# Properties

 Label 1152.2.i.k.385.4 Level $1152$ Weight $2$ Character 1152.385 Analytic conductor $9.199$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

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## Newspace parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1152.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.19876631285$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 385.4 Root $$1.73202 - 0.0102491i$$ of defining polynomial Character $$\chi$$ $$=$$ 1152.385 Dual form 1152.2.i.k.769.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.857134 + 1.50510i) q^{3} +(0.551563 + 0.955334i) q^{5} +(-1.62490 + 2.81442i) q^{7} +(-1.53064 + 2.58014i) q^{9} +O(q^{10})$$ $$q+(0.857134 + 1.50510i) q^{3} +(0.551563 + 0.955334i) q^{5} +(-1.62490 + 2.81442i) q^{7} +(-1.53064 + 2.58014i) q^{9} +(1.28869 - 2.23208i) q^{11} +(1.58731 + 2.74930i) q^{13} +(-0.965109 + 1.64901i) q^{15} +4.71601 q^{17} -5.75569 q^{19} +(-5.62873 - 0.0333075i) q^{21} +(2.35397 + 4.07719i) q^{23} +(1.89156 - 3.27627i) q^{25} +(-5.19533 - 0.0922374i) q^{27} +(-3.66250 + 6.34363i) q^{29} +(-2.93135 - 5.07724i) q^{31} +(4.46408 + 0.0264158i) q^{33} -3.58494 q^{35} -0.0714979 q^{37} +(-2.77743 + 4.74558i) q^{39} +(-1.63887 - 2.83861i) q^{41} +(-2.12088 + 3.67347i) q^{43} +(-3.30914 - 0.0391645i) q^{45} +(-4.72803 + 8.18919i) q^{47} +(-1.78062 - 3.08413i) q^{49} +(4.04225 + 7.09806i) q^{51} -6.42812 q^{53} +2.84317 q^{55} +(-4.93340 - 8.66288i) q^{57} +(-4.19606 - 7.26779i) q^{59} +(4.66250 - 8.07568i) q^{61} +(-4.77445 - 8.50035i) q^{63} +(-1.75100 + 3.03283i) q^{65} +(6.09975 + 10.5651i) q^{67} +(-4.11890 + 7.03765i) q^{69} -0.335627 q^{71} +14.8664 q^{73} +(6.55243 + 0.0387734i) q^{75} +(4.18800 + 7.25382i) q^{77} +(4.85985 - 8.41750i) q^{79} +(-4.31427 - 7.89855i) q^{81} +(-3.07022 + 5.31778i) q^{83} +(2.60117 + 4.50537i) q^{85} +(-12.6870 - 0.0750744i) q^{87} +4.42812 q^{89} -10.3169 q^{91} +(5.12919 - 8.76384i) q^{93} +(-3.17462 - 5.49861i) q^{95} +(6.39456 - 11.0757i) q^{97} +(3.78655 + 6.74151i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q + 4q^{3} - 2q^{5} + 6q^{7} - 2q^{9} + O(q^{10})$$ $$12q + 4q^{3} - 2q^{5} + 6q^{7} - 2q^{9} + 4q^{11} + 10q^{13} + 4q^{15} + 4q^{17} + 4q^{19} + 2q^{21} + 8q^{23} - 14q^{25} - 14q^{27} - 2q^{29} + 8q^{31} - 10q^{33} + 8q^{35} + 22q^{39} - 2q^{41} - 2q^{43} + 10q^{45} - 14q^{47} - 18q^{49} - 38q^{51} + 24q^{53} - 16q^{55} - 38q^{57} + 6q^{59} + 14q^{61} - 16q^{63} - 8q^{65} + 4q^{67} - 50q^{69} - 28q^{71} + 60q^{73} + 50q^{75} + 2q^{77} + 16q^{79} + 22q^{81} + 24q^{83} + 16q^{85} - 36q^{87} - 48q^{89} - 52q^{91} + 42q^{93} - 20q^{95} - 14q^{97} + 68q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$641$$ $$901$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$3$$ 0.857134 + 1.50510i 0.494867 + 0.868969i
$$4$$ 0 0
$$5$$ 0.551563 + 0.955334i 0.246666 + 0.427238i 0.962599 0.270931i $$-0.0873315\pi$$
−0.715933 + 0.698169i $$0.753998\pi$$
$$6$$ 0 0
$$7$$ −1.62490 + 2.81442i −0.614156 + 1.06375i 0.376376 + 0.926467i $$0.377170\pi$$
−0.990532 + 0.137282i $$0.956163\pi$$
$$8$$ 0 0
$$9$$ −1.53064 + 2.58014i −0.510214 + 0.860048i
$$10$$ 0 0
$$11$$ 1.28869 2.23208i 0.388555 0.672997i −0.603701 0.797211i $$-0.706308\pi$$
0.992255 + 0.124215i $$0.0396411\pi$$
$$12$$ 0 0
$$13$$ 1.58731 + 2.74930i 0.440241 + 0.762520i 0.997707 0.0676799i $$-0.0215597\pi$$
−0.557466 + 0.830200i $$0.688226\pi$$
$$14$$ 0 0
$$15$$ −0.965109 + 1.64901i −0.249190 + 0.425771i
$$16$$ 0 0
$$17$$ 4.71601 1.14380 0.571900 0.820323i $$-0.306206\pi$$
0.571900 + 0.820323i $$0.306206\pi$$
$$18$$ 0 0
$$19$$ −5.75569 −1.32045 −0.660223 0.751070i $$-0.729538\pi$$
−0.660223 + 0.751070i $$0.729538\pi$$
$$20$$ 0 0
$$21$$ −5.62873 0.0333075i −1.22829 0.00726830i
$$22$$ 0 0
$$23$$ 2.35397 + 4.07719i 0.490836 + 0.850152i 0.999944 0.0105499i $$-0.00335820\pi$$
−0.509109 + 0.860702i $$0.670025\pi$$
$$24$$ 0 0
$$25$$ 1.89156 3.27627i 0.378312 0.655255i
$$26$$ 0 0
$$27$$ −5.19533 0.0922374i −0.999842 0.0177511i
$$28$$ 0 0
$$29$$ −3.66250 + 6.34363i −0.680108 + 1.17798i 0.294839 + 0.955547i $$0.404734\pi$$
−0.974947 + 0.222435i $$0.928599\pi$$
$$30$$ 0 0
$$31$$ −2.93135 5.07724i −0.526485 0.911899i −0.999524 0.0308575i $$-0.990176\pi$$
0.473039 0.881042i $$-0.343157\pi$$
$$32$$ 0 0
$$33$$ 4.46408 + 0.0264158i 0.777096 + 0.00459840i
$$34$$ 0 0
