# Properties

 Label 784.2.i.g.753.1 Level $784$ Weight $2$ Character 784.753 Analytic conductor $6.260$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(177,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("784.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$784 = 2^{4} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 784.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$6.26027151847$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 56) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 753.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 784.753 Dual form 784.2.i.g.177.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.73205i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(1.00000 + 1.73205i) q^{5} +(1.50000 + 2.59808i) q^{9} +(-2.00000 + 3.46410i) q^{11} -2.00000 q^{13} +(-3.00000 + 5.19615i) q^{17} +(-4.00000 - 6.92820i) q^{19} +(0.500000 - 0.866025i) q^{25} +6.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(1.00000 + 1.73205i) q^{37} -2.00000 q^{41} +4.00000 q^{43} +(-3.00000 + 5.19615i) q^{45} +(4.00000 + 6.92820i) q^{47} +(-3.00000 + 5.19615i) q^{53} -8.00000 q^{55} +(-3.00000 - 5.19615i) q^{61} +(-2.00000 - 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +8.00000 q^{71} +(5.00000 - 8.66025i) q^{73} +(8.00000 + 13.8564i) q^{79} +(-4.50000 + 7.79423i) q^{81} +8.00000 q^{83} -12.0000 q^{85} +(-3.00000 - 5.19615i) q^{89} +(8.00000 - 13.8564i) q^{95} +6.00000 q^{97} -12.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{5} + 3 q^{9}+O(q^{10})$$ 2 * q + 2 * q^5 + 3 * q^9 $$2 q + 2 q^{5} + 3 q^{9} - 4 q^{11} - 4 q^{13} - 6 q^{17} - 8 q^{19} + q^{25} + 12 q^{29} - 8 q^{31} + 2 q^{37} - 4 q^{41} + 8 q^{43} - 6 q^{45} + 8 q^{47} - 6 q^{53} - 16 q^{55} - 6 q^{61} - 4 q^{65} - 4 q^{67} + 16 q^{71} + 10 q^{73} + 16 q^{79} - 9 q^{81} + 16 q^{83} - 24 q^{85} - 6 q^{89} + 16 q^{95} + 12 q^{97} - 24 q^{99}+O(q^{100})$$ 2 * q + 2 * q^5 + 3 * q^9 - 4 * q^11 - 4 * q^13 - 6 * q^17 - 8 * q^19 + q^25 + 12 * q^29 - 8 * q^31 + 2 * q^37 - 4 * q^41 + 8 * q^43 - 6 * q^45 + 8 * q^47 - 6 * q^53 - 16 * q^55 - 6 * q^61 - 4 * q^65 - 4 * q^67 + 16 * q^71 + 10 * q^73 + 16 * q^79 - 9 * q^81 + 16 * q^83 - 24 * q^85 - 6 * q^89 + 16 * q^95 + 12 * q^97 - 24 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$687$$ $$689$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ 0 0
$$5$$ 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i $$-0.0190830\pi$$
−0.550990 + 0.834512i $$0.685750\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i $$0.372704\pi$$
−0.992361 + 0.123371i $$0.960630\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i $$0.426034\pi$$
−0.957892 + 0.287129i $$0.907299\pi$$
$$18$$ 0 0
$$19$$ −4.00000 6.92820i −0.917663 1.58944i −0.802955 0.596040i $$-0.796740\pi$$
−0.114708 0.993399i $$-0.536593\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ 0 0
$$25$$ 0.500000 0.866025i 0.100000 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i $$0.421802\pi$$
−0.961625 + 0.274367i $$0.911532\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i $$-0.114098\pi$$
−0.772043 + 0.635571i $$0.780765\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −2.00000 −0.312348 −0.156174 0.987730i $$-0.549916\pi$$
−0.156174 + 0.987730i $$0.549916\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ −3.00000 + 5.19615i −0.447214 + 0.774597i
$$46$$ 0 0
$$47$$ 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i $$0.0316348\pi$$
−0.411606 + 0.911362i $$0.635032\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i $$-0.968532\pi$$
