Properties

 Label 912.2.cc.c.257.1 Level $912$ Weight $2$ Character 912.257 Analytic conductor $7.282$ Analytic rank $0$ Dimension $18$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.cc (of order $$18$$, degree $$6$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$7.28235666434$$ Analytic rank: $$0$$ Dimension: $$18$$ Relative dimension: $$3$$ over $$\Q(\zeta_{18})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ Defining polynomial: $$x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 114) Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

 Embedding label 257.1 Root $$-1.72388 + 0.168030i$$ of defining polynomial Character $$\chi$$ $$=$$ 912.257 Dual form 912.2.cc.c.401.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.67739 + 0.431705i) q^{3} +(1.14133 - 3.13578i) q^{5} +(1.07356 - 1.85947i) q^{7} +(2.62726 - 1.44827i) q^{9} +O(q^{10})$$ $$q+(-1.67739 + 0.431705i) q^{3} +(1.14133 - 3.13578i) q^{5} +(1.07356 - 1.85947i) q^{7} +(2.62726 - 1.44827i) q^{9} +(5.41799 - 3.12808i) q^{11} +(-2.56208 + 3.05336i) q^{13} +(-0.560722 + 5.75264i) q^{15} +(-0.403611 + 0.0711674i) q^{17} +(-4.34640 - 0.329887i) q^{19} +(-0.998042 + 3.58251i) q^{21} +(0.280411 + 0.770422i) q^{23} +(-4.70025 - 3.94398i) q^{25} +(-3.78171 + 3.56352i) q^{27} +(0.805141 - 4.56618i) q^{29} +(2.02597 + 1.16970i) q^{31} +(-7.73767 + 7.58597i) q^{33} +(-4.60559 - 5.48872i) q^{35} -6.01346i q^{37} +(2.97944 - 6.22774i) q^{39} +(0.926617 - 0.777524i) q^{41} +(-5.87377 - 2.13788i) q^{43} +(-1.54289 - 9.89147i) q^{45} +(7.59919 + 1.33994i) q^{47} +(1.19492 + 2.06967i) q^{49} +(0.646288 - 0.293616i) q^{51} +(-0.220516 + 0.0802612i) q^{53} +(-3.62525 - 20.5598i) q^{55} +(7.43301 - 1.32301i) q^{57} +(-0.930375 - 5.27642i) q^{59} +(7.30705 - 2.65955i) q^{61} +(0.127515 - 6.44012i) q^{63} +(6.65050 + 11.5190i) q^{65} +(-3.48689 - 0.614832i) q^{67} +(-0.802953 - 1.17124i) q^{69} +(-4.19799 - 1.52794i) q^{71} +(-4.33185 + 3.63485i) q^{73} +(9.58679 + 4.58646i) q^{75} -13.4328i q^{77} +(8.05412 + 9.59853i) q^{79} +(4.80501 - 7.60999i) q^{81} +(-8.01579 - 4.62792i) q^{83} +(-0.237488 + 1.34686i) q^{85} +(0.620710 + 8.00685i) q^{87} +(-5.61888 - 4.71480i) q^{89} +(2.92708 + 8.04207i) q^{91} +(-3.90331 - 1.08741i) q^{93} +(-5.99513 + 13.2528i) q^{95} +(-16.0734 + 2.83418i) q^{97} +(9.70416 - 16.0650i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$18q - 3q^{3} - 3q^{9} + O(q^{10})$$ $$18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$$.

 $$n$$ $$97$$ $$229$$ $$305$$ $$799$$ $$\chi(n)$$ $$e\left(\frac{17}{18}\right)$$ $$1$$ $$-1$$ $$1$$

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
$$3$$ −1.67739 + 0.431705i −0.968440 + 0.249245i
$$4$$ 0 0
$$5$$ 1.14133 3.13578i 0.510418 1.40236i −0.370384 0.928879i $$-0.620774\pi$$
0.880802 0.473484i $$-0.157004\pi$$
$$6$$ 0 0
$$7$$ 1.07356 1.85947i 0.405769 0.702812i −0.588642 0.808394i $$-0.700337\pi$$
0.994411 + 0.105582i $$0.0336704\pi$$
$$8$$ 0 0
$$9$$ 2.62726 1.44827i 0.875754 0.482758i
$$10$$ 0 0
$$11$$ 5.41799 3.12808i 1.63359 0.943151i 0.650611 0.759412i $$-0.274513\pi$$
0.982975 0.183740i $$-0.0588203\pi$$
$$12$$ 0 0
$$13$$ −2.56208 + 3.05336i −0.710592 + 0.846850i −0.993681 0.112243i $$-0.964196\pi$$
0.283089 + 0.959094i $$0.408641\pi$$
$$14$$ 0 0
$$15$$ −0.560722 + 5.75264i −0.144778 + 1.48532i
$$16$$ 0 0
$$17$$ −0.403611 + 0.0711674i −0.0978899 + 0.0172606i −0.222379 0.974960i $$-0.571382\pi$$
0.124489 + 0.992221i $$0.460271\pi$$
$$18$$ 0 0
$$19$$ −4.34640 0.329887i −0.997132 0.0756812i
$$20$$ 0 0
$$21$$ −0.998042 + 3.58251i −0.217791 + 0.781768i
$$22$$ 0 0
$$23$$ 0.280411 + 0.770422i 0.0584697 + 0.160644i 0.965488 0.260446i $$-0.0838697\pi$$
−0.907019 + 0.421090i $$0.861647\pi$$
$$24$$ 0 0
