# Properties

 Label 400.3.p.d.257.1 Level $400$ Weight $3$ Character 400.257 Analytic conductor $10.899$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(193,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("400.193");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$400 = 2^{4} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 400.p (of order $$4$$, 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: $$10.8992105744$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 20) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 257.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 400.257 Dual form 400.3.p.d.193.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.00000i) q^{3} +(-7.00000 - 7.00000i) q^{7} +7.00000i q^{9} +O(q^{10})$$ $$q+(1.00000 - 1.00000i) q^{3} +(-7.00000 - 7.00000i) q^{7} +7.00000i q^{9} -10.0000 q^{11} +(-9.00000 + 9.00000i) q^{13} +(-1.00000 - 1.00000i) q^{17} +8.00000i q^{19} -14.0000 q^{21} +(-23.0000 + 23.0000i) q^{23} +(16.0000 + 16.0000i) q^{27} -8.00000i q^{29} +14.0000 q^{31} +(-10.0000 + 10.0000i) q^{33} +(-33.0000 - 33.0000i) q^{37} +18.0000i q^{39} -14.0000 q^{41} +(-15.0000 + 15.0000i) q^{43} +(-39.0000 - 39.0000i) q^{47} +49.0000i q^{49} -2.00000 q^{51} +(7.00000 - 7.00000i) q^{53} +(8.00000 + 8.00000i) q^{57} +56.0000i q^{59} +42.0000 q^{61} +(49.0000 - 49.0000i) q^{63} +(-7.00000 - 7.00000i) q^{67} +46.0000i q^{69} -98.0000 q^{71} +(-49.0000 + 49.0000i) q^{73} +(70.0000 + 70.0000i) q^{77} -96.0000i q^{79} -31.0000 q^{81} +(-63.0000 + 63.0000i) q^{83} +(-8.00000 - 8.00000i) q^{87} -112.000i q^{89} +126.000 q^{91} +(14.0000 - 14.0000i) q^{93} +(-33.0000 - 33.0000i) q^{97} -70.0000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{3} - 14 q^{7}+O(q^{10})$$ 2 * q + 2 * q^3 - 14 * q^7 $$2 q + 2 q^{3} - 14 q^{7} - 20 q^{11} - 18 q^{13} - 2 q^{17} - 28 q^{21} - 46 q^{23} + 32 q^{27} + 28 q^{31} - 20 q^{33} - 66 q^{37} - 28 q^{41} - 30 q^{43} - 78 q^{47} - 4 q^{51} + 14 q^{53} + 16 q^{57} + 84 q^{61} + 98 q^{63} - 14 q^{67} - 196 q^{71} - 98 q^{73} + 140 q^{77} - 62 q^{81} - 126 q^{83} - 16 q^{87} + 252 q^{91} + 28 q^{93} - 66 q^{97}+O(q^{100})$$ 2 * q + 2 * q^3 - 14 * q^7 - 20 * q^11 - 18 * q^13 - 2 * q^17 - 28 * q^21 - 46 * q^23 + 32 * q^27 + 28 * q^31 - 20 * q^33 - 66 * q^37 - 28 * q^41 - 30 * q^43 - 78 * q^47 - 4 * q^51 + 14 * q^53 + 16 * q^57 + 84 * q^61 + 98 * q^63 - 14 * q^67 - 196 * q^71 - 98 * q^73 + 140 * q^77 - 62 * q^81 - 126 * q^83 - 16 * q^87 + 252 * q^91 + 28 * q^93 - 66 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$177$$ $$351$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$ $$1$$

## 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 0
$$3$$ 1.00000 1.00000i 0.333333 0.333333i −0.520518 0.853851i $$-0.674261\pi$$
0.853851 + 0.520518i $$0.174261\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −7.00000 7.00000i −1.00000 1.00000i 1.00000i $$-0.5\pi$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ 7.00000i 0.777778i
$$10$$ 0 0
$$11$$ −10.0000 −0.909091 −0.454545 0.890724i $$-0.650198\pi$$
−0.454545 + 0.890724i $$0.650198\pi$$
$$12$$ 0 0
$$13$$ −9.00000 + 9.00000i −0.692308 + 0.692308i −0.962739 0.270432i $$-0.912834\pi$$
0.270432 + 0.962739i $$0.412834\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1.00000 1.00000i −0.0588235 0.0588235i 0.677083 0.735907i $$-0.263244\pi$$
−0.735907 + 0.677083i $$0.763244\pi$$
$$18$$ 0 0
$$19$$ 8.00000i 0.421053i 0.977588 + 0.210526i $$0.0675178\pi$$
−0.977588 + 0.210526i $$0.932482\pi$$
$$20$$ 0 0
$$21$$ −14.0000 −0.666667
$$22$$ 0 0
$$23$$ −23.0000 + 23.0000i −1.00000 + 1.00000i 1.00000i $$0.5\pi$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 16.0000 + 16.0000i 0.592593 + 0.592593i
$$28$$ 0 0
$$29$$ 8.00000i 0.275862i −0.990442 0.137931i $$-0.955955\pi$$
0.990442 0.137931i $$-0.0440452\pi$$
