# Properties

 Label 400.3.p.g.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: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 50) 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.g.193.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(3.00000 - 3.00000i) q^{3} +(-3.00000 - 3.00000i) q^{7} -9.00000i q^{9} +O(q^{10})$$ $$q+(3.00000 - 3.00000i) q^{3} +(-3.00000 - 3.00000i) q^{7} -9.00000i q^{9} -12.0000 q^{11} +(12.0000 - 12.0000i) q^{13} +(-12.0000 - 12.0000i) q^{17} -20.0000i q^{19} -18.0000 q^{21} +(3.00000 - 3.00000i) q^{23} -30.0000i q^{29} +8.00000 q^{31} +(-36.0000 + 36.0000i) q^{33} +(48.0000 + 48.0000i) q^{37} -72.0000i q^{39} -48.0000 q^{41} +(-27.0000 + 27.0000i) q^{43} +(27.0000 + 27.0000i) q^{47} -31.0000i q^{49} -72.0000 q^{51} +(12.0000 - 12.0000i) q^{53} +(-60.0000 - 60.0000i) q^{57} +60.0000i q^{59} +32.0000 q^{61} +(-27.0000 + 27.0000i) q^{63} +(-3.00000 - 3.00000i) q^{67} -18.0000i q^{69} +48.0000 q^{71} +(12.0000 - 12.0000i) q^{73} +(36.0000 + 36.0000i) q^{77} -40.0000i q^{79} +81.0000 q^{81} +(93.0000 - 93.0000i) q^{83} +(-90.0000 - 90.0000i) q^{87} +30.0000i q^{89} -72.0000 q^{91} +(24.0000 - 24.0000i) q^{93} +(-12.0000 - 12.0000i) q^{97} +108.000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 6 q^{3} - 6 q^{7}+O(q^{10})$$ 2 * q + 6 * q^3 - 6 * q^7 $$2 q + 6 q^{3} - 6 q^{7} - 24 q^{11} + 24 q^{13} - 24 q^{17} - 36 q^{21} + 6 q^{23} + 16 q^{31} - 72 q^{33} + 96 q^{37} - 96 q^{41} - 54 q^{43} + 54 q^{47} - 144 q^{51} + 24 q^{53} - 120 q^{57} + 64 q^{61} - 54 q^{63} - 6 q^{67} + 96 q^{71} + 24 q^{73} + 72 q^{77} + 162 q^{81} + 186 q^{83} - 180 q^{87} - 144 q^{91} + 48 q^{93} - 24 q^{97}+O(q^{100})$$ 2 * q + 6 * q^3 - 6 * q^7 - 24 * q^11 + 24 * q^13 - 24 * q^17 - 36 * q^21 + 6 * q^23 + 16 * q^31 - 72 * q^33 + 96 * q^37 - 96 * q^41 - 54 * q^43 + 54 * q^47 - 144 * q^51 + 24 * q^53 - 120 * q^57 + 64 * q^61 - 54 * q^63 - 6 * q^67 + 96 * q^71 + 24 * q^73 + 72 * q^77 + 162 * q^81 + 186 * q^83 - 180 * q^87 - 144 * q^91 + 48 * q^93 - 24 * 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
$$3$$ 3.00000 3.00000i 1.00000 1.00000i 1.00000i $$-0.5\pi$$
1.00000 $$0$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −3.00000 3.00000i −0.428571 0.428571i 0.459570 0.888142i $$-0.348004\pi$$
−0.888142 + 0.459570i $$0.848004\pi$$
$$8$$ 0 0
$$9$$ 9.00000i 1.00000i
$$10$$ 0 0
$$11$$ −12.0000 −1.09091 −0.545455 0.838140i $$-0.683643\pi$$
−0.545455 + 0.838140i $$0.683643\pi$$
$$12$$ 0 0
$$13$$ 12.0000 12.0000i 0.923077 0.923077i −0.0741688 0.997246i $$-0.523630\pi$$
0.997246 + 0.0741688i $$0.0236304\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −12.0000 12.0000i −0.705882 0.705882i 0.259784 0.965667i $$-0.416349\pi$$
−0.965667 + 0.259784i $$0.916349\pi$$
$$18$$ 0 0
$$19$$ 20.0000i 1.05263i −0.850289 0.526316i $$-0.823573\pi$$
0.850289 0.526316i $$-0.176427\pi$$
$$20$$ 0 0
$$21$$ −18.0000 −0.857143
$$22$$ 0 0
$$23$$ 3.00000 3.00000i 0.130435 0.130435i −0.638875 0.769310i $$-0.720600\pi$$
0.769310 + 0.638875i $$0.220600\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 30.0000i 1.03448i −0.855840 0.517241i $$-0.826959\pi$$
0.855840 0.517241i $$-0.173041\pi$$
$$30$$ 0 0
$$31$$ 8.00000 0.258065 0.129032 0.991640i $$-0.458813\pi$$
0.129032 + 0.991640i $$0.458813\pi$$
$$32$$ 0 0
$$33$$ −36.0000 + 36.0000i −1.09091 + 1.09091i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 48.0000 + 48.0000i 1.29730 + 1.29730i 0.930171 + 0.367126i $$0.119658\pi$$
0.367126 + 0.930171i $$0.380342\pi$$
$$38$$ 0 0
$$39$$ 72.0000i 1.84615i
$$40$$ 0 0
$$41$$ −48.0000 −1.17073 −0.585366 0.810769i $$-0.699049\pi$$
−0.585366 + 0.810769i $$0.699049\pi$$
$$42$$ 0 0