$$25$$ −4.70025 3.94398i −0.940051 0.788796i
$$26$$ 0 0
$$27$$ −3.78171 + 3.56352i −0.727790 + 0.685800i
$$28$$ 0 0
$$29$$ 0.805141 4.56618i 0.149511 0.847919i −0.814123 0.580693i $$-0.802782\pi$$
0.963634 0.267226i $$-0.0861071\pi$$
$$30$$ 0 0
$$31$$ 2.02597 + 1.16970i 0.363875 + 0.210084i 0.670779 0.741657i $$-0.265960\pi$$
−0.306904 + 0.951740i $$0.599293\pi$$
$$32$$ 0 0
$$33$$ −7.73767 + 7.58597i −1.34695 + 1.32055i
$$34$$ 0 0
$$35$$ −4.60559 5.48872i −0.778486 0.927764i
$$36$$ 0 0
$$37$$ 6.01346i 0.988607i −0.869289 0.494303i $$-0.835423\pi$$
0.869289 0.494303i $$-0.164577\pi$$
$$38$$ 0 0
$$39$$ 2.97944 6.22774i 0.477093 0.997236i
$$40$$ 0 0
$$41$$ 0.926617 0.777524i 0.144713 0.121429i −0.567557 0.823334i $$-0.692111\pi$$
0.712270 + 0.701905i $$0.247667\pi$$
$$42$$ 0 0
$$43$$ −5.87377 2.13788i −0.895741 0.326023i −0.147196 0.989107i $$-0.547025\pi$$
−0.748545 + 0.663084i $$0.769247\pi$$
$$44$$ 0 0
$$45$$ −1.54289 9.89147i −0.230001 1.47453i
$$46$$ 0 0
$$47$$ 7.59919 + 1.33994i 1.10846 + 0.195451i 0.697767 0.716325i $$-0.254177\pi$$
0.410689 + 0.911776i $$0.365288\pi$$
$$48$$ 0 0
$$49$$ 1.19492 + 2.06967i 0.170703 + 0.295666i
$$50$$ 0 0
$$51$$ 0.646288 0.293616i 0.0904984 0.0411145i
$$52$$ 0 0
$$53$$ −0.220516 + 0.0802612i −0.0302902 + 0.0110247i −0.357121 0.934058i $$-0.616242\pi$$
0.326831 + 0.945083i $$0.394019\pi$$
$$54$$ 0 0
$$55$$ −3.62525 20.5598i −0.488828 2.77228i
$$56$$ 0 0
$$57$$ 7.43301 1.32301i 0.984526 0.175237i
$$58$$ 0 0
$$59$$ −0.930375 5.27642i −0.121124 0.686931i −0.983534 0.180721i $$-0.942157\pi$$
0.862410 0.506210i $$-0.168954\pi$$
$$60$$ 0 0
$$61$$ 7.30705 2.65955i 0.935572 0.340520i 0.171156 0.985244i $$-0.445250\pi$$
0.764416 + 0.644723i $$0.223027\pi$$
$$62$$ 0 0
$$63$$ 0.127515 6.44012i 0.0160654 0.811379i
$$64$$ 0 0
$$65$$ 6.65050 + 11.5190i 0.824893 + 1.42876i
$$66$$ 0 0
$$67$$ −3.48689 0.614832i −0.425991 0.0751137i −0.0434574 0.999055i $$-0.513837\pi$$
−0.382534 + 0.923942i $$0.624948\pi$$
$$68$$ 0 0
$$69$$ −0.802953 1.17124i −0.0966642 0.141001i
$$70$$ 0 0
$$71$$ −4.19799 1.52794i −0.498210 0.181334i 0.0806788 0.996740i $$-0.474291\pi$$
−0.578889 + 0.815407i $$0.696513\pi$$
$$72$$ 0 0
$$73$$ −4.33185 + 3.63485i −0.507005 + 0.425427i −0.860074 0.510170i $$-0.829583\pi$$
0.353069 + 0.935597i $$0.385138\pi$$
$$74$$ 0 0
$$75$$ 9.58679 + 4.58646i 1.10699 + 0.529599i
$$76$$ 0 0
$$77$$ 13.4328i 1.53081i
$$78$$ 0 0
$$79$$ 8.05412 + 9.59853i 0.906159 + 1.07992i 0.996465 + 0.0840047i $$0.0267711\pi$$
−0.0903059 + 0.995914i $$0.528784\pi$$
$$80$$ 0 0
$$81$$ 4.80501 7.60999i 0.533889 0.845554i
$$82$$ 0 0
$$83$$ −8.01579 4.62792i −0.879848 0.507980i −0.00923947 0.999957i $$-0.502941\pi$$
−0.870608 + 0.491977i $$0.836274\pi$$
$$84$$ 0 0
$$85$$ −0.237488 + 1.34686i −0.0257591 + 0.146087i
$$86$$ 0 0
$$87$$ 0.620710 + 8.00685i 0.0665471 + 0.858424i
$$88$$ 0 0
$$89$$ −5.61888 4.71480i −0.595600 0.499767i 0.294428 0.955674i $$-0.404871\pi$$
−0.890028 + 0.455906i $$0.849315\pi$$
$$90$$ 0 0
$$91$$ 2.92708 + 8.04207i 0.306841 + 0.843038i
$$92$$ 0 0
$$93$$ −3.90331 1.08741i −0.404754 0.112759i
$$94$$ 0 0
$$95$$ −5.99513 + 13.2528i −0.615087 + 1.35971i
$$96$$ 0 0
$$97$$ −16.0734 + 2.83418i −1.63201 + 0.287767i −0.913221 0.407464i $$-0.866413\pi$$
−0.718786 + 0.695231i $$0.755302\pi$$
$$98$$ 0 0
$$99$$ 9.70416 16.0650i 0.975305 1.61459i
$$100$$ 0 0
$$101$$ −3.69207 + 4.40004i −0.367375 + 0.437820i −0.917787 0.397073i $$-0.870026\pi$$
0.550412 + 0.834893i $$0.314471\pi$$
$$102$$ 0 0
$$103$$ 0.957127 0.552597i 0.0943085 0.0544490i −0.452104 0.891965i $$-0.649326\pi$$
0.546413 + 0.837516i $$0.315993\pi$$
$$104$$ 0 0
$$105$$ 10.0949 + 7.21847i 0.985158 + 0.704450i
$$106$$ 0 0
$$107$$ 3.47626 6.02105i 0.336062 0.582077i −0.647626 0.761958i $$-0.724238\pi$$