$$30$$ 0 0
$$31$$ 14.0000 0.451613 0.225806 0.974172i $$-0.427498\pi$$
0.225806 + 0.974172i $$0.427498\pi$$
$$32$$ 0 0
$$33$$ −10.0000 + 10.0000i −0.303030 + 0.303030i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −33.0000 33.0000i −0.891892 0.891892i 0.102809 0.994701i $$-0.467217\pi$$
−0.994701 + 0.102809i $$0.967217\pi$$
$$38$$ 0 0
$$39$$ 18.0000i 0.461538i
$$40$$ 0 0
$$41$$ −14.0000 −0.341463 −0.170732 0.985318i $$-0.554613\pi$$
−0.170732 + 0.985318i $$0.554613\pi$$
$$42$$ 0 0
$$43$$ −15.0000 + 15.0000i −0.348837 + 0.348837i −0.859676 0.510839i $$-0.829335\pi$$
0.510839 + 0.859676i $$0.329335\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −39.0000 39.0000i −0.829787 0.829787i 0.157700 0.987487i $$-0.449592\pi$$
−0.987487 + 0.157700i $$0.949592\pi$$
$$48$$ 0 0
$$49$$ 49.0000i 1.00000i
$$50$$ 0 0
$$51$$ −2.00000 −0.0392157
$$52$$ 0 0
$$53$$ 7.00000 7.00000i 0.132075 0.132075i −0.637979 0.770054i $$-0.720229\pi$$
0.770054 + 0.637979i $$0.220229\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 8.00000 + 8.00000i 0.140351 + 0.140351i
$$58$$ 0 0
$$59$$ 56.0000i 0.949153i 0.880214 + 0.474576i $$0.157399\pi$$
−0.880214 + 0.474576i $$0.842601\pi$$
$$60$$ 0 0
$$61$$ 42.0000 0.688525 0.344262 0.938874i $$-0.388129\pi$$
0.344262 + 0.938874i $$0.388129\pi$$
$$62$$ 0 0
$$63$$ 49.0000 49.0000i 0.777778 0.777778i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −7.00000 7.00000i −0.104478 0.104478i 0.652936 0.757413i $$-0.273537\pi$$
−0.757413 + 0.652936i $$0.773537\pi$$
$$68$$ 0 0
$$69$$ 46.0000i 0.666667i
$$70$$ 0 0
$$71$$ −98.0000 −1.38028 −0.690141 0.723675i $$-0.742451\pi$$
−0.690141 + 0.723675i $$0.742451\pi$$
$$72$$ 0 0
$$73$$ −49.0000 + 49.0000i −0.671233 + 0.671233i −0.958000 0.286767i $$-0.907419\pi$$
0.286767 + 0.958000i $$0.407419\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 70.0000 + 70.0000i 0.909091 + 0.909091i
$$78$$ 0 0
$$79$$ 96.0000i 1.21519i −0.794247 0.607595i $$-0.792134\pi$$
0.794247 0.607595i $$-0.207866\pi$$
$$80$$ 0 0
$$81$$ −31.0000 −0.382716
$$82$$ 0 0
$$83$$ −63.0000 + 63.0000i −0.759036 + 0.759036i −0.976147 0.217111i $$-0.930337\pi$$
0.217111 + 0.976147i $$0.430337\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −8.00000 8.00000i −0.0919540 0.0919540i
$$88$$ 0 0
$$89$$ 112.000i 1.25843i −0.777233 0.629213i $$-0.783377\pi$$
0.777233 0.629213i $$-0.216623\pi$$
$$90$$ 0 0
$$91$$ 126.000 1.38462
$$92$$ 0 0
$$93$$ 14.0000 14.0000i 0.150538 0.150538i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −33.0000 33.0000i −0.340206 0.340206i 0.516239 0.856445i $$-0.327332\pi$$
−0.856445 + 0.516239i $$0.827332\pi$$
$$98$$ 0 0
$$99$$ 70.0000i 0.707071i
$$100$$ 0 0
$$101$$ 26.0000 0.257426 0.128713 0.991682i $$-0.458915\pi$$
0.128713 + 0.991682i $$0.458915\pi$$
$$102$$ 0 0
$$103$$ 73.0000 73.0000i 0.708738 0.708738i −0.257532 0.966270i $$-0.582909\pi$$
0.966270 + 0.257532i $$0.0829093\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 121.000 + 121.000i 1.13084 + 1.13084i 0.990038 + 0.140804i $$0.0449686\pi$$
0.140804 + 0.990038i $$0.455031\pi$$
$$108$$ 0 0
$$109$$ 136.000i 1.24771i −0.781542 0.623853i $$-0.785566\pi$$
0.781542 0.623853i $$-0.214434\pi$$
$$110$$ 0 0
$$111$$ −66.0000 −0.594595
$$112$$ 0 0
$$113$$ 127.000 127.000i 1.12389 1.12389i 0.132743 0.991150i $$-0.457621\pi$$
0.991150 0.132743i $$-0.0423786\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −63.0000 63.0000i −0.538462 0.538462i
$$118$$ 0 0
$$119$$ 14.0000i 0.117647i
$$120$$ 0 0
$$121$$ −21.0000 −0.173554
$$122$$ 0 0
$$123$$ −14.0000 + 14.0000i −0.113821 + 0.113821i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −7.00000 7.00000i −0.0551181 0.0551181i 0.679010 0.734129i $$-0.262409\pi$$
−0.734129 + 0.679010i $$0.762409\pi$$
$$128$$ 0 0
$$129$$ 30.0000i 0.232558i
$$130$$ 0 0
$$131$$ 230.000 1.75573 0.877863 0.478913i $$-0.158969\pi$$