0.583036 + 0.812447i $$0.301865\pi$$
$$54$$ 0 0
$$55$$ −8.00000 −1.07872
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$60$$ 0 0
$$61$$ −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i $$-0.292159\pi$$
−0.991645 + 0.128994i $$0.958825\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −2.00000 3.46410i −0.248069 0.429669i
$$66$$ 0 0
$$67$$ −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i $$-0.911904\pi$$
0.717607 + 0.696449i $$0.245238\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 8.00000 0.949425 0.474713 0.880141i $$-0.342552\pi$$
0.474713 + 0.880141i $$0.342552\pi$$
$$72$$ 0 0
$$73$$ 5.00000 8.66025i 0.585206 1.01361i −0.409644 0.912245i $$-0.634347\pi$$
0.994850 0.101361i $$-0.0323196\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 8.00000 + 13.8564i 0.900070 + 1.55897i 0.827401 + 0.561611i $$0.189818\pi$$
0.0726692 + 0.997356i $$0.476848\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 8.00000 0.878114 0.439057 0.898459i $$-0.355313\pi$$
0.439057 + 0.898459i $$0.355313\pi$$
$$84$$ 0 0
$$85$$ −12.0000 −1.30158
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 8.00000 13.8564i 0.820783 1.42164i
$$96$$ 0 0
$$97$$ 6.00000 0.609208 0.304604 0.952479i $$-0.401476\pi$$
0.304604 + 0.952479i $$0.401476\pi$$
$$98$$ 0 0
$$99$$ −12.0000 −1.20605
$$100$$ 0 0
$$101$$ 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i $$-0.801608\pi$$
0.911479 + 0.411346i $$0.134941\pi$$
$$102$$ 0 0
$$103$$ 8.00000 + 13.8564i 0.788263 + 1.36531i 0.927030 + 0.374987i $$0.122353\pi$$
−0.138767 + 0.990325i $$0.544314\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i $$-0.969703\pi$$
0.415432 0.909624i $$-0.363630\pi$$
$$108$$ 0 0
$$109$$ 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i $$-0.674364\pi$$
0.999708 + 0.0241802i $$0.00769755\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −3.00000 5.19615i −0.277350 0.480384i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.50000 4.33013i −0.227273 0.393648i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.0000 1.07331
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −4.00000 6.92820i −0.349482 0.605320i 0.636676 0.771132i $$-0.280309\pi$$
−0.986157 + 0.165812i $$0.946976\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i $$-0.750827\pi$$
0.965250 + 0.261329i $$0.0841608\pi$$
$$138$$ 0 0
$$139$$ −8.00000 −0.678551 −0.339276 0.940687i $$-0.610182\pi$$
−0.339276 + 0.940687i $$0.610182\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 4.00000 6.92820i 0.334497 0.579365i
$$144$$ 0 0
$$145$$ 6.00000 + 10.3923i 0.498273 + 0.863034i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i $$-0.245707\pi$$
−0.962348 + 0.271821i $$0.912374\pi$$
$$150$$ 0 0
$$151$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$152$$ 0 0
$$153$$ −18.0000 −1.45521
$$154$$ 0 0
$$155$$ −16.0000 −1.28515
$$156$$ 0 0
$$157$$ 9.00000 15.5885i 0.718278 1.24409i −0.243403 0.969925i $$-0.578264\pi$$
0.961681 0.274169i $$-0.0884028\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −6.00000 10.3923i −0.469956 0.813988i 0.529454 0.848339i $$-0.322397\pi$$
−0.999410 + 0.0343508i $$0.989064\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 16.0000 1.23812 0.619059 0.785345i $$-0.287514\pi$$
0.619059 + 0.785345i $$0.287514\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ 12.0000 20.7846i 0.917663 1.58944i
$$172$$ 0 0
$$173$$ 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i $$0.0732068\pi$$