0.983688 + 0.179881i $$0.0575713\pi$$
$$108$$ 0 0
$$109$$ 2.42887 6.67327i 0.232644 0.639183i −0.767354 0.641223i $$-0.778427\pi$$
0.999998 + 0.00204008i $$0.000649379\pi$$
$$110$$ 0 0
$$111$$ 2.59604 + 10.0869i 0.246405 + 0.957407i
$$112$$ 0 0
$$113$$ 2.33000 0.219188 0.109594 0.993976i $$-0.465045\pi$$
0.109594 + 0.993976i $$0.465045\pi$$
$$114$$ 0 0
$$115$$ 2.73592 0.255125
$$116$$ 0 0
$$117$$ −2.30914 + 11.7326i −0.213480 + 1.08468i
$$118$$ 0 0
$$119$$ −0.300968 + 0.826903i −0.0275897 + 0.0758021i
$$120$$ 0 0
$$121$$ 14.0697 24.3695i 1.27907 2.21541i
$$122$$ 0 0
$$123$$ −1.21863 + 1.70423i −0.109881 + 0.153666i
$$124$$ 0 0
$$125$$ −3.28225 + 1.89501i −0.293573 + 0.169495i
$$126$$ 0 0
$$127$$ −0.792153 + 0.944052i −0.0702922 + 0.0837710i −0.800045 0.599941i $$-0.795191\pi$$
0.729752 + 0.683712i $$0.239635\pi$$
$$128$$ 0 0
$$129$$ 10.7755 + 1.05031i 0.948732 + 0.0924749i
$$130$$ 0 0
$$131$$ −6.34320 + 1.11848i −0.554208 + 0.0977218i −0.443736 0.896157i $$-0.646347\pi$$
−0.110472 + 0.993879i $$0.535236\pi$$
$$132$$ 0 0
$$133$$ −5.27955 + 7.72783i −0.457795 + 0.670088i
$$134$$ 0 0
$$135$$ 6.85823 + 15.9258i 0.590262 + 1.37067i
$$136$$ 0 0
$$137$$ 3.68452 + 10.1231i 0.314790 + 0.864878i 0.991672 + 0.128787i $$0.0411084\pi$$
−0.676882 + 0.736091i $$0.736669\pi$$
$$138$$ 0 0
$$139$$ −6.45972 5.42035i −0.547906 0.459748i 0.326325 0.945258i $$-0.394190\pi$$
−0.874231 + 0.485510i $$0.838634\pi$$
$$140$$ 0 0
$$141$$ −13.3253 + 1.03301i −1.12219 + 0.0869948i
$$142$$ 0 0
$$143$$ −4.33014 + 24.5575i −0.362105 + 2.05360i
$$144$$ 0 0
$$145$$ −13.3996 7.73627i −1.11278 0.642462i
$$146$$ 0 0
$$147$$ −2.89783 2.95578i −0.239009 0.243788i
$$148$$ 0 0
$$149$$ −3.41271 4.06711i −0.279580 0.333190i 0.607920 0.793998i $$-0.292004\pi$$
−0.887500 + 0.460808i $$0.847560\pi$$
$$150$$ 0 0
$$151$$ 2.55987i 0.208319i −0.994561 0.104160i $$-0.966785\pi$$
0.994561 0.104160i $$-0.0332153\pi$$
$$152$$ 0 0
$$153$$ −0.957320 + 0.771514i −0.0773948 + 0.0623732i
$$154$$ 0 0
$$155$$ 5.98021 5.01799i 0.480342 0.403055i
$$156$$ 0 0
$$157$$ 15.7565 + 5.73489i 1.25750 + 0.457694i 0.882931 0.469503i $$-0.155567\pi$$
0.374573 + 0.927197i $$0.377789\pi$$
$$158$$ 0 0
$$159$$ 0.335241 0.229827i 0.0265864 0.0182265i
$$160$$ 0 0
$$161$$ 1.73361 + 0.305683i 0.136628 + 0.0240912i
$$162$$ 0 0
$$163$$ −5.28499 9.15387i −0.413952 0.716987i 0.581365 0.813643i $$-0.302519\pi$$
−0.995318 + 0.0966559i $$0.969185\pi$$
$$164$$ 0 0
$$165$$ 14.9567 + 32.9217i 1.16438 + 2.56295i
$$166$$ 0 0
$$167$$ 10.5199 3.82893i 0.814054 0.296292i 0.0987568 0.995112i $$-0.468513\pi$$
0.715298 + 0.698820i $$0.246291\pi$$
$$168$$ 0 0
$$169$$ −0.501366 2.84339i −0.0385666 0.218722i
$$170$$ 0 0
$$171$$ −11.8969 + 5.42808i −0.909778 + 0.415095i
$$172$$ 0 0
$$173$$ 3.80558 + 21.5825i 0.289333 + 1.64089i 0.689384 + 0.724396i $$0.257881\pi$$
−0.400051 + 0.916493i $$0.631007\pi$$
$$174$$ 0 0
$$175$$ −12.3797 + 4.50585i −0.935819 + 0.340610i
$$176$$ 0 0
$$177$$ 3.83846 + 8.44895i 0.288516 + 0.635062i
$$178$$ 0 0
$$179$$ 10.6934 + 18.5215i 0.799263 + 1.38436i 0.920097 + 0.391692i $$0.128110\pi$$
−0.120833 + 0.992673i $$0.538557\pi$$
$$180$$ 0 0
$$181$$ −18.0057 3.17489i −1.33835 0.235988i −0.541775 0.840523i $$-0.682248\pi$$
−0.796578 + 0.604536i $$0.793359\pi$$
$$182$$ 0 0
$$183$$ −11.1086 + 7.61559i −0.821173 + 0.562961i
$$184$$ 0 0
$$185$$ −18.8569 6.86334i −1.38639 0.504603i
$$186$$ 0 0
$$187$$ −1.96414 + 1.64811i −0.143632 + 0.120522i
$$188$$ 0 0
$$189$$ 2.56634 + 10.8576i 0.186674 + 0.789776i
$$190$$ 0 0
$$191$$ 3.46116i 0.250441i 0.992129 + 0.125220i $$0.0399638\pi$$
−0.992129 + 0.125220i $$0.960036\pi$$
$$192$$ 0 0
$$193$$ 6.64414 + 7.91818i 0.478256 + 0.569963i 0.950190 0.311671i $$-0.100889\pi$$
−0.471934 + 0.881634i $$0.656444\pi$$