0.877863 + 0.478913i $$0.158969\pi$$
$$132$$ 0 0
$$133$$ 56.0000 56.0000i 0.421053 0.421053i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 63.0000 + 63.0000i 0.459854 + 0.459854i 0.898607 0.438753i $$-0.144580\pi$$
−0.438753 + 0.898607i $$0.644580\pi$$
$$138$$ 0 0
$$139$$ 88.0000i 0.633094i 0.948577 + 0.316547i $$0.102523\pi$$
−0.948577 + 0.316547i $$0.897477\pi$$
$$140$$ 0 0
$$141$$ −78.0000 −0.553191
$$142$$ 0 0
$$143$$ 90.0000 90.0000i 0.629371 0.629371i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 49.0000 + 49.0000i 0.333333 + 0.333333i
$$148$$ 0 0
$$149$$ 168.000i 1.12752i 0.825940 + 0.563758i $$0.190645\pi$$
−0.825940 + 0.563758i $$0.809355\pi$$
$$150$$ 0 0
$$151$$ −130.000 −0.860927 −0.430464 0.902608i $$-0.641650\pi$$
−0.430464 + 0.902608i $$0.641650\pi$$
$$152$$ 0 0
$$153$$ 7.00000 7.00000i 0.0457516 0.0457516i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 63.0000 + 63.0000i 0.401274 + 0.401274i 0.878682 0.477408i $$-0.158424\pi$$
−0.477408 + 0.878682i $$0.658424\pi$$
$$158$$ 0 0
$$159$$ 14.0000i 0.0880503i
$$160$$ 0 0
$$161$$ 322.000 2.00000
$$162$$ 0 0
$$163$$ 65.0000 65.0000i 0.398773 0.398773i −0.479027 0.877800i $$-0.659010\pi$$
0.877800 + 0.479027i $$0.159010\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −103.000 103.000i −0.616766 0.616766i 0.327934 0.944701i $$-0.393648\pi$$
−0.944701 + 0.327934i $$0.893648\pi$$
$$168$$ 0 0
$$169$$ 7.00000i 0.0414201i
$$170$$ 0 0
$$171$$ −56.0000 −0.327485
$$172$$ 0 0
$$173$$ −73.0000 + 73.0000i −0.421965 + 0.421965i −0.885880 0.463915i $$-0.846444\pi$$
0.463915 + 0.885880i $$0.346444\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 56.0000 + 56.0000i 0.316384 + 0.316384i
$$178$$ 0 0
$$179$$ 56.0000i 0.312849i −0.987690 0.156425i $$-0.950003\pi$$
0.987690 0.156425i $$-0.0499968\pi$$
$$180$$ 0 0
$$181$$ −70.0000 −0.386740 −0.193370 0.981126i $$-0.561942\pi$$
−0.193370 + 0.981126i $$0.561942\pi$$
$$182$$ 0 0
$$183$$ 42.0000 42.0000i 0.229508 0.229508i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 10.0000 + 10.0000i 0.0534759 + 0.0534759i
$$188$$ 0 0
$$189$$ 224.000i 1.18519i
$$190$$ 0 0
$$191$$ 142.000 0.743455 0.371728 0.928342i $$-0.378765\pi$$
0.371728 + 0.928342i $$0.378765\pi$$
$$192$$ 0 0
$$193$$ 63.0000 63.0000i 0.326425 0.326425i −0.524800 0.851225i $$-0.675860\pi$$
0.851225 + 0.524800i $$0.175860\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 63.0000 + 63.0000i 0.319797 + 0.319797i 0.848689 0.528892i $$-0.177392\pi$$
−0.528892 + 0.848689i $$0.677392\pi$$
$$198$$ 0 0
$$199$$ 336.000i 1.68844i −0.535995 0.844221i $$-0.680063\pi$$
0.535995 0.844221i $$-0.319937\pi$$
$$200$$ 0 0
$$201$$ −14.0000 −0.0696517
$$202$$ 0 0
$$203$$ −56.0000 + 56.0000i −0.275862 + 0.275862i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −161.000 161.000i −0.777778 0.777778i
$$208$$ 0 0
$$209$$ 80.0000i 0.382775i
$$210$$ 0 0
$$211$$ −314.000 −1.48815 −0.744076 0.668095i $$-0.767110\pi$$
−0.744076 + 0.668095i $$0.767110\pi$$
$$212$$ 0 0
$$213$$ −98.0000 + 98.0000i −0.460094 + 0.460094i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −98.0000 98.0000i −0.451613 0.451613i
$$218$$ 0 0
$$219$$ 98.0000i 0.447489i
$$220$$ 0 0
$$221$$ 18.0000 0.0814480
$$222$$ 0 0
$$223$$ −135.000 + 135.000i −0.605381 + 0.605381i −0.941736 0.336354i $$-0.890806\pi$$
0.336354 + 0.941736i $$0.390806\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 281.000 + 281.000i 1.23789 + 1.23789i 0.960864 + 0.277022i $$0.0893474\pi$$
0.277022 + 0.960864i $$0.410653\pi$$
$$228$$ 0 0
$$229$$ 168.000i 0.733624i 0.930295 + 0.366812i $$0.119551\pi$$
−0.930295 + 0.366812i $$0.880449\pi$$
$$230$$ 0 0
$$231$$ 140.000 0.606061
$$232$$ 0 0
$$233$$ −273.000 + 273.000i −1.17167 + 1.17167i −0.189863 + 0.981811i $$0.560804\pi$$
