# Properties

 Label 378.2.k.c.215.2 Level $378$ Weight $2$ Character 378.215 Analytic conductor $3.018$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(215,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("378.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$378 = 2 \cdot 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 378.k (of order $$6$$, 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: $$3.01834519640$$ 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: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 215.2 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 378.215 Dual form 378.2.k.c.269.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000i q^{8} +(1.50000 - 0.866025i) q^{10} +(2.59808 - 0.500000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 - 3.00000i) q^{17} +(6.00000 + 3.46410i) q^{19} +1.73205 q^{20} +(-5.19615 - 3.00000i) q^{23} +(1.00000 + 1.73205i) q^{25} +(2.50000 + 0.866025i) q^{28} +9.00000i q^{29} +(3.00000 - 1.73205i) q^{31} +(-0.866025 + 0.500000i) q^{32} -3.46410i q^{34} +(-0.866025 - 4.50000i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(3.46410 + 6.00000i) q^{38} +(1.50000 + 0.866025i) q^{40} -3.46410 q^{41} -8.00000 q^{43} +(-3.00000 - 5.19615i) q^{46} +(-1.73205 + 3.00000i) q^{47} +(1.00000 - 6.92820i) q^{49} +2.00000i q^{50} +(-2.59808 + 1.50000i) q^{53} +(1.73205 + 2.00000i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(-6.06218 - 10.5000i) q^{59} +(3.00000 + 1.73205i) q^{61} +3.46410 q^{62} -1.00000 q^{64} +(-7.00000 - 12.1244i) q^{67} +(1.73205 - 3.00000i) q^{68} +(1.50000 - 4.33013i) q^{70} -6.00000i q^{71} +(-10.5000 + 6.06218i) q^{73} +(-3.46410 + 2.00000i) q^{74} +6.92820i q^{76} +(-5.50000 + 9.52628i) q^{79} +(0.866025 + 1.50000i) q^{80} +(-3.00000 - 1.73205i) q^{82} +17.3205 q^{83} -6.00000 q^{85} +(-6.92820 - 4.00000i) q^{86} +(-5.19615 + 9.00000i) q^{89} -6.00000i q^{92} +(-3.00000 + 1.73205i) q^{94} +(10.3923 - 6.00000i) q^{95} -6.92820i q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{4} + 8 q^{7}+O(q^{10})$$ 4 * q + 2 * q^4 + 8 * q^7 $$4 q + 2 q^{4} + 8 q^{7} + 6 q^{10} - 2 q^{16} + 24 q^{19} + 4 q^{25} + 10 q^{28} + 12 q^{31} - 8 q^{37} + 6 q^{40} - 32 q^{43} - 12 q^{46} + 4 q^{49} - 18 q^{58} + 12 q^{61} - 4 q^{64} - 28 q^{67} + 6 q^{70} - 42 q^{73} - 22 q^{79} - 12 q^{82} - 24 q^{85} - 12 q^{94}+O(q^{100})$$ 4 * q + 2 * q^4 + 8 * q^7 + 6 * q^10 - 2 * q^16 + 24 * q^19 + 4 * q^25 + 10 * q^28 + 12 * q^31 - 8 * q^37 + 6 * q^40 - 32 * q^43 - 12 * q^46 + 4 * q^49 - 18 * q^58 + 12 * q^61 - 4 * q^64 - 28 * q^67 + 6 * q^70 - 42 * q^73 - 22 * q^79 - 12 * q^82 - 24 * q^85 - 12 * q^94

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$325$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 + 0.500000i 0.612372 + 0.353553i
$$3$$ 0 0
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ 0.866025 1.50000i 0.387298 0.670820i −0.604787 0.796387i $$-0.706742\pi$$
0.992085 + 0.125567i $$0.0400750\pi$$
$$6$$ 0 0
$$7$$ 2.00000 1.73205i 0.755929 0.654654i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 1.50000 0.866025i 0.474342 0.273861i
$$11$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 2.59808 0.500000i 0.694365 0.133631i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −1.73205 3.00000i −0.420084 0.727607i 0.575863 0.817546i $$-0.304666\pi$$
−0.995947 + 0.0899392i $$0.971333\pi$$
$$18$$ 0 0
$$19$$ 6.00000 + 3.46410i 1.37649 + 0.794719i 0.991736 0.128298i $$-0.0409513\pi$$
0.384759 + 0.923017i $$0.374285\pi$$
$$20$$ 1.73205 0.387298
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −5.19615 3.00000i −1.08347 0.625543i −0.151642 0.988436i $$-0.548456\pi$$
−0.931831 + 0.362892i $$0.881789\pi$$
$$24$$ 0 0
$$25$$ 1.00000 + 1.73205i 0.200000 + 0.346410i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 2.50000 + 0.866025i 0.472456 + 0.163663i
$$29$$ 9.00000i 1.67126i 0.549294 + 0.835629i $$0.314897\pi$$
−0.549294 + 0.835629i $$0.685103\pi$$
$$30$$ 0 0
$$31$$ 3.00000 1.73205i 0.538816 0.311086i −0.205783 0.978598i $$-0.565974\pi$$
0.744599 + 0.667512i $$0.232641\pi$$
$$32$$ −0.866025 + 0.500000i −0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ 3.46410i 0.594089i
$$35$$ −0.866025 4.50000i −0.146385 0.760639i
$$36$$ 0 0
$$37$$ −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i $$-0.939977\pi$$
0.653476 + 0.756948i $$0.273310\pi$$
$$38$$ 3.46410 + 6.00000i 0.561951 + 0.973329i
$$39$$ 0 0
$$40$$ 1.50000 + 0.866025i 0.237171 + 0.136931i