$$43$$ −27.0000 + 27.0000i −0.627907 + 0.627907i −0.947541 0.319634i $$-0.896440\pi$$
0.319634 + 0.947541i $$0.396440\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 27.0000 + 27.0000i 0.574468 + 0.574468i 0.933374 0.358906i $$-0.116850\pi$$
−0.358906 + 0.933374i $$0.616850\pi$$
$$48$$ 0 0
$$49$$ 31.0000i 0.632653i
$$50$$ 0 0
$$51$$ −72.0000 −1.41176
$$52$$ 0 0
$$53$$ 12.0000 12.0000i 0.226415 0.226415i −0.584778 0.811193i $$-0.698818\pi$$
0.811193 + 0.584778i $$0.198818\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −60.0000 60.0000i −1.05263 1.05263i
$$58$$ 0 0
$$59$$ 60.0000i 1.01695i 0.861077 + 0.508475i $$0.169790\pi$$
−0.861077 + 0.508475i $$0.830210\pi$$
$$60$$ 0 0
$$61$$ 32.0000 0.524590 0.262295 0.964988i $$-0.415521\pi$$
0.262295 + 0.964988i $$0.415521\pi$$
$$62$$ 0 0
$$63$$ −27.0000 + 27.0000i −0.428571 + 0.428571i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −3.00000 3.00000i −0.0447761 0.0447761i 0.684364 0.729140i $$-0.260080\pi$$
−0.729140 + 0.684364i $$0.760080\pi$$
$$68$$ 0 0
$$69$$ 18.0000i 0.260870i
$$70$$ 0 0
$$71$$ 48.0000 0.676056 0.338028 0.941136i $$-0.390240\pi$$
0.338028 + 0.941136i $$0.390240\pi$$
$$72$$ 0 0
$$73$$ 12.0000 12.0000i 0.164384 0.164384i −0.620122 0.784505i $$-0.712917\pi$$
0.784505 + 0.620122i $$0.212917\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 36.0000 + 36.0000i 0.467532 + 0.467532i
$$78$$ 0 0
$$79$$ 40.0000i 0.506329i −0.967423 0.253165i $$-0.918529\pi$$
0.967423 0.253165i $$-0.0814714\pi$$
$$80$$ 0 0
$$81$$ 81.0000 1.00000
$$82$$ 0 0
$$83$$ 93.0000 93.0000i 1.12048 1.12048i 0.128813 0.991669i $$-0.458883\pi$$
0.991669 0.128813i $$-0.0411167\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −90.0000 90.0000i −1.03448 1.03448i
$$88$$ 0 0
$$89$$ 30.0000i 0.337079i 0.985695 + 0.168539i $$0.0539050\pi$$
−0.985695 + 0.168539i $$0.946095\pi$$
$$90$$ 0 0
$$91$$ −72.0000 −0.791209
$$92$$ 0 0
$$93$$ 24.0000 24.0000i 0.258065 0.258065i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −12.0000 12.0000i −0.123711 0.123711i 0.642540 0.766252i $$-0.277880\pi$$
−0.766252 + 0.642540i $$0.777880\pi$$
$$98$$ 0 0
$$99$$ 108.000i 1.09091i
$$100$$ 0 0
$$101$$ −78.0000 −0.772277 −0.386139 0.922441i $$-0.626191\pi$$
−0.386139 + 0.922441i $$0.626191\pi$$
$$102$$ 0 0
$$103$$ 93.0000 93.0000i 0.902913 0.902913i −0.0927745 0.995687i $$-0.529574\pi$$
0.995687 + 0.0927745i $$0.0295736\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 27.0000 + 27.0000i 0.252336 + 0.252336i 0.821928 0.569591i $$-0.192899\pi$$
−0.569591 + 0.821928i $$0.692899\pi$$
$$108$$ 0 0
$$109$$ 160.000i 1.46789i 0.679209 + 0.733945i $$0.262323\pi$$
−0.679209 + 0.733945i $$0.737677\pi$$
$$110$$ 0 0
$$111$$ 288.000 2.59459
$$112$$ 0 0
$$113$$ 72.0000 72.0000i 0.637168 0.637168i −0.312688 0.949856i $$-0.601229\pi$$
0.949856 + 0.312688i $$0.101229\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −108.000 108.000i −0.923077 0.923077i
$$118$$ 0 0
$$119$$ 72.0000i 0.605042i
$$120$$ 0 0
$$121$$ 23.0000 0.190083
$$122$$ 0 0
$$123$$ −144.000 + 144.000i −1.17073 + 1.17073i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 117.000 + 117.000i 0.921260 + 0.921260i 0.997119 0.0758587i $$-0.0241698\pi$$
−0.0758587 + 0.997119i $$0.524170\pi$$
$$128$$ 0 0
$$129$$ 162.000i 1.25581i
$$130$$ 0 0
$$131$$ −132.000 −1.00763 −0.503817 0.863811i $$-0.668071\pi$$
−0.503817 + 0.863811i $$0.668071\pi$$
$$132$$ 0 0
$$133$$ −60.0000 + 60.0000i −0.451128 + 0.451128i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 168.000 + 168.000i 1.22628 + 1.22628i 0.965362 + 0.260916i $$0.0840245\pi$$
0.260916 + 0.965362i $$0.415975\pi$$
$$138$$ 0 0
$$139$$ 100.000i 0.719424i 0.933063 + 0.359712i $$0.117125\pi$$