$$194$$ 0 0
$$195$$ −16.1283 16.4508i −1.15497 1.17806i
$$196$$ 0 0
$$197$$ 10.2877 + 5.93959i 0.732966 + 0.423178i 0.819506 0.573070i $$-0.194248\pi$$
−0.0865400 + 0.996248i $$0.527581\pi$$
$$198$$ 0 0
$$199$$ −4.24330 + 24.0650i −0.300800 + 1.70592i 0.341845 + 0.939756i $$0.388948\pi$$
−0.642645 + 0.766164i $$0.722163\pi$$
$$200$$ 0 0
$$201$$ 6.11429 0.473995i 0.431269 0.0334330i
$$202$$ 0 0
$$203$$ −7.62630 6.39922i −0.535261 0.449137i
$$204$$ 0 0
$$205$$ −1.38057 3.79308i −0.0964230 0.264920i
$$206$$ 0 0
$$207$$ 1.85249 + 1.61799i 0.128757 + 0.112458i
$$208$$ 0 0
$$209$$ −24.5807 + 11.8085i −1.70028 + 0.816814i
$$210$$ 0 0
$$211$$ 16.3173 2.87718i 1.12333 0.198074i 0.419028 0.907973i $$-0.362371\pi$$
0.704303 + 0.709900i $$0.251260\pi$$
$$212$$ 0 0
$$213$$ 7.70128 + 0.750660i 0.527683 + 0.0514344i
$$214$$ 0 0
$$215$$ −13.4078 + 15.9788i −0.914405 + 1.08975i
$$216$$ 0 0
$$217$$ 4.35002 2.51149i 0.295299 0.170491i
$$218$$ 0 0
$$219$$ 5.69701 7.96714i 0.384968 0.538370i
$$220$$ 0 0
$$221$$ 0.816781 1.41471i 0.0549426 0.0951634i
$$222$$ 0 0
$$223$$ 4.05122 11.1306i 0.271290 0.745362i −0.726986 0.686653i $$-0.759079\pi$$
0.998275 0.0587091i $$-0.0186984\pi$$
$$224$$ 0 0
$$225$$ −18.0608 3.55461i −1.20405 0.236974i
$$226$$ 0 0
$$227$$ 23.0722 1.53135 0.765676 0.643226i $$-0.222405\pi$$
0.765676 + 0.643226i $$0.222405\pi$$
$$228$$ 0 0
$$229$$ 14.0461 0.928192 0.464096 0.885785i $$-0.346379\pi$$
0.464096 + 0.885785i $$0.346379\pi$$
$$230$$ 0 0
$$231$$ 5.79899 + 22.5320i 0.381546 + 1.48249i
$$232$$ 0 0
$$233$$ −8.06779 + 22.1661i −0.528539 + 1.45215i 0.332253 + 0.943190i $$0.392191\pi$$
−0.860792 + 0.508958i $$0.830031\pi$$
$$234$$ 0 0
$$235$$ 12.8749 22.3001i 0.839869 1.45470i
$$236$$ 0 0
$$237$$ −17.6536 12.6235i −1.14673 0.819981i
$$238$$ 0 0
$$239$$ 23.6023 13.6268i 1.52670 0.881443i 0.527206 0.849738i $$-0.323240\pi$$
0.999497 0.0317050i $$-0.0100937\pi$$
$$240$$ 0 0
$$241$$ 13.6728 16.2946i 0.880739 1.04962i −0.117659 0.993054i $$-0.537539\pi$$
0.998399 0.0565704i $$-0.0180165\pi$$
$$242$$ 0 0
$$243$$ −4.77459 + 14.8392i −0.306290 + 0.951938i
$$244$$ 0 0
$$245$$ 7.85381 1.38484i 0.501762 0.0884741i
$$246$$ 0 0
$$247$$ 12.1431 12.4259i 0.772645 0.790643i
$$248$$ 0 0
$$249$$ 15.4435 + 4.30236i 0.978692 + 0.272651i
$$250$$ 0 0
$$251$$ −0.848967 2.33252i −0.0535863 0.147227i 0.910012 0.414583i $$-0.136072\pi$$
−0.963598 + 0.267355i $$0.913850\pi$$
$$252$$ 0 0
$$253$$ 3.92920 + 3.29699i 0.247027 + 0.207280i
$$254$$ 0 0
$$255$$ −0.183087 2.36173i −0.0114654 0.147897i
$$256$$ 0 0
$$257$$ 1.95465 11.0854i 0.121928 0.691488i −0.861157 0.508339i $$-0.830260\pi$$
0.983085 0.183149i $$-0.0586291\pi$$
$$258$$ 0 0
$$259$$ −11.1818 6.45583i −0.694805 0.401146i
$$260$$ 0 0
$$261$$ −4.49777 13.1626i −0.278405 0.814746i
$$262$$ 0 0
$$263$$ −7.57578 9.02847i −0.467143 0.556719i 0.480109 0.877209i $$-0.340597\pi$$
−0.947252 + 0.320490i $$0.896153\pi$$
$$264$$ 0 0
$$265$$ 0.783093i 0.0481050i
$$266$$ 0 0
$$267$$ 11.4604 + 5.48285i 0.701367 + 0.335545i
$$268$$ 0 0
$$269$$ 8.96522 7.52271i 0.546619 0.458668i −0.327175 0.944964i $$-0.606097\pi$$
0.873794 + 0.486296i $$0.161652\pi$$
$$270$$ 0 0
$$271$$ 29.1999 + 10.6279i 1.77377 + 0.645598i 0.999925 + 0.0122180i $$0.00388921\pi$$
0.773841 + 0.633380i $$0.218333\pi$$
$$272$$ 0 0
$$273$$ −8.38165 12.2260i −0.507280 0.739954i
$$274$$ 0 0
$$275$$ −37.8030 6.66569i −2.27961 0.401956i
$$276$$ 0 0
$$277$$ 1.91965 + 3.32494i 0.115341 + 0.199776i 0.917916 0.396775i $$-0.129871\pi$$
−0.802575 + 0.596551i $$0.796537\pi$$
$$278$$ 0 0
$$279$$ 7.01680 + 0.138933i 0.420085 + 0.00831773i
$$280$$ 0 0
$$281$$ 23.0658 8.39528i 1.37599 0.500820i 0.455031 0.890475i $$-0.349628\pi$$
0.920961 + 0.389655i $$0.127406\pi$$
$$282$$ 0 0
