 0.112037i
$$718$$ 0 0
$$719$$ 7.50000 12.9904i 0.279703 0.484459i −0.691608 0.722273i $$-0.743097\pi$$
0.971311 + 0.237814i $$0.0764307\pi$$
$$720$$ 0 0
$$721$$ 64.0000 2.38348
$$722$$ 0 0
$$723$$ 10.0000i 0.371904i
$$724$$ −2.00000 + 3.46410i −0.0743294 + 0.128742i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −12.1244 7.00000i −0.449667 0.259616i 0.258022 0.966139i $$-0.416929\pi$$
−0.707690 + 0.706523i $$0.750263\pi$$
$$728$$ 0 0
$$729$$ −13.0000 −0.481481
$$730$$ 0 0
$$731$$ 12.0000 + 20.7846i 0.443836 + 0.768747i
$$732$$ 17.3205 10.0000i 0.640184 0.369611i
$$733$$ 32.0000i 1.18195i −0.806691 0.590973i $$-0.798744\pi$$
0.806691 0.590973i $$-0.201256\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 5.19615 3.00000i 0.191403 0.110506i
$$738$$ 0 0
$$739$$ 17.5000 30.3109i 0.643748 1.11500i −0.340841 0.940121i $$-0.610712\pi$$
0.984589 0.174883i $$-0.0559548\pi$$
$$740$$ 0 0
$$741$$ 14.0000 + 10.3923i 0.514303 + 0.381771i
$$742$$ 0 0
$$743$$ −20.7846 12.0000i −0.762513 0.440237i 0.0676840 0.997707i $$-0.478439\pi$$
−0.830197 + 0.557470i $$0.811772\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 10.3923 6.00000i 0.380235 0.219529i
$$748$$ 36.0000i 1.31629i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 3.50000 + 6.06218i 0.127717 + 0.221212i 0.922792 0.385299i $$-0.125902\pi$$
−0.795075 + 0.606511i $$0.792568\pi$$
$$752$$ 24.0000i 0.875190i
$$753$$ 30.0000i 1.09326i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −16.0000 27.7128i −0.581914 1.00791i
$$757$$ 8.66025 + 5.00000i 0.314762 + 0.181728i 0.649056 0.760741i $$-0.275164\pi$$
−0.334293 + 0.942469i $$0.608498\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 6.00000 0.217500 0.108750 0.994069i $$-0.465315\pi$$
0.108750 + 0.994069i $$0.465315\pi$$
$$762$$ 0 0
$$763$$ −38.1051 22.0000i −1.37950 0.796453i
$$764$$ 15.0000 + 25.9808i 0.542681 + 0.939951i
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 30.0000i 1.08324i
$$768$$ 32.0000i 1.15470i
$$769$$ 14.5000 + 25.1147i 0.522883 + 0.905661i 0.999645 + 0.0266282i $$0.00847701\pi$$
−0.476762 + 0.879032i $$0.658190\pi$$
$$770$$ 0 0
$$771$$ 36.0000 1.29651
$$772$$ 32.0000i 1.15171i
$$773$$ −25.9808 + 15.0000i −0.934463 + 0.539513i −0.888220 0.459418i $$-0.848058\pi$$
−0.0462427 + 0.998930i $$0.514725\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −55.4256 32.0000i −1.98838 1.14799i
$$778$$ 0 0
$$779$$ 24.0000 10.3923i 0.859889 0.372343i
$$780$$ 0 0
$$781$$ 4.50000 7.79423i 0.161023 0.278899i
$$782$$ 0 0
$$783$$ 10.3923 6.00000i 0.371391 0.214423i
$$784$$ 18.0000 31.1769i 0.642857 1.11346i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 34.0000i 1.21197i −0.795476 0.605985i $$-0.792779\pi$$
0.795476 0.605985i $$-0.207221\pi$$
$$788$$ −31.1769 + 18.0000i −1.11063 + 0.641223i
$$789$$ 18.0000 + 31.1769