# Properties

 Label 668.2.e.a.21.5 Level $668$ Weight $2$ Character 668.21 Analytic conductor $5.334$ Analytic rank $0$ Dimension $1148$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$668 = 2^{2} \cdot 167$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 668.e (of order $$83$$, degree $$82$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.33400685502$$ Analytic rank: $$0$$ Dimension: $$1148$$ Relative dimension: $$14$$ over $$\Q(\zeta_{83})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

## Embedding invariants

 Embedding label 21.5 Character $$\chi$$ $$=$$ 668.21 Dual form 668.2.e.a.509.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.69992 - 0.259356i) q^{3} +(-0.724427 - 0.859660i) q^{5} +(-2.54038 + 3.52451i) q^{7} +(-0.0410528 - 0.0128253i) q^{9} +O(q^{10})$$ $$q+(-1.69992 - 0.259356i) q^{3} +(-0.724427 - 0.859660i) q^{5} +(-2.54038 + 3.52451i) q^{7} +(-0.0410528 - 0.0128253i) q^{9} +(3.97566 - 3.75611i) q^{11} +(0.411828 - 3.09047i) q^{13} +(1.00851 + 1.64924i) q^{15} +(-3.90237 + 5.87032i) q^{17} +(4.29909 + 0.993475i) q^{19} +(5.23254 - 5.33251i) q^{21} +(1.11800 + 5.29258i) q^{23} +(0.633303 - 3.68213i) q^{25} +(4.70218 + 2.29586i) q^{27} +(0.0318815 - 0.150927i) q^{29} +(9.99434 - 1.91437i) q^{31} +(-7.73247 + 5.35398i) q^{33} +(4.87020 - 0.369385i) q^{35} +(4.21572 - 1.31704i) q^{37} +(-1.50161 + 5.14674i) q^{39} +(8.59220 - 3.41695i) q^{41} +(-0.170641 - 0.0604876i) q^{43} +(0.0187143 + 0.0445825i) q^{45} +(0.0288402 - 0.114848i) q^{47} +(-3.75518 - 11.2663i) q^{49} +(8.15621 - 8.96697i) q^{51} +(0.180465 + 0.135337i) q^{53} +(-6.10906 - 0.696690i) q^{55} +(-7.05044 - 2.80382i) q^{57} +(0.557327 + 0.838386i) q^{59} +(-0.548065 - 0.702708i) q^{61} +(0.149493 - 0.112109i) q^{63} +(-2.95510 + 1.88479i) q^{65} +(1.41050 - 1.67380i) q^{67} +(-0.527839 - 9.28692i) q^{69} +(0.759892 + 8.00647i) q^{71} +(-0.447602 + 0.798365i) q^{73} +(-2.03154 + 6.09506i) q^{75} +(3.13877 + 23.5542i) q^{77} +(5.29749 + 0.200609i) q^{79} +(-7.29180 - 5.04886i) q^{81} +(2.99997 - 0.813991i) q^{83} +(7.87346 - 0.897906i) q^{85} +(-0.0933398 + 0.248295i) q^{87} +(-6.10917 + 9.99046i) q^{89} +(9.84619 + 9.30246i) q^{91} +(-17.4861 + 0.662173i) q^{93} +(-2.26032 - 4.41545i) q^{95} +(17.0247 + 3.26100i) q^{97} +(-0.211385 + 0.103210i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$1148q - 2q^{5} - 14q^{9} + O(q^{10})$$ $$1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$335$$ $$\chi(n)$$ $$e\left(\frac{23}{83}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.69992 0.259356i −0.981449 0.149739i −0.359795 0.933031i $$-0.617153\pi$$
−0.621654 + 0.783292i $$0.713539\pi$$
$$4$$ 0 0
$$5$$ −0.724427 0.859660i −0.323973 0.384452i 0.578150 0.815931i $$-0.303775\pi$$
−0.902123 + 0.431479i $$0.857992\pi$$
$$6$$ 0 0
$$7$$ −2.54038 + 3.52451i −0.960172 + 1.33214i −0.0169925 + 0.999856i $$0.505409\pi$$
−0.943180 + 0.332283i $$0.892181\pi$$
$$8$$ 0 0
$$9$$ −0.0410528 0.0128253i −0.0136843 0.00427512i
$$10$$ 0 0
$$11$$ 3.97566 3.75611i 1.19871 1.13251i 0.210789 0.977532i $$-0.432397\pi$$
0.987918 0.154979i $$-0.0495310\pi$$
$$12$$ 0 0
$$13$$ 0.411828 3.09047i 0.114221 0.857143i −0.836690 0.547677i $$-0.815512\pi$$
0.950910 0.309466i $$-0.100150\pi$$
$$14$$ 0 0
$$15$$ 1.00851 + 1.64924i 0.260396 + 0.425831i
$$16$$ 0 0
$$17$$ −3.90237 + 5.87032i −0.946463 + 1.42376i −0.0410853 + 0.999156i $$0.513082\pi$$
−0.905378 + 0.424607i $$0.860412\pi$$
$$18$$ 0 0
$$19$$ 4.29909 + 0.993475i 0.986278 + 0.227919i 0.687326 0.726349i $$-0.258784\pi$$
0.298952 + 0.954268i $$0.403363\pi$$
$$20$$ 0 0
$$21$$ 5.23254 5.33251i 1.14183 1.16365i
$$22$$ 0 0
$$23$$ 1.11800 + 5.29258i 0.233118 + 1.10358i 0.924527 + 0.381116i $$0.124460\pi$$
−0.691409 + 0.722463i $$0.743010\pi$$
$$24$$ 0 0
$$25$$ 0.633303 3.68213i 0.126661 0.736425i
$$26$$ 0 0
$$27$$ 4.70218 + 2.29586i 0.904935 + 0.441838i
$$28$$ 0 0
$$29$$ 0.0318815 0.150927i 0.00592025 0.0280264i −0.975349 0.220669i $$-0.929176\pi$$
0.981269 + 0.192643i $$0.0617059\pi$$
$$30$$ 0 0
$$31$$ 9.99434 1.91437i 1.79504 0.343830i 0.821124 0.570750i $$-0.193348\pi$$
0.973913 + 0.226920i $$0.0728657\pi$$
$$32$$ 0 0
$$33$$ −7.73247 + 5.35398i −1.34605 + 0.932008i
$$34$$ 0 0
$$35$$ 4.87020 0.369385i 0.823213 0.0624374i
$$36$$ 0 0
$$37$$ 4.21572 1.31704i 0.693059 0.216520i 0.0686776 0.997639i $$-0.478122\pi$$
0.624382 + 0.781119i $$0.285351\pi$$
$$38$$ 0 0
$$39$$ −1.50161 + 5.14674i −0.240450 + 0.824139i
$$40$$ 0 0
$$41$$ 8.59220 3.41695i 1.34188 0.533638i 0.415280 0.909694i $$-0.363684\pi$$
0.926597 + 0.376056i $$0.122720\pi$$