−0.981811 + 0.189863i $$0.939196\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −96.0000 96.0000i −0.405063 0.405063i
$$238$$ 0 0
$$239$$ 288.000i 1.20502i 0.798111 + 0.602510i $$0.205833\pi$$
−0.798111 + 0.602510i $$0.794167\pi$$
$$240$$ 0 0
$$241$$ −446.000 −1.85062 −0.925311 0.379209i $$-0.876196\pi$$
−0.925311 + 0.379209i $$0.876196\pi$$
$$242$$ 0 0
$$243$$ −175.000 + 175.000i −0.720165 + 0.720165i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −72.0000 72.0000i −0.291498 0.291498i
$$248$$ 0 0
$$249$$ 126.000i 0.506024i
$$250$$ 0 0
$$251$$ 150.000 0.597610 0.298805 0.954314i $$-0.403412\pi$$
0.298805 + 0.954314i $$0.403412\pi$$
$$252$$ 0 0
$$253$$ 230.000 230.000i 0.909091 0.909091i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −161.000 161.000i −0.626459 0.626459i 0.320716 0.947175i $$-0.396076\pi$$
−0.947175 + 0.320716i $$0.896076\pi$$
$$258$$ 0 0
$$259$$ 462.000i 1.78378i
$$260$$ 0 0
$$261$$ 56.0000 0.214559
$$262$$ 0 0
$$263$$ −151.000 + 151.000i −0.574144 + 0.574144i −0.933284 0.359139i $$-0.883070\pi$$
0.359139 + 0.933284i $$0.383070\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −112.000 112.000i −0.419476 0.419476i
$$268$$ 0 0
$$269$$ 376.000i 1.39777i 0.715234 + 0.698885i $$0.246320\pi$$
−0.715234 + 0.698885i $$0.753680\pi$$
$$270$$ 0 0
$$271$$ −210.000 −0.774908 −0.387454 0.921889i $$-0.626645\pi$$
−0.387454 + 0.921889i $$0.626645\pi$$
$$272$$ 0 0
$$273$$ 126.000 126.000i 0.461538 0.461538i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −129.000 129.000i −0.465704 0.465704i 0.434816 0.900520i $$-0.356814\pi$$
−0.900520 + 0.434816i $$0.856814\pi$$
$$278$$ 0 0
$$279$$ 98.0000i 0.351254i
$$280$$ 0 0
$$281$$ −174.000 −0.619217 −0.309609 0.950864i $$-0.600198\pi$$
−0.309609 + 0.950864i $$0.600198\pi$$
$$282$$ 0 0
$$283$$ 113.000 113.000i 0.399293 0.399293i −0.478690 0.877984i $$-0.658888\pi$$
0.877984 + 0.478690i $$0.158888\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 98.0000 + 98.0000i 0.341463 + 0.341463i
$$288$$ 0 0
$$289$$ 287.000i 0.993080i
$$290$$ 0 0
$$291$$ −66.0000 −0.226804
$$292$$ 0 0
$$293$$ −345.000 + 345.000i −1.17747 + 1.17747i −0.197089 + 0.980386i $$0.563149\pi$$
−0.980386 + 0.197089i $$0.936851\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −160.000 160.000i −0.538721 0.538721i
$$298$$ 0 0
$$299$$ 414.000i 1.38462i
$$300$$ 0 0
$$301$$ 210.000 0.697674
$$302$$ 0 0
$$303$$ 26.0000 26.0000i 0.0858086 0.0858086i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −327.000 327.000i −1.06515 1.06515i −0.997725 0.0674220i $$-0.978523\pi$$
−0.0674220 0.997725i $$-0.521477\pi$$
$$308$$ 0 0
$$309$$ 146.000i 0.472492i
$$310$$ 0 0
$$311$$ −2.00000 −0.00643087 −0.00321543 0.999995i $$-0.501024\pi$$
−0.00321543 + 0.999995i $$0.501024\pi$$
$$312$$ 0 0
$$313$$ −81.0000 + 81.0000i −0.258786 + 0.258786i −0.824560 0.565774i $$-0.808577\pi$$
0.565774 + 0.824560i $$0.308577\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 159.000 + 159.000i 0.501577 + 0.501577i 0.911928 0.410351i $$-0.134594\pi$$
−0.410351 + 0.911928i $$0.634594\pi$$
$$318$$ 0 0
$$319$$ 80.0000i 0.250784i
$$320$$ 0 0
$$321$$ 242.000 0.753894
$$322$$ 0 0
$$323$$ 8.00000 8.00000i 0.0247678 0.0247678i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −136.000 136.000i −0.415902 0.415902i
$$328$$ 0 0
$$329$$ 546.000i 1.65957i
$$330$$ 0 0
$$331$$ 182.000 0.549849 0.274924 0.961466i $$-0.411347\pi$$
0.274924 + 0.961466i $$0.411347\pi$$
$$332$$ 0 0
$$333$$ 231.000 231.000i 0.693694 0.693694i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 447.000 + 447.000i 1.32641 + 1.32641i 0.908479 + 0.417930i $$0.137244\pi$$
0.417930 + 0.908479i $$0.362756\pi$$
$$338$$ 0 0
$$339$$ 254.000i 0.749263i
$$340$$ 0 0
$$341$$ −140.000 −0.410557
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 25.0000 + 25.0000i 0.0720461 + 0.0720461i 0.742212 0.670166i $$-0.233777\pi$$
