# Properties

 Label 1008.2.s.r.865.2 Level $1008$ Weight $2$ Character 1008.865 Analytic conductor $8.049$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(289,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1008.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1008.s (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: $$8.04892052375$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-19})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} - 4x^{2} - 5x + 25$$ x^4 - x^3 - 4*x^2 - 5*x + 25 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 168) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 865.2 Root $$2.13746 + 0.656712i$$ of defining polynomial Character $$\chi$$ $$=$$ 1008.865 Dual form 1008.2.s.r.289.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.63746 + 2.83616i) q^{5} +(1.50000 + 2.17945i) q^{7} +O(q^{10})$$ $$q+(1.63746 + 2.83616i) q^{5} +(1.50000 + 2.17945i) q^{7} +(-1.63746 + 2.83616i) q^{11} +6.27492 q^{13} +(-2.00000 + 3.46410i) q^{17} +(-3.13746 - 5.43424i) q^{19} +(-2.00000 - 3.46410i) q^{23} +(-2.86254 + 4.95807i) q^{25} -5.27492 q^{29} +(-0.500000 + 0.866025i) q^{31} +(-3.72508 + 7.82300i) q^{35} +(1.13746 + 1.97014i) q^{37} +4.54983 q^{41} -0.274917 q^{43} +(3.00000 + 5.19615i) q^{47} +(-2.50000 + 6.53835i) q^{49} +(4.63746 - 8.03231i) q^{53} -10.7251 q^{55} +(0.637459 - 1.10411i) q^{59} +(-5.00000 - 8.66025i) q^{61} +(10.2749 + 17.7967i) q^{65} +(-0.137459 + 0.238085i) q^{67} +2.00000 q^{71} +(2.13746 - 3.70219i) q^{73} +(-8.63746 + 0.685484i) q^{77} +(5.77492 + 10.0025i) q^{79} +7.27492 q^{83} -13.0997 q^{85} +(-5.27492 - 9.13642i) q^{89} +(9.41238 + 13.6759i) q^{91} +(10.2749 - 17.7967i) q^{95} +8.72508 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - q^{5} + 6 q^{7}+O(q^{10})$$ 4 * q - q^5 + 6 * q^7 $$4 q - q^{5} + 6 q^{7} + q^{11} + 10 q^{13} - 8 q^{17} - 5 q^{19} - 8 q^{23} - 19 q^{25} - 6 q^{29} - 2 q^{31} - 30 q^{35} - 3 q^{37} - 12 q^{41} + 14 q^{43} + 12 q^{47} - 10 q^{49} + 11 q^{53} - 58 q^{55} - 5 q^{59} - 20 q^{61} + 26 q^{65} + 7 q^{67} + 8 q^{71} + q^{73} - 27 q^{77} + 8 q^{79} + 14 q^{83} + 8 q^{85} - 6 q^{89} + 15 q^{91} + 26 q^{95} + 50 q^{97}+O(q^{100})$$ 4 * q - q^5 + 6 * q^7 + q^11 + 10 * q^13 - 8 * q^17 - 5 * q^19 - 8 * q^23 - 19 * q^25 - 6 * q^29 - 2 * q^31 - 30 * q^35 - 3 * q^37 - 12 * q^41 + 14 * q^43 + 12 * q^47 - 10 * q^49 + 11 * q^53 - 58 * q^55 - 5 * q^59 - 20 * q^61 + 26 * q^65 + 7 * q^67 + 8 * q^71 + q^73 - 27 * q^77 + 8 * q^79 + 14 * q^83 + 8 * q^85 - 6 * q^89 + 15 * q^91 + 26 * q^95 + 50 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$577$$ $$757$$ $$785$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 1.63746 + 2.83616i 0.732294 + 1.26837i 0.955901 + 0.293691i $$0.0948835\pi$$
−0.223607 + 0.974679i $$0.571783\pi$$
$$6$$ 0 0
$$7$$ 1.50000 + 2.17945i 0.566947 + 0.823754i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.63746 + 2.83616i −0.493712 + 0.855135i −0.999974 0.00724520i $$-0.997694\pi$$
0.506261 + 0.862380i $$0.331027\pi$$
$$12$$ 0 0
$$13$$ 6.27492 1.74035 0.870174 0.492744i $$-0.164006\pi$$
0.870174 + 0.492744i $$0.164006\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i $$-0.994540\pi$$
0.514782 + 0.857321i $$0.327873\pi$$
$$18$$ 0 0
$$19$$ −3.13746 5.43424i −0.719782 1.24670i −0.961086 0.276250i $$-0.910908\pi$$
0.241303 0.970450i $$-0.422425\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i $$-0.303595\pi$$
−0.995639 + 0.0932891i $$0.970262\pi$$
$$24$$ 0 0
$$25$$ −2.86254 + 4.95807i −0.572508 + 0.991613i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −5.27492 −0.979528 −0.489764 0.871855i $$-0.662917\pi$$
−0.489764 + 0.871855i $$0.662917\pi$$
$$30$$ 0 0
$$31$$ −0.500000 + 0.866025i −0.0898027 + 0.155543i −0.907428 0.420208i $$-0.861957\pi$$