−0.933063 + 0.359712i $$0.882875\pi$$
$$140$$ 0 0
$$141$$ 162.000 1.14894
$$142$$ 0 0
$$143$$ −144.000 + 144.000i −1.00699 + 1.00699i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −93.0000 93.0000i −0.632653 0.632653i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 248.000 1.64238 0.821192 0.570652i $$-0.193309\pi$$
0.821192 + 0.570652i $$0.193309\pi$$
$$152$$ 0 0
$$153$$ −108.000 + 108.000i −0.705882 + 0.705882i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −72.0000 72.0000i −0.458599 0.458599i 0.439597 0.898195i $$-0.355121\pi$$
−0.898195 + 0.439597i $$0.855121\pi$$
$$158$$ 0 0
$$159$$ 72.0000i 0.452830i
$$160$$ 0 0
$$161$$ −18.0000 −0.111801
$$162$$ 0 0
$$163$$ 93.0000 93.0000i 0.570552 0.570552i −0.361731 0.932283i $$-0.617814\pi$$
0.932283 + 0.361731i $$0.117814\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −3.00000 3.00000i −0.0179641 0.0179641i 0.698068 0.716032i $$-0.254043\pi$$
−0.716032 + 0.698068i $$0.754043\pi$$
$$168$$ 0 0
$$169$$ 119.000i 0.704142i
$$170$$ 0 0
$$171$$ −180.000 −1.05263
$$172$$ 0 0
$$173$$ −168.000 + 168.000i −0.971098 + 0.971098i −0.999594 0.0284957i $$-0.990928\pi$$
0.0284957 + 0.999594i $$0.490928\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 180.000 + 180.000i 1.01695 + 1.01695i
$$178$$ 0 0
$$179$$ 300.000i 1.67598i 0.545687 + 0.837989i $$0.316269\pi$$
−0.545687 + 0.837989i $$0.683731\pi$$
$$180$$ 0 0
$$181$$ 142.000 0.784530 0.392265 0.919852i $$-0.371692\pi$$
0.392265 + 0.919852i $$0.371692\pi$$
$$182$$ 0 0
$$183$$ 96.0000 96.0000i 0.524590 0.524590i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 144.000 + 144.000i 0.770053 + 0.770053i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −192.000 −1.00524 −0.502618 0.864509i $$-0.667630\pi$$
−0.502618 + 0.864509i $$0.667630\pi$$
$$192$$ 0 0
$$193$$ 132.000 132.000i 0.683938 0.683938i −0.276947 0.960885i $$-0.589323\pi$$
0.960885 + 0.276947i $$0.0893227\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −132.000 132.000i −0.670051 0.670051i 0.287677 0.957728i $$-0.407117\pi$$
−0.957728 + 0.287677i $$0.907117\pi$$
$$198$$ 0 0
$$199$$ 160.000i 0.804020i −0.915635 0.402010i $$-0.868312\pi$$
0.915635 0.402010i $$-0.131688\pi$$
$$200$$ 0 0
$$201$$ −18.0000 −0.0895522
$$202$$ 0 0
$$203$$ −90.0000 + 90.0000i −0.443350 + 0.443350i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −27.0000 27.0000i −0.130435 0.130435i
$$208$$ 0 0
$$209$$ 240.000i 1.14833i
$$210$$ 0 0
$$211$$ 28.0000 0.132701 0.0663507 0.997796i $$-0.478864\pi$$
0.0663507 + 0.997796i $$0.478864\pi$$
$$212$$ 0 0
$$213$$ 144.000 144.000i 0.676056 0.676056i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −24.0000 24.0000i −0.110599 0.110599i
$$218$$ 0 0
$$219$$ 72.0000i 0.328767i
$$220$$ 0 0
$$221$$ −288.000 −1.30317
$$222$$ 0 0
$$223$$ −117.000 + 117.000i −0.524664 + 0.524664i −0.918976 0.394313i $$-0.870983\pi$$
0.394313 + 0.918976i $$0.370983\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −93.0000 93.0000i −0.409692 0.409692i 0.471939 0.881631i $$-0.343554\pi$$
−0.881631 + 0.471939i $$0.843554\pi$$
$$228$$ 0 0
$$229$$ 370.000i 1.61572i −0.589374 0.807860i $$-0.700626\pi$$
0.589374 0.807860i $$-0.299374\pi$$
$$230$$ 0 0
$$231$$ 216.000 0.935065
$$232$$ 0 0
$$233$$ 252.000 252.000i 1.08155 1.08155i 0.0851794 0.996366i $$-0.472854\pi$$
0.996366 0.0851794i $$-0.0271464\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −120.000 120.000i −0.506329 0.506329i
$$238$$ 0 0
$$239$$ 360.000i 1.50628i −0.657862 0.753138i $$-0.728539\pi$$
0.657862 0.753138i $$-0.271461\pi$$
$$240$$ 0 0
$$241$$ 32.0000 0.132780 0.0663900 0.997794i $$-0.478852\pi$$
0.0663900 + 0.997794i $$0.478852\pi$$
$$242$$ 0 0