−0.289412 + 0.957205i $$0.593460\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i $$-0.881096\pi$$
0.781551 + 0.623841i $$0.214429\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −2.00000 + 3.46410i −0.147043 + 0.254686i
$$186$$ 0 0
$$187$$ −12.0000 20.7846i −0.877527 1.51992i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −8.00000 13.8564i −0.578860 1.00261i −0.995610 0.0935936i $$-0.970165\pi$$
0.416751 0.909021i $$-0.363169\pi$$
$$192$$ 0 0
$$193$$ 7.00000 12.1244i 0.503871 0.872730i −0.496119 0.868255i $$-0.665242\pi$$
0.999990 0.00447566i $$-0.00142465\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −2.00000 3.46410i −0.139686 0.241943i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 32.0000 2.21349
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 4.00000 + 6.92820i 0.272798 + 0.472500i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 6.00000 10.3923i 0.403604 0.699062i
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 3.00000 0.200000
$$226$$ 0 0
$$227$$ 4.00000 6.92820i 0.265489 0.459841i −0.702202 0.711977i $$-0.747800\pi$$
0.967692 + 0.252136i $$0.0811332\pi$$
$$228$$ 0 0
$$229$$ 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i $$-0.0594799\pi$$
−0.652183 + 0.758062i $$0.726147\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 11.0000 + 19.0526i 0.720634 + 1.24817i 0.960746 + 0.277429i $$0.0894825\pi$$
−0.240112 + 0.970745i $$0.577184\pi$$
$$234$$ 0 0
$$235$$ −8.00000 + 13.8564i −0.521862 + 0.903892i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −8.00000 −0.517477 −0.258738 0.965947i $$-0.583307\pi$$
−0.258738 + 0.965947i $$0.583307\pi$$
$$240$$ 0 0
$$241$$ 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i $$-0.728952\pi$$
0.980917 + 0.194429i $$0.0622852\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 8.00000 + 13.8564i 0.509028 + 0.881662i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 1.00000 + 1.73205i 0.0623783 + 0.108042i 0.895528 0.445005i $$-0.146798\pi$$
−0.833150 + 0.553047i $$0.813465\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 9.00000 + 15.5885i 0.557086 + 0.964901i
$$262$$ 0 0
$$263$$ 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i $$-0.568182\pi$$
0.952517 0.304487i $$-0.0984850\pi$$
$$264$$ 0 0
$$265$$ −12.0000 −0.737154
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −7.00000 + 12.1244i −0.426798 + 0.739235i −0.996586 0.0825561i $$-0.973692\pi$$
0.569789 + 0.821791i $$0.307025\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 2.00000 + 3.46410i 0.120605 + 0.208893i
$$276$$ 0 0
$$277$$ −11.0000 + 19.0526i −0.660926 + 1.14476i 0.319447 + 0.947604i $$0.396503\pi$$
−0.980373 + 0.197153i $$0.936830\pi$$
$$278$$ 0 0
$$279$$ −24.0000 −1.43684
$$280$$ 0 0
$$281$$ −6.00000 −0.357930 −0.178965 0.983855i $$-0.557275\pi$$
−0.178965 + 0.983855i $$0.557275\pi$$
$$282$$ 0 0
$$283$$ −8.00000 + 13.8564i −0.475551 + 0.823678i −0.999608 0.0280052i $$-0.991084\pi$$
0.524057 + 0.851683i $$0.324418\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −9.50000 16.4545i −0.558824 0.967911i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −18.0000 −1.05157 −0.525786 0.850617i $$-0.676229\pi$$
−0.525786 + 0.850617i $$0.676229\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 6.00000 10.3923i 0.343559 0.595062i
$$306$$ 0 0
$$307$$ −8.00000 −0.456584 −0.228292 0.973593i $$-0.573314\pi$$
−0.228292 + 0.973593i $$0.573314\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −4.00000 + 6.92820i −0.226819 + 0.392862i −0.956864 0.290537i $$-0.906166\pi$$