$$41$$ −3.46410 −0.541002 −0.270501 0.962720i $$-0.587189\pi$$
−0.270501 + 0.962720i $$0.587189\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ −3.00000 5.19615i −0.442326 0.766131i
$$47$$ −1.73205 + 3.00000i −0.252646 + 0.437595i −0.964253 0.264982i $$-0.914634\pi$$
0.711608 + 0.702577i $$0.247967\pi$$
$$48$$ 0 0
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ 2.00000i 0.282843i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −2.59808 + 1.50000i −0.356873 + 0.206041i −0.667708 0.744423i $$-0.732725\pi$$
0.310835 + 0.950464i $$0.399391\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.73205 + 2.00000i 0.231455 + 0.267261i
$$57$$ 0 0
$$58$$ −4.50000 + 7.79423i −0.590879 + 1.02343i
$$59$$ −6.06218 10.5000i −0.789228 1.36698i −0.926440 0.376442i $$-0.877147\pi$$
0.137212 0.990542i $$-0.456186\pi$$
$$60$$ 0 0
$$61$$ 3.00000 + 1.73205i 0.384111 + 0.221766i 0.679605 0.733578i $$-0.262151\pi$$
−0.295495 + 0.955344i $$0.595484\pi$$
$$62$$ 3.46410 0.439941
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i $$-0.840109\pi$$
0.0212861 0.999773i $$-0.493224\pi$$
$$68$$ 1.73205 3.00000i 0.210042 0.363803i
$$69$$ 0 0
$$70$$ 1.50000 4.33013i 0.179284 0.517549i
$$71$$ 6.00000i 0.712069i −0.934473 0.356034i $$-0.884129\pi$$
0.934473 0.356034i $$-0.115871\pi$$
$$72$$ 0 0
$$73$$ −10.5000 + 6.06218i −1.22893 + 0.709524i −0.966807 0.255510i $$-0.917757\pi$$
−0.262126 + 0.965034i $$0.584423\pi$$
$$74$$ −3.46410 + 2.00000i −0.402694 + 0.232495i
$$75$$ 0 0
$$76$$ 6.92820i 0.794719i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i $$0.379047\pi$$
−0.989705 + 0.143120i $$0.954286\pi$$
$$80$$ 0.866025 + 1.50000i 0.0968246 + 0.167705i
$$81$$ 0 0
$$82$$ −3.00000 1.73205i −0.331295 0.191273i
$$83$$ 17.3205 1.90117 0.950586 0.310460i $$-0.100483\pi$$
0.950586 + 0.310460i $$0.100483\pi$$
$$84$$ 0 0
$$85$$ −6.00000 −0.650791
$$86$$ −6.92820 4.00000i −0.747087 0.431331i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −5.19615 + 9.00000i −0.550791 + 0.953998i 0.447427 + 0.894321i $$0.352341\pi$$
−0.998218 + 0.0596775i $$0.980993\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 6.00000i 0.625543i
$$93$$ 0 0
$$94$$ −3.00000 + 1.73205i −0.309426 + 0.178647i
$$95$$ 10.3923 6.00000i 1.06623 0.615587i
$$96$$ 0 0
$$97$$ 6.92820i 0.703452i −0.936103 0.351726i $$-0.885595\pi$$
0.936103 0.351726i $$-0.114405\pi$$
$$98$$ 4.33013 5.50000i 0.437409 0.555584i
$$99$$ 0 0
$$100$$ −1.00000 + 1.73205i −0.100000 + 0.173205i
$$101$$ 2.59808 + 4.50000i 0.258518 + 0.447767i 0.965845 0.259120i $$-0.0834325\pi$$
−0.707327 + 0.706887i $$0.750099\pi$$
$$102$$ 0 0
$$103$$ 9.00000 + 5.19615i 0.886796 + 0.511992i 0.872893 0.487911i $$-0.162241\pi$$
0.0139031 + 0.999903i $$0.495574\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −3.00000 −0.291386
$$107$$ 2.59808 + 1.50000i 0.251166 + 0.145010i 0.620298 0.784366i $$-0.287012\pi$$
−0.369132 + 0.929377i $$0.620345\pi$$
$$108$$ 0 0
$$109$$ −8.00000 13.8564i −0.766261 1.32720i −0.939577 0.342337i $$-0.888782\pi$$
0.173316 0.984866i $$-0.444552\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0.500000 + 2.59808i 0.0472456 + 0.245495i
$$113$$ 18.0000i 1.69330i 0.532152 + 0.846649i $$0.321383\pi$$
−0.532152 + 0.846649i $$0.678617\pi$$
$$114$$ 0 0
$$115$$ −9.00000 + 5.19615i −0.839254 + 0.484544i
$$116$$ −7.79423 + 4.50000i −0.723676 + 0.417815i
$$117$$ 0 0
$$118$$ 12.1244i 1.11614i
$$119$$ −8.66025 3.00000i −0.793884 0.275010i
$$120$$ 0 0
$$121$$ −5.50000 + 9.52628i −0.500000 + 0.866025i
$$122$$ 1.73205 + 3.00000i 0.156813 + 0.271607i
$$123$$ 0 0
$$124$$ 3.00000 + 1.73205i 0.269408 + 0.155543i
$$125$$ 12.1244 1.08444
$$126$$ 0 0
$$127$$ −7.00000 −0.621150 −0.310575 0.950549i $$-0.600522\pi$$
−0.310575 + 0.950549i $$0.600522\pi$$
$$128$$ −0.866025 0.500000i −0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 5.19615 9.00000i 0.453990 0.786334i −0.544640 0.838670i $$-0.683334\pi$$
0.998630 + 0.0523366i $$0.0166669\pi$$
$$132$$ 0 0
$$133$$ 18.0000 3.46410i 1.56080 0.300376i
$$134$$ 14.0000i 1.20942i
$$135$$ 0 0
$$136$$ 3.00000 1.73205i 0.257248 0.148522i
$$137$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$138$$ 0 0
$$139$$ 10.3923i 0.881464i −0.897639 0.440732i $$-0.854719\pi$$
0.897639 0.440732i $$-0.145281\pi$$
$$140$$ 3.46410 3.00000i 0.292770 0.253546i
$$141$$ 0 0
$$142$$ 3.00000 5.19615i 0.251754 0.436051i
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 13.5000 + 7.79423i 1.12111 + 0.647275i
$$146$$ −12.1244 −1.00342
$$147$$ 0 0
$$148$$ −4.00000 −0.328798