0.817625 + 0.575751i $$0.195290\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −3.72508 + 7.82300i −0.629654 + 1.32233i
$$36$$ 0 0
$$37$$ 1.13746 + 1.97014i 0.186997 + 0.323888i 0.944248 0.329236i $$-0.106791\pi$$
−0.757251 + 0.653124i $$0.773458\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 4.54983 0.710565 0.355282 0.934759i $$-0.384385\pi$$
0.355282 + 0.934759i $$0.384385\pi$$
$$42$$ 0 0
$$43$$ −0.274917 −0.0419245 −0.0209622 0.999780i $$-0.506673\pi$$
−0.0209622 + 0.999780i $$0.506673\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i $$-0.0224970\pi$$
−0.559908 + 0.828554i $$0.689164\pi$$
$$48$$ 0 0
$$49$$ −2.50000 + 6.53835i −0.357143 + 0.934050i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 4.63746 8.03231i 0.637004 1.10332i −0.349083 0.937092i $$-0.613507\pi$$
0.986087 0.166231i $$-0.0531598\pi$$
$$54$$ 0 0
$$55$$ −10.7251 −1.44617
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0.637459 1.10411i 0.0829900 0.143743i −0.821543 0.570147i $$-0.806886\pi$$
0.904533 + 0.426404i $$0.140220\pi$$
$$60$$ 0 0
$$61$$ −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i $$-0.945525\pi$$
0.345207 0.938527i $$-0.387809\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 10.2749 + 17.7967i 1.27445 + 2.20741i
$$66$$ 0 0
$$67$$ −0.137459 + 0.238085i −0.0167932 + 0.0290867i −0.874300 0.485386i $$-0.838679\pi$$
0.857507 + 0.514473i $$0.172012\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ 0 0
$$73$$ 2.13746 3.70219i 0.250171 0.433308i −0.713402 0.700755i $$-0.752847\pi$$
0.963573 + 0.267447i $$0.0861800\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −8.63746 + 0.685484i −0.984330 + 0.0781181i
$$78$$ 0 0
$$79$$ 5.77492 + 10.0025i 0.649729 + 1.12536i 0.983188 + 0.182599i $$0.0584509\pi$$
−0.333459 + 0.942765i $$0.608216\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 7.27492 0.798526 0.399263 0.916836i $$-0.369266\pi$$
0.399263 + 0.916836i $$0.369266\pi$$
$$84$$ 0 0
$$85$$ −13.0997 −1.42086
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −5.27492 9.13642i −0.559140 0.968459i −0.997568 0.0696929i $$-0.977798\pi$$
0.438428 0.898766i $$-0.355535\pi$$
$$90$$ 0 0
$$91$$ 9.41238 + 13.6759i 0.986685 + 1.43362i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 10.2749 17.7967i 1.05418 1.82590i
$$96$$ 0 0
$$97$$ 8.72508 0.885898 0.442949 0.896547i $$-0.353932\pi$$
0.442949 + 0.896547i $$0.353932\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i $$-0.929823\pi$$
0.677284 + 0.735721i $$0.263157\pi$$
$$102$$ 0 0
$$103$$ 5.41238 + 9.37451i 0.533297 + 0.923698i 0.999244 + 0.0388850i $$0.0123806\pi$$
−0.465946 + 0.884813i $$0.654286\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 7.91238 + 13.7046i 0.764918 + 1.32488i 0.940290 + 0.340375i $$0.110554\pi$$
−0.175372 + 0.984502i $$0.556113\pi$$
$$108$$ 0 0
$$109$$ −8.41238 + 14.5707i −0.805759 + 1.39562i 0.110018 + 0.993930i $$0.464909\pi$$
−0.915777 + 0.401687i $$0.868424\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 4.54983 0.428012 0.214006 0.976832i $$-0.431349\pi$$
0.214006 + 0.976832i $$0.431349\pi$$
$$114$$ 0 0
$$115$$ 6.54983 11.3446i 0.610775 1.05789i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −10.5498 + 0.837253i −0.967102 + 0.0767509i
$$120$$ 0 0
$$121$$ 0.137459 + 0.238085i 0.0124962 + 0.0216441i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −2.37459 −0.212389
$$126$$ 0 0
$$127$$ 6.45017 0.572360 0.286180 0.958176i $$-0.407615\pi$$
0.286180 + 0.958176i $$0.407615\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −3.63746 6.30026i −0.317806 0.550457i 0.662224 0.749306i $$-0.269613\pi$$
−0.980030 + 0.198850i $$0.936279\pi$$
$$132$$ 0 0
$$133$$ 7.13746 14.9893i 0.618896 1.29974i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0.725083 1.25588i 0.0619480 0.107297i −0.833388 0.552688i $$-0.813602\pi$$