−0.670166 + 0.742212i $$0.733777\pi$$
$$348$$ 0 0
$$349$$ 200.000i 0.573066i −0.958070 0.286533i $$-0.907497\pi$$
0.958070 0.286533i $$-0.0925028\pi$$
$$350$$ 0 0
$$351$$ −288.000 −0.820513
$$352$$ 0 0
$$353$$ −321.000 + 321.000i −0.909348 + 0.909348i −0.996220 0.0868711i $$-0.972313\pi$$
0.0868711 + 0.996220i $$0.472313\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 14.0000 + 14.0000i 0.0392157 + 0.0392157i
$$358$$ 0 0
$$359$$ 112.000i 0.311978i 0.987759 + 0.155989i $$0.0498564\pi$$
−0.987759 + 0.155989i $$0.950144\pi$$
$$360$$ 0 0
$$361$$ 297.000 0.822715
$$362$$ 0 0
$$363$$ −21.0000 + 21.0000i −0.0578512 + 0.0578512i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 377.000 + 377.000i 1.02725 + 1.02725i 0.999618 + 0.0276297i $$0.00879594\pi$$
0.0276297 + 0.999618i $$0.491204\pi$$
$$368$$ 0 0
$$369$$ 98.0000i 0.265583i
$$370$$ 0 0
$$371$$ −98.0000 −0.264151
$$372$$ 0 0
$$373$$ −217.000 + 217.000i −0.581769 + 0.581769i −0.935389 0.353620i $$-0.884951\pi$$
0.353620 + 0.935389i $$0.384951\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 72.0000 + 72.0000i 0.190981 + 0.190981i
$$378$$ 0 0
$$379$$ 56.0000i 0.147757i 0.997267 + 0.0738786i $$0.0235377\pi$$
−0.997267 + 0.0738786i $$0.976462\pi$$
$$380$$ 0 0
$$381$$ −14.0000 −0.0367454
$$382$$ 0 0
$$383$$ 57.0000 57.0000i 0.148825 0.148825i −0.628768 0.777593i $$-0.716440\pi$$
0.777593 + 0.628768i $$0.216440\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −105.000 105.000i −0.271318 0.271318i
$$388$$ 0 0
$$389$$ 312.000i 0.802057i −0.916066 0.401028i $$-0.868653\pi$$
0.916066 0.401028i $$-0.131347\pi$$
$$390$$ 0 0
$$391$$ 46.0000 0.117647
$$392$$ 0 0
$$393$$ 230.000 230.000i 0.585242 0.585242i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −193.000 193.000i −0.486146 0.486146i 0.420942 0.907088i $$-0.361700\pi$$
−0.907088 + 0.420942i $$0.861700\pi$$
$$398$$ 0 0
$$399$$ 112.000i 0.280702i
$$400$$ 0 0
$$401$$ −30.0000 −0.0748130 −0.0374065 0.999300i $$-0.511910\pi$$
−0.0374065 + 0.999300i $$0.511910\pi$$
$$402$$ 0 0
$$403$$ −126.000 + 126.000i −0.312655 + 0.312655i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 330.000 + 330.000i 0.810811 + 0.810811i
$$408$$ 0 0
$$409$$ 432.000i 1.05623i 0.849171 + 0.528117i $$0.177102\pi$$
−0.849171 + 0.528117i $$0.822898\pi$$
$$410$$ 0 0
$$411$$ 126.000 0.306569
$$412$$ 0 0
$$413$$ 392.000 392.000i 0.949153 0.949153i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 88.0000 + 88.0000i 0.211031 + 0.211031i
$$418$$ 0 0
$$419$$ 168.000i 0.400955i 0.979698 + 0.200477i $$0.0642493\pi$$
−0.979698 + 0.200477i $$0.935751\pi$$
$$420$$ 0 0
$$421$$ −454.000 −1.07838 −0.539192 0.842183i $$-0.681270\pi$$
−0.539192 + 0.842183i $$0.681270\pi$$
$$422$$ 0 0
$$423$$ 273.000 273.000i 0.645390 0.645390i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −294.000 294.000i −0.688525 0.688525i
$$428$$ 0 0
$$429$$ 180.000i 0.419580i
$$430$$ 0 0
$$431$$ 494.000 1.14617 0.573086 0.819495i $$-0.305746\pi$$
0.573086 + 0.819495i $$0.305746\pi$$
$$432$$ 0 0
$$433$$ 511.000 511.000i 1.18014 1.18014i 0.200431 0.979708i $$-0.435766\pi$$
0.979708 0.200431i $$-0.0642341\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −184.000 184.000i −0.421053 0.421053i
$$438$$ 0 0
$$439$$ 176.000i 0.400911i −0.979703 0.200456i $$-0.935758\pi$$
0.979703 0.200456i $$-0.0642422\pi$$
$$440$$ 0 0
$$441$$ −343.000 −0.777778
$$442$$ 0 0
$$443$$ 177.000 177.000i 0.399549 0.399549i −0.478525 0.878074i $$-0.658828\pi$$
0.878074 + 0.478525i $$0.158828\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 168.000 + 168.000i 0.375839 + 0.375839i
$$448$$ 0 0
$$449$$ 608.000i 1.35412i −0.735928 0.677060i $$-0.763254\pi$$
0.735928 0.677060i $$-0.236746\pi$$
$$450$$ 0 0
$$451$$ 140.000 0.310421
$$452$$ 0 0
$$453$$ −130.000 + 130.000i −0.286976 + 0.286976i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −609.000 609.000i −1.33260 1.33260i −0.903033 0.429571i $$-0.858665\pi$$