$$149$$ 12.9904 + 7.50000i 1.06421 + 0.614424i 0.926595 0.376061i $$-0.122722\pi$$
0.137619 + 0.990485i $$0.456055\pi$$
$$150$$ 0 0
$$151$$ 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i $$-0.0611289\pi$$
−0.656101 + 0.754673i $$0.727796\pi$$
$$152$$ −3.46410 + 6.00000i −0.280976 + 0.486664i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 6.00000i 0.481932i
$$156$$ 0 0
$$157$$ 9.00000 5.19615i 0.718278 0.414698i −0.0958404 0.995397i $$-0.530554\pi$$
0.814119 + 0.580699i $$0.197221\pi$$
$$158$$ −9.52628 + 5.50000i −0.757870 + 0.437557i
$$159$$ 0 0
$$160$$ 1.73205i 0.136931i
$$161$$ −15.5885 + 3.00000i −1.22854 + 0.236433i
$$162$$ 0 0
$$163$$ −1.00000 + 1.73205i −0.0783260 + 0.135665i −0.902528 0.430632i $$-0.858291\pi$$
0.824202 + 0.566296i $$0.191624\pi$$
$$164$$ −1.73205 3.00000i −0.135250 0.234261i
$$165$$ 0 0
$$166$$ 15.0000 + 8.66025i 1.16423 + 0.672166i
$$167$$ −17.3205 −1.34030 −0.670151 0.742225i $$-0.733770\pi$$
−0.670151 + 0.742225i $$0.733770\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ −5.19615 3.00000i −0.398527 0.230089i
$$171$$ 0 0
$$172$$ −4.00000 6.92820i −0.304997 0.528271i
$$173$$ −2.59808 + 4.50000i −0.197528 + 0.342129i −0.947726 0.319084i $$-0.896625\pi$$
0.750198 + 0.661213i $$0.229958\pi$$
$$174$$ 0 0
$$175$$ 5.00000 + 1.73205i 0.377964 + 0.130931i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −9.00000 + 5.19615i −0.674579 + 0.389468i
$$179$$ 12.9904 7.50000i 0.970947 0.560576i 0.0714220 0.997446i $$-0.477246\pi$$
0.899525 + 0.436870i $$0.143913\pi$$
$$180$$ 0 0
$$181$$ 17.3205i 1.28742i 0.765268 + 0.643712i $$0.222606\pi$$
−0.765268 + 0.643712i $$0.777394\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 3.00000 5.19615i 0.221163 0.383065i
$$185$$ 3.46410 + 6.00000i 0.254686 + 0.441129i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −3.46410 −0.252646
$$189$$ 0 0
$$190$$ 12.0000 0.870572
$$191$$ −5.19615 3.00000i −0.375980 0.217072i 0.300088 0.953912i $$-0.402984\pi$$
−0.676068 + 0.736839i $$0.736317\pi$$
$$192$$ 0 0
$$193$$ −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i $$-0.283859\pi$$
−0.987945 + 0.154805i $$0.950525\pi$$
$$194$$ 3.46410 6.00000i 0.248708 0.430775i
$$195$$ 0 0
$$196$$ 6.50000 2.59808i 0.464286 0.185577i
$$197$$ 3.00000i 0.213741i 0.994273 + 0.106871i $$0.0340831\pi$$
−0.994273 + 0.106871i $$0.965917\pi$$
$$198$$ 0 0
$$199$$ 7.50000 4.33013i 0.531661 0.306955i −0.210032 0.977695i $$-0.567357\pi$$
0.741693 + 0.670740i $$0.234023\pi$$
$$200$$ −1.73205 + 1.00000i −0.122474 + 0.0707107i
$$201$$ 0 0
$$202$$ 5.19615i 0.365600i
$$203$$ 15.5885 + 18.0000i 1.09410 + 1.26335i
$$204$$ 0 0
$$205$$ −3.00000 + 5.19615i −0.209529 + 0.362915i
$$206$$ 5.19615 + 9.00000i 0.362033 + 0.627060i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 16.0000 1.10149 0.550743 0.834675i $$-0.314345\pi$$
0.550743 + 0.834675i $$0.314345\pi$$
$$212$$ −2.59808 1.50000i −0.178437 0.103020i
$$213$$ 0 0
$$214$$ 1.50000 + 2.59808i 0.102538 + 0.177601i
$$215$$ −6.92820 + 12.0000i −0.472500 + 0.818393i
$$216$$ 0 0
$$217$$ 3.00000 8.66025i 0.203653 0.587896i
$$218$$ 16.0000i 1.08366i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 15.5885i 1.04388i −0.852982 0.521940i $$-0.825208\pi$$
0.852982 0.521940i $$-0.174792\pi$$
$$224$$ −0.866025 + 2.50000i −0.0578638 + 0.167038i
$$225$$ 0 0
$$226$$ −9.00000 + 15.5885i −0.598671 + 1.03693i
$$227$$ −12.9904 22.5000i −0.862202 1.49338i −0.869799 0.493406i $$-0.835752\pi$$
0.00759708 0.999971i $$-0.497582\pi$$
$$228$$ 0 0
$$229$$ −3.00000 1.73205i −0.198246 0.114457i 0.397591 0.917563i $$-0.369846\pi$$
−0.595837 + 0.803105i $$0.703180\pi$$
$$230$$ −10.3923 −0.685248
$$231$$ 0 0
$$232$$ −9.00000 −0.590879
$$233$$ 25.9808 + 15.0000i 1.70206 + 0.982683i 0.943676 + 0.330870i $$0.107342\pi$$
0.758380 + 0.651813i $$0.225991\pi$$
$$234$$ 0 0
$$235$$ 3.00000 + 5.19615i 0.195698 + 0.338960i
$$236$$ 6.06218 10.5000i 0.394614 0.683492i
$$237$$ 0 0
$$238$$ −6.00000 6.92820i −0.388922 0.449089i
$$239$$ 24.0000i 1.55243i 0.630468 + 0.776215i $$0.282863\pi$$
−0.630468 + 0.776215i $$0.717137\pi$$
$$240$$ 0 0
$$241$$ 1.50000 0.866025i 0.0966235 0.0557856i −0.450910 0.892570i $$-0.648900\pi$$
0.547533 + 0.836784i $$0.315567\pi$$
$$242$$ −9.52628 + 5.50000i −0.612372 + 0.353553i
$$243$$ 0 0
$$244$$ 3.46410i 0.221766i
$$245$$ −9.52628 7.50000i −0.608612 0.479157i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 1.73205 + 3.00000i 0.109985 + 0.190500i
$$249$$ 0 0
$$250$$ 10.5000 + 6.06218i 0.664078 + 0.383406i