0.895336 + 0.445391i $$0.146935\pi$$
$$138$$ 0 0
$$139$$ −8.27492 −0.701869 −0.350935 0.936400i $$-0.614136\pi$$
−0.350935 + 0.936400i $$0.614136\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −10.2749 + 17.7967i −0.859232 + 1.48823i
$$144$$ 0 0
$$145$$ −8.63746 14.9605i −0.717302 1.24240i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −7.27492 12.6005i −0.595984 1.03228i −0.993407 0.114640i $$-0.963429\pi$$
0.397423 0.917636i $$-0.369905\pi$$
$$150$$ 0 0
$$151$$ 11.1873 19.3770i 0.910409 1.57687i 0.0969217 0.995292i $$-0.469100\pi$$
0.813487 0.581583i $$-0.197566\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3.27492 −0.263048
$$156$$ 0 0
$$157$$ 0.274917 0.476171i 0.0219408 0.0380026i −0.854847 0.518881i $$-0.826349\pi$$
0.876787 + 0.480878i $$0.159682\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 4.54983 9.55505i 0.358577 0.753044i
$$162$$ 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
$$167$$ −6.00000 −0.464294 −0.232147 0.972681i $$-0.574575\pi$$
−0.232147 + 0.972681i $$0.574575\pi$$
$$168$$ 0 0
$$169$$ 26.3746 2.02881
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −11.2749 19.5287i −0.857216 1.48474i −0.874574 0.484892i $$-0.838859\pi$$
0.0173577 0.999849i $$-0.494475\pi$$
$$174$$ 0 0
$$175$$ −15.0997 + 1.19834i −1.14143 + 0.0905857i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 8.27492 14.3326i 0.618496 1.07127i −0.371264 0.928527i $$-0.621075\pi$$
0.989760 0.142740i $$-0.0455912\pi$$
$$180$$ 0 0
$$181$$ −18.8248 −1.39923 −0.699616 0.714519i $$-0.746646\pi$$
−0.699616 + 0.714519i $$0.746646\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −3.72508 + 6.45203i −0.273874 + 0.474363i
$$186$$ 0 0
$$187$$ −6.54983 11.3446i −0.478971 0.829603i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −2.27492 3.94027i −0.164607 0.285108i 0.771909 0.635734i $$-0.219302\pi$$
−0.936516 + 0.350626i $$0.885969\pi$$
$$192$$ 0 0
$$193$$ −0.225083 + 0.389855i −0.0162018 + 0.0280624i −0.874013 0.485903i $$-0.838491\pi$$
0.857811 + 0.513966i $$0.171824\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1.45017 0.103320 0.0516600 0.998665i $$-0.483549\pi$$
0.0516600 + 0.998665i $$0.483549\pi$$
$$198$$ 0 0
$$199$$ −2.54983 + 4.41644i −0.180753 + 0.313073i −0.942137 0.335228i $$-0.891187\pi$$
0.761384 + 0.648301i $$0.224520\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −7.91238 11.4964i −0.555340 0.806890i
$$204$$ 0 0
$$205$$ 7.45017 + 12.9041i 0.520342 + 0.901259i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 20.5498 1.42146
$$210$$ 0 0
$$211$$ 27.6495 1.90347 0.951735 0.306921i $$-0.0992986\pi$$
0.951735 + 0.306921i $$0.0992986\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −0.450166 0.779710i −0.0307010 0.0531758i
$$216$$ 0 0
$$217$$ −2.63746 + 0.209313i −0.179042 + 0.0142091i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −12.5498 + 21.7370i −0.844193 + 1.46219i
$$222$$ 0 0
$$223$$ 1.27492 0.0853748 0.0426874 0.999088i $$-0.486408\pi$$
0.0426874 + 0.999088i $$0.486408\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 5.63746 9.76436i 0.374171 0.648084i −0.616031 0.787722i $$-0.711261\pi$$
0.990203 + 0.139638i $$0.0445939\pi$$
$$228$$ 0 0
$$229$$ −9.13746 15.8265i −0.603820 1.04585i −0.992237 0.124363i $$-0.960311\pi$$
0.388416 0.921484i $$-0.373022\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −0.274917 0.476171i −0.0180104 0.0311950i 0.856880 0.515516i $$-0.172400\pi$$
−0.874890 + 0.484321i $$0.839067\pi$$
$$234$$ 0 0
$$235$$ −9.82475 + 17.0170i −0.640896 + 1.11006i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 15.4502 0.999388 0.499694 0.866202i $$-0.333446\pi$$
0.499694 + 0.866202i $$0.333446\pi$$
$$240$$ 0 0
$$241$$ −4.91238 + 8.50848i −0.316434 + 0.548080i −0.979741 0.200267i $$-0.935819\pi$$