$$35$$ −3.58494 −0.605966
$$36$$ 0 0
$$37$$ −0.0714979 −0.0117542 −0.00587709 0.999983i $$-0.501871\pi$$
−0.00587709 + 0.999983i $$0.501871\pi$$
$$38$$ 0 0
$$39$$ −2.77743 + 4.74558i −0.444745 + 0.759901i
$$40$$ 0 0
$$41$$ −1.63887 2.83861i −0.255949 0.443317i 0.709204 0.705004i $$-0.249055\pi$$
−0.965153 + 0.261687i $$0.915721\pi$$
$$42$$ 0 0
$$43$$ −2.12088 + 3.67347i −0.323431 + 0.560198i −0.981193 0.193027i $$-0.938170\pi$$
0.657763 + 0.753225i $$0.271503\pi$$
$$44$$ 0 0
$$45$$ −3.30914 0.0391645i −0.493298 0.00583830i
$$46$$ 0 0
$$47$$ −4.72803 + 8.18919i −0.689654 + 1.19452i 0.282296 + 0.959327i $$0.408904\pi$$
−0.971950 + 0.235188i $$0.924429\pi$$
$$48$$ 0 0
$$49$$ −1.78062 3.08413i −0.254375 0.440590i
$$50$$ 0 0
$$51$$ 4.04225 + 7.09806i 0.566029 + 0.993927i
$$52$$ 0 0
$$53$$ −6.42812 −0.882970 −0.441485 0.897269i $$-0.645548\pi$$
−0.441485 + 0.897269i $$0.645548\pi$$
$$54$$ 0 0
$$55$$ 2.84317 0.383373
$$56$$ 0 0
$$57$$ −4.93340 8.66288i −0.653445 1.14743i
$$58$$ 0 0
$$59$$ −4.19606 7.26779i −0.546281 0.946186i −0.998525 0.0542918i $$-0.982710\pi$$
0.452244 0.891894i $$-0.350623\pi$$
$$60$$ 0 0
$$61$$ 4.66250 8.07568i 0.596971 1.03398i −0.396294 0.918124i $$-0.629704\pi$$
0.993265 0.115861i $$-0.0369628\pi$$
$$62$$ 0 0
$$63$$ −4.77445 8.50035i −0.601524 1.07094i
$$64$$ 0 0
$$65$$ −1.75100 + 3.03283i −0.217185 + 0.376176i
$$66$$ 0 0
$$67$$ 6.09975 + 10.5651i 0.745203 + 1.29073i 0.950100 + 0.311945i $$0.100981\pi$$
−0.204897 + 0.978783i $$0.565686\pi$$
$$68$$ 0 0
$$69$$ −4.11890 + 7.03765i −0.495858 + 0.847233i
$$70$$ 0 0
$$71$$ −0.335627 −0.0398316 −0.0199158 0.999802i $$-0.506340\pi$$
−0.0199158 + 0.999802i $$0.506340\pi$$
$$72$$ 0 0
$$73$$ 14.8664 1.73998 0.869989 0.493071i $$-0.164126\pi$$
0.869989 + 0.493071i $$0.164126\pi$$
$$74$$ 0 0
$$75$$ 6.55243 + 0.0387734i 0.756610 + 0.00447717i
$$76$$ 0 0
$$77$$ 4.18800 + 7.25382i 0.477266 + 0.826650i
$$78$$ 0 0
$$79$$ 4.85985 8.41750i 0.546776 0.947043i −0.451717 0.892161i $$-0.649188\pi$$
0.998493 0.0548820i $$-0.0174783\pi$$
$$80$$ 0 0
$$81$$ −4.31427 7.89855i −0.479364 0.877616i
$$82$$ 0 0
$$83$$ −3.07022 + 5.31778i −0.337000 + 0.583702i −0.983867 0.178901i $$-0.942746\pi$$
0.646867 + 0.762603i $$0.276079\pi$$
$$84$$ 0 0
$$85$$ 2.60117 + 4.50537i 0.282137 + 0.488676i
$$86$$ 0 0
$$87$$ −12.6870 0.0750744i −1.36019 0.00804882i
$$88$$ 0 0
$$89$$ 4.42812 0.469379 0.234690 0.972070i $$-0.424593\pi$$
0.234690 + 0.972070i $$0.424593\pi$$
$$90$$ 0 0
$$91$$ −10.3169 −1.08151
$$92$$ 0 0
$$93$$ 5.12919 8.76384i 0.531872 0.908768i
$$94$$ 0 0
$$95$$ −3.17462 5.49861i −0.325709 0.564145i
$$96$$ 0 0
$$97$$ 6.39456 11.0757i 0.649270 1.12457i −0.334028 0.942563i $$-0.608408\pi$$
0.983298 0.182005i $$-0.0582586\pi$$
$$98$$ 0 0
$$99$$ 3.78655 + 6.74151i 0.380563 + 0.677548i
$$100$$ 0 0
$$101$$ 3.80137 6.58417i 0.378250 0.655149i −0.612557 0.790426i $$-0.709859\pi$$
0.990808 + 0.135277i $$0.0431925\pi$$
$$102$$ 0 0
$$103$$ 5.62490 + 9.74262i 0.554238 + 0.959969i 0.997962 + 0.0638053i $$0.0203237\pi$$
−0.443724 + 0.896163i $$0.646343\pi$$
$$104$$ 0 0
$$105$$ −3.07278 5.39569i −0.299872 0.526566i
$$106$$ 0 0
$$107$$ −2.81493 −0.272130 −0.136065 0.990700i $$-0.543446\pi$$
−0.136065 + 0.990700i $$0.543446\pi$$
$$108$$ 0 0
$$109$$ −15.6539 −1.49937 −0.749685 0.661795i $$-0.769795\pi$$
−0.749685 + 0.661795i $$0.769795\pi$$
$$110$$ 0 0
$$111$$ −0.0612833 0.107611i −0.00581675 0.0102140i
$$112$$ 0 0
$$113$$ 10.1828 + 17.6370i 0.957913 + 1.65915i 0.727557 + 0.686047i $$0.240656\pi$$
0.230355 + 0.973107i $$0.426011\pi$$
$$114$$ 0 0
$$115$$ −2.59672 + 4.49765i −0.242145 + 0.419408i
$$116$$ 0 0
$$117$$ −9.52320 0.112709i −0.880420 0.0104200i
$$118$$ 0 0
$$119$$ −7.66306 + 13.2728i −0.702472 + 1.21672i
$$120$$ 0 0
$$121$$ 2.17855 + 3.77337i 0.198050 + 0.343033i
$$122$$ 0 0
$$123$$ 2.86766 4.89974i 0.258568 0.441795i
$$124$$ 0 0
$$125$$ 9.68887 0.866599
$$126$$ 0 0
$$127$$ 3.09888 0.274981 0.137491 0.990503i $$-0.456096\pi$$
0.137491 + 0.990503i $$0.456096\pi$$
$$128$$ 0 0
$$129$$ −7.34680 0.0434741i −0.646850 0.00382768i
$$130$$ 0 0
$$131$$ 0.251085 + 0.434893i 0.0219374 + 0.0379968i 0.876786 0.480881i $$-0.159683\pi$$
−0.854848 + 0.518878i $$0.826350\pi$$
$$132$$ 0 0
$$133$$ 9.35244 16.1989i 0.810960 1.40462i
$$134$$ 0 0
$$135$$ −2.77743 5.01416i −0.239043 0.431550i
$$136$$ 0 0