$$42$$ 0 0
$$43$$ −0.170641 0.0604876i −0.0260224 0.00922427i 0.321061 0.947058i $$-0.395961\pi$$
−0.347084 + 0.937834i $$0.612828\pi$$
$$44$$ 0 0
$$45$$ 0.0187143 + 0.0445825i 0.00278976 + 0.00664596i
$$46$$ 0 0
$$47$$ 0.0288402 0.114848i 0.00420677 0.0167523i −0.967748 0.251921i $$-0.918938\pi$$
0.971955 + 0.235169i $$0.0755642\pi$$
$$48$$ 0 0
$$49$$ −3.75518 11.2663i −0.536454 1.60947i
$$50$$ 0 0
$$51$$ 8.15621 8.96697i 1.14210 1.25563i
$$52$$ 0 0
$$53$$ 0.180465 + 0.135337i 0.0247887 + 0.0185899i 0.612288 0.790634i $$-0.290249\pi$$
−0.587500 + 0.809224i $$0.699888\pi$$
$$54$$ 0 0
$$55$$ −6.10906 0.696690i −0.823745 0.0939416i
$$56$$ 0 0
$$57$$ −7.05044 2.80382i −0.933853 0.371375i
$$58$$ 0 0
$$59$$ 0.557327 + 0.838386i 0.0725579 + 0.109149i 0.867270 0.497837i $$-0.165872\pi$$
−0.794713 + 0.606986i $$0.792378\pi$$
$$60$$ 0 0
$$61$$ −0.548065 0.702708i −0.0701725 0.0899726i 0.752158 0.658983i $$-0.229013\pi$$
−0.822330 + 0.569010i $$0.807326\pi$$
$$62$$ 0 0
$$63$$ 0.149493 0.112109i 0.0188343 0.0141245i
$$64$$ 0 0
$$65$$ −2.95510 + 1.88479i −0.366535 + 0.233779i
$$66$$ 0 0
$$67$$ 1.41050 1.67380i 0.172319 0.204488i −0.671665 0.740855i $$-0.734421\pi$$
0.843985 + 0.536367i $$0.180204\pi$$
$$68$$ 0 0
$$69$$ −0.527839 9.28692i −0.0635444 1.11801i
$$70$$ 0 0
$$71$$ 0.759892 + 8.00647i 0.0901826 + 0.950194i 0.919937 + 0.392065i $$0.128239\pi$$
−0.829755 + 0.558128i $$0.811520\pi$$
$$72$$ 0 0
$$73$$ −0.447602 + 0.798365i −0.0523879 + 0.0934415i −0.897207 0.441611i $$-0.854407\pi$$
0.844819 + 0.535053i $$0.179708\pi$$
$$74$$ 0 0
$$75$$ −2.03154 + 6.09506i −0.234583 + 0.703797i
$$76$$ 0 0
$$77$$ 3.13877 + 23.5542i 0.357696 + 2.68425i
$$78$$ 0 0
$$79$$ 5.29749 + 0.200609i 0.596014 + 0.0225702i 0.334127 0.942528i $$-0.391559\pi$$
0.261888 + 0.965098i $$0.415655\pi$$
$$80$$ 0 0
$$81$$ −7.29180 5.04886i −0.810200 0.560984i
$$82$$ 0 0
$$83$$ 2.99997 0.813991i 0.329290 0.0893471i −0.0933808 0.995630i $$-0.529767\pi$$
0.422671 + 0.906283i $$0.361093\pi$$
$$84$$ 0 0
$$85$$ 7.87346 0.897906i 0.853997 0.0973916i
$$86$$ 0 0
$$87$$ −0.0933398 + 0.248295i −0.0100071 + 0.0266200i
$$88$$ 0 0
$$89$$ −6.10917 + 9.99046i −0.647570 + 1.05899i 0.345150 + 0.938547i $$0.387828\pi$$
−0.992721 + 0.120439i $$0.961570\pi$$
$$90$$ 0 0
$$91$$ 9.84619 + 9.30246i 1.03216 + 0.975163i
$$92$$ 0 0
$$93$$ −17.4861 + 0.662173i −1.81322 + 0.0686642i
$$94$$ 0 0
$$95$$ −2.26032 4.41545i −0.231904 0.453016i
$$96$$ 0 0
$$97$$ 17.0247 + 3.26100i 1.72860 + 0.331104i 0.953650 0.300920i $$-0.0972936\pi$$
0.774949 + 0.632024i $$0.217776\pi$$
$$98$$ 0 0
$$99$$ −0.211385 + 0.103210i −0.0212450 + 0.0103730i
$$100$$ 0 0
$$101$$ −5.24763 + 1.86015i −0.522159 + 0.185092i −0.582111 0.813110i $$-0.697773\pi$$
0.0599514 + 0.998201i $$0.480905\pi$$
$$102$$ 0 0
$$103$$ −0.253172 + 13.3759i −0.0249458 + 1.31797i 0.739447 + 0.673215i $$0.235087\pi$$
−0.764393 + 0.644751i $$0.776961\pi$$
$$104$$ 0 0
$$105$$ −8.37474 0.635190i −0.817291 0.0619882i
$$106$$ 0 0
$$107$$ −0.362987 19.1777i −0.0350913 1.85398i −0.392152 0.919900i $$-0.628269\pi$$
0.357061 0.934081i $$-0.383779\pi$$
$$108$$ 0 0
$$109$$ −5.98037 + 11.6824i −0.572816 + 1.11897i 0.405931 + 0.913904i $$0.366947\pi$$
−0.978747 + 0.205071i $$0.934258\pi$$
$$110$$ 0 0
$$111$$ −7.50796 + 1.14549i −0.712624 + 0.108725i
$$112$$ 0 0
$$113$$ −9.13471 7.99819i −0.859321 0.752407i 0.111104 0.993809i $$-0.464561\pi$$
−0.970425 + 0.241402i $$0.922393\pi$$
$$114$$ 0 0
$$115$$ 3.73992 4.79518i 0.348749 0.447153i
$$116$$ 0 0
$$117$$ −0.0565431 + 0.121591i −0.00522741 + 0.0112411i
$$118$$ 0 0
$$119$$ −10.7765 28.6668i −0.987880 2.62788i
$$120$$ 0 0
$$121$$ 1.07329 18.8838i 0.0975722 1.71671i
$$122$$ 0 0
$$123$$ −15.4923 + 3.58010i −1.39689 + 0.322807i
$$124$$ 0 0
$$125$$ −8.47423 + 4.96414i −0.757958 + 0.444006i
$$126$$ 0 0
$$127$$ −0.0565232 + 0.595546i −0.00501562 + 0.0528462i −0.997683 0.0680287i $$-0.978329\pi$$
0.992668 + 0.120875i $$0.0385700\pi$$
$$128$$ 0 0
$$129$$ 0.274387 + 0.147081i 0.0241585 + 0.0129497i
$$130$$ 0 0
$$131$$ −2.50237 2.75111i −0.218633 0.240366i 0.620614 0.784116i $$-0.286883\pi$$
−0.839247 + 0.543750i $$0.817004\pi$$
$$132$$ 0 0
$$133$$ −14.4228 + 12.6284i −1.25062 + 1.09502i
$$134$$ 0 0
$$135$$ −1.43273 5.70546i −0.123310 0.491048i
$$136$$ 0 0
$$137$$ −4.07494 13.9668i −0.348145 1.19326i −0.926126 0.377214i $$-0.876882\pi$$
0.577981 0.816050i $$-0.303841\pi$$
$$138$$ 0 0
$$139$$ −12.7574 + 5.64142i −1.08207 + 0.478499i −0.867106 0.498124i $$-0.834023\pi$$
−0.214961 + 0.976623i $$0.568962\pi$$
$$140$$ 0 0
$$141$$ −0.0788125 + 0.187753i −0.00663721 + 0.0158116i