$$283$$ 4.03563 + 22.8872i 0.239894 + 1.36050i 0.832059 + 0.554688i $$0.187162\pi$$
−0.592165 + 0.805817i $$0.701727\pi$$
$$284$$ 0 0
$$285$$ 4.33484 24.8183i 0.256774 1.47011i
$$286$$ 0 0
$$287$$ −0.450998 2.55773i −0.0266215 0.150978i
$$288$$ 0 0
$$289$$ −15.8169 + 5.75689i −0.930408 + 0.338641i
$$290$$ 0 0
$$291$$ 25.7378 11.6930i 1.50878 0.685455i
$$292$$ 0 0
$$293$$ 5.48661 + 9.50309i 0.320531 + 0.555177i 0.980598 0.196031i $$-0.0628052\pi$$
−0.660066 + 0.751207i $$0.729472\pi$$
$$294$$ 0 0
$$295$$ −17.6075 3.10468i −1.02515 0.180762i
$$296$$ 0 0
$$297$$ −9.34230 + 31.1366i −0.542095 + 1.80673i
$$298$$ 0 0
$$299$$ −3.07081 1.11768i −0.177590 0.0646374i
$$300$$ 0 0
$$301$$ −10.2812 + 8.62693i −0.592597 + 0.497248i
$$302$$ 0 0
$$303$$ 4.29352 8.97446i 0.246656 0.515569i
$$304$$ 0 0
$$305$$ 25.9487i 1.48582i
$$306$$ 0 0
$$307$$ 0.351542 + 0.418952i 0.0200636 + 0.0239108i 0.775983 0.630754i $$-0.217254\pi$$
−0.755919 + 0.654665i $$0.772810\pi$$
$$308$$ 0 0
$$309$$ −1.36691 + 1.34012i −0.0777610 + 0.0762366i
$$310$$ 0 0
$$311$$ −12.1908 7.03836i −0.691277 0.399109i 0.112813 0.993616i $$-0.464014\pi$$
−0.804090 + 0.594507i $$0.797347\pi$$
$$312$$ 0 0
$$313$$ −3.23018 + 18.3193i −0.182580 + 1.03547i 0.746444 + 0.665448i $$0.231759\pi$$
−0.929025 + 0.370018i $$0.879352\pi$$
$$314$$ 0 0
$$315$$ −20.0493 7.75016i −1.12965 0.436672i
$$316$$ 0 0
$$317$$ −20.8301 17.4785i −1.16993 0.981690i −0.169940 0.985454i $$-0.554357\pi$$
−0.999993 + 0.00376423i $$0.998802\pi$$
$$318$$ 0 0
$$319$$ −9.92113 27.2581i −0.555477 1.52616i
$$320$$ 0 0
$$321$$ −3.23171 + 11.6004i −0.180377 + 0.647469i
$$322$$ 0 0
$$323$$ 1.77773 0.176176i 0.0989155 0.00980270i
$$324$$ 0 0
$$325$$ 24.0848 4.24680i 1.33598 0.235570i
$$326$$ 0 0
$$327$$ −1.19328 + 12.2422i −0.0659883 + 0.676996i
$$328$$ 0 0
$$329$$ 10.6498 12.6919i 0.587142 0.699729i
$$330$$ 0 0
$$331$$ −25.4221 + 14.6775i −1.39733 + 0.806746i −0.994112 0.108360i $$-0.965440\pi$$
−0.403214 + 0.915106i $$0.632107\pi$$
$$332$$ 0 0
$$333$$ −8.70914 15.7989i −0.477258 0.865776i
$$334$$ 0 0
$$335$$ −5.90767 + 10.2324i −0.322770 + 0.559055i
$$336$$ 0 0
$$337$$ 4.60842 12.6615i 0.251037 0.689717i −0.748607 0.663014i $$-0.769277\pi$$
0.999643 0.0267031i $$-0.00850087\pi$$
$$338$$ 0 0
$$339$$ −3.90832 + 1.00587i −0.212271 + 0.0546316i
$$340$$ 0 0
$$341$$ 14.6356 0.792562
$$342$$ 0 0
$$343$$ 20.1612 1.08860
$$344$$ 0 0
$$345$$ −4.58919 + 1.18111i −0.247074 + 0.0635888i
$$346$$ 0 0
$$347$$ −2.06013 + 5.66016i −0.110594 + 0.303854i −0.982627 0.185594i $$-0.940579\pi$$
0.872033 + 0.489447i $$0.162801\pi$$
$$348$$ 0 0
$$349$$ −14.3065 + 24.7795i −0.765808 + 1.32642i 0.174010 + 0.984744i $$0.444328\pi$$
−0.939818 + 0.341675i $$0.889006\pi$$
$$350$$ 0 0
$$351$$ −1.19169 20.6769i −0.0636078 1.10365i
$$352$$ 0 0
$$353$$ 14.6066 8.43315i 0.777433 0.448851i −0.0580867 0.998312i $$-0.518500\pi$$
0.835520 + 0.549460i $$0.185167\pi$$
$$354$$ 0 0
$$355$$ −9.58259 + 11.4201i −0.508591 + 0.606115i
$$356$$ 0 0
$$357$$ 0.147862 1.51697i 0.00782569 0.0802864i
$$358$$ 0 0
$$359$$ 16.2813 2.87084i 0.859295 0.151517i 0.273397 0.961901i $$-0.411853\pi$$
0.585898 + 0.810385i $$0.300742\pi$$
$$360$$ 0 0
$$361$$ 18.7823 + 2.86764i 0.988545 + 0.150928i
$$362$$ 0 0
$$363$$ −13.0800 + 46.9511i −0.686521 + 2.46429i
$$364$$ 0 0
$$365$$ 6.45403 + 17.7323i 0.337819 + 0.928151i
$$366$$ 0 0
$$367$$ 7.32428 + 6.14580i 0.382324 + 0.320808i 0.813614 0.581405i $$-0.197497\pi$$
−0.431290 + 0.902213i $$0.641941\pi$$
$$368$$ 0 0
$$369$$ 1.30840 3.38475i 0.0681124 0.176203i
$$370$$ 0 0
$$371$$ −0.0874947 + 0.496207i −0.00454250 + 0.0257618i
$$372$$ 0 0
$$373$$ 3.75197 + 2.16620i 0.194270 + 0.112162i 0.593980 0.804480i $$-0.297556\pi$$
−0.399710 + 0.916642i $$0.630889\pi$$
$$374$$ 0 0