$$251$$ 8.66025 0.546630 0.273315 0.961925i $$-0.411880\pi$$
0.273315 + 0.961925i $$0.411880\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −6.06218 3.50000i −0.380375 0.219610i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 10.3923 18.0000i 0.648254 1.12281i −0.335285 0.942117i $$-0.608833\pi$$
0.983540 0.180693i $$-0.0578339\pi$$
$$258$$ 0 0
$$259$$ 2.00000 + 10.3923i 0.124274 + 0.645746i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 9.00000 5.19615i 0.556022 0.321019i
$$263$$ 15.5885 9.00000i 0.961225 0.554964i 0.0646755 0.997906i $$-0.479399\pi$$
0.896550 + 0.442943i $$0.146065\pi$$
$$264$$ 0 0
$$265$$ 5.19615i 0.319197i
$$266$$ 17.3205 + 6.00000i 1.06199 + 0.367884i
$$267$$ 0 0
$$268$$ 7.00000 12.1244i 0.427593 0.740613i
$$269$$ −0.866025 1.50000i −0.0528025 0.0914566i 0.838416 0.545031i $$-0.183482\pi$$
−0.891219 + 0.453574i $$0.850149\pi$$
$$270$$ 0 0
$$271$$ 10.5000 + 6.06218i 0.637830 + 0.368251i 0.783778 0.621041i $$-0.213290\pi$$
−0.145948 + 0.989292i $$0.546623\pi$$
$$272$$ 3.46410 0.210042
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i $$-0.243925\pi$$
−0.960810 + 0.277207i $$0.910591\pi$$
$$278$$ 5.19615 9.00000i 0.311645 0.539784i
$$279$$ 0 0
$$280$$ 4.50000 0.866025i 0.268926 0.0517549i
$$281$$ 18.0000i 1.07379i −0.843649 0.536895i $$-0.819597\pi$$
0.843649 0.536895i $$-0.180403\pi$$
$$282$$ 0 0
$$283$$ 6.00000 3.46410i 0.356663 0.205919i −0.310953 0.950425i $$-0.600648\pi$$
0.667616 + 0.744506i $$0.267315\pi$$
$$284$$ 5.19615 3.00000i 0.308335 0.178017i
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −6.92820 + 6.00000i −0.408959 + 0.354169i
$$288$$ 0 0
$$289$$ 2.50000 4.33013i 0.147059 0.254713i
$$290$$ 7.79423 + 13.5000i 0.457693 + 0.792747i
$$291$$ 0 0
$$292$$ −10.5000 6.06218i −0.614466 0.354762i
$$293$$ −29.4449 −1.72019 −0.860094 0.510136i $$-0.829595\pi$$
−0.860094 + 0.510136i $$0.829595\pi$$
$$294$$ 0 0
$$295$$ −21.0000 −1.22267
$$296$$ −3.46410 2.00000i −0.201347 0.116248i
$$297$$ 0 0
$$298$$ 7.50000 + 12.9904i 0.434463 + 0.752513i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −16.0000 + 13.8564i −0.922225 + 0.798670i
$$302$$ 8.00000i 0.460348i
$$303$$ 0 0
$$304$$ −6.00000 + 3.46410i −0.344124 + 0.198680i
$$305$$ 5.19615 3.00000i 0.297531 0.171780i
$$306$$ 0 0
$$307$$ 6.92820i 0.395413i −0.980261 0.197707i $$-0.936651\pi$$
0.980261 0.197707i $$-0.0633494\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 3.00000 5.19615i 0.170389 0.295122i
$$311$$ −6.92820 12.0000i −0.392862 0.680458i 0.599963 0.800027i $$-0.295182\pi$$
−0.992826 + 0.119570i $$0.961848\pi$$
$$312$$ 0 0
$$313$$ −19.5000 11.2583i −1.10221 0.636358i −0.165406 0.986226i $$-0.552893\pi$$
−0.936799 + 0.349867i $$0.886227\pi$$
$$314$$ 10.3923 0.586472
$$315$$ 0 0
$$316$$ −11.0000 −0.618798
$$317$$ 5.19615 + 3.00000i 0.291845 + 0.168497i 0.638774 0.769395i $$-0.279442\pi$$
−0.346929 + 0.937892i $$0.612775\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −0.866025 + 1.50000i −0.0484123 + 0.0838525i
$$321$$ 0 0
$$322$$ −15.0000 5.19615i −0.835917 0.289570i
$$323$$ 24.0000i 1.33540i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −1.73205 + 1.00000i −0.0959294 + 0.0553849i
$$327$$ 0 0
$$328$$ 3.46410i 0.191273i
$$329$$ 1.73205 + 9.00000i 0.0954911 + 0.496186i
$$330$$ 0 0
$$331$$ −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i $$-0.921953\pi$$
0.695266 + 0.718752i $$0.255287\pi$$
$$332$$ 8.66025 + 15.0000i 0.475293 + 0.823232i
$$333$$ 0 0
$$334$$ −15.0000 8.66025i −0.820763 0.473868i
$$335$$ −24.2487 −1.32485
$$336$$ 0 0
$$337$$ −23.0000 −1.25289 −0.626445 0.779466i $$-0.715491\pi$$
−0.626445 + 0.779466i $$0.715491\pi$$
$$338$$ 11.2583 + 6.50000i 0.612372 + 0.353553i
$$339$$ 0 0
$$340$$ −3.00000 5.19615i −0.162698 0.281801i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 8.00000i 0.431331i
$$345$$ 0 0
$$346$$ −4.50000 + 2.59808i −0.241921 + 0.139673i
$$347$$ 28.5788 16.5000i 1.53419 0.885766i 0.535031 0.844833i $$-0.320300\pi$$
0.999162 0.0409337i $$-0.0130332\pi$$
$$348$$ 0 0
$$349$$ 3.46410i 0.185429i −0.995693 0.0927146i $$-0.970446\pi$$
0.995693 0.0927146i $$-0.0295544\pi$$
$$350$$ 3.46410 + 4.00000i 0.185164 + 0.213809i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −1.73205 3.00000i −0.0921878 0.159674i 0.816244 0.577708i $$-0.196053\pi$$
−0.908431 + 0.418034i $$0.862719\pi$$
$$354$$ 0 0
$$355$$ −9.00000 5.19615i −0.477670 0.275783i
$$356$$ −10.3923 −0.550791
$$357$$ 0 0
$$358$$ 15.0000 0.792775