$$137$$ −4.88868 + 8.46744i −0.417668 + 0.723423i −0.995704 0.0925885i $$-0.970486\pi$$
0.578036 + 0.816011i $$0.303819\pi$$
$$138$$ 0 0
$$139$$ −0.188498 0.326488i −0.0159882 0.0276924i 0.857921 0.513782i $$-0.171756\pi$$
−0.873909 + 0.486090i $$0.838423\pi$$
$$140$$ 0 0
$$141$$ −16.3781 0.0969159i −1.37928 0.00816179i
$$142$$ 0 0
$$143$$ 8.18221 0.684231
$$144$$ 0 0
$$145$$ −8.08038 −0.671039
$$146$$ 0 0
$$147$$ 3.11569 5.32353i 0.256978 0.439077i
$$148$$ 0 0
$$149$$ 4.83712 + 8.37814i 0.396272 + 0.686364i 0.993263 0.115885i $$-0.0369703\pi$$
−0.596990 + 0.802248i $$0.703637\pi$$
$$150$$ 0 0
$$151$$ 8.42915 14.5997i 0.685954 1.18811i −0.287181 0.957876i $$-0.592718\pi$$
0.973136 0.230232i $$-0.0739484\pi$$
$$152$$ 0 0
$$153$$ −7.21852 + 12.1680i −0.583583 + 0.983723i
$$154$$ 0 0
$$155$$ 3.23364 5.60083i 0.259732 0.449870i
$$156$$ 0 0
$$157$$ −4.36262 7.55628i −0.348175 0.603057i 0.637750 0.770243i $$-0.279865\pi$$
−0.985925 + 0.167187i $$0.946532\pi$$
$$158$$ 0 0
$$159$$ −5.50976 9.67495i −0.436952 0.767273i
$$160$$ 0 0
$$161$$ −15.2999 −1.20580
$$162$$ 0 0
$$163$$ −12.2063 −0.956067 −0.478034 0.878342i $$-0.658650\pi$$
−0.478034 + 0.878342i $$0.658650\pi$$
$$164$$ 0 0
$$165$$ 2.43698 + 4.27925i 0.189719 + 0.333140i
$$166$$ 0 0
$$167$$ 11.3806 + 19.7118i 0.880657 + 1.52534i 0.850612 + 0.525794i $$0.176232\pi$$
0.0300447 + 0.999549i $$0.490435\pi$$
$$168$$ 0 0
$$169$$ 1.46088 2.53033i 0.112376 0.194640i
$$170$$ 0 0
$$171$$ 8.80990 14.8505i 0.673710 1.13565i
$$172$$ 0 0
$$173$$ −11.9797 + 20.7494i −0.910798 + 1.57755i −0.0978588 + 0.995200i $$0.531199\pi$$
−0.812939 + 0.582348i $$0.802134\pi$$
$$174$$ 0 0
$$175$$ 6.14720 + 10.6473i 0.464684 + 0.804857i
$$176$$ 0 0
$$177$$ 7.34215 12.5450i 0.551870 0.942937i
$$178$$ 0 0
$$179$$ 10.9992 0.822121 0.411061 0.911608i $$-0.365158\pi$$
0.411061 + 0.911608i $$0.365158\pi$$
$$180$$ 0 0
$$181$$ 22.2168 1.65136 0.825679 0.564140i $$-0.190792\pi$$
0.825679 + 0.564140i $$0.190792\pi$$
$$182$$ 0 0
$$183$$ 16.1511 + 0.0955726i 1.19392 + 0.00706493i
$$184$$ 0 0
$$185$$ −0.0394356 0.0683044i −0.00289936 0.00502184i
$$186$$ 0 0
$$187$$ 6.07748 10.5265i 0.444429 0.769774i
$$188$$ 0 0
$$189$$ 8.70151 14.4720i 0.632942 1.05268i
$$190$$ 0 0
$$191$$ 5.48760 9.50479i 0.397068 0.687743i −0.596294 0.802766i $$-0.703361\pi$$
0.993363 + 0.115023i $$0.0366942\pi$$
$$192$$ 0 0
$$193$$ −7.11682 12.3267i −0.512280 0.887294i −0.999899 0.0142378i $$-0.995468\pi$$
0.487619 0.873057i $$-0.337866\pi$$
$$194$$ 0 0
$$195$$ −6.06555 0.0358923i −0.434363 0.00257030i
$$196$$ 0 0
$$197$$ 8.15037 0.580690 0.290345 0.956922i $$-0.406230\pi$$
0.290345 + 0.956922i $$0.406230\pi$$
$$198$$ 0 0
$$199$$ 6.09200 0.431850 0.215925 0.976410i $$-0.430723\pi$$
0.215925 + 0.976410i $$0.430723\pi$$
$$200$$ 0 0
$$201$$ −10.6732 + 18.2364i −0.752827 + 1.28630i
$$202$$ 0 0
$$203$$ −11.9024 20.6156i −0.835385 1.44693i
$$204$$ 0 0
$$205$$ 1.80788 3.13135i 0.126268 0.218703i
$$206$$ 0 0
$$207$$ −14.1228 0.167147i −0.981603 0.0116175i
$$208$$ 0 0
$$209$$ −7.41730 + 12.8471i −0.513066 + 0.888656i
$$210$$ 0 0
$$211$$ 3.01985 + 5.23054i 0.207895 + 0.360085i 0.951051 0.309033i $$-0.100005\pi$$
−0.743156 + 0.669118i $$0.766672\pi$$
$$212$$ 0 0
$$213$$ −0.287677 0.505151i −0.0197113 0.0346124i
$$214$$ 0 0
$$215$$ −4.67918 −0.319118
$$216$$ 0 0
$$217$$ 19.0526 1.29338
$$218$$ 0 0
$$219$$ 12.7425 + 22.3754i 0.861057 + 1.51199i
$$220$$ 0 0
$$221$$ 7.48578 + 12.9657i 0.503548 + 0.872170i
$$222$$ 0 0
$$223$$ 10.5391 18.2542i 0.705749 1.22239i −0.260671 0.965428i $$-0.583944\pi$$
0.966420 0.256966i $$-0.0827228\pi$$
$$224$$ 0 0
$$225$$ 5.55796 + 9.89529i 0.370530 + 0.659686i
$$226$$ 0 0
$$227$$ 14.9946 25.9713i 0.995224 1.72378i 0.413069 0.910700i $$-0.364457\pi$$
0.582155 0.813078i $$-0.302210\pi$$
$$228$$ 0 0
$$229$$ 9.53170 + 16.5094i 0.629873 + 1.09097i 0.987577 + 0.157136i $$0.0502262\pi$$
−0.357704 + 0.933835i $$0.616440\pi$$
$$230$$ 0 0
$$231$$ −7.32804 + 12.5208i −0.482150 + 0.823811i
$$232$$ 0 0
$$233$$ 7.91098 0.518266 0.259133 0.965842i $$-0.416563\pi$$
0.259133 + 0.965842i $$0.416563\pi$$
$$234$$ 0 0
$$235$$ −10.4312 −0.680457
$$236$$ 0 0
$$237$$ 16.8347 + 0.0996179i 1.09353 + 0.00647088i
$$238$$ 0 0
$$239$$ 2.96685 + 5.13873i 0.191910 + 0.332397i 0.945883 0.324508i $$-0.105199\pi$$
−0.753973 + 0.656905i $$0.771865\pi$$
$$240$$ 0 0
$$241$$ −14.2494 + 24.6808i −0.917888 + 1.58983i −0.115270 + 0.993334i $$0.536773\pi$$