$$375$$ 4.68752 4.59562i 0.242062 0.237317i
$$376$$ 0 0
$$377$$ 11.8794 + 14.1573i 0.611819 + 0.729138i
$$378$$ 0 0
$$379$$ 5.96818i 0.306565i −0.988182 0.153282i $$-0.951016\pi$$
0.988182 0.153282i $$-0.0489844\pi$$
$$380$$ 0 0
$$381$$ 0.921197 1.92552i 0.0471943 0.0986472i
$$382$$ 0 0
$$383$$ −3.37004 + 2.82780i −0.172201 + 0.144494i −0.724815 0.688944i $$-0.758075\pi$$
0.552614 + 0.833437i $$0.313630\pi$$
$$384$$ 0 0
$$385$$ −42.1222 15.3312i −2.14675 0.781351i
$$386$$ 0 0
$$387$$ −18.5282 + 2.89006i −0.941839 + 0.146910i
$$388$$ 0 0
$$389$$ −14.5009 2.55689i −0.735223 0.129640i −0.206515 0.978443i $$-0.566212\pi$$
−0.528708 + 0.848804i $$0.677323\pi$$
$$390$$ 0 0
$$391$$ −0.168006 0.290994i −0.00849641 0.0147162i
$$392$$ 0 0
$$393$$ 10.1572 4.61451i 0.512361 0.232771i
$$394$$ 0 0
$$395$$ 39.2913 14.3009i 1.97696 0.719554i
$$396$$ 0 0
$$397$$ 1.74751 + 9.91059i 0.0877048 + 0.497398i 0.996740 + 0.0806794i $$0.0257090\pi$$
−0.909035 + 0.416719i $$0.863180\pi$$
$$398$$ 0 0
$$399$$ 5.51971 15.2418i 0.276331 0.763043i
$$400$$ 0 0
$$401$$ −2.58090 14.6370i −0.128884 0.730937i −0.978925 0.204221i $$-0.934534\pi$$
0.850041 0.526717i $$-0.176577\pi$$
$$402$$ 0 0
$$403$$ −8.76220 + 3.18918i −0.436476 + 0.158864i
$$404$$ 0 0
$$405$$ −18.3791 23.7529i −0.913267 1.18029i
$$406$$ 0 0
$$407$$ −18.8106 32.5809i −0.932405 1.61497i
$$408$$ 0 0
$$409$$ −9.81162 1.73005i −0.485153 0.0855456i −0.0742787 0.997238i $$-0.523665\pi$$
−0.410874 + 0.911692i $$0.634777\pi$$
$$410$$ 0 0
$$411$$ −10.5506 15.3898i −0.520422 0.759123i
$$412$$ 0 0
$$413$$ −10.8101 3.93457i −0.531932 0.193607i
$$414$$ 0 0
$$415$$ −23.6608 + 19.8538i −1.16146 + 0.974583i
$$416$$ 0 0
$$417$$ 13.1754 + 6.30333i 0.645204 + 0.308676i
$$418$$ 0 0
$$419$$ 8.34847i 0.407849i 0.978987 + 0.203925i $$0.0653698\pi$$
−0.978987 + 0.203925i $$0.934630\pi$$
$$420$$ 0 0
$$421$$ 23.4446 + 27.9402i 1.14262 + 1.36172i 0.922384 + 0.386273i $$0.126238\pi$$
0.220234 + 0.975447i $$0.429318\pi$$
$$422$$ 0 0
$$423$$ 21.9057 7.48533i 1.06509 0.363949i
$$424$$ 0 0
$$425$$ 2.17775 + 1.25733i 0.105637 + 0.0609893i
$$426$$ 0 0
$$427$$ 2.89924 16.4424i 0.140304 0.795705i
$$428$$ 0 0
$$429$$ −3.33825 43.0617i −0.161172 2.07904i
$$430$$ 0 0
$$431$$ −8.05751 6.76105i −0.388116 0.325668i 0.427762 0.903891i $$-0.359302\pi$$
−0.815879 + 0.578223i $$0.803746\pi$$
$$432$$ 0 0
$$433$$ −12.6127 34.6530i −0.606126 1.66532i −0.738611 0.674132i $$-0.764518\pi$$
0.132485 0.991185i $$-0.457704\pi$$
$$434$$ 0 0
$$435$$ 25.8161 + 7.19205i 1.23779 + 0.344832i
$$436$$ 0 0
$$437$$ −0.964625 3.44107i −0.0461443 0.164608i
$$438$$ 0 0
$$439$$ −13.1107 + 2.31177i −0.625739 + 0.110335i −0.477522 0.878620i $$-0.658465\pi$$
−0.148218 + 0.988955i $$0.547354\pi$$
$$440$$ 0 0
$$441$$ 6.13681 + 3.70698i 0.292229 + 0.176523i
$$442$$ 0 0
$$443$$ −4.79891 + 5.71912i −0.228003 + 0.271724i −0.867902 0.496736i $$-0.834532\pi$$
0.639899 + 0.768459i $$0.278976\pi$$
$$444$$ 0 0
$$445$$ −21.1976 + 12.2384i −1.00486 + 0.580156i
$$446$$ 0 0
$$447$$ 7.48023 + 5.34883i 0.353803 + 0.252991i
$$448$$ 0 0
$$449$$ 12.1781 21.0931i 0.574722 0.995447i −0.421350 0.906898i $$-0.638444\pi$$
0.996072 0.0885490i $$-0.0282230\pi$$
$$450$$ 0 0
$$451$$ 2.58825 7.11115i 0.121876 0.334851i
$$452$$ 0 0
$$453$$ 1.10511 + 4.29390i 0.0519226 + 0.201745i
$$454$$ 0 0
$$455$$ 28.5589 1.33886
$$456$$ 0 0
$$457$$ −34.8127 −1.62847 −0.814236 0.580534i $$-0.802844\pi$$
−0.814236 + 0.580534i $$0.802844\pi$$
$$458$$ 0 0
$$459$$ 1.27273 1.70741i 0.0594060 0.0796950i
$$460$$ 0 0
$$461$$ 0.765028 2.10190i 0.0356309 0.0978951i −0.920601 0.390503i $$-0.872301\pi$$
0.956232 + 0.292608i $$0.0945232\pi$$
$$462$$ 0 0
$$463$$ −1.84091 + 3.18854i −0.0855541 + 0.148184i −0.905627 0.424075i $$-0.860599\pi$$
0.820073 + 0.572259i $$0.193933\pi$$