$$359$$ −20.7846 12.0000i −1.09697 0.633336i −0.161546 0.986865i $$-0.551648\pi$$
−0.935423 + 0.353529i $$0.884981\pi$$
$$360$$ 0 0
$$361$$ 14.5000 + 25.1147i 0.763158 + 1.32183i
$$362$$ −8.66025 + 15.0000i −0.455173 + 0.788382i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 21.0000i 1.09919i
$$366$$ 0 0
$$367$$ −7.50000 + 4.33013i −0.391497 + 0.226031i −0.682808 0.730597i $$-0.739242\pi$$
0.291312 + 0.956628i $$0.405908\pi$$
$$368$$ 5.19615 3.00000i 0.270868 0.156386i
$$369$$ 0 0
$$370$$ 6.92820i 0.360180i
$$371$$ −2.59808 + 7.50000i −0.134885 + 0.389381i
$$372$$ 0 0
$$373$$ −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i $$-0.951392\pi$$
0.625917 + 0.779890i $$0.284725\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −3.00000 1.73205i −0.154713 0.0893237i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −14.0000 −0.719132 −0.359566 0.933120i $$-0.617075\pi$$
−0.359566 + 0.933120i $$0.617075\pi$$
$$380$$ 10.3923 + 6.00000i 0.533114 + 0.307794i
$$381$$ 0 0
$$382$$ −3.00000 5.19615i −0.153493 0.265858i
$$383$$ −8.66025 + 15.0000i −0.442518 + 0.766464i −0.997876 0.0651476i $$-0.979248\pi$$
0.555357 + 0.831612i $$0.312581\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 10.0000i 0.508987i
$$387$$ 0 0
$$388$$ 6.00000 3.46410i 0.304604 0.175863i
$$389$$ −18.1865 + 10.5000i −0.922094 + 0.532371i −0.884302 0.466915i $$-0.845366\pi$$
−0.0377914 + 0.999286i $$0.512032\pi$$
$$390$$ 0 0
$$391$$ 20.7846i 1.05112i
$$392$$ 6.92820 + 1.00000i 0.349927 + 0.0505076i
$$393$$ 0 0
$$394$$ −1.50000 + 2.59808i −0.0755689 + 0.130889i
$$395$$ 9.52628 + 16.5000i 0.479319 + 0.830205i
$$396$$ 0 0
$$397$$ −24.0000 13.8564i −1.20453 0.695433i −0.242967 0.970034i $$-0.578121\pi$$
−0.961558 + 0.274601i $$0.911454\pi$$
$$398$$ 8.66025 0.434099
$$399$$ 0 0
$$400$$ −2.00000 −0.100000
$$401$$ −5.19615 3.00000i −0.259483 0.149813i 0.364615 0.931158i $$-0.381200\pi$$
−0.624099 + 0.781345i $$0.714534\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −2.59808 + 4.50000i −0.129259 + 0.223883i
$$405$$ 0 0
$$406$$ 4.50000 + 23.3827i 0.223331 + 1.16046i
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −13.5000 + 7.79423i −0.667532 + 0.385400i −0.795141 0.606425i $$-0.792603\pi$$
0.127609 + 0.991825i $$0.459270\pi$$
$$410$$ −5.19615 + 3.00000i −0.256620 + 0.148159i
$$411$$ 0 0
$$412$$ 10.3923i 0.511992i
$$413$$ −30.3109 10.5000i −1.49150 0.516671i
$$414$$ 0 0
$$415$$ 15.0000 25.9808i 0.736321 1.27535i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 3.46410 0.169232 0.0846162 0.996414i $$-0.473034\pi$$
0.0846162 + 0.996414i $$0.473034\pi$$
$$420$$ 0 0
$$421$$ 32.0000 1.55958 0.779792 0.626038i $$-0.215325\pi$$
0.779792 + 0.626038i $$0.215325\pi$$
$$422$$ 13.8564 + 8.00000i 0.674519 + 0.389434i
$$423$$ 0 0
$$424$$ −1.50000 2.59808i −0.0728464 0.126174i
$$425$$ 3.46410 6.00000i 0.168034 0.291043i
$$426$$ 0 0
$$427$$ 9.00000 1.73205i 0.435541 0.0838198i
$$428$$ 3.00000i 0.145010i
$$429$$ 0 0
$$430$$ −12.0000 + 6.92820i −0.578691 + 0.334108i
$$431$$ −31.1769 + 18.0000i −1.50174 + 0.867029i −0.501741 + 0.865018i $$0.667307\pi$$
−0.999998 + 0.00201168i $$0.999360\pi$$
$$432$$ 0 0
$$433$$ 1.73205i 0.0832370i 0.999134 + 0.0416185i $$0.0132514\pi$$
−0.999134 + 0.0416185i $$0.986749\pi$$
$$434$$ 6.92820 6.00000i 0.332564 0.288009i
$$435$$ 0 0
$$436$$ 8.00000 13.8564i 0.383131 0.663602i
$$437$$ −20.7846 36.0000i −0.994263 1.72211i
$$438$$ 0 0
$$439$$ −27.0000 15.5885i −1.28864 0.743996i −0.310228 0.950662i $$-0.600405\pi$$
−0.978412 + 0.206666i $$0.933739\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 7.79423 + 4.50000i 0.370315 + 0.213801i 0.673596 0.739100i $$-0.264749\pi$$
−0.303281 + 0.952901i $$0.598082\pi$$
$$444$$ 0 0
$$445$$ 9.00000 + 15.5885i 0.426641 + 0.738964i
$$446$$ 7.79423 13.5000i 0.369067 0.639244i
$$447$$ 0 0
$$448$$ −2.00000 + 1.73205i −0.0944911 + 0.0818317i
$$449$$ 6.00000i 0.283158i −0.989927 0.141579i $$-0.954782\pi$$
0.989927 0.141579i $$-0.0452178\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −15.5885 + 9.00000i −0.733219 + 0.423324i
$$453$$ 0 0
$$454$$ 25.9808i 1.21934i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 20.5000 35.5070i 0.958950 1.66095i 0.233890 0.972263i $$-0.424854\pi$$
0.725059 0.688686i $$-0.241812\pi$$
$$458$$ −1.73205 3.00000i −0.0809334 0.140181i
$$459$$ 0 0
$$460$$ −9.00000 5.19615i −0.419627 0.242272i
$$461$$ 22.5167 1.04871 0.524353 0.851501i $$-0.324307\pi$$
0.524353 + 0.851501i $$0.324307\pi$$
$$462$$ 0 0