−0.802618 + 0.596494i $$0.796560\pi$$
$$242$$ 0 0
$$243$$ 8.19018 13.2635i 0.525400 0.850855i
$$244$$ 0 0
$$245$$ 1.96425 3.40218i 0.125491 0.217357i
$$246$$ 0 0
$$247$$ −9.13607 15.8241i −0.581314 1.00687i
$$248$$ 0 0
$$249$$ −10.6354 0.0629338i −0.673989 0.00398827i
$$250$$ 0 0
$$251$$ 15.6924 0.990498 0.495249 0.868751i $$-0.335077\pi$$
0.495249 + 0.868751i $$0.335077\pi$$
$$252$$ 0 0
$$253$$ 12.1341 0.762866
$$254$$ 0 0
$$255$$ −4.55146 + 7.77673i −0.285024 + 0.486997i
$$256$$ 0 0
$$257$$ 11.5645 + 20.0304i 0.721377 + 1.24946i 0.960448 + 0.278459i $$0.0898237\pi$$
−0.239071 + 0.971002i $$0.576843\pi$$
$$258$$ 0 0
$$259$$ 0.116177 0.201225i 0.00721890 0.0125035i
$$260$$ 0 0
$$261$$ −10.7615 19.1596i −0.666120 1.18595i
$$262$$ 0 0
$$263$$ 12.0737 20.9122i 0.744494 1.28950i −0.205937 0.978565i $$-0.566024\pi$$
0.950431 0.310936i $$-0.100642\pi$$
$$264$$ 0 0
$$265$$ −3.54551 6.14100i −0.217799 0.377239i
$$266$$ 0 0
$$267$$ 3.79549 + 6.66475i 0.232280 + 0.407876i
$$268$$ 0 0
$$269$$ −9.45599 −0.576542 −0.288271 0.957549i $$-0.593080\pi$$
−0.288271 + 0.957549i $$0.593080\pi$$
$$270$$ 0 0
$$271$$ −15.5750 −0.946115 −0.473057 0.881032i $$-0.656850\pi$$
−0.473057 + 0.881032i $$0.656850\pi$$
$$272$$ 0 0
$$273$$ −8.84298 15.5280i −0.535201 0.939795i
$$274$$ 0 0
$$275$$ −4.87526 8.44420i −0.293989 0.509205i
$$276$$ 0 0
$$277$$ 2.87862 4.98592i 0.172960 0.299575i −0.766494 0.642252i $$-0.778000\pi$$
0.939453 + 0.342677i $$0.111334\pi$$
$$278$$ 0 0
$$279$$ 17.5868 + 0.208144i 1.05290 + 0.0124613i
$$280$$ 0 0
$$281$$ 5.99712 10.3873i 0.357758 0.619656i −0.629828 0.776735i $$-0.716874\pi$$
0.987586 + 0.157079i $$0.0502078\pi$$
$$282$$ 0 0
$$283$$ −0.604018 1.04619i −0.0359051 0.0621895i 0.847514 0.530772i $$-0.178098\pi$$
−0.883420 + 0.468583i $$0.844765\pi$$
$$284$$ 0 0
$$285$$ 5.55487 9.49117i 0.329042 0.562208i
$$286$$ 0 0
$$287$$ 10.6520 0.628771
$$288$$ 0 0
$$289$$ 5.24075 0.308279
$$290$$ 0 0
$$291$$ 22.1510 + 0.131077i 1.29852 + 0.00768386i
$$292$$ 0 0
$$293$$ −10.4657 18.1272i −0.611415 1.05900i −0.991002 0.133846i $$-0.957267\pi$$
0.379587 0.925156i $$-0.376066\pi$$
$$294$$ 0 0
$$295$$ 4.62878 8.01728i 0.269498 0.466784i
$$296$$ 0 0
$$297$$ −6.90106 + 11.4775i −0.400440 + 0.665993i
$$298$$ 0 0
$$299$$ −7.47295 + 12.9435i −0.432172 + 0.748544i
$$300$$ 0 0
$$301$$ −6.89244 11.9381i −0.397274 0.688098i
$$302$$ 0 0
$$303$$ 13.1681 + 0.0779211i 0.756488 + 0.00447645i
$$304$$ 0 0
$$305$$ 10.2866 0.589011
$$306$$ 0 0
$$307$$ 5.12445 0.292468 0.146234 0.989250i $$-0.453285\pi$$
0.146234 + 0.989250i $$0.453285\pi$$
$$308$$ 0 0
$$309$$ −9.84230 + 16.8168i −0.559909 + 0.956672i
$$310$$ 0 0
$$311$$ −4.70739 8.15344i −0.266931 0.462339i 0.701136 0.713027i $$-0.252676\pi$$
−0.968068 + 0.250688i $$0.919343\pi$$
$$312$$ 0 0
$$313$$ −9.48986 + 16.4369i −0.536398 + 0.929069i 0.462696 + 0.886517i $$0.346882\pi$$
−0.999094 + 0.0425521i $$0.986451\pi$$
$$314$$ 0 0
$$315$$ 5.48726 9.24967i 0.309172 0.521160i
$$316$$ 0 0
$$317$$ 14.2294 24.6461i 0.799205 1.38426i −0.120930 0.992661i $$-0.538588\pi$$
0.920135 0.391602i $$-0.128079\pi$$
$$318$$ 0 0
$$319$$ 9.43965 + 16.3499i 0.528519 + 0.915421i
$$320$$ 0 0
$$321$$ −2.41278 4.23675i −0.134668 0.236472i
$$322$$ 0 0
$$323$$ −27.1439 −1.51033
$$324$$ 0 0
$$325$$ 12.0100 0.666193
$$326$$ 0 0
$$327$$ −13.4175 23.5606i −0.741988 1.30291i
$$328$$ 0 0
$$329$$ −15.3652 26.6133i −0.847110 1.46724i
$$330$$ 0 0
$$331$$ 0.837151 1.44999i 0.0460140 0.0796986i −0.842101 0.539320i $$-0.818681\pi$$
0.888115 + 0.459621i $$0.152015\pi$$
$$332$$ 0 0
$$333$$ 0.109438 0.184475i 0.00599715 0.0101092i
$$334$$ 0 0
$$335$$ −6.72878 + 11.6546i −0.367633 + 0.636758i
$$336$$ 0 0
$$337$$ −15.1064 26.1651i −0.822899 1.42530i −0.903514 0.428558i $$-0.859022\pi$$
0.0806146 0.996745i $$-0.474312\pi$$
$$338$$ 0 0
$$339$$ −17.8175 + 30.4434i −0.967714 + 1.65346i
$$340$$ 0 0
$$341$$ −15.1104 −0.818273
$$342$$ 0 0
$$343$$ −11.1753 −0.603408
$$344$$ 0 0
$$345$$ −8.99514 0.0532279i −0.484282 0.00286570i
$$346$$ 0 0
$$347$$ 8.46076 + 14.6545i 0.454197 + 0.786693i 0.998642 0.0521042i $$-0.0165928\pi$$
−0.544444 + 0.838797i $$0.683259\pi$$
$$348$$ 0 0
$$349$$ 8.92436 15.4574i 0.477710 0.827418i −0.521964 0.852968i $$-0.674800\pi$$
0.999674 + 0.0255500i $$0.00813369\pi$$
$$350$$ 0 0
$$351$$ −7.99302 14.4300i −0.426636 0.770214i