$$243$$ 243.000 243.000i 1.00000 1.00000i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −240.000 240.000i −0.971660 0.971660i
$$248$$ 0 0
$$249$$ 558.000i 2.24096i
$$250$$ 0 0
$$251$$ −252.000 −1.00398 −0.501992 0.864872i $$-0.667399\pi$$
−0.501992 + 0.864872i $$0.667399\pi$$
$$252$$ 0 0
$$253$$ −36.0000 + 36.0000i −0.142292 + 0.142292i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −192.000 192.000i −0.747082 0.747082i 0.226848 0.973930i $$-0.427158\pi$$
−0.973930 + 0.226848i $$0.927158\pi$$
$$258$$ 0 0
$$259$$ 288.000i 1.11197i
$$260$$ 0 0
$$261$$ −270.000 −1.03448
$$262$$ 0 0
$$263$$ 333.000 333.000i 1.26616 1.26616i 0.318104 0.948056i $$-0.396954\pi$$
0.948056 0.318104i $$-0.103046\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 90.0000 + 90.0000i 0.337079 + 0.337079i
$$268$$ 0 0
$$269$$ 480.000i 1.78439i 0.451654 + 0.892193i $$0.350834\pi$$
−0.451654 + 0.892193i $$0.649166\pi$$
$$270$$ 0 0
$$271$$ 88.0000 0.324723 0.162362 0.986731i $$-0.448089\pi$$
0.162362 + 0.986731i $$0.448089\pi$$
$$272$$ 0 0
$$273$$ −216.000 + 216.000i −0.791209 + 0.791209i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 288.000 + 288.000i 1.03971 + 1.03971i 0.999178 + 0.0405330i $$0.0129056\pi$$
0.0405330 + 0.999178i $$0.487094\pi$$
$$278$$ 0 0
$$279$$ 72.0000i 0.258065i
$$280$$ 0 0
$$281$$ −288.000 −1.02491 −0.512456 0.858714i $$-0.671264\pi$$
−0.512456 + 0.858714i $$0.671264\pi$$
$$282$$ 0 0
$$283$$ −117.000 + 117.000i −0.413428 + 0.413428i −0.882931 0.469503i $$-0.844433\pi$$
0.469503 + 0.882931i $$0.344433\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 144.000 + 144.000i 0.501742 + 0.501742i
$$288$$ 0 0
$$289$$ 1.00000i 0.00346021i
$$290$$ 0 0
$$291$$ −72.0000 −0.247423
$$292$$ 0 0
$$293$$ −168.000 + 168.000i −0.573379 + 0.573379i −0.933071 0.359692i $$-0.882882\pi$$
0.359692 + 0.933071i $$0.382882\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 72.0000i 0.240803i
$$300$$ 0 0
$$301$$ 162.000 0.538206
$$302$$ 0 0
$$303$$ −234.000 + 234.000i −0.772277 + 0.772277i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −243.000 243.000i −0.791531 0.791531i 0.190212 0.981743i $$-0.439082\pi$$
−0.981743 + 0.190212i $$0.939082\pi$$
$$308$$ 0 0
$$309$$ 558.000i 1.80583i
$$310$$ 0 0
$$311$$ −552.000 −1.77492 −0.887460 0.460885i $$-0.847532\pi$$
−0.887460 + 0.460885i $$0.847532\pi$$
$$312$$ 0 0
$$313$$ −48.0000 + 48.0000i −0.153355 + 0.153355i −0.779614 0.626260i $$-0.784585\pi$$
0.626260 + 0.779614i $$0.284585\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 228.000 + 228.000i 0.719243 + 0.719243i 0.968450 0.249207i $$-0.0801700\pi$$
−0.249207 + 0.968450i $$0.580170\pi$$
$$318$$ 0 0
$$319$$ 360.000i 1.12853i
$$320$$ 0 0
$$321$$ 162.000 0.504673
$$322$$ 0 0
$$323$$ −240.000 + 240.000i −0.743034 + 0.743034i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 480.000 + 480.000i 1.46789 + 1.46789i
$$328$$ 0 0
$$329$$ 162.000i 0.492401i
$$330$$ 0 0
$$331$$ 148.000 0.447130 0.223565 0.974689i $$-0.428231\pi$$
0.223565 + 0.974689i $$0.428231\pi$$
$$332$$ 0 0
$$333$$ 432.000 432.000i 1.29730 1.29730i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −192.000 192.000i −0.569733 0.569733i 0.362321 0.932054i $$-0.381985\pi$$
−0.932054 + 0.362321i $$0.881985\pi$$
$$338$$ 0 0
$$339$$ 432.000i 1.27434i
$$340$$ 0 0
$$341$$ −96.0000 −0.281525
$$342$$ 0 0
$$343$$ −240.000 + 240.000i −0.699708 + 0.699708i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 117.000 + 117.000i 0.337176 + 0.337176i 0.855303 0.518128i $$-0.173371\pi$$
−0.518128 + 0.855303i $$0.673371\pi$$
$$348$$ 0 0
$$349$$ 130.000i 0.372493i −0.982503 0.186246i $$-0.940368\pi$$
0.982503 0.186246i $$-0.0596323\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −288.000 + 288.000i −0.815864 + 0.815864i −0.985506 0.169642i $$-0.945739\pi$$