$$464$$ 0 0
$$465$$ −7.86484 + 10.9988i −0.364723 + 0.510058i
$$466$$ 0 0
$$467$$ 11.3948 6.57879i 0.527288 0.304430i −0.212623 0.977134i $$-0.568201\pi$$
0.739911 + 0.672704i $$0.234867\pi$$
$$468$$ 0 0
$$469$$ −4.88666 + 5.82369i −0.225645 + 0.268913i
$$470$$ 0 0
$$471$$ −28.9055 2.81748i −1.33190 0.129823i
$$472$$ 0 0
$$473$$ −38.5115 + 6.79061i −1.77076 + 0.312233i
$$474$$ 0 0
$$475$$ 19.1281 + 18.6927i 0.877658 + 0.857678i
$$476$$ 0 0
$$477$$ −0.463112 + 0.530234i −0.0212045 + 0.0242778i
$$478$$ 0 0
$$479$$ 11.4643 + 31.4978i 0.523816 + 1.43917i 0.866240 + 0.499628i $$0.166530\pi$$
−0.342424 + 0.939546i $$0.611248\pi$$
$$480$$ 0 0
$$481$$ 18.3613 + 15.4069i 0.837202 + 0.702496i
$$482$$ 0 0
$$483$$ −3.03991 + 0.235661i −0.138321 + 0.0107229i
$$484$$ 0 0
$$485$$ −9.45772 + 53.6374i −0.429453 + 2.43555i
$$486$$ 0 0
$$487$$ 15.2052 + 8.77875i 0.689015 + 0.397803i 0.803243 0.595651i $$-0.203106\pi$$
−0.114228 + 0.993455i $$0.536439\pi$$
$$488$$ 0 0
$$489$$ 12.8168 + 13.0730i 0.579594 + 0.591183i
$$490$$ 0 0
$$491$$ −15.8204 18.8540i −0.713964 0.850869i 0.280065 0.959981i $$-0.409644\pi$$
−0.994030 + 0.109112i $$0.965199\pi$$
$$492$$ 0 0
$$493$$ 1.90026i 0.0855834i
$$494$$ 0 0
$$495$$ −39.3007 48.7656i −1.76643 2.19185i
$$496$$ 0 0
$$497$$ −7.34797 + 6.16568i −0.329602 + 0.276569i
$$498$$ 0 0
$$499$$ −13.8001 5.02282i −0.617777 0.224852i 0.0141259 0.999900i $$-0.495503\pi$$
−0.631902 + 0.775048i $$0.717726\pi$$
$$500$$ 0 0
$$501$$ −15.9930 + 10.9641i −0.714514 + 0.489840i
$$502$$ 0 0
$$503$$ 4.24201 + 0.747980i 0.189142 + 0.0333508i 0.267417 0.963581i $$-0.413830\pi$$
−0.0782748 + 0.996932i $$0.524941\pi$$
$$504$$ 0 0
$$505$$ 9.58368 + 16.5994i 0.426468 + 0.738665i
$$506$$ 0 0
$$507$$ 2.06849 + 4.55303i 0.0918650 + 0.202207i
$$508$$ 0 0
$$509$$ −4.35756 + 1.58602i −0.193145 + 0.0702991i −0.436782 0.899567i $$-0.643882\pi$$
0.243637 + 0.969867i $$0.421660\pi$$
$$510$$ 0 0
$$511$$ 2.10837 + 11.9572i 0.0932690 + 0.528955i
$$512$$ 0 0
$$513$$ 17.6124 14.2409i 0.777605 0.628753i
$$514$$ 0 0
$$515$$ −0.640425 3.63203i −0.0282205 0.160047i
$$516$$ 0 0
$$517$$ 45.3638 16.5111i 1.99510 0.726156i
$$518$$ 0 0
$$519$$ −15.7007 34.5594i −0.689185 1.51699i
$$520$$ 0 0
$$521$$ −0.205968 0.356747i −0.00902363 0.0156294i 0.861478 0.507794i $$-0.169539\pi$$
−0.870502 + 0.492165i $$0.836206\pi$$
$$522$$ 0 0
$$523$$ 19.2248 + 3.38986i 0.840643 + 0.148228i 0.577359 0.816490i $$-0.304083\pi$$
0.263284 + 0.964718i $$0.415194\pi$$
$$524$$ 0 0
$$525$$ 18.8204 12.9025i 0.821390 0.563109i
$$526$$ 0 0
$$527$$ −0.900948 0.327918i −0.0392459 0.0142843i
$$528$$ 0 0
$$529$$ 17.1041 14.3520i 0.743657 0.624002i
$$530$$ 0 0
$$531$$ −10.0860 12.5151i −0.437697 0.543109i
$$532$$ 0 0
$$533$$ 4.82137i 0.208837i
$$534$$ 0 0
$$535$$ −14.9131 17.7728i −0.644751 0.768385i
$$536$$ 0 0
$$537$$ −25.9328 26.4514i −1.11908 1.14146i
$$538$$ 0 0
$$539$$ 12.9481 + 7.47562i 0.557716 + 0.321998i
$$540$$ 0 0
$$541$$ −3.15633 + 17.9005i −0.135701 + 0.769601i 0.838667 + 0.544644i $$0.183335\pi$$
−0.974369 + 0.224957i $$0.927776\pi$$
$$542$$ 0 0
$$543$$ 31.5732 2.44763i 1.35493 0.105038i
$$544$$ 0 0
$$545$$ −18.1538 15.2328i −0.777622 0.652502i
$$546$$ 0 0
$$547$$ −1.42436 3.91340i −0.0609014 0.167325i 0.905510 0.424324i $$-0.139488\pi$$
−0.966412 + 0.256999i $$0.917266\pi$$
$$548$$ 0 0
$$549$$ 15.3458 17.5699i 0.654942 0.749867i
$$550$$ 0 0
$$551$$ −5.00579 + 19.5808i −0.213254 + 0.834172i
$$552$$ 0 0
$$553$$ 26.4948 4.67174i 1.12667 0.198663i
$$554$$ 0 0
$$555$$ 34.5932 + 3.37188i 1.46840 + 0.143128i
$$556$$ 0 0
$$557$$ 9.16196 10.9188i 0.388205 0.462644i −0.536181 0.844103i $$-0.680134\pi$$
0.924386 + 0.381459i $$0.124578\pi$$
$$558$$ 0 0
$$559$$ 21.5767 12.4573i 0.912599 0.526889i