−0.429571 0.903033i $$-0.641335\pi$$
$$458$$ 0 0
$$459$$ 32.0000i 0.0697168i
$$460$$ 0 0
$$461$$ 490.000 1.06291 0.531453 0.847088i $$-0.321646\pi$$
0.531453 + 0.847088i $$0.321646\pi$$
$$462$$ 0 0
$$463$$ −7.00000 + 7.00000i −0.0151188 + 0.0151188i −0.714626 0.699507i $$-0.753403\pi$$
0.699507 + 0.714626i $$0.253403\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 25.0000 + 25.0000i 0.0535332 + 0.0535332i 0.733367 0.679833i $$-0.237948\pi$$
−0.679833 + 0.733367i $$0.737948\pi$$
$$468$$ 0 0
$$469$$ 98.0000i 0.208955i
$$470$$ 0 0
$$471$$ 126.000 0.267516
$$472$$ 0 0
$$473$$ 150.000 150.000i 0.317125 0.317125i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 49.0000 + 49.0000i 0.102725 + 0.102725i
$$478$$ 0 0
$$479$$ 128.000i 0.267223i 0.991034 + 0.133612i $$0.0426575\pi$$
−0.991034 + 0.133612i $$0.957343\pi$$
$$480$$ 0 0
$$481$$ 594.000 1.23493
$$482$$ 0 0
$$483$$ 322.000 322.000i 0.666667 0.666667i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 249.000 + 249.000i 0.511294 + 0.511294i 0.914923 0.403629i $$-0.132251\pi$$
−0.403629 + 0.914923i $$0.632251\pi$$
$$488$$ 0 0
$$489$$ 130.000i 0.265849i
$$490$$ 0 0
$$491$$ −650.000 −1.32383 −0.661914 0.749579i $$-0.730256\pi$$
−0.661914 + 0.749579i $$0.730256\pi$$
$$492$$ 0 0
$$493$$ −8.00000 + 8.00000i −0.0162272 + 0.0162272i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 686.000 + 686.000i 1.38028 + 1.38028i
$$498$$ 0 0
$$499$$ 632.000i 1.26653i −0.773934 0.633267i $$-0.781714\pi$$
0.773934 0.633267i $$-0.218286\pi$$
$$500$$ 0 0
$$501$$ −206.000 −0.411178
$$502$$ 0 0
$$503$$ −471.000 + 471.000i −0.936382 + 0.936382i −0.998094 0.0617123i $$-0.980344\pi$$
0.0617123 + 0.998094i $$0.480344\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 7.00000 + 7.00000i 0.0138067 + 0.0138067i
$$508$$ 0 0
$$509$$ 8.00000i 0.0157171i −0.999969 0.00785855i $$-0.997499\pi$$
0.999969 0.00785855i $$-0.00250148\pi$$
$$510$$ 0 0
$$511$$ 686.000 1.34247
$$512$$ 0 0
$$513$$ −128.000 + 128.000i −0.249513 + 0.249513i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 390.000 + 390.000i 0.754352 + 0.754352i
$$518$$ 0 0
$$519$$ 146.000i 0.281310i
$$520$$ 0 0
$$521$$ −366.000 −0.702495 −0.351248 0.936283i $$-0.614242\pi$$
−0.351248 + 0.936283i $$0.614242\pi$$
$$522$$ 0 0
$$523$$ 273.000 273.000i 0.521989 0.521989i −0.396183 0.918172i $$-0.629665\pi$$
0.918172 + 0.396183i $$0.129665\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −14.0000 14.0000i −0.0265655 0.0265655i
$$528$$ 0 0
$$529$$ 529.000i 1.00000i
$$530$$ 0 0
$$531$$ −392.000 −0.738230
$$532$$ 0 0
$$533$$ 126.000 126.000i 0.236398 0.236398i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −56.0000 56.0000i −0.104283 0.104283i
$$538$$ 0 0
$$539$$ 490.000i 0.909091i
$$540$$ 0 0
$$541$$ 394.000 0.728281 0.364140 0.931344i $$-0.381363\pi$$
0.364140 + 0.931344i $$0.381363\pi$$
$$542$$ 0 0
$$543$$ −70.0000 + 70.0000i −0.128913 + 0.128913i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −231.000 231.000i −0.422303 0.422303i 0.463693 0.885996i $$-0.346524\pi$$
−0.885996 + 0.463693i $$0.846524\pi$$
$$548$$ 0 0
$$549$$ 294.000i 0.535519i
$$550$$ 0 0
$$551$$ 64.0000 0.116152
$$552$$ 0 0
$$553$$ −672.000 + 672.000i −1.21519 + 1.21519i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 735.000 + 735.000i 1.31957 + 1.31957i 0.914116 + 0.405453i $$0.132886\pi$$
0.405453 + 0.914116i $$0.367114\pi$$
$$558$$ 0 0
$$559$$ 270.000i 0.483005i
$$560$$ 0 0
$$561$$ 20.0000 0.0356506
$$562$$ 0 0
$$563$$ 609.000 609.000i 1.08171 1.08171i 0.0853545 0.996351i $$-0.472798\pi$$
0.996351 0.0853545i $$-0.0272023\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 217.000 + 217.000i 0.382716 + 0.382716i
$$568$$ 0 0
$$569$$ 560.000i 0.984183i 0.870544 + 0.492091i $$0.163767\pi$$