$$463$$ 23.0000 1.06890 0.534450 0.845200i $$-0.320519\pi$$
0.534450 + 0.845200i $$0.320519\pi$$
$$464$$ −7.79423 4.50000i −0.361838 0.208907i
$$465$$ 0 0
$$466$$ 15.0000 + 25.9808i 0.694862 + 1.20354i
$$467$$ −2.59808 + 4.50000i −0.120225 + 0.208235i −0.919856 0.392256i $$-0.871695\pi$$
0.799632 + 0.600491i $$0.205028\pi$$
$$468$$ 0 0
$$469$$ −35.0000 12.1244i −1.61615 0.559851i
$$470$$ 6.00000i 0.276759i
$$471$$ 0 0
$$472$$ 10.5000 6.06218i 0.483302 0.279034i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 13.8564i 0.635776i
$$476$$ −1.73205 9.00000i −0.0793884 0.412514i
$$477$$ 0 0
$$478$$ −12.0000 + 20.7846i −0.548867 + 0.950666i
$$479$$ 6.92820 + 12.0000i 0.316558 + 0.548294i 0.979767 0.200140i $$-0.0641396\pi$$
−0.663210 + 0.748434i $$0.730806\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 1.73205 0.0788928
$$483$$ 0 0
$$484$$ −11.0000 −0.500000
$$485$$ −10.3923 6.00000i −0.471890 0.272446i
$$486$$ 0 0
$$487$$ −0.500000 0.866025i −0.0226572 0.0392434i 0.854475 0.519493i $$-0.173879\pi$$
−0.877132 + 0.480250i $$0.840546\pi$$
$$488$$ −1.73205 + 3.00000i −0.0784063 + 0.135804i
$$489$$ 0 0
$$490$$ −4.50000 11.2583i −0.203289 0.508600i
$$491$$ 3.00000i 0.135388i −0.997706 0.0676941i $$-0.978436\pi$$
0.997706 0.0676941i $$-0.0215642\pi$$
$$492$$ 0 0
$$493$$ 27.0000 15.5885i 1.21602 0.702069i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 3.46410i 0.155543i
$$497$$ −10.3923 12.0000i −0.466159 0.538274i
$$498$$ 0 0
$$499$$ 7.00000 12.1244i 0.313363 0.542761i −0.665725 0.746197i $$-0.731878\pi$$
0.979088 + 0.203436i $$0.0652110\pi$$
$$500$$ 6.06218 + 10.5000i 0.271109 + 0.469574i
$$501$$ 0 0
$$502$$ 7.50000 + 4.33013i 0.334741 + 0.193263i
$$503$$ 27.7128 1.23565 0.617827 0.786314i $$-0.288013\pi$$
0.617827 + 0.786314i $$0.288013\pi$$
$$504$$ 0 0
$$505$$ 9.00000 0.400495
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −3.50000 6.06218i −0.155287 0.268966i
$$509$$ 17.3205 30.0000i 0.767718 1.32973i −0.171080 0.985257i $$-0.554726\pi$$
0.938798 0.344469i $$-0.111941\pi$$
$$510$$ 0 0
$$511$$ −10.5000 + 30.3109i −0.464493 + 1.34087i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 18.0000 10.3923i 0.793946 0.458385i
$$515$$ 15.5885 9.00000i 0.686909 0.396587i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −3.46410 + 10.0000i −0.152204 + 0.439375i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.73205 + 3.00000i 0.0758825 + 0.131432i 0.901470 0.432842i $$-0.142489\pi$$
−0.825587 + 0.564275i $$0.809156\pi$$
$$522$$ 0 0
$$523$$ 18.0000 + 10.3923i 0.787085 + 0.454424i 0.838935 0.544231i $$-0.183179\pi$$
−0.0518503 + 0.998655i $$0.516512\pi$$
$$524$$ 10.3923 0.453990
$$525$$ 0 0
$$526$$ 18.0000 0.784837
$$527$$ −10.3923 6.00000i −0.452696 0.261364i
$$528$$ 0 0
$$529$$ 6.50000 + 11.2583i 0.282609 + 0.489493i
$$530$$ −2.59808 + 4.50000i −0.112853 + 0.195468i
$$531$$ 0 0
$$532$$ 12.0000 + 13.8564i 0.520266 + 0.600751i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 4.50000 2.59808i 0.194552 0.112325i
$$536$$ 12.1244 7.00000i 0.523692 0.302354i
$$537$$ 0 0
$$538$$ 1.73205i 0.0746740i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 17.0000 29.4449i 0.730887 1.26593i −0.225617 0.974216i $$-0.572440\pi$$
0.956504 0.291718i $$-0.0942267\pi$$
$$542$$ 6.06218 + 10.5000i 0.260393 + 0.451014i
$$543$$ 0 0
$$544$$ 3.00000 + 1.73205i 0.128624 + 0.0742611i
$$545$$ −27.7128 −1.18709
$$546$$ 0 0
$$547$$ 8.00000 0.342055 0.171028 0.985266i $$-0.445291\pi$$
0.171028 + 0.985266i $$0.445291\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −31.1769 + 54.0000i −1.32818 + 2.30048i
$$552$$ 0 0
$$553$$ 5.50000 + 28.5788i 0.233884 + 1.21530i
$$554$$ 8.00000i 0.339887i
$$555$$ 0 0
$$556$$ 9.00000 5.19615i 0.381685 0.220366i
$$557$$ 15.5885 9.00000i 0.660504 0.381342i −0.131965 0.991254i $$-0.542129\pi$$
0.792469 + 0.609912i $$0.208795\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 4.33013 + 1.50000i 0.182981 + 0.0633866i
$$561$$ 0 0
$$562$$ 9.00000 15.5885i 0.379642 0.657559i
$$563$$ 2.59808 + 4.50000i 0.109496 + 0.189652i 0.915566 0.402167i $$-0.131743\pi$$
−0.806070 + 0.591820i $$0.798410\pi$$
$$564$$ 0 0
$$565$$ 27.0000 + 15.5885i 1.13590 + 0.655811i
$$566$$ 6.92820 0.291214
$$567$$ 0 0
$$568$$ 6.00000 0.251754
$$569$$ 36.3731 + 21.0000i 1.52484 + 0.880366i 0.999567 + 0.0294311i $$0.00936956\pi$$
0.525271 + 0.850935i $$0.323964\pi$$
$$570$$ 0 0
$$571$$ 20.0000 + 34.6410i 0.836974 + 1.44968i 0.892413 + 0.451219i $$0.149011\pi$$