$$142$$ 0 0
$$143$$ −9.97088 13.8335i −0.833807 1.15682i
$$144$$ 0 0
$$145$$ −0.152842 + 0.0819281i −0.0126928 + 0.00680376i
$$146$$ 0 0
$$147$$ 3.46151 + 20.1258i 0.285500 + 1.65995i
$$148$$ 0 0
$$149$$ 14.0286 + 8.94759i 1.14927 + 0.733016i 0.968132 0.250442i $$-0.0805760\pi$$
0.181139 + 0.983458i $$0.442022\pi$$
$$150$$ 0 0
$$151$$ 2.42211 + 4.32019i 0.197108 + 0.351572i 0.952922 0.303214i $$-0.0980599\pi$$
−0.755814 + 0.654786i $$0.772759\pi$$
$$152$$ 0 0
$$153$$ 0.235492 0.190944i 0.0190384 0.0154369i
$$154$$ 0 0
$$155$$ −8.88587 7.20492i −0.713730 0.578713i
$$156$$ 0 0
$$157$$ −4.93351 10.6091i −0.393737 0.846695i −0.998726 0.0504609i $$-0.983931\pi$$
0.604989 0.796234i $$-0.293177\pi$$
$$158$$ 0 0
$$159$$ −0.271675 0.276866i −0.0215452 0.0219569i
$$160$$ 0 0
$$161$$ −21.4939 9.50477i −1.69395 0.749081i
$$162$$ 0 0
$$163$$ 18.5886 + 10.8891i 1.45597 + 0.852899i 0.999325 0.0367480i $$-0.0116999\pi$$
0.456650 + 0.889647i $$0.349049\pi$$
$$164$$ 0 0
$$165$$ 10.2042 + 2.76874i 0.794397 + 0.215546i
$$166$$ 0 0
$$167$$ −3.88125 + 12.3262i −0.300340 + 0.953832i
$$168$$ 0 0
$$169$$ 3.16494 + 0.858752i 0.243457 + 0.0660578i
$$170$$ 0 0
$$171$$ −0.163748 0.0959222i −0.0125221 0.00733535i
$$172$$ 0 0
$$173$$ 5.91298 + 2.61477i 0.449556 + 0.198797i 0.616803 0.787118i $$-0.288428\pi$$
−0.167247 + 0.985915i $$0.553488\pi$$
$$174$$ 0 0
$$175$$ 11.3688 + 11.5861i 0.859404 + 0.875824i
$$176$$ 0 0
$$177$$ −0.729971 1.56973i −0.0548680 0.117989i
$$178$$ 0 0
$$179$$ 5.95683 + 4.82997i 0.445234 + 0.361009i 0.826007 0.563660i $$-0.190607\pi$$
−0.380773 + 0.924669i $$0.624342\pi$$
$$180$$ 0 0
$$181$$ 11.2305 9.10601i 0.834756 0.676844i −0.113783 0.993506i $$-0.536297\pi$$
0.948539 + 0.316661i $$0.102562\pi$$
$$182$$ 0 0
$$183$$ 0.749414 + 1.33669i 0.0553983 + 0.0988111i
$$184$$ 0 0
$$185$$ −4.18618 2.66999i −0.307774 0.196301i
$$186$$ 0 0
$$187$$ 6.53510 + 37.9961i 0.477894 + 2.77855i
$$188$$ 0 0
$$189$$ −20.0371 + 10.7405i −1.45748 + 0.781258i
$$190$$ 0 0
$$191$$ −3.81289 5.28999i −0.275891 0.382770i 0.650392 0.759599i $$-0.274605\pi$$
−0.926283 + 0.376829i $$0.877014\pi$$
$$192$$ 0 0
$$193$$ 8.10430 19.3066i 0.583360 1.38972i −0.314423 0.949283i $$-0.601811\pi$$
0.897783 0.440439i $$-0.145177\pi$$
$$194$$ 0 0
$$195$$ 5.51226 2.43757i 0.394741 0.174558i
$$196$$ 0 0
$$197$$ −6.79435 23.2876i −0.484077 1.65917i −0.725095 0.688649i $$-0.758204\pi$$
0.241017 0.970521i $$-0.422519\pi$$
$$198$$ 0 0
$$199$$ −2.13212 8.49061i −0.151142 0.601883i −0.997588 0.0694088i $$-0.977889\pi$$
0.846446 0.532475i $$-0.178738\pi$$
$$200$$ 0 0
$$201$$ −2.83184 + 2.47951i −0.199743 + 0.174891i
$$202$$ 0 0
$$203$$ 0.450952 + 0.495778i 0.0316506 + 0.0347968i
$$204$$ 0 0
$$205$$ −9.16184 4.91105i −0.639890 0.343002i
$$206$$ 0 0
$$207$$ 0.0219824 0.231614i 0.00152788 0.0160983i
$$208$$ 0 0
$$209$$ 20.8233 12.1981i 1.44038 0.843763i
$$210$$ 0 0
$$211$$ −21.9127 + 5.06379i −1.50853 + 0.348606i −0.896791 0.442454i $$-0.854108\pi$$
−0.611739 + 0.791060i $$0.709530\pi$$
$$212$$ 0 0
$$213$$ 0.784772 13.8074i 0.0537717 0.946070i
$$214$$ 0 0
$$215$$ 0.0716178 + 0.190512i 0.00488429 + 0.0129928i
$$216$$ 0 0
$$217$$ −18.6422 + 40.0883i −1.26552 + 2.72137i
$$218$$ 0 0
$$219$$ 0.967948 1.24107i 0.0654079 0.0838636i
$$220$$ 0 0
$$221$$ 16.5350 + 14.4777i 1.11226 + 0.973877i
$$222$$ 0 0
$$223$$ 25.6470 3.91295i 1.71745 0.262031i 0.784006 0.620753i $$-0.213173\pi$$
0.933444 + 0.358723i $$0.116788\pi$$
$$224$$ 0 0
$$225$$ −0.0732234 + 0.143039i −0.00488156 + 0.00953594i
$$226$$ 0 0
$$227$$ 0.502403 + 26.5435i 0.0333457 + 1.76176i 0.489638 + 0.871926i $$0.337129\pi$$
−0.456293 + 0.889830i $$0.650823\pi$$
$$228$$ 0 0
$$229$$ 19.3624 + 1.46856i 1.27950 + 0.0970451i 0.697762 0.716330i $$-0.254179\pi$$
0.581740 + 0.813375i $$0.302372\pi$$
$$230$$ 0 0
$$231$$ 0.773270 40.8543i 0.0508774 2.68801i
$$232$$ 0 0
$$233$$ 6.76873 2.39934i 0.443434 0.157186i −0.103012 0.994680i $$-0.532848\pi$$
0.546446 + 0.837494i $$0.315980\pi$$
$$234$$ 0 0
$$235$$ −0.119623 + 0.0584063i −0.00780335 + 0.00381001i
$$236$$ 0 0
$$237$$ −8.95328 1.71495i −0.581578 0.111398i
$$238$$ 0 0
$$239$$ 1.59414 + 3.11409i 0.103116 + 0.201434i 0.935988 0.352033i $$-0.114509\pi$$
−0.832871 + 0.553467i $$0.813305\pi$$
$$240$$ 0 0
$$241$$ 17.2838 0.654514i 1.11335 0.0421610i 0.525248 0.850949i $$-0.323972\pi$$
0.588100 + 0.808788i $$0.299876\pi$$
$$242$$ 0 0
$$243$$ −0.324872 0.306932i −0.0208406 0.0196897i
$$244$$ 0 0
$$245$$ −6.96486 + 11.3898i −0.444969 + 0.727668i
$$246$$ 0 0
$$247$$ 4.84079 12.8771i 0.308012 0.819349i
$$248$$ 0 0