0.730044 + 0.683400i $$0.239499\pi$$
$$312$$ 0 0
$$313$$ −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i $$-0.296152\pi$$
−0.993186 + 0.116543i $$0.962819\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −15.0000 25.9808i −0.842484 1.45922i −0.887788 0.460252i $$-0.847759\pi$$
0.0453045 0.998973i $$-0.485574\pi$$
$$318$$ 0 0
$$319$$ −12.0000 + 20.7846i −0.671871 + 1.16371i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 48.0000 2.67079
$$324$$ 0 0
$$325$$ −1.00000 + 1.73205i −0.0554700 + 0.0960769i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i $$-0.201729\pi$$
−0.915742 + 0.401768i $$0.868396\pi$$
$$332$$ 0 0
$$333$$ −3.00000 + 5.19615i −0.164399 + 0.284747i
$$334$$ 0 0
$$335$$ −8.00000 −0.437087
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −16.0000 27.7128i −0.866449 1.50073i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i $$-0.728946\pi$$
0.980921 + 0.194409i $$0.0622790\pi$$
$$348$$ 0 0
$$349$$ 30.0000 1.60586 0.802932 0.596071i $$-0.203272\pi$$
0.802932 + 0.596071i $$0.203272\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −7.00000 + 12.1244i −0.372572 + 0.645314i −0.989960 0.141344i $$-0.954858\pi$$
0.617388 + 0.786659i $$0.288191\pi$$
$$354$$ 0 0
$$355$$ 8.00000 + 13.8564i 0.424596 + 0.735422i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$360$$ 0 0
$$361$$ −22.5000 + 38.9711i −1.18421 + 2.05111i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 20.0000 1.04685
$$366$$ 0 0
$$367$$ −8.00000 + 13.8564i −0.417597 + 0.723299i −0.995697 0.0926670i $$-0.970461\pi$$
0.578101 + 0.815966i $$0.303794\pi$$
$$368$$ 0 0
$$369$$ −3.00000 5.19615i −0.156174 0.270501i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 13.0000 + 22.5167i 0.673114 + 1.16587i 0.977016 + 0.213165i $$0.0683772\pi$$
−0.303902 + 0.952703i $$0.598289\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i $$0.0434398\pi$$
−0.377531 + 0.925997i $$0.623227\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 6.00000 + 10.3923i 0.304997 + 0.528271i
$$388$$ 0 0
$$389$$ 1.00000 1.73205i 0.0507020 0.0878185i −0.839561 0.543266i $$-0.817187\pi$$
0.890263 + 0.455448i $$0.150521\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −16.0000 + 27.7128i −0.805047 + 1.39438i
$$396$$ 0 0
$$397$$ −7.00000 12.1244i −0.351320 0.608504i 0.635161 0.772380i $$-0.280934\pi$$
−0.986481 + 0.163876i $$0.947600\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i $$-0.315043\pi$$
−0.998350 + 0.0574304i $$0.981709\pi$$
$$402$$ 0 0
$$403$$ 8.00000 13.8564i 0.398508 0.690237i
$$404$$ 0 0
$$405$$ −18.0000 −0.894427
$$406$$ 0 0
$$407$$ −8.00000 −0.396545
$$408$$ 0 0
$$409$$ −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i $$-0.945837\pi$$
0.639430 + 0.768849i $$0.279170\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 8.00000 + 13.8564i 0.392705 + 0.680184i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −16.0000 −0.781651 −0.390826 0.920465i $$-0.627810\pi$$
−0.390826 + 0.920465i $$0.627810\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 0 0
$$423$$ −12.0000 + 20.7846i −0.583460 + 1.01058i
$$424$$ 0 0
$$425$$ 3.00000 + 5.19615i 0.145521 + 0.252050i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −4.00000 + 6.92820i −0.192673 + 0.333720i −0.946135 0.323772i $$-0.895049\pi$$
0.753462 + 0.657491i $$0.228382\pi$$
$$432$$ 0 0
$$433$$ −10.0000 −0.480569 −0.240285 0.970702i $$-0.577241\pi$$
−0.240285 + 0.970702i $$0.577241\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i $$-0.972552\pi$$