0.663307 + 0.748347i $$0.269152\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −22.6375 + 3.61587i −1.44625 + 0.231010i
$$246$$ 0 0
$$247$$ −19.6873 34.0994i −1.25267 2.16969i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −18.3746 −1.15979 −0.579897 0.814690i $$-0.696907\pi$$
−0.579897 + 0.814690i $$0.696907\pi$$
$$252$$ 0 0
$$253$$ 13.0997 0.823569
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 5.54983 + 9.61260i 0.346189 + 0.599617i 0.985569 0.169274i $$-0.0541422\pi$$
−0.639380 + 0.768891i $$0.720809\pi$$
$$258$$ 0 0
$$259$$ −2.58762 + 5.43424i −0.160787 + 0.337667i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 4.72508 8.18408i 0.291361 0.504652i −0.682771 0.730633i $$-0.739225\pi$$
0.974132 + 0.225980i $$0.0725586\pi$$
$$264$$ 0 0
$$265$$ 30.3746 1.86590
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 10.3625 17.9484i 0.631815 1.09434i −0.355365 0.934728i $$-0.615643\pi$$
0.987180 0.159609i $$-0.0510232\pi$$
$$270$$ 0 0
$$271$$ 0.637459 + 1.10411i 0.0387229 + 0.0670699i 0.884737 0.466090i $$-0.154338\pi$$
−0.846014 + 0.533160i $$0.821004\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −9.37459 16.2373i −0.565309 0.979144i
$$276$$ 0 0
$$277$$ 13.4124 23.2309i 0.805872 1.39581i −0.109830 0.993950i $$-0.535030\pi$$
0.915701 0.401860i $$-0.131636\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 26.5498 1.58383 0.791915 0.610631i $$-0.209084\pi$$
0.791915 + 0.610631i $$0.209084\pi$$
$$282$$ 0 0
$$283$$ −12.9622 + 22.4512i −0.770523 + 1.33459i 0.166753 + 0.985999i $$0.446672\pi$$
−0.937276 + 0.348587i $$0.886662\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 6.82475 + 9.91613i 0.402852 + 0.585331i
$$288$$ 0 0
$$289$$ 0.500000 + 0.866025i 0.0294118 + 0.0509427i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 27.8248 1.62554 0.812770 0.582585i $$-0.197959\pi$$
0.812770 + 0.582585i $$0.197959\pi$$
$$294$$ 0 0
$$295$$ 4.17525 0.243092
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −12.5498 21.7370i −0.725776 1.25708i
$$300$$ 0 0
$$301$$ −0.412376 0.599168i −0.0237689 0.0345355i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 16.3746 28.3616i 0.937606 1.62398i
$$306$$ 0 0
$$307$$ −11.3746 −0.649182 −0.324591 0.945854i $$-0.605227\pi$$
−0.324591 + 0.945854i $$0.605227\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 2.27492 3.94027i 0.128999 0.223432i −0.794290 0.607539i $$-0.792157\pi$$
0.923289 + 0.384106i $$0.125490\pi$$
$$312$$ 0 0
$$313$$ 9.77492 + 16.9307i 0.552511 + 0.956977i 0.998093 + 0.0617357i $$0.0196636\pi$$
−0.445582 + 0.895241i $$0.647003\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −13.9124 24.0969i −0.781397 1.35342i −0.931128 0.364692i $$-0.881174\pi$$
0.149731 0.988727i $$-0.452159\pi$$
$$318$$ 0 0
$$319$$ 8.63746 14.9605i 0.483605 0.837628i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 25.0997 1.39658
$$324$$ 0 0
$$325$$ −17.9622 + 31.1115i −0.996364 + 1.72575i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −6.82475 + 14.3326i −0.376261 + 0.790181i
$$330$$ 0 0
$$331$$ 0.587624 + 1.01779i 0.0322987 + 0.0559431i 0.881723 0.471768i $$-0.156384\pi$$
−0.849424 + 0.527711i $$0.823051\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −0.900331 −0.0491903
$$336$$ 0 0
$$337$$ −24.0997 −1.31279 −0.656396 0.754416i $$-0.727920\pi$$
−0.656396 + 0.754416i $$0.727920\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −1.63746 2.83616i −0.0886734 0.153587i
$$342$$ 0 0
$$343$$ −18.0000 + 4.35890i −0.971909 + 0.235358i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −15.0997 + 26.1534i −0.810593 + 1.40399i 0.101857 + 0.994799i $$0.467522\pi$$
−0.912450 + 0.409189i $$0.865812\pi$$
$$348$$ 0 0
$$349$$ −6.00000 −0.321173 −0.160586 0.987022i $$-0.551338\pi$$
−0.160586 + 0.987022i $$0.551338\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −10.2749 + 17.7967i −0.546879 + 0.947222i 0.451607 + 0.892217i $$0.350851\pi$$