0.169642 + 0.985506i $$0.445739\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 216.000 + 216.000i 0.605042 + 0.605042i
$$358$$ 0 0
$$359$$ 120.000i 0.334262i 0.985935 + 0.167131i $$0.0534503\pi$$
−0.985935 + 0.167131i $$0.946550\pi$$
$$360$$ 0 0
$$361$$ −39.0000 −0.108033
$$362$$ 0 0
$$363$$ 69.0000 69.0000i 0.190083 0.190083i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −213.000 213.000i −0.580381 0.580381i 0.354627 0.935008i $$-0.384608\pi$$
−0.935008 + 0.354627i $$0.884608\pi$$
$$368$$ 0 0
$$369$$ 432.000i 1.17073i
$$370$$ 0 0
$$371$$ −72.0000 −0.194070
$$372$$ 0 0
$$373$$ −168.000 + 168.000i −0.450402 + 0.450402i −0.895488 0.445086i $$-0.853173\pi$$
0.445086 + 0.895488i $$0.353173\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −360.000 360.000i −0.954907 0.954907i
$$378$$ 0 0
$$379$$ 20.0000i 0.0527704i −0.999652 0.0263852i $$-0.991600\pi$$
0.999652 0.0263852i $$-0.00839965\pi$$
$$380$$ 0 0
$$381$$ 702.000 1.84252
$$382$$ 0 0
$$383$$ 123.000 123.000i 0.321149 0.321149i −0.528059 0.849208i $$-0.677080\pi$$
0.849208 + 0.528059i $$0.177080\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 243.000 + 243.000i 0.627907 + 0.627907i
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ −72.0000 −0.184143
$$392$$ 0 0
$$393$$ −396.000 + 396.000i −1.00763 + 1.00763i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 108.000 + 108.000i 0.272040 + 0.272040i 0.829921 0.557881i $$-0.188385\pi$$
−0.557881 + 0.829921i $$0.688385\pi$$
$$398$$ 0 0
$$399$$ 360.000i 0.902256i
$$400$$ 0 0
$$401$$ −18.0000 −0.0448878 −0.0224439 0.999748i $$-0.507145\pi$$
−0.0224439 + 0.999748i $$0.507145\pi$$
$$402$$ 0 0
$$403$$ 96.0000 96.0000i 0.238213 0.238213i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −576.000 576.000i −1.41523 1.41523i
$$408$$ 0 0
$$409$$ 80.0000i 0.195599i 0.995206 + 0.0977995i $$0.0311804\pi$$
−0.995206 + 0.0977995i $$0.968820\pi$$
$$410$$ 0 0
$$411$$ 1008.00 2.45255
$$412$$ 0 0
$$413$$ 180.000 180.000i 0.435835 0.435835i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 300.000 + 300.000i 0.719424 + 0.719424i
$$418$$ 0 0
$$419$$ 540.000i 1.28878i 0.764696 + 0.644391i $$0.222889\pi$$
−0.764696 + 0.644391i $$0.777111\pi$$
$$420$$ 0 0
$$421$$ −608.000 −1.44418 −0.722090 0.691799i $$-0.756818\pi$$
−0.722090 + 0.691799i $$0.756818\pi$$
$$422$$ 0 0
$$423$$ 243.000 243.000i 0.574468 0.574468i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −96.0000 96.0000i −0.224824 0.224824i
$$428$$ 0 0
$$429$$ 864.000i 2.01399i
$$430$$ 0 0
$$431$$ −312.000 −0.723898 −0.361949 0.932198i $$-0.617889\pi$$
−0.361949 + 0.932198i $$0.617889\pi$$
$$432$$ 0 0
$$433$$ 252.000 252.000i 0.581986 0.581986i −0.353463 0.935449i $$-0.614996\pi$$
0.935449 + 0.353463i $$0.114996\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −60.0000 60.0000i −0.137300 0.137300i
$$438$$ 0 0
$$439$$ 40.0000i 0.0911162i −0.998962 0.0455581i $$-0.985493\pi$$
0.998962 0.0455581i $$-0.0145066\pi$$
$$440$$ 0 0
$$441$$ −279.000 −0.632653
$$442$$ 0 0
$$443$$ 213.000 213.000i 0.480813 0.480813i −0.424578 0.905391i $$-0.639578\pi$$
0.905391 + 0.424578i $$0.139578\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 480.000i 1.06904i 0.845155 + 0.534521i $$0.179508\pi$$
−0.845155 + 0.534521i $$0.820492\pi$$
$$450$$ 0 0
$$451$$ 576.000 1.27716
$$452$$ 0 0
$$453$$ 744.000 744.000i 1.64238 1.64238i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −432.000 432.000i −0.945295 0.945295i 0.0532840 0.998579i $$-0.483031\pi$$
−0.998579 + 0.0532840i $$0.983031\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 222.000 0.481562 0.240781 0.970579i $$-0.422596\pi$$