$$249$$ −5.31082 + 0.605658i −0.336560 + 0.0383820i
$$250$$ 0 0
$$251$$ −3.56203 + 0.966496i −0.224834 + 0.0610047i −0.372499 0.928033i $$-0.621499\pi$$
0.147665 + 0.989037i $$0.452824\pi$$
$$252$$ 0 0
$$253$$ 24.3243 + 16.8422i 1.52926 + 1.05886i
$$254$$ 0 0
$$255$$ −13.6171 0.515662i −0.852738 0.0322920i
$$256$$ 0 0
$$257$$ 2.08825 + 15.6708i 0.130261 + 0.977517i 0.927492 + 0.373842i $$0.121960\pi$$
−0.797231 + 0.603674i $$0.793703\pi$$
$$258$$ 0 0
$$259$$ −6.06760 + 18.2041i −0.377022 + 1.13115i
$$260$$ 0 0
$$261$$ −0.00324451 + 0.00578707i −0.000200830 + 0.000358211i
$$262$$ 0 0
$$263$$ −2.44048 25.7137i −0.150487 1.58558i −0.677372 0.735640i $$-0.736881\pi$$
0.526886 0.849936i $$-0.323360\pi$$
$$264$$ 0 0
$$265$$ −0.0143899 0.253180i −0.000883968 0.0155527i
$$266$$ 0 0
$$267$$ 12.9762 15.3985i 0.794129 0.942375i
$$268$$ 0 0
$$269$$ 8.26750 5.27309i 0.504078 0.321506i −0.261114 0.965308i $$-0.584090\pi$$
0.765192 + 0.643802i $$0.222644\pi$$
$$270$$ 0 0
$$271$$ −11.7338 + 8.79958i −0.712778 + 0.534536i −0.893536 0.448991i $$-0.851783\pi$$
0.180758 + 0.983528i $$0.442145\pi$$
$$272$$ 0 0
$$273$$ −14.3251 18.3671i −0.866994 1.11163i
$$274$$ 0 0
$$275$$ −11.3127 17.0176i −0.682180 1.02620i
$$276$$ 0 0
$$277$$ −2.26907 0.902366i −0.136335 0.0542179i 0.300368 0.953823i $$-0.402890\pi$$
−0.436704 + 0.899605i $$0.643854\pi$$
$$278$$ 0 0
$$279$$ −0.434848 0.0495910i −0.0260337 0.00296893i
$$280$$ 0 0
$$281$$ 3.68087 + 2.76041i 0.219582 + 0.164672i 0.704081 0.710120i $$-0.251359\pi$$
−0.484499 + 0.874792i $$0.660998\pi$$
$$282$$ 0 0
$$283$$ 20.1125 22.1117i 1.19556 1.31441i 0.258184 0.966096i $$-0.416876\pi$$
0.937379 0.348310i $$-0.113244\pi$$
$$284$$ 0 0
$$285$$ 2.69719 + 8.09214i 0.159768 + 0.479337i
$$286$$ 0 0
$$287$$ −9.78437 + 38.9636i −0.577553 + 2.29995i
$$288$$ 0 0
$$289$$ −12.6523 30.1413i −0.744256 1.77302i
$$290$$ 0 0
$$291$$ −28.0949 9.95890i −1.64695 0.583801i
$$292$$ 0 0
$$293$$ 3.39053 1.34835i 0.198077 0.0787713i −0.268388 0.963311i $$-0.586491\pi$$
0.466465 + 0.884539i $$0.345527\pi$$
$$294$$ 0 0
$$295$$ 0.316985 1.08646i 0.0184556 0.0632562i
$$296$$ 0 0
$$297$$ 27.3178 8.53438i 1.58514 0.495215i
$$298$$ 0 0
$$299$$ 16.8170 1.27550i 0.972552 0.0737641i
$$300$$ 0 0
$$301$$ 0.646680 0.447763i 0.0372740 0.0258086i
$$302$$ 0 0
$$303$$ 9.40300 1.80110i 0.540188 0.103470i
$$304$$ 0 0
$$305$$ −0.207058 + 0.980210i −0.0118561 + 0.0561267i
$$306$$ 0 0
$$307$$ 0.897746 + 0.438327i 0.0512371 + 0.0250167i 0.464189 0.885736i $$-0.346346\pi$$
−0.412952 + 0.910753i $$0.635502\pi$$
$$308$$ 0 0
$$309$$ 3.89949 22.6723i 0.221834 1.28978i
$$310$$ 0 0
$$311$$ 4.77983 + 22.6277i 0.271039 + 1.28310i 0.874235 + 0.485503i $$0.161364\pi$$
−0.603196 + 0.797593i $$0.706106\pi$$
$$312$$ 0 0
$$313$$ 8.25408 8.41178i 0.466548 0.475462i −0.439739 0.898126i $$-0.644929\pi$$
0.906287 + 0.422664i $$0.138905\pi$$
$$314$$ 0 0
$$315$$ −0.204672 0.0472977i −0.0115320 0.00266492i
$$316$$ 0 0
$$317$$ −4.14208 + 6.23091i −0.232642 + 0.349963i −0.930512 0.366262i $$-0.880637\pi$$
0.697870 + 0.716225i $$0.254131\pi$$
$$318$$ 0 0
$$319$$ −0.440148 0.719784i −0.0246436 0.0403002i
$$320$$ 0 0
$$321$$ −4.35681 + 32.6947i −0.243174 + 1.82484i
$$322$$ 0 0
$$323$$ −22.6086 + 21.3601i −1.25798 + 1.18851i
$$324$$ 0 0
$$325$$ −11.1187 3.47361i −0.616754 0.192681i
$$326$$ 0 0
$$327$$ 13.1961 18.3081i 0.729744 1.01244i
$$328$$ 0 0
$$329$$ 0.331518 + 0.393405i 0.0182772 + 0.0216891i
$$330$$ 0 0
$$331$$ 17.0057 + 2.59455i 0.934718 + 0.142610i 0.600263 0.799802i $$-0.295062\pi$$
0.334454 + 0.942412i $$0.391448\pi$$
$$332$$ 0 0
$$333$$ −0.189958 −0.0104096
$$334$$ 0 0
$$335$$ −2.46070 −0.134443
$$336$$ 0 0
$$337$$ −24.1738 3.68819i −1.31683 0.200909i −0.545914 0.837841i $$-0.683817\pi$$
−0.770919 + 0.636933i $$0.780203\pi$$
$$338$$ 0 0
$$339$$ 13.4539 + 15.9654i 0.730715 + 0.867123i
$$340$$ 0 0
$$341$$ 32.5435 45.1507i 1.76233 2.44505i
$$342$$ 0 0
$$343$$ 20.2191 + 6.31669i 1.09173 + 0.341069i
$$344$$ 0 0
$$345$$ −7.60121 + 7.18145i −0.409236 + 0.386636i
$$346$$ 0 0
$$347$$ 1.62901 12.2245i 0.0874496 0.656246i −0.891629 0.452766i $$-0.850437\pi$$
0.979079 0.203480i $$-0.0652253\pi$$
$$348$$ 0 0
$$349$$ 12.4654 + 20.3850i 0.667259 + 1.09118i 0.989501 + 0.144527i $$0.0461661\pi$$
−0.322241 + 0.946658i $$0.604436\pi$$
$$350$$ 0 0
$$351$$ 9.03177 13.5865i 0.482080 0.725192i
$$352$$ 0 0
$$353$$ −3.91764 0.905325i −0.208515 0.0481856i 0.119606 0.992821i $$-0.461837\pi$$
−0.328121 + 0.944636i $$0.606415\pi$$
$$354$$ 0 0
$$355$$ 6.33236 6.45335i 0.336087 0.342508i
$$356$$ 0 0