$$352$$ 0 0
$$353$$ −6.93593 + 12.0134i −0.369162 + 0.639407i −0.989435 0.144979i $$-0.953689\pi$$
0.620273 + 0.784386i $$0.287022\pi$$
$$354$$ 0 0
$$355$$ −0.185119 0.320636i −0.00982510 0.0170176i
$$356$$ 0 0
$$357$$ −26.5452 0.157079i −1.40492 0.00831348i
$$358$$ 0 0
$$359$$ −0.333139 −0.0175824 −0.00879120 0.999961i $$-0.502798\pi$$
−0.00879120 + 0.999961i $$0.502798\pi$$
$$360$$ 0 0
$$361$$ 14.1280 0.743577
$$362$$ 0 0
$$363$$ −3.81197 + 6.51322i −0.200077 + 0.341855i
$$364$$ 0 0
$$365$$ 8.19974 + 14.2024i 0.429194 + 0.743386i
$$366$$ 0 0
$$367$$ 10.5763 18.3188i 0.552081 0.956232i −0.446043 0.895011i $$-0.647167\pi$$
0.998124 0.0612208i $$-0.0194994\pi$$
$$368$$ 0 0
$$369$$ 9.83256 + 0.116371i 0.511862 + 0.00605801i
$$370$$ 0 0
$$371$$ 10.4451 18.0914i 0.542281 0.939258i
$$372$$ 0 0
$$373$$ 4.33750 + 7.51278i 0.224587 + 0.388997i 0.956196 0.292729i $$-0.0945632\pi$$
−0.731608 + 0.681725i $$0.761230\pi$$
$$374$$ 0 0
$$375$$ 8.30467 + 14.5827i 0.428851 + 0.753048i
$$376$$ 0 0
$$377$$ −23.2541 −1.19765
$$378$$ 0 0
$$379$$ 14.2538 0.732168 0.366084 0.930582i $$-0.380698\pi$$
0.366084 + 0.930582i $$0.380698\pi$$
$$380$$ 0 0
$$381$$ 2.65616 + 4.66412i 0.136079 + 0.238950i
$$382$$ 0 0
$$383$$ 5.11696 + 8.86283i 0.261464 + 0.452869i 0.966631 0.256172i $$-0.0824613\pi$$
−0.705167 + 0.709041i $$0.749128\pi$$
$$384$$ 0 0
$$385$$ −4.61988 + 8.00187i −0.235451 + 0.407813i
$$386$$ 0 0
$$387$$ −6.23177 11.0949i −0.316778 0.563987i
$$388$$ 0 0
$$389$$ 1.62675 2.81761i 0.0824793 0.142858i −0.821835 0.569726i $$-0.807049\pi$$
0.904314 + 0.426867i $$0.140383\pi$$
$$390$$ 0 0
$$391$$ 11.1013 + 19.2281i 0.561418 + 0.972405i
$$392$$ 0 0
$$393$$ −0.439342 + 0.750670i −0.0221619 + 0.0378663i
$$394$$ 0 0
$$395$$ 10.7220 0.539484
$$396$$ 0 0
$$397$$ −30.8709 −1.54936 −0.774682 0.632351i $$-0.782090\pi$$
−0.774682 + 0.632351i $$0.782090\pi$$
$$398$$ 0 0
$$399$$ 32.3972 + 0.191708i 1.62189 + 0.00959739i
$$400$$ 0 0
$$401$$ −2.01000 3.48143i −0.100375 0.173854i 0.811464 0.584402i $$-0.198671\pi$$
−0.911839 + 0.410548i $$0.865338\pi$$
$$402$$ 0 0
$$403$$ 9.30592 16.1183i 0.463561 0.802911i
$$404$$ 0 0
$$405$$ 5.16616 8.47812i 0.256709 0.421281i
$$406$$ 0 0
$$407$$ −0.0921386 + 0.159589i −0.00456714 + 0.00791052i
$$408$$ 0 0
$$409$$ −3.33949 5.78416i −0.165127 0.286008i 0.771573 0.636140i $$-0.219470\pi$$
−0.936700 + 0.350132i $$0.886137\pi$$
$$410$$ 0 0
$$411$$ −16.9346 0.100209i −0.835322 0.00494294i
$$412$$ 0 0
$$413$$ 27.2728 1.34201
$$414$$ 0 0
$$415$$ −6.77367 −0.332507
$$416$$ 0 0
$$417$$ 0.329829 0.563553i 0.0161518 0.0275973i
$$418$$ 0 0
$$419$$ 17.0507 + 29.5327i 0.832982 + 1.44277i 0.895663 + 0.444733i $$0.146701\pi$$
−0.0626815 + 0.998034i $$0.519965\pi$$
$$420$$ 0 0
$$421$$ 9.34688 16.1893i 0.455539 0.789017i −0.543180 0.839616i $$-0.682780\pi$$
0.998719 + 0.0505996i $$0.0161132\pi$$
$$422$$ 0 0
$$423$$ −13.8924 24.7337i −0.675469 1.20259i
$$424$$ 0 0
$$425$$ 8.92060 15.4509i 0.432713 0.749481i
$$426$$ 0 0
$$427$$ 15.1522 + 26.2444i 0.733267 + 1.27006i
$$428$$ 0 0
$$429$$ 7.01325 + 12.3150i 0.338603 + 0.594575i
$$430$$ 0 0
$$431$$ −6.49967 −0.313078 −0.156539 0.987672i $$-0.550034\pi$$
−0.156539 + 0.987672i $$0.550034\pi$$
$$432$$ 0 0
$$433$$ 28.3266 1.36129 0.680645 0.732613i $$-0.261700\pi$$
0.680645 + 0.732613i $$0.261700\pi$$
$$434$$ 0 0
$$435$$ −6.92597 12.1618i −0.332075 0.583112i
$$436$$ 0 0
$$437$$ −13.5487 23.4670i −0.648122 1.12258i
$$438$$ 0 0
$$439$$ 3.82047 6.61724i 0.182341 0.315824i −0.760336 0.649530i $$-0.774966\pi$$
0.942677 + 0.333706i $$0.108299\pi$$
$$440$$ 0 0
$$441$$ 10.6830 + 0.126436i 0.508714 + 0.00602075i
$$442$$ 0 0
$$443$$ −6.94625 + 12.0313i −0.330026 + 0.571623i −0.982517 0.186175i $$-0.940391\pi$$
0.652490 + 0.757797i $$0.273724\pi$$
$$444$$ 0 0
$$445$$ 2.44238 + 4.23033i 0.115780 + 0.200537i
$$446$$ 0 0
$$447$$ −8.46386 + 14.4615i −0.400327 + 0.684007i
$$448$$ 0 0
$$449$$ 11.8869 0.560976 0.280488 0.959857i $$-0.409504\pi$$
0.280488 + 0.959857i $$0.409504\pi$$
$$450$$ 0 0
$$451$$ −8.44800 −0.397801
$$452$$ 0 0
$$453$$ 29.1989 + 0.172782i 1.37188 + 0.00811801i
$$454$$ 0 0
$$455$$ −5.69042 9.85610i −0.266771 0.462061i
$$456$$ 0 0
$$457$$ 0.860741 1.49085i 0.0402638 0.0697389i −0.845191 0.534464i $$-0.820514\pi$$
0.885455 + 0.464725i $$0.153847\pi$$
$$458$$ 0 0
$$459$$ −24.5012 0.434992i −1.14362 0.0203037i
$$460$$ 0 0