−0.998486 + 0.0550049i $$0.982483\pi$$
$$354$$ 0 0
$$355$$ 3.27492 + 5.67232i 0.173815 + 0.301056i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 9.82475 + 17.0170i 0.518531 + 0.898121i 0.999768 + 0.0215311i $$0.00685409\pi$$
−0.481238 + 0.876590i $$0.659813\pi$$
$$360$$ 0 0
$$361$$ −10.1873 + 17.6449i −0.536173 + 0.928679i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 14.0000 0.732793
$$366$$ 0 0
$$367$$ 11.0498 19.1389i 0.576797 0.999041i −0.419047 0.907964i $$-0.637636\pi$$
0.995844 0.0910767i $$-0.0290308\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 24.4622 1.94136i 1.27001 0.100791i
$$372$$ 0 0
$$373$$ 3.13746 + 5.43424i 0.162451 + 0.281374i 0.935747 0.352671i $$-0.114727\pi$$
−0.773296 + 0.634045i $$0.781393\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −33.0997 −1.70472
$$378$$ 0 0
$$379$$ −13.1752 −0.676767 −0.338384 0.941008i $$-0.609880\pi$$
−0.338384 + 0.941008i $$0.609880\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −5.27492 9.13642i −0.269536 0.466849i 0.699206 0.714920i $$-0.253537\pi$$
−0.968742 + 0.248070i $$0.920204\pi$$
$$384$$ 0 0
$$385$$ −16.0876 23.3748i −0.819901 1.19129i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1.00000 + 1.73205i −0.0507020 + 0.0878185i −0.890263 0.455448i $$-0.849479\pi$$
0.839561 + 0.543266i $$0.182813\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −18.9124 + 32.7572i −0.951585 + 1.64819i
$$396$$ 0 0
$$397$$ 1.68729 + 2.92248i 0.0846828 + 0.146675i 0.905256 0.424867i $$-0.139679\pi$$
−0.820573 + 0.571541i $$0.806346\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 12.0000 + 20.7846i 0.599251 + 1.03793i 0.992932 + 0.118686i $$0.0378683\pi$$
−0.393680 + 0.919247i $$0.628798\pi$$
$$402$$ 0 0
$$403$$ −3.13746 + 5.43424i −0.156288 + 0.270699i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −7.45017 −0.369291
$$408$$ 0 0
$$409$$ −5.22508 + 9.05011i −0.258364 + 0.447499i −0.965804 0.259274i $$-0.916517\pi$$
0.707440 + 0.706773i $$0.249850\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 3.36254 0.266857i 0.165460 0.0131312i
$$414$$ 0 0
$$415$$ 11.9124 + 20.6328i 0.584756 + 1.01283i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 28.5498 1.39475 0.697375 0.716706i $$-0.254351\pi$$
0.697375 + 0.716706i $$0.254351\pi$$
$$420$$ 0 0
$$421$$ 8.82475 0.430092 0.215046 0.976604i $$-0.431010\pi$$
0.215046 + 0.976604i $$0.431010\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −11.4502 19.8323i −0.555415 0.962006i
$$426$$ 0 0
$$427$$ 11.3746 23.8876i 0.550455 1.15600i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 8.82475 15.2849i 0.425073 0.736249i −0.571354 0.820704i $$-0.693582\pi$$
0.996427 + 0.0844552i $$0.0269150\pi$$
$$432$$ 0 0
$$433$$ 3.17525 0.152593 0.0762963 0.997085i $$-0.475690\pi$$
0.0762963 + 0.997085i $$0.475690\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −12.5498 + 21.7370i −0.600340 + 1.03982i
$$438$$ 0 0
$$439$$ 8.63746 + 14.9605i 0.412243 + 0.714027i 0.995135 0.0985236i $$-0.0314120\pi$$
−0.582891 + 0.812550i $$0.698079\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 3.18729 + 5.52055i 0.151433 + 0.262289i 0.931754 0.363089i $$-0.118278\pi$$
−0.780322 + 0.625378i $$0.784945\pi$$
$$444$$ 0 0
$$445$$ 17.2749 29.9210i 0.818910 1.41839i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −20.5498 −0.969807 −0.484903 0.874568i $$-0.661145\pi$$
−0.484903 + 0.874568i $$0.661145\pi$$
$$450$$ 0 0
$$451$$ −7.45017 + 12.9041i −0.350815 + 0.607629i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −23.3746 + 49.0887i −1.09582 + 2.30131i
$$456$$ 0 0
$$457$$ −18.3248 31.7394i −0.857196 1.48471i −0.874593 0.484858i $$-0.838871\pi$$
0.0173972 0.999849i $$-0.494462\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 3.64950 0.169974 0.0849872 0.996382i $$-0.472915\pi$$