0.240781 + 0.970579i $$0.422596\pi$$
$$462$$ 0 0
$$463$$ 213.000 213.000i 0.460043 0.460043i −0.438626 0.898670i $$-0.644535\pi$$
0.898670 + 0.438626i $$0.144535\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −3.00000 3.00000i −0.00642398 0.00642398i 0.703887 0.710311i $$-0.251446\pi$$
−0.710311 + 0.703887i $$0.751446\pi$$
$$468$$ 0 0
$$469$$ 18.0000i 0.0383795i
$$470$$ 0 0
$$471$$ −432.000 −0.917197
$$472$$ 0 0
$$473$$ 324.000 324.000i 0.684989 0.684989i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −108.000 108.000i −0.226415 0.226415i
$$478$$ 0 0
$$479$$ 240.000i 0.501044i 0.968111 + 0.250522i $$0.0806022\pi$$
−0.968111 + 0.250522i $$0.919398\pi$$
$$480$$ 0 0
$$481$$ 1152.00 2.39501
$$482$$ 0 0
$$483$$ −54.0000 + 54.0000i −0.111801 + 0.111801i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 627.000 + 627.000i 1.28747 + 1.28747i 0.936316 + 0.351158i $$0.114212\pi$$
0.351158 + 0.936316i $$0.385788\pi$$
$$488$$ 0 0
$$489$$ 558.000i 1.14110i
$$490$$ 0 0
$$491$$ 588.000 1.19756 0.598778 0.800915i $$-0.295653\pi$$
0.598778 + 0.800915i $$0.295653\pi$$
$$492$$ 0 0
$$493$$ −360.000 + 360.000i −0.730223 + 0.730223i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −144.000 144.000i −0.289738 0.289738i
$$498$$ 0 0
$$499$$ 460.000i 0.921844i −0.887441 0.460922i $$-0.847519\pi$$
0.887441 0.460922i $$-0.152481\pi$$
$$500$$ 0 0
$$501$$ −18.0000 −0.0359281
$$502$$ 0 0
$$503$$ −627.000 + 627.000i −1.24652 + 1.24652i −0.289275 + 0.957246i $$0.593414\pi$$
−0.957246 + 0.289275i $$0.906586\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −357.000 357.000i −0.704142 0.704142i
$$508$$ 0 0
$$509$$ 450.000i 0.884086i 0.896994 + 0.442043i $$0.145746\pi$$
−0.896994 + 0.442043i $$0.854254\pi$$
$$510$$ 0 0
$$511$$ −72.0000 −0.140900
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −324.000 324.000i −0.626692 0.626692i
$$518$$ 0 0
$$519$$ 1008.00i 1.94220i
$$520$$ 0 0
$$521$$ −558.000 −1.07102 −0.535509 0.844530i $$-0.679880\pi$$
−0.535509 + 0.844530i $$0.679880\pi$$
$$522$$ 0 0
$$523$$ 123.000 123.000i 0.235182 0.235182i −0.579670 0.814851i $$-0.696818\pi$$
0.814851 + 0.579670i $$0.196818\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −96.0000 96.0000i −0.182163 0.182163i
$$528$$ 0 0
$$529$$ 511.000i 0.965974i
$$530$$ 0 0
$$531$$ 540.000 1.01695
$$532$$ 0 0
$$533$$ −576.000 + 576.000i −1.08068 + 1.08068i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 900.000 + 900.000i 1.67598 + 1.67598i
$$538$$ 0 0
$$539$$ 372.000i 0.690167i
$$540$$ 0 0
$$541$$ 542.000 1.00185 0.500924 0.865491i $$-0.332994\pi$$
0.500924 + 0.865491i $$0.332994\pi$$
$$542$$ 0 0
$$543$$ 426.000 426.000i 0.784530 0.784530i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 147.000 + 147.000i 0.268739 + 0.268739i 0.828592 0.559853i $$-0.189142\pi$$
−0.559853 + 0.828592i $$0.689142\pi$$
$$548$$ 0 0
$$549$$ 288.000i 0.524590i
$$550$$ 0 0
$$551$$ −600.000 −1.08893
$$552$$ 0 0
$$553$$ −120.000 + 120.000i −0.216998 + 0.216998i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 288.000 + 288.000i 0.517056 + 0.517056i 0.916679 0.399624i $$-0.130859\pi$$
−0.399624 + 0.916679i $$0.630859\pi$$
$$558$$ 0 0
$$559$$ 648.000i 1.15921i
$$560$$ 0 0
$$561$$ 864.000 1.54011
$$562$$ 0 0
$$563$$ −477.000 + 477.000i −0.847247 + 0.847247i −0.989789 0.142542i $$-0.954472\pi$$
0.142542 + 0.989789i $$0.454472\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −243.000 243.000i −0.428571 0.428571i
$$568$$ 0 0
$$569$$ 240.000i 0.421793i −0.977508 0.210896i $$-0.932362\pi$$
0.977508 0.210896i $$-0.0676382\pi$$
$$570$$ 0 0
$$571$$ −692.000 −1.21191 −0.605954 0.795499i $$-0.707209\pi$$
−0.605954 + 0.795499i $$0.707209\pi$$
$$572$$ 0 0