$$357$$ 10.8843 + 51.5261i 0.576057 + 2.72705i
$$358$$ 0 0
$$359$$ −0.743703 + 4.32401i −0.0392512 + 0.228213i −0.998527 0.0542586i $$-0.982720\pi$$
0.959276 + 0.282471i $$0.0911542\pi$$
$$360$$ 0 0
$$361$$ 0.421578 + 0.205837i 0.0221883 + 0.0108335i
$$362$$ 0 0
$$363$$ −6.72214 + 31.8225i −0.352821 + 1.67025i
$$364$$ 0 0
$$365$$ 1.01058 0.193571i 0.0528960 0.0101320i
$$366$$ 0 0
$$367$$ −24.7729 + 17.1528i −1.29313 + 0.895368i −0.998190 0.0601460i $$-0.980843\pi$$
−0.294945 + 0.955514i $$0.595301\pi$$
$$368$$ 0 0
$$369$$ −0.396557 + 0.0300773i −0.0206439 + 0.00156576i
$$370$$ 0 0
$$371$$ −0.935444 + 0.292243i −0.0485658 + 0.0151725i
$$372$$ 0 0
$$373$$ −6.93563 + 23.7718i −0.359113 + 1.23086i 0.557194 + 0.830382i $$0.311878\pi$$
−0.916308 + 0.400475i $$0.868845\pi$$
$$374$$ 0 0
$$375$$ 15.6930 6.24079i 0.810382 0.322273i
$$376$$ 0 0
$$377$$ −0.453306 0.160685i −0.0233464 0.00827569i
$$378$$ 0 0
$$379$$ −8.26649 19.6930i −0.424621 1.01156i −0.983269 0.182158i $$-0.941692\pi$$
0.558648 0.829405i $$-0.311320\pi$$
$$380$$ 0 0
$$381$$ 0.250543 0.997721i 0.0128357 0.0511148i
$$382$$ 0 0
$$383$$ −0.851737 2.55539i −0.0435217 0.130574i 0.924680 0.380745i $$-0.124332\pi$$
−0.968202 + 0.250171i $$0.919513\pi$$
$$384$$ 0 0
$$385$$ 17.9748 19.7616i 0.916080 1.00714i
$$386$$ 0 0
$$387$$ 0.00622949 + 0.00467171i 0.000316663 + 0.000237476i
$$388$$ 0 0
$$389$$ 4.74278 + 0.540877i 0.240469 + 0.0274236i 0.232709 0.972546i $$-0.425241\pi$$
0.00775940 + 0.999970i $$0.497530\pi$$
$$390$$ 0 0
$$391$$ −35.4320 14.0906i −1.79187 0.712592i
$$392$$ 0 0
$$393$$ 3.54031 + 5.32568i 0.178585 + 0.268645i
$$394$$ 0 0
$$395$$ −3.66519 4.69937i −0.184416 0.236451i
$$396$$ 0 0
$$397$$ −9.11239 + 6.83369i −0.457338 + 0.342973i −0.803605 0.595163i $$-0.797088\pi$$
0.346267 + 0.938136i $$0.387449\pi$$
$$398$$ 0 0
$$399$$ 27.7929 17.7265i 1.39138 0.887437i
$$400$$ 0 0
$$401$$ −19.3822 + 23.0004i −0.967901 + 1.14859i 0.0209657 + 0.999780i $$0.493326\pi$$
−0.988867 + 0.148805i $$0.952457\pi$$
$$402$$ 0 0
$$403$$ −1.80034 31.6756i −0.0896815 1.57788i
$$404$$ 0 0
$$405$$ 0.942074 + 9.92600i 0.0468120 + 0.493227i
$$406$$ 0 0
$$407$$ 11.8133 21.0708i 0.585564 1.04444i
$$408$$ 0 0
$$409$$ 3.26876 9.80698i 0.161630 0.484924i −0.836368 0.548168i $$-0.815325\pi$$
0.997998 + 0.0632442i $$0.0201447\pi$$
$$410$$ 0 0
$$411$$ 3.30469 + 24.7993i 0.163008 + 1.22326i
$$412$$ 0 0
$$413$$ −4.37072 0.165513i −0.215069 0.00814436i
$$414$$ 0 0
$$415$$ −2.87302 1.98928i −0.141031 0.0976500i
$$416$$ 0 0
$$417$$ 23.1496 6.28126i 1.13364 0.307594i
$$418$$ 0 0
$$419$$ −8.64432 + 0.985817i −0.422303 + 0.0481603i −0.321871 0.946784i $$-0.604312\pi$$
−0.100432 + 0.994944i $$0.532022\pi$$
$$420$$ 0 0
$$421$$ 1.38513 3.68461i 0.0675072 0.179577i −0.897975 0.440047i $$-0.854962\pi$$
0.965482 + 0.260470i $$0.0838775\pi$$
$$422$$ 0 0
$$423$$ −0.00265694 + 0.00434495i −0.000129185 + 0.000211259i
$$424$$ 0 0
$$425$$ 19.1439 + 18.0867i 0.928615 + 0.877334i
$$426$$ 0 0
$$427$$ 3.86899 0.146513i 0.187234 0.00709028i
$$428$$ 0 0
$$429$$ 13.3619 + 26.1019i 0.645117 + 1.26021i
$$430$$ 0 0
$$431$$ −14.0396 2.68921i −0.676262 0.129535i −0.161507 0.986872i $$-0.551635\pi$$
−0.514755 + 0.857337i $$0.672117\pi$$
$$432$$ 0 0
$$433$$ −11.3423 + 5.53791i −0.545075 + 0.266135i −0.690621 0.723217i $$-0.742663\pi$$
0.145546 + 0.989352i $$0.453506\pi$$
$$434$$ 0 0
$$435$$ 0.281067 0.0996308i 0.0134761 0.00477693i
$$436$$ 0 0
$$437$$ −0.451686 + 23.8640i −0.0216071 + 1.14157i
$$438$$ 0 0
$$439$$ 25.1248 + 1.90561i 1.19914 + 0.0909500i 0.660000 0.751266i $$-0.270556\pi$$
0.539141 + 0.842216i $$0.318749\pi$$
$$440$$ 0 0
$$441$$ 0.00966581 + 0.510675i 0.000460277 + 0.0243179i
$$442$$ 0 0
$$443$$ 4.18149 8.16838i 0.198669 0.388091i −0.769404 0.638763i $$-0.779447\pi$$
0.968072 + 0.250671i $$0.0806513\pi$$
$$444$$ 0 0
$$445$$ 13.0140 1.98555i 0.616925 0.0941240i
$$446$$ 0 0
$$447$$ −21.5269 18.8486i −1.01819 0.891508i
$$448$$ 0 0
$$449$$ −1.45182 + 1.86147i −0.0685155 + 0.0878481i −0.821562 0.570120i $$-0.806897\pi$$
0.753046 + 0.657968i $$0.228584\pi$$
$$450$$ 0 0
$$451$$ 21.3252 45.8579i 1.00417 2.15937i
$$452$$ 0 0
$$453$$ −2.99692 7.97215i −0.140808 0.374565i
$$454$$ 0 0
$$455$$ 0.864109 15.2033i 0.0405101 0.712743i
$$456$$ 0 0
$$457$$ −6.23312 + 1.44041i −0.291573 + 0.0673795i −0.368408 0.929664i $$-0.620097\pi$$
0.0768347 + 0.997044i $$0.475519\pi$$
$$458$$ 0 0
$$459$$ −31.8271 + 18.6440i −1.48556 + 0.870229i
$$460$$ 0 0
$$461$$ 1.77021 18.6515i 0.0824470 0.868689i −0.854554 0.519362i $$-0.826169\pi$$
0.937001 0.349326i $$-0.113590\pi$$
$$462$$ 0 0