$$461$$ −15.8265 + 27.4123i −0.737113 + 1.27672i 0.216677 + 0.976243i $$0.430478\pi$$
−0.953790 + 0.300474i $$0.902855\pi$$
$$462$$ 0 0
$$463$$ 1.71702 + 2.97396i 0.0797966 + 0.138212i 0.903162 0.429300i $$-0.141240\pi$$
−0.823366 + 0.567511i $$0.807906\pi$$
$$464$$ 0 0
$$465$$ 11.2015 + 0.0662837i 0.519456 + 0.00307383i
$$466$$ 0 0
$$467$$ −15.5333 −0.718797 −0.359398 0.933184i $$-0.617018\pi$$
−0.359398 + 0.933184i $$0.617018\pi$$
$$468$$ 0 0
$$469$$ −39.6460 −1.83068
$$470$$ 0 0
$$471$$ 7.63359 13.0429i 0.351737 0.600986i
$$472$$ 0 0
$$473$$ 5.46631 + 9.46792i 0.251341 + 0.435335i
$$474$$ 0 0
$$475$$ −10.8872 + 18.8572i −0.499540 + 0.865228i
$$476$$ 0 0
$$477$$ 9.83914 16.5855i 0.450503 0.759396i
$$478$$ 0 0
$$479$$ −16.6927 + 28.9126i −0.762710 + 1.32105i 0.178739 + 0.983897i $$0.442798\pi$$
−0.941449 + 0.337156i $$0.890535\pi$$
$$480$$ 0 0
$$481$$ −0.113489 0.196569i −0.00517467 0.00896280i
$$482$$ 0 0
$$483$$ −13.1140 23.0278i −0.596710 1.04780i
$$484$$ 0 0
$$485$$ 14.1080 0.640612
$$486$$ 0 0
$$487$$ −20.0794 −0.909883 −0.454941 0.890521i $$-0.650340\pi$$
−0.454941 + 0.890521i $$0.650340\pi$$
$$488$$ 0 0
$$489$$ −10.4624 18.3716i −0.473126 0.830793i
$$490$$ 0 0
$$491$$ −2.10538 3.64663i −0.0950146 0.164570i 0.814600 0.580023i $$-0.196956\pi$$
−0.909615 + 0.415453i $$0.863623\pi$$
$$492$$ 0 0
$$493$$ −17.2724 + 29.9166i −0.777908 + 1.34738i
$$494$$ 0 0
$$495$$ −4.35188 + 7.33579i −0.195602 + 0.329719i
$$496$$ 0 0
$$497$$ 0.545361 0.944593i 0.0244628 0.0423708i
$$498$$ 0 0
$$499$$ −5.24770 9.08928i −0.234919 0.406892i 0.724330 0.689453i $$-0.242149\pi$$
−0.959249 + 0.282561i $$0.908816\pi$$
$$500$$ 0 0
$$501$$ −19.9134 + 34.0245i −0.889667 + 1.52010i
$$502$$ 0 0
$$503$$ −34.5118 −1.53881 −0.769403 0.638764i $$-0.779446\pi$$
−0.769403 + 0.638764i $$0.779446\pi$$
$$504$$ 0 0
$$505$$ 8.38677 0.373206
$$506$$ 0 0
$$507$$ 5.06056 + 0.0299454i 0.224748 + 0.00132992i
$$508$$ 0 0
$$509$$ −2.62702 4.55013i −0.116440 0.201681i 0.801914 0.597439i $$-0.203815\pi$$
−0.918355 + 0.395758i $$0.870482\pi$$
$$510$$ 0 0
$$511$$ −24.1564 + 41.8402i −1.06862 + 1.85090i
$$512$$ 0 0
$$513$$ 29.9027 + 0.530890i 1.32024 + 0.0234394i
$$514$$ 0 0
$$515$$ −6.20497 + 10.7473i −0.273424 + 0.473584i
$$516$$ 0 0
$$517$$ 12.1859 + 21.1066i 0.535937 + 0.928269i
$$518$$ 0 0
$$519$$ −41.4981 0.245561i −1.82156 0.0107789i
$$520$$ 0 0
$$521$$ −12.9218 −0.566113 −0.283056 0.959103i $$-0.591348\pi$$
−0.283056 + 0.959103i $$0.591348\pi$$
$$522$$ 0 0
$$523$$ 5.10475 0.223215 0.111607 0.993752i $$-0.464400\pi$$
0.111607 + 0.993752i $$0.464400\pi$$
$$524$$ 0 0
$$525$$ −10.7562 + 18.3783i −0.469439 + 0.802093i
$$526$$ 0 0
$$527$$ −13.8243 23.9443i −0.602194 1.04303i
$$528$$ 0 0
$$529$$ 0.417694 0.723468i 0.0181606 0.0314551i
$$530$$ 0 0
$$531$$ 25.1746 + 0.297947i 1.09248 + 0.0129298i
$$532$$ 0 0
$$533$$ 5.20281 9.01153i 0.225359 0.390333i
$$534$$ 0 0
$$535$$ −1.55261 2.68920i −0.0671252 0.116264i
$$536$$ 0 0
$$537$$ 9.42782 + 16.5549i 0.406840 + 0.714398i
$$538$$ 0 0
$$539$$ −9.17869 −0.395354
$$540$$ 0 0
$$541$$ −37.9746 −1.63266 −0.816328 0.577589i $$-0.803994\pi$$
−0.816328 + 0.577589i $$0.803994\pi$$
$$542$$ 0 0
$$543$$ 19.0427 + 33.4384i 0.817202 + 1.43498i
$$544$$ 0 0
$$545$$ −8.63410 14.9547i −0.369844 0.640589i
$$546$$ 0 0
$$547$$ 15.9350 27.6003i 0.681332 1.18010i −0.293243 0.956038i $$-0.594734\pi$$
0.974575 0.224063i $$-0.0719323\pi$$
$$548$$ 0 0
$$549$$ 13.6998 + 24.3909i 0.584693 + 1.04098i
$$550$$ 0 0
$$551$$ 21.0802 36.5120i 0.898046 1.55546i
$$552$$ 0 0
$$553$$ 15.7936 + 27.3553i 0.671611 + 1.16326i
$$554$$ 0 0
$$555$$ 0.0690032 0.117900i 0.00292902 0.00500459i
$$556$$ 0 0
$$557$$ −11.5906 −0.491111 −0.245555 0.969383i $$-0.578970\pi$$
−0.245555 + 0.969383i $$0.578970\pi$$
$$558$$ 0 0
$$559$$ −13.4660 −0.569550
$$560$$ 0 0
$$561$$ 21.0526 + 0.124577i 0.888843 + 0.00525965i
$$562$$ 0 0
$$563$$ 1.25138 + 2.16745i 0.0527392 + 0.0913470i 0.891190 0.453631i $$-0.149871\pi$$
−0.838451 + 0.544978i $$0.816538\pi$$
$$564$$ 0 0
$$565$$ −11.2328 + 19.4559i −0.472569 + 0.818514i
$$566$$ 0 0
$$567$$ 29.2401 + 0.692223i 1.22797 + 0.0290706i
$$568$$ 0 0
$$569$$ 12.9597 22.4469i 0.543301 0.941024i −0.455411 0.890281i $$-0.650508\pi$$
0.998712 0.0507432i $$-0.0161590\pi$$
$$570$$ 0 0
$$571$$ 5.03679 + 8.72398i 0.210783 + 0.365087i 0.951960 0.306223i $$-0.0990653\pi$$