−0.870544 + 0.492091i $$0.836233\pi$$
$$570$$ 0 0
$$571$$ −938.000 −1.64273 −0.821366 0.570401i $$-0.806788\pi$$
−0.821366 + 0.570401i $$0.806788\pi$$
$$572$$ 0 0
$$573$$ 142.000 142.000i 0.247818 0.247818i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −97.0000 97.0000i −0.168111 0.168111i 0.618038 0.786149i $$-0.287928\pi$$
−0.786149 + 0.618038i $$0.787928\pi$$
$$578$$ 0 0
$$579$$ 126.000i 0.217617i
$$580$$ 0 0
$$581$$ 882.000 1.51807
$$582$$ 0 0
$$583$$ −70.0000 + 70.0000i −0.120069 + 0.120069i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −39.0000 39.0000i −0.0664395 0.0664395i 0.673106 0.739546i $$-0.264960\pi$$
−0.739546 + 0.673106i $$0.764960\pi$$
$$588$$ 0 0
$$589$$ 112.000i 0.190153i
$$590$$ 0 0
$$591$$ 126.000 0.213198
$$592$$ 0 0
$$593$$ 479.000 479.000i 0.807757 0.807757i −0.176537 0.984294i $$-0.556489\pi$$
0.984294 + 0.176537i $$0.0564895\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −336.000 336.000i −0.562814 0.562814i
$$598$$ 0 0
$$599$$ 1040.00i 1.73623i 0.496366 + 0.868114i $$0.334668\pi$$
−0.496366 + 0.868114i $$0.665332\pi$$
$$600$$ 0 0
$$601$$ −430.000 −0.715474 −0.357737 0.933822i $$-0.616452\pi$$
−0.357737 + 0.933822i $$0.616452\pi$$
$$602$$ 0 0
$$603$$ 49.0000 49.0000i 0.0812604 0.0812604i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −423.000 423.000i −0.696870 0.696870i 0.266864 0.963734i $$-0.414012\pi$$
−0.963734 + 0.266864i $$0.914012\pi$$
$$608$$ 0 0
$$609$$ 112.000i 0.183908i
$$610$$ 0 0
$$611$$ 702.000 1.14894
$$612$$ 0 0
$$613$$ −249.000 + 249.000i −0.406199 + 0.406199i −0.880411 0.474212i $$-0.842733\pi$$
0.474212 + 0.880411i $$0.342733\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −321.000 321.000i −0.520259 0.520259i 0.397390 0.917650i $$-0.369916\pi$$
−0.917650 + 0.397390i $$0.869916\pi$$
$$618$$ 0 0
$$619$$ 600.000i 0.969305i 0.874707 + 0.484653i $$0.161054\pi$$
−0.874707 + 0.484653i $$0.838946\pi$$
$$620$$ 0 0
$$621$$ −736.000 −1.18519
$$622$$ 0 0
$$623$$ −784.000 + 784.000i −1.25843 + 1.25843i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −80.0000 80.0000i −0.127592 0.127592i
$$628$$ 0 0
$$629$$ 66.0000i 0.104928i
$$630$$ 0 0
$$631$$ 638.000 1.01109 0.505547 0.862799i $$-0.331291\pi$$
0.505547 + 0.862799i $$0.331291\pi$$
$$632$$ 0 0
$$633$$ −314.000 + 314.000i −0.496051 + 0.496051i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −441.000 441.000i −0.692308 0.692308i
$$638$$ 0 0
$$639$$ 686.000i 1.07355i
$$640$$ 0 0
$$641$$ 482.000 0.751950 0.375975 0.926630i $$-0.377308\pi$$
0.375975 + 0.926630i $$0.377308\pi$$
$$642$$ 0 0
$$643$$ 33.0000 33.0000i 0.0513219 0.0513219i −0.680980 0.732302i $$-0.738446\pi$$
0.732302 + 0.680980i $$0.238446\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −7.00000 7.00000i −0.0108192 0.0108192i 0.701677 0.712496i $$-0.252435\pi$$
−0.712496 + 0.701677i $$0.752435\pi$$
$$648$$ 0 0
$$649$$ 560.000i 0.862866i
$$650$$ 0 0
$$651$$ −196.000 −0.301075
$$652$$ 0 0
$$653$$ 471.000 471.000i 0.721286 0.721286i −0.247581 0.968867i $$-0.579636\pi$$
0.968867 + 0.247581i $$0.0796356\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −343.000 343.000i −0.522070 0.522070i
$$658$$ 0 0
$$659$$ 328.000i 0.497724i 0.968539 + 0.248862i $$0.0800565\pi$$
−0.968539 + 0.248862i $$0.919943\pi$$
$$660$$ 0 0
$$661$$ −742.000 −1.12254 −0.561271 0.827632i $$-0.689687\pi$$
−0.561271 + 0.827632i $$0.689687\pi$$
$$662$$ 0 0
$$663$$ 18.0000 18.0000i 0.0271493 0.0271493i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 184.000 + 184.000i 0.275862 + 0.275862i
$$668$$ 0 0
$$669$$ 270.000i 0.403587i
$$670$$ 0 0
$$671$$ −420.000 −0.625931
$$672$$ 0 0
$$673$$ 287.000 287.000i 0.426449 0.426449i −0.460968 0.887417i $$-0.652498\pi$$
0.887417 + 0.460968i $$0.152498\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −577.000 577.000i −0.852290 0.852290i 0.138125 0.990415i $$-0.455892\pi$$