$$463$$ 24.8760 + 13.3344i 1.15609 + 0.619700i 0.934683 0.355482i $$-0.115683\pi$$
0.221403 + 0.975182i $$0.428936\pi$$
$$464$$ 0 0
$$465$$ 13.2366 + 14.5524i 0.613834 + 0.674851i
$$466$$ 0 0
$$467$$ 3.72059 3.25768i 0.172168 0.150748i −0.568342 0.822792i $$-0.692415\pi$$
0.740511 + 0.672045i $$0.234584\pi$$
$$468$$ 0 0
$$469$$ 2.31614 + 9.22339i 0.106949 + 0.425897i
$$470$$ 0 0
$$471$$ 5.63505 + 19.3141i 0.259649 + 0.889945i
$$472$$ 0 0
$$473$$ −0.905607 + 0.400467i −0.0416399 + 0.0184135i
$$474$$ 0 0
$$475$$ 6.38072 15.2006i 0.292768 0.697452i
$$476$$ 0 0
$$477$$ −0.00567284 0.00787047i −0.000259741 0.000360364i
$$478$$ 0 0
$$479$$ −8.28183 + 4.43933i −0.378406 + 0.202838i −0.650628 0.759396i $$-0.725494\pi$$
0.272222 + 0.962234i $$0.412241\pi$$
$$480$$ 0 0
$$481$$ −2.33412 13.5709i −0.106427 0.618782i
$$482$$ 0 0
$$483$$ 34.0727 + 21.7319i 1.55036 + 0.988836i
$$484$$ 0 0
$$485$$ −9.52981 16.9978i −0.432726 0.771832i
$$486$$ 0 0
$$487$$ 11.2279 9.10388i 0.508783 0.412536i −0.340684 0.940178i $$-0.610659\pi$$
0.849467 + 0.527642i $$0.176924\pi$$
$$488$$ 0 0
$$489$$ −28.7750 23.3316i −1.30125 1.05509i
$$490$$ 0 0
$$491$$ 8.72505 + 18.7624i 0.393756 + 0.846735i 0.998725 + 0.0504863i $$0.0160771\pi$$
−0.604969 + 0.796249i $$0.706814\pi$$
$$492$$ 0 0
$$493$$ 0.761576 + 0.776127i 0.0342996 + 0.0349550i
$$494$$ 0 0
$$495$$ 0.241858 + 0.106952i 0.0108707 + 0.00480713i
$$496$$ 0 0
$$497$$ −30.1493 17.6612i −1.35238 0.792214i
$$498$$ 0 0
$$499$$ 8.02173 + 2.17656i 0.359102 + 0.0974362i 0.436844 0.899537i $$-0.356096\pi$$
−0.0777417 + 0.996974i $$0.524771\pi$$
$$500$$ 0 0
$$501$$ 9.79469 19.9470i 0.437595 0.891165i
$$502$$ 0 0
$$503$$ −3.03912 0.824612i −0.135508 0.0367676i 0.193465 0.981107i $$-0.438028\pi$$
−0.328972 + 0.944340i $$0.606702\pi$$
$$504$$ 0 0
$$505$$ 5.40062 + 3.16364i 0.240325 + 0.140780i
$$506$$ 0 0
$$507$$ −5.15742 2.28065i −0.229049 0.101287i
$$508$$ 0 0
$$509$$ 9.31439 + 9.49236i 0.412853 + 0.420741i 0.888487 0.458902i $$-0.151757\pi$$
−0.475634 + 0.879643i $$0.657781\pi$$
$$510$$ 0 0
$$511$$ −1.67676 3.60572i −0.0741757 0.159508i
$$512$$ 0 0
$$513$$ 17.9342 + 14.5416i 0.791815 + 0.642026i
$$514$$ 0 0
$$515$$ 11.6821 9.47221i 0.514776 0.417396i
$$516$$ 0 0
$$517$$ −0.316724 0.564924i −0.0139295 0.0248453i
$$518$$ 0 0
$$519$$ −9.37344 5.97847i −0.411448 0.262426i
$$520$$ 0 0
$$521$$ −6.06561 35.2665i −0.265739 1.54505i −0.744810 0.667276i $$-0.767460\pi$$
0.479071 0.877776i $$-0.340974\pi$$
$$522$$ 0 0
$$523$$ 20.5508 11.0159i 0.898624 0.481692i 0.0428733 0.999081i $$-0.486349\pi$$
0.855751 + 0.517389i $$0.173096\pi$$
$$524$$ 0 0
$$525$$ −16.3212 22.6440i −0.712316 0.988263i
$$526$$ 0 0
$$527$$ −27.7637 + 66.1406i −1.20940 + 2.88113i
$$528$$ 0 0
$$529$$ −5.72640 + 2.53226i −0.248974 + 0.110098i
$$530$$ 0 0
$$531$$ −0.0121272 0.0415660i −0.000526277 0.00180381i
$$532$$ 0 0
$$533$$ −7.02148 27.9612i −0.304134 1.21113i
$$534$$ 0 0
$$535$$ −16.2234 + 14.2049i −0.701398 + 0.614132i
$$536$$ 0 0
$$537$$ −8.87345 9.75550i −0.382918 0.420981i
$$538$$ 0 0
$$539$$ −57.2469 30.6862i −2.46580 1.32175i
$$540$$ 0 0
$$541$$ −2.86426 + 30.1787i −0.123144 + 1.29749i 0.693548 + 0.720411i $$0.256047\pi$$
−0.816692 + 0.577074i $$0.804194\pi$$
$$542$$ 0 0
$$543$$ −21.4526 + 12.5668i −0.920620 + 0.539292i
$$544$$ 0 0
$$545$$ 14.3753 3.32198i 0.615769 0.142298i
$$546$$ 0 0
$$547$$ 0.132164 2.32532i 0.00565091 0.0994234i −0.994325 0.106387i $$-0.966072\pi$$
0.999976 + 0.00696320i $$0.00221647\pi$$
$$548$$ 0 0
$$549$$ 0.0134871 + 0.0358772i 0.000575615 + 0.00153120i
$$550$$ 0 0
$$551$$ 0.287003 0.617174i 0.0122268 0.0262925i
$$552$$ 0 0
$$553$$ −14.1647 + 18.1614i −0.602343 + 0.772302i
$$554$$ 0 0
$$555$$ 6.42369 + 5.62447i 0.272671 + 0.238746i
$$556$$ 0 0
$$557$$ 11.2179 1.71151i 0.475317 0.0725190i 0.0912578 0.995827i $$-0.470911\pi$$
0.384060 + 0.923308i $$0.374526\pi$$
$$558$$ 0 0
$$559$$ −0.257210 + 0.502450i −0.0108788 + 0.0212514i
$$560$$ 0 0
$$561$$ −1.25462 66.2853i −0.0529699 2.79857i
$$562$$ 0 0
$$563$$ −46.3977 3.51908i −1.95543 0.148311i −0.962860 0.270001i $$-0.912976\pi$$
−0.992568 + 0.121690i $$0.961169\pi$$
$$564$$ 0 0
$$565$$ −0.258301 + 13.6469i −0.0108668 + 0.574127i
$$566$$ 0 0
$$567$$ 36.3187 12.8740i 1.52524 0.540657i
$$568$$ 0 0
$$569$$ −8.46771 + 4.13439i −0.354985 + 0.173323i −0.607598 0.794245i $$-0.707867\pi$$
0.252613 + 0.967567i $$0.418710\pi$$
$$570$$ 0 0
$$571$$ −22.8941 4.38525i −0.958088 0.183517i −0.314815 0.949153i $$-0.601942\pi$$
−0.643274 + 0.765636i $$0.722424\pi$$
$$572$$ 0 0
$$573$$ 5.10962 + 9.98144i 0.213457 + 0.416981i