−0.741177 + 0.671310i $$0.765732\pi$$
$$572$$ 0 0
$$573$$ 19.0093 + 0.112486i 0.794123 + 0.00469915i
$$574$$ 0 0
$$575$$ 17.8106 0.742755
$$576$$ 0 0
$$577$$ −23.4726 −0.977177 −0.488588 0.872514i $$-0.662488\pi$$
−0.488588 + 0.872514i $$0.662488\pi$$
$$578$$ 0 0
$$579$$ 12.4528 21.2771i 0.517521 0.884248i
$$580$$ 0 0
$$581$$ −9.97762 17.2818i −0.413942 0.716968i
$$582$$ 0 0
$$583$$ −8.28385 + 14.3481i −0.343082 + 0.594236i
$$584$$ 0 0
$$585$$ −5.14497 9.16001i −0.212718 0.378720i
$$586$$ 0 0
$$587$$ −12.4138 + 21.5012i −0.512370 + 0.887451i 0.487527 + 0.873108i $$0.337899\pi$$
−0.999897 + 0.0143435i $$0.995434\pi$$
$$588$$ 0 0
$$589$$ 16.8719 + 29.2230i 0.695195 + 1.20411i
$$590$$ 0 0
$$591$$ 6.98596 + 12.2671i 0.287364 + 0.504601i
$$592$$ 0 0
$$593$$ −7.70977 −0.316602 −0.158301 0.987391i $$-0.550602\pi$$
−0.158301 + 0.987391i $$0.550602\pi$$
$$594$$ 0 0
$$595$$ −16.9066 −0.693104
$$596$$ 0 0
$$597$$ 5.22166 + 9.16906i 0.213708 + 0.375265i
$$598$$ 0 0
$$599$$ 14.7176 + 25.4916i 0.601344 + 1.04156i 0.992618 + 0.121284i $$0.0387013\pi$$
−0.391274 + 0.920274i $$0.627965\pi$$
$$600$$ 0 0
$$601$$ −1.76388 + 3.05514i −0.0719503 + 0.124622i −0.899756 0.436393i $$-0.856256\pi$$
0.827806 + 0.561015i $$0.189589\pi$$
$$602$$ 0 0
$$603$$ −36.5959 0.433121i −1.49030 0.0176381i
$$604$$ 0 0
$$605$$ −2.40322 + 4.16250i −0.0977047 + 0.169230i
$$606$$ 0 0
$$607$$ 13.3211 + 23.0728i 0.540687 + 0.936497i 0.998865 + 0.0476362i $$0.0151688\pi$$
−0.458178 + 0.888860i $$0.651498\pi$$
$$608$$ 0 0
$$609$$ 20.8265 35.5846i 0.843932 1.44196i
$$610$$ 0 0
$$611$$ −30.0194 −1.21446
$$612$$ 0 0
$$613$$ 0.706406 0.0285315 0.0142657 0.999898i $$-0.495459\pi$$
0.0142657 + 0.999898i $$0.495459\pi$$
$$614$$ 0 0
$$615$$ 6.26258 + 0.0370583i 0.252532 + 0.00149433i
$$616$$ 0 0
$$617$$ 8.58480 + 14.8693i 0.345611 + 0.598616i 0.985465 0.169881i $$-0.0543383\pi$$
−0.639853 + 0.768497i $$0.721005\pi$$
$$618$$ 0 0
$$619$$ 4.17800 7.23651i 0.167928 0.290860i −0.769763 0.638330i $$-0.779626\pi$$
0.937691 + 0.347470i $$0.112959\pi$$
$$620$$ 0 0
$$621$$ −11.8536 21.3995i −0.475667 0.858731i
$$622$$ 0 0
$$623$$ −7.19526 + 12.4626i −0.288272 + 0.499302i
$$624$$ 0 0
$$625$$ −4.11377 7.12526i −0.164551 0.285010i
$$626$$ 0 0
$$627$$ −25.6938 0.152041i −1.02611 0.00607193i
$$628$$ 0 0
$$629$$ −0.337185 −0.0134444
$$630$$ 0 0
$$631$$ −23.9865 −0.954889 −0.477444 0.878662i $$-0.658437\pi$$
−0.477444 + 0.878662i $$0.658437\pi$$
$$632$$ 0 0
$$633$$ −5.28406 + 9.02845i −0.210022 + 0.358849i
$$634$$ 0 0
$$635$$ 1.70923 + 2.96047i 0.0678286 + 0.117483i
$$636$$ 0 0
$$637$$ 5.65281 9.79095i 0.223972 0.387932i
$$638$$ 0 0
$$639$$ 0.513724 0.865965i 0.0203226 0.0342570i
$$640$$ 0 0
$$641$$ 6.58068 11.3981i 0.259921 0.450197i −0.706299 0.707913i $$-0.749637\pi$$
0.966221 + 0.257716i $$0.0829700\pi$$
$$642$$ 0 0
$$643$$ −7.85931 13.6127i −0.309941 0.536834i 0.668408 0.743795i $$-0.266976\pi$$
−0.978349 + 0.206961i $$0.933643\pi$$
$$644$$ 0 0
$$645$$ −4.01069 7.04263i −0.157921 0.277303i
$$646$$ 0 0
$$647$$ 23.5146 0.924455 0.462228 0.886761i $$-0.347050\pi$$
0.462228 + 0.886761i $$0.347050\pi$$
$$648$$ 0 0
$$649$$ −21.6297 −0.849040
$$650$$ 0 0
$$651$$ 16.3307 + 28.6761i 0.640049 + 1.12390i
$$652$$ 0 0
$$653$$ −13.1340 22.7487i −0.513971 0.890224i −0.999869 0.0162084i $$-0.994840\pi$$
0.485897 0.874016i $$-0.338493\pi$$
$$654$$ 0 0
$$655$$ −0.276979 + 0.479741i −0.0108224 + 0.0187450i
$$656$$ 0 0
$$657$$ −22.7551 + 38.3574i −0.887761 + 1.49646i
$$658$$ 0 0
$$659$$ −13.2710 + 22.9860i −0.516963 + 0.895406i 0.482843 + 0.875707i $$0.339604\pi$$
−0.999806 + 0.0196993i $$0.993729\pi$$
$$660$$ 0 0
$$661$$ 0.981745 + 1.70043i 0.0381855 + 0.0661392i 0.884487 0.466566i $$-0.154509\pi$$
−0.846301 + 0.532705i $$0.821176\pi$$
$$662$$ 0 0
$$663$$ −13.0984 + 22.3802i −0.508700 + 0.869175i
$$664$$ 0 0
$$665$$ 20.6338 0.800145
$$666$$ 0 0
$$667$$ −34.4856 −1.33529
$$668$$ 0 0
$$669$$ 36.5078 + 0.216032i 1.41147 + 0.00835227i
$$670$$ 0 0
$$671$$ −12.0170 20.8141i −0.463912 0.803519i
$$672$$ 0 0
$$673$$ −18.9859 + 32.8846i −0.731854 + 1.26761i 0.224236 + 0.974535i $$0.428011\pi$$
−0.956090 + 0.293073i $$0.905322\pi$$
$$674$$ 0 0
$$675$$ −10.1295 + 16.8469i −0.389883 + 0.648436i
$$676$$ 0 0
$$677$$ −13.5894 + 23.5375i −0.522282 + 0.904619i 0.477382 + 0.878696i $$0.341586\pi$$
−0.999664 + 0.0259229i $$0.991748\pi$$
$$678$$ 0 0