−0.0554391 + 0.998462i $$0.517656\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −9.00000 + 1.73205i −0.375653 + 0.0722944i
$$575$$ 12.0000i 0.500435i
$$576$$ 0 0
$$577$$ −13.5000 + 7.79423i −0.562012 + 0.324478i −0.753953 0.656929i $$-0.771855\pi$$
0.191940 + 0.981407i $$0.438522\pi$$
$$578$$ 4.33013 2.50000i 0.180110 0.103986i
$$579$$ 0 0
$$580$$ 15.5885i 0.647275i
$$581$$ 34.6410 30.0000i 1.43715 1.24461i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −6.06218 10.5000i −0.250855 0.434493i
$$585$$ 0 0
$$586$$ −25.5000 14.7224i −1.05340 0.608178i
$$587$$ 36.3731 1.50128 0.750639 0.660713i $$-0.229746\pi$$
0.750639 + 0.660713i $$0.229746\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ −18.1865 10.5000i −0.748728 0.432278i
$$591$$ 0 0
$$592$$ −2.00000 3.46410i −0.0821995 0.142374i
$$593$$ 12.1244 21.0000i 0.497888 0.862367i −0.502109 0.864804i $$-0.667443\pi$$
0.999997 + 0.00243746i $$0.000775869\pi$$
$$594$$ 0 0
$$595$$ −12.0000 + 10.3923i −0.491952 + 0.426043i
$$596$$ 15.0000i 0.614424i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −20.7846 + 12.0000i −0.849236 + 0.490307i −0.860393 0.509631i $$-0.829782\pi$$
0.0111569 + 0.999938i $$0.496449\pi$$
$$600$$ 0 0
$$601$$ 1.73205i 0.0706518i −0.999376 0.0353259i $$-0.988753\pi$$
0.999376 0.0353259i $$-0.0112469\pi$$
$$602$$ −20.7846 + 4.00000i −0.847117 + 0.163028i
$$603$$ 0 0
$$604$$ −4.00000 + 6.92820i −0.162758 + 0.281905i
$$605$$ 9.52628 + 16.5000i 0.387298 + 0.670820i
$$606$$ 0 0
$$607$$ −28.5000 16.4545i −1.15678 0.667867i −0.206249 0.978499i $$-0.566126\pi$$
−0.950530 + 0.310633i $$0.899459\pi$$
$$608$$ −6.92820 −0.280976
$$609$$ 0 0
$$610$$ 6.00000 0.242933
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −4.00000 6.92820i −0.161558 0.279827i 0.773869 0.633345i $$-0.218319\pi$$
−0.935428 + 0.353518i $$0.884985\pi$$
$$614$$ 3.46410 6.00000i 0.139800 0.242140i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 6.00000i 0.241551i 0.992680 + 0.120775i $$0.0385381\pi$$
−0.992680 + 0.120775i $$0.961462\pi$$
$$618$$ 0 0
$$619$$ 18.0000 10.3923i 0.723481 0.417702i −0.0925515 0.995708i $$-0.529502\pi$$
0.816033 + 0.578006i $$0.196169\pi$$
$$620$$ 5.19615 3.00000i 0.208683 0.120483i
$$621$$ 0 0
$$622$$ 13.8564i 0.555591i
$$623$$ 5.19615 + 27.0000i 0.208179 + 1.08173i
$$624$$ 0 0
$$625$$ 5.50000 9.52628i 0.220000 0.381051i
$$626$$ −11.2583 19.5000i −0.449973 0.779377i
$$627$$ 0 0
$$628$$ 9.00000 + 5.19615i 0.359139 + 0.207349i
$$629$$ 13.8564 0.552491
$$630$$ 0 0
$$631$$ 20.0000 0.796187 0.398094 0.917345i $$-0.369672\pi$$
0.398094 + 0.917345i $$0.369672\pi$$
$$632$$ −9.52628 5.50000i −0.378935 0.218778i
$$633$$ 0 0
$$634$$ 3.00000 + 5.19615i 0.119145 + 0.206366i
$$635$$ −6.06218 + 10.5000i −0.240570 + 0.416680i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1.50000 + 0.866025i −0.0592927 + 0.0342327i
$$641$$ −10.3923 + 6.00000i −0.410471 + 0.236986i −0.690992 0.722862i $$-0.742826\pi$$
0.280521 + 0.959848i $$0.409493\pi$$
$$642$$ 0 0
$$643$$ 27.7128i 1.09289i 0.837496 + 0.546443i $$0.184019\pi$$
−0.837496 + 0.546443i $$0.815981\pi$$
$$644$$ −10.3923 12.0000i −0.409514 0.472866i
$$645$$ 0 0
$$646$$ 12.0000 20.7846i 0.472134 0.817760i
$$647$$ −5.19615 9.00000i −0.204282 0.353827i 0.745622 0.666369i $$-0.232153\pi$$
−0.949904 + 0.312543i $$0.898819\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −2.00000 −0.0783260
$$653$$ −12.9904 7.50000i −0.508353 0.293498i 0.223803 0.974634i $$-0.428153\pi$$
−0.732156 + 0.681137i $$0.761486\pi$$
$$654$$ 0 0
$$655$$ −9.00000 15.5885i −0.351659 0.609091i
$$656$$ 1.73205 3.00000i 0.0676252 0.117130i
$$657$$ 0 0
$$658$$ −3.00000 + 8.66025i −0.116952 + 0.337612i
$$659$$ 27.0000i 1.05177i 0.850555 + 0.525885i $$0.176266\pi$$
−0.850555 + 0.525885i $$0.823734\pi$$
$$660$$ 0 0
$$661$$ −12.0000 + 6.92820i −0.466746 + 0.269476i −0.714877 0.699251i $$-0.753517\pi$$
0.248131 + 0.968727i $$0.420184\pi$$
$$662$$ −8.66025 + 5.00000i −0.336590 + 0.194331i
$$663$$ 0 0
$$664$$ 17.3205i 0.672166i
$$665$$ 10.3923 30.0000i 0.402996 1.16335i
$$666$$ 0 0
$$667$$ 27.0000 46.7654i 1.04544 1.81076i
$$668$$ −8.66025 15.0000i −0.335075 0.580367i
$$669$$ 0 0
$$670$$ −21.0000 12.1244i −0.811301 0.468405i
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −5.00000 −0.192736 −0.0963679 0.995346i $$-0.530723\pi$$
−0.0963679 + 0.995346i $$0.530723\pi$$
$$674$$ −19.9186 11.5000i −0.767235 0.442963i
$$675$$ 0 0
$$676$$ 6.50000 + 11.2583i 0.250000 + 0.433013i
$$677$$ 12.9904 22.5000i 0.499261 0.864745i −0.500739 0.865598i $$-0.666938\pi$$