$$574$$ 0 0
$$575$$ 20.1960 0.764793i 0.842230 0.0318941i
$$576$$ 0 0
$$577$$ −2.97414 2.80990i −0.123815 0.116978i 0.622349 0.782740i $$-0.286179\pi$$
−0.746164 + 0.665763i $$0.768106\pi$$
$$578$$ 0 0
$$579$$ −18.7839 + 30.7178i −0.780634 + 1.27659i
$$580$$ 0 0
$$581$$ −4.75215 + 12.6413i −0.197152 + 0.524448i
$$582$$ 0 0
$$583$$ 1.22581 0.139794i 0.0507677 0.00578966i
$$584$$ 0 0
$$585$$ 0.145488 0.0394756i 0.00601519 0.00163212i
$$586$$ 0 0
$$587$$ 35.9399 + 24.8849i 1.48340 + 1.02711i 0.987304 + 0.158839i $$0.0507751\pi$$
0.496094 + 0.868269i $$0.334767\pi$$
$$588$$ 0 0
$$589$$ 44.8684 + 1.69910i 1.84877 + 0.0700104i
$$590$$ 0 0
$$591$$ 5.51007 + 41.3491i 0.226654 + 1.70088i
$$592$$ 0 0
$$593$$ −6.44363 + 19.3323i −0.264608 + 0.793881i 0.729352 + 0.684139i $$0.239822\pi$$
−0.993960 + 0.109742i $$0.964998\pi$$
$$594$$ 0 0
$$595$$ −16.8369 + 30.0311i −0.690245 + 1.23115i
$$596$$ 0 0
$$597$$ 1.42235 + 14.9863i 0.0582128 + 0.613350i
$$598$$ 0 0
$$599$$ −0.0653149 1.14916i −0.00266869 0.0469536i 0.996778 0.0802064i $$-0.0255579\pi$$
−0.999447 + 0.0332528i $$0.989413\pi$$
$$600$$ 0 0
$$601$$ 10.3476 12.2793i 0.422087 0.500881i −0.511474 0.859299i $$-0.670900\pi$$
0.933561 + 0.358418i $$0.116684\pi$$
$$602$$ 0 0
$$603$$ −0.0793718 + 0.0506241i −0.00323227 + 0.00206157i
$$604$$ 0 0
$$605$$ −17.0112 + 12.7572i −0.691602 + 0.518656i
$$606$$ 0 0
$$607$$ 26.1737 + 33.5589i 1.06236 + 1.36212i 0.928592 + 0.371103i $$0.121020\pi$$
0.133766 + 0.991013i $$0.457293\pi$$
$$608$$ 0 0
$$609$$ −0.637998 0.959739i −0.0258530 0.0388906i
$$610$$ 0 0
$$611$$ −0.343058 0.136427i −0.0138786 0.00551927i
$$612$$ 0 0
$$613$$ −42.3561 4.83038i −1.71075 0.195097i −0.797730 0.603015i $$-0.793966\pi$$
−0.913019 + 0.407918i $$0.866255\pi$$
$$614$$ 0 0
$$615$$ 14.3007 + 10.7246i 0.576659 + 0.432456i
$$616$$ 0 0
$$617$$ 29.1406 32.0373i 1.17316 1.28977i 0.224136 0.974558i $$-0.428044\pi$$
0.949020 0.315215i $$-0.102077\pi$$
$$618$$ 0 0
$$619$$ −12.4233 37.2724i −0.499333 1.49810i −0.831846 0.555006i $$-0.812716\pi$$
0.332514 0.943098i $$-0.392103\pi$$
$$620$$ 0 0
$$621$$ −6.89398 + 27.4534i −0.276646 + 1.10167i
$$622$$ 0 0
$$623$$ −19.6919 46.9113i −0.788938 1.87946i
$$624$$ 0 0
$$625$$ −7.20104 2.55258i −0.288042 0.102103i
$$626$$ 0 0
$$627$$ −38.5616 + 15.3352i −1.54000 + 0.612429i
$$628$$ 0 0
$$629$$ −8.71984 + 29.8872i −0.347683 + 1.19168i
$$630$$ 0 0
$$631$$ −34.1169 + 10.6585i −1.35817 + 0.424308i −0.888639 0.458607i $$-0.848348\pi$$
−0.469532 + 0.882915i $$0.655577\pi$$
$$632$$ 0 0
$$633$$ 38.5631 2.92485i 1.53274 0.116253i
$$634$$ 0 0
$$635$$ 0.552915 0.382839i 0.0219417 0.0151925i
$$636$$ 0 0
$$637$$ −36.3648 + 6.96548i −1.44082 + 0.275982i
$$638$$ 0 0
$$639$$ 0.0714901 0.338434i 0.00282811 0.0133882i
$$640$$ 0 0
$$641$$ −14.2526 6.95889i −0.562944 0.274859i 0.135198 0.990819i $$-0.456833\pi$$
−0.698142 + 0.715959i $$0.745990\pi$$
$$642$$ 0 0
$$643$$ −0.478272 + 2.78075i −0.0188612 + 0.109662i −0.993433 0.114411i $$-0.963502\pi$$
0.974572 + 0.224073i $$0.0719356\pi$$
$$644$$ 0 0
$$645$$ −0.0723341 0.342429i −0.00284815 0.0134831i
$$646$$ 0 0
$$647$$ −25.5993 + 26.0884i −1.00641 + 1.02564i −0.00674061 + 0.999977i $$0.502146\pi$$
−0.999671 + 0.0256631i $$0.991830\pi$$
$$648$$ 0 0
$$649$$ 5.36482 + 1.23975i 0.210588 + 0.0486646i
$$650$$ 0 0
$$651$$ 42.0874 63.3120i 1.64954 2.48139i
$$652$$ 0 0
$$653$$ 1.28593 + 2.10291i 0.0503224 + 0.0822934i 0.877303 0.479938i $$-0.159341\pi$$
−0.826980 + 0.562231i $$0.809943\pi$$
$$654$$ 0 0
$$655$$ −0.552240 + 4.14417i −0.0215778 + 0.161926i
$$656$$ 0 0
$$657$$ 0.0286146 0.0270344i 0.00111636 0.00105471i
$$658$$ 0 0
$$659$$ −42.2943 13.2132i −1.64755 0.514714i −0.673145 0.739511i $$-0.735057\pi$$
−0.974406 + 0.224797i $$0.927828\pi$$
$$660$$ 0 0
$$661$$ 24.8920 34.5351i 0.968188 1.34326i 0.0291027 0.999576i $$-0.490735\pi$$
0.939086 0.343683i $$-0.111675\pi$$
$$662$$ 0 0
$$663$$ −24.3532 28.8994i −0.945801 1.12236i
$$664$$ 0 0
$$665$$ 21.3044 + 3.25040i 0.826148 + 0.126045i
$$666$$ 0 0
$$667$$ 0.834436 0.0323095
$$668$$ 0 0
$$669$$ −44.6127 −1.72483
$$670$$ 0 0
$$671$$ −4.81837 0.735137i −0.186011 0.0283796i
$$672$$ 0 0
$$673$$ −1.57957 1.87443i −0.0608878 0.0722541i 0.733393 0.679805i $$-0.237935\pi$$
−0.794281 + 0.607550i $$0.792152\pi$$
$$674$$ 0 0
$$675$$ 11.4315 15.8600i 0.440000 0.610453i
$$676$$ 0 0
$$677$$ −25.5706 7.98854i −0.982757 0.307024i −0.235730 0.971818i $$-0.575748\pi$$
−0.747027 + 0.664794i $$0.768519\pi$$
$$678$$ 0 0
$$679$$ −54.7426 + 51.7196i −2.10083 + 1.98482i
$$680$$ 0 0
$$681$$ 6.03018 45.2521i 0.231077 1.73407i