0.423556 0.905870i $$-0.360782\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i $$0.159903\pi$$
−0.0212481 + 0.999774i $$0.506764\pi$$
$$444$$ 0 0
$$445$$ 6.00000 10.3923i 0.284427 0.492642i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 34.0000 1.60456 0.802280 0.596948i $$-0.203620\pi$$
0.802280 + 0.596948i $$0.203620\pi$$
$$450$$ 0 0
$$451$$ 4.00000 6.92820i 0.188353 0.326236i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 19.0000 + 32.9090i 0.888783 + 1.53942i 0.841316 + 0.540544i $$0.181781\pi$$
0.0474665 + 0.998873i $$0.484885\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 30.0000 1.39724 0.698620 0.715493i $$-0.253798\pi$$
0.698620 + 0.715493i $$0.253798\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 4.00000 + 6.92820i 0.185098 + 0.320599i 0.943610 0.331061i $$-0.107406\pi$$
−0.758512 + 0.651660i $$0.774073\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −8.00000 + 13.8564i −0.367840 + 0.637118i
$$474$$ 0 0
$$475$$ −8.00000 −0.367065
$$476$$ 0 0
$$477$$ −18.0000 −0.824163
$$478$$ 0 0
$$479$$ 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i $$-0.648611\pi$$
0.998392 0.0566937i $$-0.0180558\pi$$
$$480$$ 0 0
$$481$$ −2.00000 3.46410i −0.0911922 0.157949i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 6.00000 + 10.3923i 0.272446 + 0.471890i
$$486$$ 0 0
$$487$$ −8.00000 + 13.8564i −0.362515 + 0.627894i −0.988374 0.152042i $$-0.951415\pi$$
0.625859 + 0.779936i $$0.284748\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ 0 0
$$493$$ −18.0000 + 31.1769i −0.810679 + 1.40414i
$$494$$ 0 0
$$495$$ −12.0000 20.7846i −0.539360 0.934199i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i $$-0.195204\pi$$
−0.907314 + 0.420455i $$0.861871\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 40.0000 1.78351 0.891756 0.452517i $$-0.149474\pi$$
0.891756 + 0.452517i $$0.149474\pi$$
$$504$$ 0 0
$$505$$ 4.00000 0.177998
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 17.0000 + 29.4449i 0.753512 + 1.30512i 0.946111 + 0.323843i $$0.104975\pi$$
−0.192599 + 0.981278i $$0.561692\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −16.0000 + 27.7128i −0.705044 + 1.22117i
$$516$$ 0 0
$$517$$ −32.0000 −1.40736
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i $$-0.704321\pi$$
0.993011 + 0.118020i $$0.0376547\pi$$
$$522$$ 0 0
$$523$$ 16.0000 + 27.7128i 0.699631 + 1.21180i 0.968594 + 0.248646i $$0.0799857\pi$$
−0.268963 + 0.963150i $$0.586681\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −24.0000 41.5692i −1.04546 1.81078i
$$528$$ 0 0
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 4.00000 0.173259
$$534$$ 0 0
$$535$$ 12.0000 20.7846i 0.518805 0.898597i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −7.00000 12.1244i −0.300954 0.521267i 0.675399 0.737453i $$-0.263972\pi$$
−0.976352 + 0.216186i $$0.930638\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 20.0000 0.856706
$$546$$ 0 0
$$547$$ −36.0000 −1.53925 −0.769624 0.638497i $$-0.779557\pi$$
−0.769624 + 0.638497i $$0.779557\pi$$
$$548$$ 0 0
$$549$$ 9.00000 15.5885i 0.384111 0.665299i
$$550$$ 0 0
$$551$$ −24.0000 41.5692i −1.02243 1.77091i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −7.00000 + 12.1244i −0.296600 + 0.513725i −0.975356 0.220638i $$-0.929186\pi$$
0.678756 + 0.734364i $$0.262519\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −16.0000 + 27.7128i −0.674320 + 1.16796i 0.302348 + 0.953198i $$0.402230\pi$$
−0.976667 + 0.214758i $$0.931104\pi$$
$$564$$ 0 0