$$573$$ −576.000 + 576.000i −1.00524 + 1.00524i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 168.000 + 168.000i 0.291161 + 0.291161i 0.837539 0.546378i $$-0.183994\pi$$
−0.546378 + 0.837539i $$0.683994\pi$$
$$578$$ 0 0
$$579$$ 792.000i 1.36788i
$$580$$ 0 0
$$581$$ −558.000 −0.960413
$$582$$ 0 0
$$583$$ −144.000 + 144.000i −0.246998 + 0.246998i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −213.000 213.000i −0.362862 0.362862i 0.502004 0.864866i $$-0.332596\pi$$
−0.864866 + 0.502004i $$0.832596\pi$$
$$588$$ 0 0
$$589$$ 160.000i 0.271647i
$$590$$ 0 0
$$591$$ −792.000 −1.34010
$$592$$ 0 0
$$593$$ 312.000 312.000i 0.526138 0.526138i −0.393280 0.919419i $$-0.628660\pi$$
0.919419 + 0.393280i $$0.128660\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −480.000 480.000i −0.804020 0.804020i
$$598$$ 0 0
$$599$$ 240.000i 0.400668i −0.979728 0.200334i $$-0.935797\pi$$
0.979728 0.200334i $$-0.0642027\pi$$
$$600$$ 0 0
$$601$$ −608.000 −1.01165 −0.505824 0.862637i $$-0.668811\pi$$
−0.505824 + 0.862637i $$0.668811\pi$$
$$602$$ 0 0
$$603$$ −27.0000 + 27.0000i −0.0447761 + 0.0447761i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 267.000 + 267.000i 0.439868 + 0.439868i 0.891968 0.452099i $$-0.149325\pi$$
−0.452099 + 0.891968i $$0.649325\pi$$
$$608$$ 0 0
$$609$$ 540.000i 0.886700i
$$610$$ 0 0
$$611$$ 648.000 1.06056
$$612$$ 0 0
$$613$$ −228.000 + 228.000i −0.371941 + 0.371941i −0.868184 0.496243i $$-0.834713\pi$$
0.496243 + 0.868184i $$0.334713\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 348.000 + 348.000i 0.564019 + 0.564019i 0.930447 0.366427i $$-0.119419\pi$$
−0.366427 + 0.930447i $$0.619419\pi$$
$$618$$ 0 0
$$619$$ 940.000i 1.51858i −0.650753 0.759289i $$-0.725547\pi$$
0.650753 0.759289i $$-0.274453\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 90.0000 90.0000i 0.144462 0.144462i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 720.000 + 720.000i 1.14833 + 1.14833i
$$628$$ 0 0
$$629$$ 1152.00i 1.83148i
$$630$$ 0 0
$$631$$ 808.000 1.28051 0.640254 0.768164i $$-0.278829\pi$$
0.640254 + 0.768164i $$0.278829\pi$$
$$632$$ 0 0
$$633$$ 84.0000 84.0000i 0.132701 0.132701i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −372.000 372.000i −0.583987 0.583987i
$$638$$ 0 0
$$639$$ 432.000i 0.676056i
$$640$$ 0 0
$$641$$ −768.000 −1.19813 −0.599064 0.800701i $$-0.704460\pi$$
−0.599064 + 0.800701i $$0.704460\pi$$
$$642$$ 0 0
$$643$$ −477.000 + 477.000i −0.741835 + 0.741835i −0.972931 0.231096i $$-0.925769\pi$$
0.231096 + 0.972931i $$0.425769\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 627.000 + 627.000i 0.969088 + 0.969088i 0.999536 0.0304482i $$-0.00969348\pi$$
−0.0304482 + 0.999536i $$0.509693\pi$$
$$648$$ 0 0
$$649$$ 720.000i 1.10940i
$$650$$ 0 0
$$651$$ −144.000 −0.221198
$$652$$ 0 0
$$653$$ 12.0000 12.0000i 0.0183767 0.0183767i −0.697859 0.716235i $$-0.745864\pi$$
0.716235 + 0.697859i $$0.245864\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −108.000 108.000i −0.164384 0.164384i
$$658$$ 0 0
$$659$$ 540.000i 0.819423i 0.912215 + 0.409712i $$0.134371\pi$$
−0.912215 + 0.409712i $$0.865629\pi$$
$$660$$ 0 0
$$661$$ 352.000 0.532526 0.266263 0.963900i $$-0.414211\pi$$
0.266263 + 0.963900i $$0.414211\pi$$
$$662$$ 0 0
$$663$$ −864.000 + 864.000i −1.30317 + 1.30317i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −90.0000 90.0000i −0.134933 0.134933i
$$668$$ 0 0
$$669$$ 702.000i 1.04933i
$$670$$ 0 0
$$671$$ −384.000 −0.572280
$$672$$ 0 0
$$673$$ 732.000 732.000i 1.08767 1.08767i 0.0918988 0.995768i $$-0.470706\pi$$
0.995768 0.0918988i $$-0.0292936\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 108.000 + 108.000i 0.159527 + 0.159527i 0.782357 0.622830i $$-0.214017\pi$$