1.00000 0.000853228i $$0.000271591\pi$$
$$678$$ 0 0
$$679$$ −12.0000 13.8564i −0.460518 0.531760i
$$680$$ 6.00000i 0.230089i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 7.79423 4.50000i 0.298238 0.172188i −0.343413 0.939184i $$-0.611583\pi$$
0.641651 + 0.766997i $$0.278250\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −0.866025 18.5000i −0.0330650 0.706333i
$$687$$ 0 0
$$688$$ 4.00000 6.92820i 0.152499 0.264135i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −24.0000 13.8564i −0.913003 0.527123i −0.0316069 0.999500i $$-0.510062\pi$$
−0.881396 + 0.472378i $$0.843396\pi$$
$$692$$ −5.19615 −0.197528
$$693$$ 0 0
$$694$$ 33.0000 1.25266
$$695$$ −15.5885 9.00000i −0.591304 0.341389i
$$696$$ 0 0
$$697$$ 6.00000 + 10.3923i 0.227266 + 0.393637i
$$698$$ 1.73205 3.00000i 0.0655591 0.113552i
$$699$$ 0 0
$$700$$ 1.00000 + 5.19615i 0.0377964 + 0.196396i
$$701$$ 27.0000i 1.01978i 0.860241 + 0.509888i $$0.170313\pi$$
−0.860241 + 0.509888i $$0.829687\pi$$
$$702$$ 0 0
$$703$$ −24.0000 + 13.8564i −0.905177 + 0.522604i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 3.46410i 0.130373i
$$707$$ 12.9904 + 4.50000i 0.488554 + 0.169240i
$$708$$ 0 0
$$709$$ −14.0000 + 24.2487i −0.525781 + 0.910679i 0.473768 + 0.880650i $$0.342894\pi$$
−0.999549 + 0.0300298i $$0.990440\pi$$
$$710$$ −5.19615 9.00000i −0.195008 0.337764i
$$711$$ 0 0
$$712$$ −9.00000 5.19615i −0.337289 0.194734i
$$713$$ −20.7846 −0.778390
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.9904 + 7.50000i 0.485473 + 0.280288i
$$717$$ 0 0
$$718$$ −12.0000 20.7846i −0.447836 0.775675i
$$719$$ −24.2487 + 42.0000i −0.904324 + 1.56634i −0.0825027 + 0.996591i $$0.526291\pi$$
−0.821822 + 0.569745i $$0.807042\pi$$
$$720$$ 0 0
$$721$$ 27.0000 5.19615i 1.00553 0.193515i
$$722$$ 29.0000i 1.07927i
$$723$$ 0 0
$$724$$ −15.0000 + 8.66025i −0.557471 + 0.321856i
$$725$$ −15.5885 + 9.00000i −0.578941 + 0.334252i
$$726$$ 0 0
$$727$$ 12.1244i 0.449667i 0.974397 + 0.224834i $$0.0721839\pi$$
−0.974397 + 0.224834i $$0.927816\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −10.5000 + 18.1865i −0.388622 + 0.673114i
$$731$$ 13.8564 + 24.0000i 0.512498 + 0.887672i
$$732$$ 0 0
$$733$$ −6.00000 3.46410i −0.221615 0.127950i 0.385083 0.922882i $$-0.374173\pi$$
−0.606698 + 0.794933i $$0.707506\pi$$
$$734$$ −8.66025 −0.319656
$$735$$ 0 0
$$736$$ 6.00000 0.221163
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 5.00000 + 8.66025i 0.183928 + 0.318573i 0.943215 0.332184i $$-0.107785\pi$$
−0.759287 + 0.650756i $$0.774452\pi$$
$$740$$ −3.46410 + 6.00000i −0.127343 + 0.220564i
$$741$$ 0 0
$$742$$ −6.00000 + 5.19615i −0.220267 + 0.190757i
$$743$$ 36.0000i 1.32071i 0.750953 + 0.660356i $$0.229595\pi$$
−0.750953 + 0.660356i $$0.770405\pi$$
$$744$$ 0 0
$$745$$ 22.5000 12.9904i 0.824336 0.475931i
$$746$$ −12.1244 + 7.00000i −0.443904 + 0.256288i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 7.79423 1.50000i 0.284795 0.0548088i
$$750$$ 0 0
$$751$$ −3.50000 + 6.06218i −0.127717 + 0.221212i −0.922792 0.385299i $$-0.874098\pi$$
0.795075 + 0.606511i $$0.207432\pi$$
$$752$$ −1.73205 3.00000i −0.0631614 0.109399i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 13.8564 0.504286
$$756$$ 0 0
$$757$$ −38.0000 −1.38113 −0.690567 0.723269i $$-0.742639\pi$$
−0.690567 + 0.723269i $$0.742639\pi$$
$$758$$ −12.1244 7.00000i −0.440376 0.254251i
$$759$$ 0 0
$$760$$ 6.00000 + 10.3923i 0.217643 + 0.376969i
$$761$$ 17.3205 30.0000i 0.627868 1.08750i −0.360111 0.932910i $$-0.617261\pi$$
0.987979 0.154590i $$-0.0494055\pi$$
$$762$$ 0 0
$$763$$ −40.0000 13.8564i −1.44810 0.501636i
$$764$$ 6.00000i 0.217072i
$$765$$ 0 0
$$766$$ −15.0000 + 8.66025i −0.541972 + 0.312908i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 48.4974i 1.74886i −0.485150 0.874431i $$-0.661235\pi$$
0.485150 0.874431i $$-0.338765\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 5.00000 8.66025i 0.179954 0.311689i
$$773$$ −6.92820 12.0000i −0.249190 0.431610i 0.714111 0.700032i $$-0.246831\pi$$
−0.963301 + 0.268422i $$0.913498\pi$$
$$774$$ 0 0
$$775$$ 6.00000 + 3.46410i 0.215526 + 0.124434i
$$776$$ 6.92820 0.248708
$$777$$ 0 0
$$778$$ −21.0000 −0.752886
$$779$$ −20.7846 12.0000i −0.744686 0.429945i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −10.3923 + 18.0000i −0.371628 + 0.643679i
$$783$$ 0 0
$$784$$ 5.50000 + 4.33013i 0.196429 + 0.154647i
$$785$$ 18.0000i 0.642448i
$$786$$ 0 0
$$787$$ 3.00000 1.73205i 0.106938 0.0617409i −0.445577 0.895244i $$-0.647001\pi$$
0.552515 + 0.833503i