0.0849872 + 0.996382i $$0.472915\pi$$
$$462$$ 0 0
$$463$$ −13.1752 −0.612306 −0.306153 0.951982i $$-0.599042\pi$$
−0.306153 + 0.951982i $$0.599042\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −20.2749 35.1172i −0.938211 1.62503i −0.768805 0.639483i $$-0.779148\pi$$
−0.169406 0.985546i $$-0.554185\pi$$
$$468$$ 0 0
$$469$$ −0.725083 + 0.0575438i −0.0334812 + 0.00265713i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0.450166 0.779710i 0.0206986 0.0358511i
$$474$$ 0 0
$$475$$ 35.9244 1.64833
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 2.72508 4.71998i 0.124512 0.215661i −0.797030 0.603940i $$-0.793597\pi$$
0.921542 + 0.388278i $$0.126930\pi$$
$$480$$ 0 0
$$481$$ 7.13746 + 12.3624i 0.325440 + 0.563679i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 14.2870 + 24.7457i 0.648738 + 1.12365i
$$486$$ 0 0
$$487$$ 0.500000 0.866025i 0.0226572 0.0392434i −0.854475 0.519493i $$-0.826121\pi$$
0.877132 + 0.480250i $$0.159454\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 36.9244 1.66638 0.833188 0.552990i $$-0.186513\pi$$
0.833188 + 0.552990i $$0.186513\pi$$
$$492$$ 0 0
$$493$$ 10.5498 18.2728i 0.475141 0.822968i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 3.00000 + 4.35890i 0.134568 + 0.195523i
$$498$$ 0 0
$$499$$ 16.1375 + 27.9509i 0.722412 + 1.25125i 0.960030 + 0.279896i $$0.0902998\pi$$
−0.237619 + 0.971359i $$0.576367\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −37.6495 −1.67871 −0.839354 0.543585i $$-0.817067\pi$$
−0.839354 + 0.543585i $$0.817067\pi$$
$$504$$ 0 0
$$505$$ −19.6495 −0.874391
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −5.63746 9.76436i −0.249876 0.432798i 0.713615 0.700538i $$-0.247057\pi$$
−0.963491 + 0.267740i $$0.913723\pi$$
$$510$$ 0 0
$$511$$ 11.2749 0.894797i 0.498773 0.0395835i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −17.7251 + 30.7007i −0.781060 + 1.35284i
$$516$$ 0 0
$$517$$ −19.6495 −0.864184
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −7.27492 + 12.6005i −0.318720 + 0.552039i −0.980221 0.197905i $$-0.936586\pi$$
0.661501 + 0.749944i $$0.269920\pi$$
$$522$$ 0 0
$$523$$ −8.86254 15.3504i −0.387532 0.671225i 0.604585 0.796541i $$-0.293339\pi$$
−0.992117 + 0.125316i $$0.960006\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −2.00000 3.46410i −0.0871214 0.150899i
$$528$$ 0 0
$$529$$ 3.50000 6.06218i 0.152174 0.263573i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 28.5498 1.23663
$$534$$ 0 0
$$535$$ −25.9124 + 44.8816i −1.12029 + 1.94040i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −14.4502 17.7967i −0.622413 0.766557i
$$540$$ 0 0
$$541$$ 4.13746 + 7.16629i 0.177883 + 0.308103i 0.941155 0.337974i $$-0.109742\pi$$
−0.763272 + 0.646077i $$0.776408\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −55.0997 −2.36021
$$546$$ 0 0
$$547$$ 28.0000 1.19719 0.598597 0.801050i $$-0.295725\pi$$
0.598597 + 0.801050i $$0.295725\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 16.5498 + 28.6652i 0.705047 + 1.22118i
$$552$$ 0 0
$$553$$ −13.1375 + 27.5898i −0.558662 + 1.17324i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −14.9124 + 25.8290i −0.631858 + 1.09441i 0.355314 + 0.934747i $$0.384374\pi$$
−0.987172 + 0.159663i $$0.948959\pi$$
$$558$$ 0 0
$$559$$ −1.72508 −0.0729632
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −7.63746 + 13.2285i −0.321881 + 0.557513i −0.980876 0.194633i $$-0.937648\pi$$
0.658996 + 0.752147i $$0.270982\pi$$
$$564$$ 0 0
$$565$$ 7.45017 + 12.9041i 0.313431 + 0.542878i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 5.72508 + 9.91613i 0.240008 + 0.415706i 0.960716 0.277532i $$-0.0895166\pi$$
−0.720708 + 0.693238i $$0.756183\pi$$
$$570$$ 0 0
$$571$$ 4.13746 7.16629i 0.173147 0.299900i −0.766371 0.642398i $$-0.777940\pi$$