−0.622830 + 0.782357i $$0.714017\pi$$
$$678$$ 0 0
$$679$$ 72.0000i 0.106038i
$$680$$ 0 0
$$681$$ −558.000 −0.819383
$$682$$ 0 0
$$683$$ 933.000 933.000i 1.36603 1.36603i 0.500016 0.866016i $$-0.333327\pi$$
0.866016 0.500016i $$-0.166673\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −1110.00 1110.00i −1.61572 1.61572i
$$688$$ 0 0
$$689$$ 288.000i 0.417997i
$$690$$ 0 0
$$691$$ 68.0000 0.0984081 0.0492041 0.998789i $$-0.484332\pi$$
0.0492041 + 0.998789i $$0.484332\pi$$
$$692$$ 0 0
$$693$$ 324.000 324.000i 0.467532 0.467532i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 576.000 + 576.000i 0.826399 + 0.826399i
$$698$$ 0 0
$$699$$ 1512.00i 2.16309i
$$700$$ 0 0
$$701$$ 192.000 0.273894 0.136947 0.990578i $$-0.456271\pi$$
0.136947 + 0.990578i $$0.456271\pi$$
$$702$$ 0 0
$$703$$ 960.000 960.000i 1.36558 1.36558i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 234.000 + 234.000i 0.330976 + 0.330976i
$$708$$ 0 0
$$709$$ 50.0000i 0.0705219i 0.999378 + 0.0352609i $$0.0112262\pi$$
−0.999378 + 0.0352609i $$0.988774\pi$$
$$710$$ 0 0
$$711$$ −360.000 −0.506329
$$712$$ 0 0
$$713$$ 24.0000 24.0000i 0.0336606 0.0336606i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −1080.00 1080.00i −1.50628 1.50628i
$$718$$ 0 0
$$719$$ 840.000i 1.16829i −0.811650 0.584145i $$-0.801430\pi$$
0.811650 0.584145i $$-0.198570\pi$$
$$720$$ 0 0
$$721$$ −558.000 −0.773925
$$722$$ 0 0
$$723$$ 96.0000 96.0000i 0.132780 0.132780i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −963.000 963.000i −1.32462 1.32462i −0.909989 0.414633i $$-0.863910\pi$$
−0.414633 0.909989i $$-0.636090\pi$$
$$728$$ 0 0
$$729$$ 729.000i 1.00000i
$$730$$ 0 0
$$731$$ 648.000 0.886457
$$732$$ 0 0
$$733$$ 72.0000 72.0000i 0.0982265 0.0982265i −0.656286 0.754512i $$-0.727873\pi$$
0.754512 + 0.656286i $$0.227873\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 36.0000 + 36.0000i 0.0488467 + 0.0488467i
$$738$$ 0 0
$$739$$ 20.0000i 0.0270636i −0.999908 0.0135318i $$-0.995693\pi$$
0.999908 0.0135318i $$-0.00430744\pi$$
$$740$$ 0 0
$$741$$ −1440.00 −1.94332
$$742$$ 0 0
$$743$$ 243.000 243.000i 0.327052 0.327052i −0.524412 0.851465i $$-0.675715\pi$$
0.851465 + 0.524412i $$0.175715\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −837.000 837.000i −1.12048 1.12048i
$$748$$ 0 0
$$749$$ 162.000i 0.216288i
$$750$$ 0 0
$$751$$ −1072.00 −1.42743 −0.713715 0.700436i $$-0.752989\pi$$
−0.713715 + 0.700436i $$0.752989\pi$$
$$752$$ 0 0
$$753$$ −756.000 + 756.000i −1.00398 + 1.00398i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 408.000 + 408.000i 0.538970 + 0.538970i 0.923226 0.384257i $$-0.125542\pi$$
−0.384257 + 0.923226i $$0.625542\pi$$
$$758$$ 0 0
$$759$$ 216.000i 0.284585i
$$760$$ 0 0
$$761$$ 1362.00 1.78975 0.894875 0.446317i $$-0.147264\pi$$
0.894875 + 0.446317i $$0.147264\pi$$
$$762$$ 0 0
$$763$$ 480.000 480.000i 0.629096 0.629096i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 720.000 + 720.000i 0.938722 + 0.938722i
$$768$$ 0 0
$$769$$ 370.000i 0.481144i 0.970631 + 0.240572i $$0.0773351\pi$$
−0.970631 + 0.240572i $$0.922665\pi$$
$$770$$ 0 0
$$771$$ −1152.00 −1.49416
$$772$$ 0 0
$$773$$ 132.000 132.000i 0.170763 0.170763i −0.616551 0.787315i $$-0.711471\pi$$
0.787315 + 0.616551i $$0.211471\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −864.000 864.000i −1.11197 1.11197i
$$778$$ 0 0
$$779$$ 960.000i 1.23235i
$$780$$ 0 0
$$781$$ −576.000 −0.737516
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −93.0000 93.0000i −0.118170 0.118170i 0.645549 0.763719i $$-0.276629\pi$$
−0.763719 + 0.645549i $$0.776629\pi$$
$$788$$ 0 0
$$789$$ 1998.00i 2.53232i
$$790$$ 0 0
$$791$$ −432.000 −0.546144
$$792$$ 0 0
$$793$$ 384.000 384.000i