$$679$$ 20.7811 + 35.9939i 0.797505 + 1.38132i
$$680$$ 0 0
$$681$$ 51.9418 + 0.307361i 1.99041 + 0.0117781i
$$682$$ 0 0
$$683$$ 46.9121 1.79504 0.897520 0.440974i $$-0.145367\pi$$
0.897520 + 0.440974i $$0.145367\pi$$
$$684$$ 0 0
$$685$$ −10.7857 −0.412099
$$686$$ 0 0
$$687$$ −16.6783 + 28.4969i −0.636317 + 1.08722i
$$688$$ 0 0
$$689$$ −10.2034 17.6728i −0.388719 0.673282i
$$690$$ 0 0
$$691$$ 12.6750 21.9538i 0.482181 0.835161i −0.517610 0.855617i $$-0.673178\pi$$
0.999791 + 0.0204552i $$0.00651153\pi$$
$$692$$ 0 0
$$693$$ −25.1262 0.297375i −0.954466 0.0112963i
$$694$$ 0 0
$$695$$ 0.207937 0.360157i 0.00788750 0.0136616i
$$696$$ 0 0
$$697$$ −7.72895 13.3869i −0.292755 0.507066i
$$698$$ 0 0
$$699$$ 6.78078 + 11.9068i 0.256472 + 0.450357i
$$700$$ 0 0
$$701$$ −44.2840 −1.67258 −0.836292 0.548284i $$-0.815281\pi$$
−0.836292 + 0.548284i $$0.815281\pi$$
$$702$$ 0 0
$$703$$ 0.411520 0.0155208
$$704$$ 0 0
$$705$$ −8.94095 15.7000i −0.336736 0.591296i
$$706$$ 0 0
$$707$$ 12.3537 + 21.3973i 0.464609 + 0.804727i
$$708$$ 0 0
$$709$$ −7.80457 + 13.5179i −0.293107 + 0.507676i −0.974543 0.224202i $$-0.928022\pi$$
0.681436 + 0.731878i $$0.261356\pi$$
$$710$$ 0 0
$$711$$ 14.2797 + 25.4233i 0.535530 + 0.953448i
$$712$$ 0 0
$$713$$ 13.8006 23.9033i 0.516836 0.895185i
$$714$$ 0 0
$$715$$ 4.51300 + 7.81675i 0.168777 + 0.292330i
$$716$$ 0 0
$$717$$ −5.19131 + 8.86999i −0.193873 + 0.331256i
$$718$$ 0 0
$$719$$ −21.1560 −0.788985 −0.394493 0.918899i $$-0.629080\pi$$
−0.394493 + 0.918899i $$0.629080\pi$$
$$720$$ 0 0
$$721$$ −36.5597 −1.36155
$$722$$ 0 0
$$723$$ −49.3607 0.292087i −1.83574 0.0108628i
$$724$$ 0 0
$$725$$ 13.8556 + 23.9987i 0.514586 + 0.891289i
$$726$$ 0 0
$$727$$ 12.9909 22.5009i 0.481805 0.834511i −0.517977 0.855395i $$-0.673315\pi$$
0.999782 + 0.0208834i $$0.00664789\pi$$
$$728$$ 0 0
$$729$$ 26.9830 + 0.958408i 0.999370 + 0.0354966i
$$730$$ 0 0
$$731$$ −10.0021 + 17.3241i −0.369940 + 0.640755i
$$732$$ 0 0
$$733$$ −5.41447 9.37814i −0.199988 0.346390i 0.748536 0.663094i $$-0.230757\pi$$
−0.948524 + 0.316704i $$0.897424\pi$$
$$734$$ 0 0
$$735$$ 6.80425 + 0.0402635i 0.250978 + 0.00148514i
$$736$$ 0 0
$$737$$ 31.4427 1.15821
$$738$$ 0 0
$$739$$ 11.4520 0.421270 0.210635 0.977565i $$-0.432447\pi$$
0.210635 + 0.977565i $$0.432447\pi$$
$$740$$ 0 0
$$741$$ 15.9860 27.3141i 0.587262 1.00341i
$$742$$ 0 0
$$743$$ −24.0077 41.5826i −0.880758 1.52552i −0.850500 0.525975i $$-0.823701\pi$$
−0.0302573 0.999542i $$-0.509633\pi$$
$$744$$ 0 0
$$745$$ −5.33595 + 9.24213i −0.195494 + 0.338605i
$$746$$ 0 0
$$747$$ −9.02122 16.0612i −0.330069 0.587649i
$$748$$ 0 0
$$749$$ 4.57399 7.92239i 0.167130 0.289478i
$$750$$ 0 0
$$751$$ −22.5881 39.1238i −0.824253 1.42765i −0.902489 0.430713i $$-0.858262\pi$$
0.0782360 0.996935i $$-0.475071\pi$$
$$752$$ 0 0
$$753$$ 13.4505 + 23.6187i 0.490164 + 0.860712i
$$754$$ 0 0
$$755$$ 18.5968 0.676807
$$756$$ 0 0
$$757$$ −16.5457 −0.601365 −0.300682 0.953724i $$-0.597214\pi$$
−0.300682 + 0.953724i $$0.597214\pi$$
$$758$$ 0 0
$$759$$ 10.4006 + 18.2631i 0.377517 + 0.662907i
$$760$$ 0 0
$$761$$ −20.6826 35.8234i −0.749745 1.29860i −0.947945 0.318435i $$-0.896843\pi$$
0.198200 0.980162i $$-0.436491\pi$$
$$762$$ 0 0
$$763$$ 25.4361 44.0565i 0.920847 1.59495i
$$764$$ 0 0
$$765$$ −15.6060 0.184700i −0.564234 0.00667785i
$$766$$ 0 0
$$767$$ 13.3209 23.0725i 0.480990 0.833100i
$$768$$ 0 0
$$769$$ −3.22518 5.58617i −0.116303 0.201443i 0.801997 0.597328i $$-0.203771\pi$$
−0.918300 + 0.395886i $$0.870438\pi$$
$$770$$ 0 0
$$771$$ −20.2353 + 34.5745i −0.728758 + 1.24517i
$$772$$ 0 0
$$773$$ 0.949001 0.0341332 0.0170666 0.999854i $$-0.494567\pi$$
0.0170666 + 0.999854i $$0.494567\pi$$
$$774$$ 0 0
$$775$$ −22.1792 −0.796702
$$776$$ 0 0
$$777$$ 0.402443 + 0.00238142i 0.0144375 + 8.54329e-5i
$$778$$ 0 0
$$779$$ 9.43285 + 16.3382i 0.337967 + 0.585376i
$$780$$ 0 0
$$781$$ −0.432519 + 0.749145i −0.0154767 + 0.0268065i
$$782$$ 0 0
$$783$$ 19.6130 32.6195i 0.700912 1.16572i
$$784$$ 0 0
$$785$$ 4.81251 8.33552i 0.171766 0.297507i
$$786$$ 0 0
$$787$$ 17.6992 + 30.6559i 0.630909 + 1.09277i 0.987366 + 0.158454i $$0.0506511\pi$$
−0.356458 + 0.934312i $$0.616016\pi$$
$$788$$ 0 0
$$789$$ 41.8237 + 0.247488i 1.48896 + 0.00881080i
$$790$$ 0 0
$$791$$ −66.1840 −2.35323
$$792$$ 0 0
$$793$$ 29.6033 1.05125
$$794$$ 0 0
$$795$$ 6.20383 10.6000i 0.220027 0.375943i
$$796$$ 0 0