$$682$$ 0 0
$$683$$ −17.6330 28.8357i −0.674709 1.10337i −0.988110 0.153747i $$-0.950866\pi$$
0.313401 0.949621i $$-0.398532\pi$$
$$684$$ 0 0
$$685$$ −9.05472 + 13.6210i −0.345963 + 0.520431i
$$686$$ 0 0
$$687$$ −32.5336 7.51818i −1.24123 0.286836i
$$688$$ 0 0
$$689$$ 0.492575 0.501986i 0.0187656 0.0191241i
$$690$$ 0 0
$$691$$ 2.49949 + 11.8326i 0.0950852 + 0.450133i 0.999714 + 0.0239314i $$0.00761831\pi$$
−0.904628 + 0.426201i $$0.859852\pi$$
$$692$$ 0 0
$$693$$ 0.173236 1.00722i 0.00658068 0.0382611i
$$694$$ 0 0
$$695$$ 14.0915 + 6.88022i 0.534521 + 0.260981i
$$696$$ 0 0
$$697$$ −13.4713 + 63.7732i −0.510263 + 2.41558i
$$698$$ 0 0
$$699$$ −12.1286 + 2.32317i −0.458745 + 0.0878702i
$$700$$ 0 0
$$701$$ −35.3826 + 24.4990i −1.33638 + 0.925314i −0.999866 0.0163632i $$-0.994791\pi$$
−0.336517 + 0.941677i $$0.609249\pi$$
$$702$$ 0 0
$$703$$ 19.4322 1.47385i 0.732898 0.0555874i
$$704$$ 0 0
$$705$$ 0.218498 0.0682611i 0.00822909 0.00257086i
$$706$$ 0 0
$$707$$ 6.77487 23.2208i 0.254795 0.873308i
$$708$$ 0 0
$$709$$ 20.8149 8.27769i 0.781721 0.310875i 0.0556101 0.998453i $$-0.482290\pi$$
0.726111 + 0.687577i $$0.241326\pi$$
$$710$$ 0 0
$$711$$ −0.214904 0.0761777i −0.00805952 0.00285689i
$$712$$ 0 0
$$713$$ 21.3056 + 50.7556i 0.797899 + 1.90081i
$$714$$ 0 0
$$715$$ −4.66898 + 18.5930i −0.174610 + 0.695337i
$$716$$ 0 0
$$717$$ −1.90225 5.70715i −0.0710408 0.213138i
$$718$$ 0 0
$$719$$ 2.45184 2.69557i 0.0914383 0.100528i −0.692330 0.721581i $$-0.743416\pi$$
0.783768 + 0.621054i $$0.213295\pi$$
$$720$$ 0 0
$$721$$ −46.5003 34.8721i −1.73176 1.29871i
$$722$$ 0 0
$$723$$ −29.5509 3.37004i −1.09901 0.125333i
$$724$$ 0 0
$$725$$ −0.535541 0.212974i −0.0198895 0.00790966i
$$726$$ 0 0
$$727$$ −0.559928 0.842298i −0.0207666 0.0312391i 0.822252 0.569124i $$-0.192718\pi$$
−0.843018 + 0.537885i $$0.819224\pi$$
$$728$$ 0 0
$$729$$ 16.8361 + 21.5867i 0.623561 + 0.799507i
$$730$$ 0 0
$$731$$ 1.02098 0.765670i 0.0377624 0.0283193i
$$732$$ 0 0
$$733$$ 13.2342 8.44089i 0.488816 0.311771i −0.270245 0.962792i $$-0.587105\pi$$
0.759060 + 0.651020i $$0.225659\pi$$
$$734$$ 0 0
$$735$$ 14.7937 17.5554i 0.545674 0.647539i
$$736$$ 0 0
$$737$$ −0.679340 11.9525i −0.0250238 0.440274i
$$738$$ 0 0
$$739$$ −4.18215 44.0645i −0.153843 1.62094i −0.655033 0.755601i $$-0.727345\pi$$
0.501190 0.865337i $$-0.332896\pi$$
$$740$$ 0 0
$$741$$ −11.5687 + 20.6345i −0.424987 + 0.758027i
$$742$$ 0 0
$$743$$ −9.19392 + 27.5837i −0.337292 + 1.01195i 0.633852 + 0.773455i $$0.281473\pi$$
−0.971144 + 0.238494i $$0.923346\pi$$
$$744$$ 0 0
$$745$$ −2.47082 18.5417i −0.0905239 0.679317i
$$746$$ 0 0
$$747$$ −0.133597 0.00505913i −0.00488805 0.000185104i
$$748$$ 0 0
$$749$$ 68.5142 + 47.4393i 2.50345 + 1.73340i
$$750$$ 0 0
$$751$$ −41.5790 + 11.2818i −1.51724 + 0.411677i −0.920495 0.390754i $$-0.872214\pi$$
−0.596745 + 0.802431i $$0.703540\pi$$
$$752$$ 0 0
$$753$$ 6.30583 0.719131i 0.229797 0.0262066i
$$754$$ 0 0
$$755$$ 1.95925 5.21185i 0.0713046 0.189679i
$$756$$ 0 0
$$757$$ −0.255296 + 0.417492i −0.00927890 + 0.0151740i −0.857740 0.514084i $$-0.828132\pi$$
0.848461 + 0.529258i $$0.177530\pi$$
$$758$$ 0 0
$$759$$ −36.9812 34.9390i −1.34233 1.26821i
$$760$$ 0 0
$$761$$ −31.8648 + 1.20667i −1.15510 + 0.0437419i −0.608430 0.793608i $$-0.708200\pi$$
−0.546667 + 0.837350i $$0.684104\pi$$
$$762$$ 0 0
$$763$$ −25.9824 50.7557i −0.940626 1.83748i
$$764$$ 0 0
$$765$$ −0.334743 0.0641184i −0.0121027 0.00231820i
$$766$$ 0 0
$$767$$ 2.82053 1.37713i 0.101844 0.0497254i
$$768$$ 0 0
$$769$$ −15.4122 + 5.46321i −0.555778 + 0.197008i −0.597142 0.802136i $$-0.703697\pi$$
0.0413642 + 0.999144i $$0.486830\pi$$
$$770$$ 0 0
$$771$$ 0.514462 27.1807i 0.0185279 0.978888i
$$772$$ 0 0
$$773$$ 22.3872 + 1.69798i 0.805211 + 0.0610720i 0.471796 0.881708i $$-0.343606\pi$$
0.333416 + 0.942780i $$0.391799\pi$$
$$774$$ 0 0
$$775$$ −0.719488 38.0128i −0.0258448 1.36546i
$$776$$ 0 0
$$777$$ 15.0358 29.3718i 0.539405 1.05371i
$$778$$ 0 0
$$779$$ 40.3333 6.15363i 1.44509 0.220477i
$$780$$ 0 0
$$781$$ 33.0943 + 28.9768i 1.18421 + 1.03687i
$$782$$ 0 0
$$783$$ 0.496419 0.636490i 0.0177406 0.0227463i
$$784$$ 0 0
$$785$$ −5.54622 + 11.9266i −0.197953 + 0.425679i
$$786$$ 0 0
$$787$$ −5.94201 15.8064i −0.211810 0.563439i 0.786739 0.617285i $$-0.211768\pi$$
−0.998549 + 0.0538464i $$0.982852\pi$$
$$788$$ 0 0
$$789$$ −2.52039 + 44.3442i −0.0897281 + 1.57870i
$$790$$ 0 0
$$791$$ 51.3953 11.8769i 1.82741 0.422295i
$$792$$ 0 0
$$793$$ −2.39741 + 1.40438i −0.0851345 + 0.0498712i
$$794$$ 0 0
$$795$$ −0.0412020 + 0.434117i −0.00146128 + 0.0153966i
$$796$$ 0