$$565$$ 2.00000 + 3.46410i 0.0841406 + 0.145736i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −13.0000 22.5167i −0.544988 0.943948i −0.998608 0.0527519i $$-0.983201\pi$$
0.453619 0.891196i $$-0.350133\pi$$
$$570$$ 0 0
$$571$$ 14.0000 24.2487i 0.585882 1.01478i −0.408883 0.912587i $$-0.634082\pi$$
0.994765 0.102190i $$-0.0325850\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −7.00000 + 12.1244i −0.291414 + 0.504744i −0.974144 0.225927i $$-0.927459\pi$$
0.682730 + 0.730670i $$0.260792\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −12.0000 20.7846i −0.496989 0.860811i
$$584$$ 0 0
$$585$$ 6.00000 10.3923i 0.248069 0.429669i
$$586$$ 0 0
$$587$$ −24.0000 −0.990586 −0.495293 0.868726i $$-0.664939\pi$$
−0.495293 + 0.868726i $$0.664939\pi$$
$$588$$ 0 0
$$589$$ 64.0000 2.63707
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 17.0000 + 29.4449i 0.698106 + 1.20916i 0.969122 + 0.246581i $$0.0793071\pi$$
−0.271016 + 0.962575i $$0.587360\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i $$-0.996449\pi$$
0.509631 + 0.860393i $$0.329782\pi$$
$$600$$ 0 0
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ −12.0000 −0.488678
$$604$$ 0 0
$$605$$ 5.00000 8.66025i 0.203279 0.352089i
$$606$$ 0 0
$$607$$ −16.0000 27.7128i −0.649420 1.12483i −0.983262 0.182199i $$-0.941678\pi$$
0.333842 0.942629i $$-0.391655\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −8.00000 13.8564i −0.323645 0.560570i
$$612$$ 0 0
$$613$$ 9.00000 15.5885i 0.363507 0.629612i −0.625029 0.780602i $$-0.714913\pi$$
0.988535 + 0.150990i $$0.0482461\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −38.0000 −1.52982 −0.764911 0.644136i $$-0.777217\pi$$
−0.764911 + 0.644136i $$0.777217\pi$$
$$618$$ 0 0
$$619$$ 16.0000 27.7128i 0.643094 1.11387i −0.341644 0.939829i $$-0.610984\pi$$
0.984738 0.174042i $$-0.0556830\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 9.50000 + 16.4545i 0.380000 + 0.658179i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ −24.0000 −0.955425 −0.477712 0.878516i $$-0.658534\pi$$
−0.477712 + 0.878516i $$0.658534\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 8.00000 + 13.8564i 0.317470 + 0.549875i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 12.0000 + 20.7846i 0.474713 + 0.822226i
$$640$$ 0 0
$$641$$ 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i $$-0.631488\pi$$
0.993899 0.110291i $$-0.0351782\pi$$
$$642$$ 0 0
$$643$$ 16.0000 0.630978 0.315489 0.948929i $$-0.397831\pi$$
0.315489 + 0.948929i $$0.397831\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 16.0000 27.7128i 0.629025 1.08950i −0.358723 0.933444i $$-0.616788\pi$$
0.987748 0.156059i $$-0.0498790\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 13.0000 + 22.5167i 0.508729 + 0.881145i 0.999949 + 0.0101092i $$0.00321793\pi$$
−0.491220 + 0.871036i $$0.663449\pi$$
$$654$$ 0 0
$$655$$ 8.00000 13.8564i 0.312586 0.541415i
$$656$$ 0 0
$$657$$ 30.0000 1.17041
$$658$$ 0 0
$$659$$ 12.0000 0.467454 0.233727 0.972302i $$-0.424908\pi$$
0.233727 + 0.972302i $$0.424908\pi$$
$$660$$ 0 0
$$661$$ 1.00000 1.73205i 0.0388955 0.0673690i −0.845922 0.533306i $$-0.820949\pi$$
0.884818 + 0.465937i $$0.154283\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 24.0000 0.926510
$$672$$ 0 0
$$673$$ −14.0000 −0.539660 −0.269830 0.962908i $$-0.586968\pi$$
−0.269830 + 0.962908i $$0.586968\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i $$-0.203449\pi$$
−0.917899 + 0.396813i $$0.870116\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 18.0000 31.1769i 0.688751 1.19295i −0.283491 0.958975i $$-0.591493\pi$$