−0.990415 + 0.138125i $$0.955892\pi$$
$$678$$ 0 0
$$679$$ 462.000i 0.680412i
$$680$$ 0 0
$$681$$ 562.000 0.825257
$$682$$ 0 0
$$683$$ −399.000 + 399.000i −0.584187 + 0.584187i −0.936051 0.351864i $$-0.885548\pi$$
0.351864 + 0.936051i $$0.385548\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 168.000 + 168.000i 0.244541 + 0.244541i
$$688$$ 0 0
$$689$$ 126.000i 0.182874i
$$690$$ 0 0
$$691$$ −378.000 −0.547033 −0.273517 0.961867i $$-0.588187\pi$$
−0.273517 + 0.961867i $$0.588187\pi$$
$$692$$ 0 0
$$693$$ −490.000 + 490.000i −0.707071 + 0.707071i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 14.0000 + 14.0000i 0.0200861 + 0.0200861i
$$698$$ 0 0
$$699$$ 546.000i 0.781116i
$$700$$ 0 0
$$701$$ −470.000 −0.670471 −0.335235 0.942134i $$-0.608816\pi$$
−0.335235 + 0.942134i $$0.608816\pi$$
$$702$$ 0 0
$$703$$ 264.000 264.000i 0.375533 0.375533i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −182.000 182.000i −0.257426 0.257426i
$$708$$ 0 0
$$709$$ 1192.00i 1.68124i 0.541624 + 0.840621i $$0.317810\pi$$
−0.541624 + 0.840621i $$0.682190\pi$$
$$710$$ 0 0
$$711$$ 672.000 0.945148
$$712$$ 0 0
$$713$$ −322.000 + 322.000i −0.451613 + 0.451613i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 288.000 + 288.000i 0.401674 + 0.401674i
$$718$$ 0 0
$$719$$ 608.000i 0.845619i 0.906219 + 0.422809i $$0.138956\pi$$
−0.906219 + 0.422809i $$0.861044\pi$$
$$720$$ 0 0
$$721$$ −1022.00 −1.41748
$$722$$ 0 0
$$723$$ −446.000 + 446.000i −0.616874 + 0.616874i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 441.000 + 441.000i 0.606602 + 0.606602i 0.942057 0.335454i $$-0.108890\pi$$
−0.335454 + 0.942057i $$0.608890\pi$$
$$728$$ 0 0
$$729$$ 71.0000i 0.0973937i
$$730$$ 0 0
$$731$$ 30.0000 0.0410397
$$732$$ 0 0
$$733$$ −361.000 + 361.000i −0.492497 + 0.492497i −0.909092 0.416595i $$-0.863223\pi$$
0.416595 + 0.909092i $$0.363223\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 70.0000 + 70.0000i 0.0949796 + 0.0949796i
$$738$$ 0 0
$$739$$ 920.000i 1.24493i −0.782649 0.622463i $$-0.786132\pi$$
0.782649 0.622463i $$-0.213868\pi$$
$$740$$ 0 0
$$741$$ −144.000 −0.194332
$$742$$ 0 0
$$743$$ −343.000 + 343.000i −0.461642 + 0.461642i −0.899193 0.437551i $$-0.855846\pi$$
0.437551 + 0.899193i $$0.355846\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −441.000 441.000i −0.590361 0.590361i
$$748$$ 0 0
$$749$$ 1694.00i 2.26168i
$$750$$ 0 0
$$751$$ −786.000 −1.04660 −0.523302 0.852147i $$-0.675300\pi$$
−0.523302 + 0.852147i $$0.675300\pi$$
$$752$$ 0 0
$$753$$ 150.000 150.000i 0.199203 0.199203i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 63.0000 + 63.0000i 0.0832232 + 0.0832232i 0.747493 0.664270i $$-0.231257\pi$$
−0.664270 + 0.747493i $$0.731257\pi$$
$$758$$ 0 0
$$759$$ 460.000i 0.606061i
$$760$$ 0 0
$$761$$ −398.000 −0.522996 −0.261498 0.965204i $$-0.584216\pi$$
−0.261498 + 0.965204i $$0.584216\pi$$
$$762$$ 0 0
$$763$$ −952.000 + 952.000i −1.24771 + 1.24771i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −504.000 504.000i −0.657106 0.657106i
$$768$$ 0 0
$$769$$ 704.000i 0.915475i 0.889087 + 0.457737i $$0.151340\pi$$
−0.889087 + 0.457737i $$0.848660\pi$$
$$770$$ 0 0
$$771$$ −322.000 −0.417639
$$772$$ 0 0
$$773$$ −825.000 + 825.000i −1.06727 + 1.06727i −0.0697026 + 0.997568i $$0.522205\pi$$
−0.997568 + 0.0697026i $$0.977795\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 462.000 + 462.000i 0.594595 + 0.594595i
$$778$$ 0 0
$$779$$ 112.000i 0.143774i
$$780$$ 0 0
$$781$$ 980.000 1.25480
$$782$$ 0 0
$$783$$ 128.000 128.000i 0.163474 0.163474i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −71.0000 71.0000i −0.0902160 0.0902160i 0.660559 0.750775i $$-0.270320\pi$$
−0.750775 + 0.660559i $$0.770320\pi$$
$$788$$ 0 0
$$789$$ 302.000i 0.382763i
$$790$$ 0 0
$$791$$ −1778.00 −2.24779
$$792$$ 0 0
$$793$$ −378.000 +