0.939519 + 0.342498i $$0.111273\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 22.9003 0.955010
$$576$$ 0 0
$$577$$ 12.5000 21.6506i 0.520382 0.901328i −0.479337 0.877631i $$-0.659123\pi$$
0.999719 0.0236970i $$-0.00754370\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 10.9124 + 15.8553i 0.452722 + 0.657789i
$$582$$ 0 0
$$583$$ 15.1873 + 26.3052i 0.628993 + 1.08945i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 9.27492 0.382817 0.191408 0.981510i $$-0.438695\pi$$
0.191408 + 0.981510i $$0.438695\pi$$
$$588$$ 0 0
$$589$$ 6.27492 0.258553
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −0.274917 0.476171i −0.0112895 0.0195540i 0.860325 0.509745i $$-0.170260\pi$$
−0.871615 + 0.490191i $$0.836927\pi$$
$$594$$ 0 0
$$595$$ −19.6495 28.5501i −0.805551 1.17044i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −11.2749 + 19.5287i −0.460681 + 0.797922i −0.998995 0.0448219i $$-0.985728\pi$$
0.538314 + 0.842744i $$0.319061\pi$$
$$600$$ 0 0
$$601$$ 4.09967 0.167229 0.0836145 0.996498i $$-0.473354\pi$$
0.0836145 + 0.996498i $$0.473354\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −0.450166 + 0.779710i −0.0183018 + 0.0316997i
$$606$$ 0 0
$$607$$ −3.50000 6.06218i −0.142061 0.246056i 0.786212 0.617957i $$-0.212039\pi$$
−0.928272 + 0.371901i $$0.878706\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 18.8248 + 32.6054i 0.761568 + 1.31907i
$$612$$ 0 0
$$613$$ 4.27492 7.40437i 0.172662 0.299060i −0.766688 0.642020i $$-0.778096\pi$$
0.939350 + 0.342961i $$0.111430\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ 0 0
$$619$$ 14.4124 24.9630i 0.579282 1.00335i −0.416280 0.909237i $$-0.636666\pi$$
0.995562 0.0941097i $$-0.0300004\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 12.0000 25.2011i 0.480770 1.00966i
$$624$$ 0 0
$$625$$ 10.4244 + 18.0556i 0.416977 + 0.722225i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −9.09967 −0.362828
$$630$$ 0 0
$$631$$ −19.8248 −0.789211 −0.394605 0.918851i $$-0.629119\pi$$
−0.394605 + 0.918851i $$0.629119\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 10.5619 + 18.2937i 0.419135 + 0.725964i
$$636$$ 0 0
$$637$$ −15.6873 + 41.0276i −0.621553 + 1.62557i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −1.82475 + 3.16056i −0.0720734 + 0.124835i −0.899810 0.436282i $$-0.856295\pi$$
0.827736 + 0.561117i $$0.189628\pi$$
$$642$$ 0 0
$$643$$ −5.37459 −0.211953 −0.105976 0.994369i $$-0.533797\pi$$
−0.105976 + 0.994369i $$0.533797\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 17.0000 29.4449i 0.668339 1.15760i −0.310029 0.950727i $$-0.600339\pi$$
0.978368 0.206870i $$-0.0663277\pi$$
$$648$$ 0 0
$$649$$ 2.08762 + 3.61587i 0.0819464 + 0.141935i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −3.46221 5.99672i −0.135487 0.234670i 0.790297 0.612725i $$-0.209926\pi$$
−0.925783 + 0.378055i $$0.876593\pi$$
$$654$$ 0 0
$$655$$ 11.9124 20.6328i 0.465455 0.806192i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −42.1993 −1.64385 −0.821926 0.569594i $$-0.807101\pi$$
−0.821926 + 0.569594i $$0.807101\pi$$
$$660$$ 0 0
$$661$$ −3.58762 + 6.21395i −0.139542 + 0.241695i −0.927323 0.374261i $$-0.877896\pi$$
0.787781 + 0.615955i $$0.211230\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 54.1993 4.30136i 2.10176 0.166799i
$$666$$ 0 0
$$667$$ 10.5498 + 18.2728i 0.408491 + 0.707528i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 32.7492 1.26427
$$672$$ 0 0
$$673$$ 41.5498 1.60163 0.800814 0.598913i $$-0.204400\pi$$
0.800814 + 0.598913i $$0.204400\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −6.63746 11.4964i −0.255098 0.441843i 0.709824 0.704379i $$-0.248774\pi$$
−0.964922 + 0.262536i $$0.915441\pi$$
$$678$$ 0 0
$$679$$ 13.0876 + 19.0159i 0.502257 + 0.729762i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −6.08762 + 10.5441i −0.232936 + 0.403458i −0.958671 0.284517i $$-0.908167\pi$$