0.972242 0.233977i $$-0.0751739\pi$$
$$684$$ 0 0
$$685$$ 12.0000 0.458496
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 6.00000 10.3923i 0.228582 0.395915i
$$690$$ 0 0
$$691$$ 4.00000 + 6.92820i 0.152167 + 0.263561i 0.932024 0.362397i $$-0.118041\pi$$
−0.779857 + 0.625958i $$0.784708\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −8.00000 13.8564i −0.303457 0.525603i
$$696$$ 0 0
$$697$$ 6.00000 10.3923i 0.227266 0.393637i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −42.0000 −1.58632 −0.793159 0.609015i $$-0.791565\pi$$
−0.793159 + 0.609015i $$0.791565\pi$$
$$702$$ 0 0
$$703$$ 8.00000 13.8564i 0.301726 0.522604i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −15.0000 25.9808i −0.563337 0.975728i −0.997202 0.0747503i $$-0.976184\pi$$
0.433865 0.900978i $$-0.357149\pi$$
$$710$$ 0 0
$$711$$ −24.0000 + 41.5692i −0.900070 + 1.55897i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 16.0000 0.598366
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −4.00000 6.92820i −0.149175 0.258378i 0.781748 0.623595i $$-0.214328\pi$$
−0.930923 + 0.365216i $$0.880995\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 3.00000 5.19615i 0.111417 0.192980i
$$726$$ 0 0
$$727$$ 16.0000 0.593407 0.296704 0.954970i $$-0.404113\pi$$
0.296704 + 0.954970i $$0.404113\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ −12.0000 + 20.7846i −0.443836 + 0.768747i
$$732$$ 0 0
$$733$$ 13.0000 + 22.5167i 0.480166 + 0.831672i 0.999741 0.0227529i $$-0.00724310\pi$$
−0.519575 + 0.854425i $$0.673910\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −8.00000 13.8564i −0.294684 0.510407i
$$738$$ 0 0
$$739$$ 26.0000 45.0333i 0.956425 1.65658i 0.225354 0.974277i $$-0.427646\pi$$
0.731072 0.682300i $$-0.239020\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −32.0000 −1.17397 −0.586983 0.809599i $$-0.699684\pi$$
−0.586983 + 0.809599i $$0.699684\pi$$
$$744$$ 0 0
$$745$$ 6.00000 10.3923i 0.219823 0.380745i
$$746$$ 0 0
$$747$$ 12.0000 + 20.7846i 0.439057 + 0.760469i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −4.00000 6.92820i −0.145962 0.252814i 0.783769 0.621052i $$-0.213294\pi$$
−0.929731 + 0.368238i $$0.879961\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −2.00000 −0.0726912 −0.0363456 0.999339i $$-0.511572\pi$$
−0.0363456 + 0.999339i $$0.511572\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −15.0000 25.9808i −0.543750 0.941802i −0.998684 0.0512772i $$-0.983671\pi$$
0.454935 0.890525i $$-0.349663\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −18.0000 31.1769i −0.650791 1.12720i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 22.0000 0.793340 0.396670 0.917961i $$-0.370166\pi$$
0.396670 + 0.917961i $$0.370166\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 25.0000 43.3013i 0.899188 1.55744i 0.0706526 0.997501i $$-0.477492\pi$$
0.828535 0.559937i $$-0.189175\pi$$
$$774$$ 0 0
$$775$$ 4.00000 + 6.92820i 0.143684 + 0.248868i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 8.00000 + 13.8564i 0.286630 + 0.496457i
$$780$$ 0 0
$$781$$ −16.0000 + 27.7128i −0.572525 + 0.991642i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 36.0000 1.28490
$$786$$ 0 0
$$787$$ 20.0000 34.6410i 0.712923 1.23482i −0.250832 0.968031i $$-0.580704\pi$$
0.963755 0.266788i $$-0.0859624\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 6.00000 + 10.3923i 0.213066 + 0.369042i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 30.0000 1.06265 0.531327 0.847167i $$-0.321693\pi$$
0.531327 + 0.847167i $$0.321693\pi$$
$$798$$