0.725735 + 0.687975i $$0.241500\pi$$
$$684$$ 0 0
$$685$$ 4.74917 0.181457
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 29.0997 50.4021i 1.10861 1.92017i
$$690$$ 0 0
$$691$$ −5.41238 9.37451i −0.205896 0.356623i 0.744522 0.667598i $$-0.232678\pi$$
−0.950418 + 0.310975i $$0.899344\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −13.5498 23.4690i −0.513975 0.890230i
$$696$$ 0 0
$$697$$ −9.09967 + 15.7611i −0.344675 + 0.596994i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 12.9244 0.488149 0.244074 0.969757i $$-0.421516\pi$$
0.244074 + 0.969757i $$0.421516\pi$$
$$702$$ 0 0
$$703$$ 7.13746 12.3624i 0.269194 0.466258i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −15.8248 + 1.25588i −0.595151 + 0.0472322i
$$708$$ 0 0
$$709$$ 14.0997 + 24.4213i 0.529524 + 0.917163i 0.999407 + 0.0344340i $$0.0109628\pi$$
−0.469883 + 0.882729i $$0.655704\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 4.00000 0.149801
$$714$$ 0 0
$$715$$ −67.2990 −2.51684
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −14.0997 24.4213i −0.525829 0.910762i −0.999547 0.0300860i $$-0.990422\pi$$
0.473718 0.880676i $$-0.342911\pi$$
$$720$$ 0 0
$$721$$ −12.3127 + 25.8578i −0.458549 + 0.962993i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 15.0997 26.1534i 0.560788 0.971313i
$$726$$ 0 0
$$727$$ −31.5498 −1.17012 −0.585059 0.810991i $$-0.698929\pi$$
−0.585059 + 0.810991i $$0.698929\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0.549834 0.952341i 0.0203364 0.0352236i
$$732$$ 0 0
$$733$$ −2.96221 5.13070i −0.109412 0.189507i 0.806120 0.591752i $$-0.201563\pi$$
−0.915532 + 0.402245i $$0.868230\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −0.450166 0.779710i −0.0165821 0.0287210i
$$738$$ 0 0
$$739$$ 0.687293 1.19043i 0.0252825 0.0437905i −0.853107 0.521735i $$-0.825285\pi$$
0.878390 + 0.477945i $$0.158618\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −44.1993 −1.62152 −0.810758 0.585381i $$-0.800945\pi$$
−0.810758 + 0.585381i $$0.800945\pi$$
$$744$$ 0 0
$$745$$ 23.8248 41.2657i 0.872871 1.51186i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −18.0000 + 37.8016i −0.657706 + 1.38124i
$$750$$ 0 0
$$751$$ −5.22508 9.05011i −0.190666 0.330243i 0.754805 0.655949i $$-0.227731\pi$$
−0.945471 + 0.325706i $$0.894398\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 73.2749 2.66675
$$756$$ 0 0
$$757$$ −22.0000 −0.799604 −0.399802 0.916602i $$-0.630921\pi$$
−0.399802 + 0.916602i $$0.630921\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −12.5498 21.7370i −0.454931 0.787964i 0.543753 0.839245i $$-0.317003\pi$$
−0.998684 + 0.0512814i $$0.983669\pi$$
$$762$$ 0 0
$$763$$ −44.3746 + 3.52165i −1.60647 + 0.127492i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 4.00000 6.92820i 0.144432 0.250163i
$$768$$ 0 0
$$769$$ −32.6495 −1.17737 −0.588686 0.808362i $$-0.700354\pi$$
−0.588686 + 0.808362i $$0.700354\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1.54983 2.68439i 0.0557437 0.0965509i −0.836807 0.547498i $$-0.815580\pi$$
0.892551 + 0.450947i $$0.148914\pi$$
$$774$$ 0 0
$$775$$ −2.86254 4.95807i −0.102826 0.178099i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −14.2749 24.7249i −0.511452 0.885861i
$$780$$ 0 0
$$781$$ −3.27492 + 5.67232i −0.117186 + 0.202972i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 1.80066 0.0642684
$$786$$ 0 0
$$787$$ 1.27492 2.20822i 0.0454459 0.0787146i −0.842408 0.538841i $$-0.818862\pi$$
0.887854 + 0.460126i $$0.152196\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 6.82475 + 9.91613i 0.242660 + 0.352577i
$$792$$ 0 0
$$793$$ −31.3746 54.3424i −1.11414 1.92975i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 31.4743 1.11488 0.557438 0.830219i $$-0.311785\pi$$
0.557438 +