$$560$$ 0 0
$$561$$ 2.58313 3.61245i 0.109060 0.152518i
$$562$$ 0 0
$$563$$ 3.28307 5.68645i 0.138365 0.239655i −0.788513 0.615018i $$-0.789149\pi$$
0.926878 + 0.375363i $$0.122482\pi$$
$$564$$ 0 0
$$565$$ 2.65930 7.30637i 0.111878 0.307381i
$$566$$ 0 0
$$567$$ −8.99204 17.1046i −0.377630 0.718324i
$$568$$ 0 0
$$569$$ 45.7506 1.91797 0.958983 0.283465i $$-0.0914840\pi$$
0.958983 + 0.283465i $$0.0914840\pi$$
$$570$$ 0 0
$$571$$ −5.82547 −0.243788 −0.121894 0.992543i $$-0.538897\pi$$
−0.121894 + 0.992543i $$0.538897\pi$$
$$572$$ 0 0
$$573$$ −1.49420 5.80571i −0.0624212 0.242537i
$$574$$ 0 0
$$575$$ 1.72053 4.72712i 0.0717510 0.197134i
$$576$$ 0 0
$$577$$ −17.9425 + 31.0773i −0.746956 + 1.29377i 0.202320 + 0.979319i $$0.435152\pi$$
−0.949276 + 0.314446i $$0.898181\pi$$
$$578$$ 0 0
$$579$$ −14.5631 10.4135i −0.605223 0.432772i
$$580$$ 0 0
$$581$$ −17.2109 + 9.93674i −0.714030 + 0.412245i
$$582$$ 0 0
$$583$$ −0.943689 + 1.12464i −0.0390836 + 0.0465780i
$$584$$ 0 0
$$585$$ 34.1553 + 20.6317i 1.41215 + 0.853015i
$$586$$ 0 0
$$587$$ −29.5771 + 5.21525i −1.22078 + 0.215256i −0.746661 0.665205i $$-0.768344\pi$$
−0.474118 + 0.880461i $$0.657233\pi$$
$$588$$ 0 0
$$589$$ −8.41982 5.75231i −0.346932 0.237020i
$$590$$ 0 0
$$591$$ −19.8206 5.52176i −0.815309 0.227135i
$$592$$ 0 0
$$593$$ −0.268437 0.737526i −0.0110234 0.0302866i 0.934059 0.357119i $$-0.116241\pi$$
−0.945082 + 0.326832i $$0.894019\pi$$
$$594$$ 0 0
$$595$$ 2.24948 + 1.88754i 0.0922198 + 0.0773816i
$$596$$ 0 0
$$597$$ −3.27130 42.1981i −0.133886 1.72706i
$$598$$ 0 0
$$599$$ 2.35948 13.3813i 0.0964057 0.546744i −0.897902 0.440196i $$-0.854909\pi$$
0.994308 0.106548i $$-0.0339798\pi$$
$$600$$ 0 0
$$601$$ 1.41283 + 0.815696i 0.0576304 + 0.0332729i 0.528538 0.848909i $$-0.322740\pi$$
−0.470908 + 0.882182i $$0.656074\pi$$
$$602$$ 0 0
$$603$$ −10.0514 + 3.43464i −0.409325 + 0.139869i
$$604$$ 0 0
$$605$$ −60.3592 71.9333i −2.45395 2.92450i
$$606$$ 0 0
$$607$$ 23.6670i 0.960615i 0.877100 + 0.480308i $$0.159475\pi$$
−0.877100 + 0.480308i $$0.840525\pi$$
$$608$$ 0 0
$$609$$ 15.5548 + 7.44167i 0.630314 + 0.301552i
$$610$$ 0 0
$$611$$ −23.5610 + 19.7700i −0.953177 + 0.799811i
$$612$$ 0 0
$$613$$ 14.7136 + 5.35532i 0.594278 + 0.216299i 0.621610 0.783327i $$-0.286479\pi$$
−0.0273321 + 0.999626i $$0.508701\pi$$
$$614$$ 0 0
$$615$$ 3.95324 + 5.76646i 0.159410 + 0.232526i
$$616$$ 0 0
$$617$$ 19.6258 + 3.46056i 0.790105 + 0.139317i 0.554117 0.832439i $$-0.313056\pi$$
0.235988 + 0.971756i $$0.424167\pi$$
$$618$$ 0 0
$$619$$ 3.55524 + 6.15786i 0.142897 + 0.247505i 0.928587 0.371116i $$-0.121025\pi$$
−0.785689 + 0.618621i $$0.787691\pi$$
$$620$$ 0 0
$$621$$ −3.80585 1.91426i −0.152723 0.0768168i
$$622$$ 0 0
$$623$$ −14.7992 + 5.38648i −0.592919 + 0.215805i
$$624$$ 0 0
$$625$$ −3.13111 17.7574i −0.125244 0.710297i
$$626$$ 0 0
$$627$$ 36.1335 30.4191i 1.44303 1.21482i
$$628$$ 0 0
$$629$$ 0.427962 + 2.42710i 0.0170640 + 0.0967746i
$$630$$ 0 0
$$631$$ 1.16675 0.424661i 0.0464474 0.0169055i −0.318692 0.947858i $$-0.603244\pi$$
0.365139 + 0.930953i $$0.381021\pi$$
$$632$$ 0 0
$$633$$ −26.1284 + 11.8704i −1.03851 + 0.471807i
$$634$$ 0 0
$$635$$ 2.05623 + 3.56149i 0.0815989 + 0.141334i
$$636$$ 0 0
$$637$$ −9.38092 1.65411i −0.371685 0.0655382i
$$638$$ 0 0
$$639$$ −13.2421 + 2.06553i −0.523849 + 0.0817112i
$$640$$ 0 0
$$641$$ −7.06477 2.57137i −0.279042 0.101563i 0.198708 0.980059i $$-0.436325\pi$$
−0.477750 + 0.878496i $$0.658548\pi$$
$$642$$ 0 0
$$643$$ 9.31005 7.81206i 0.367153 0.308078i −0.440481 0.897762i $$-0.645192\pi$$
0.807634 + 0.589684i $$0.200748\pi$$
$$644$$ 0 0
$$645$$ 15.5920 32.5909i 0.613933 1.28327i
$$646$$ 0 0
$$647$$ 38.1298i 1.49904i −0.661983 0.749519i $$-0.730285\pi$$
0.661983 0.749519i $$-0.269715\pi$$
$$648$$ 0 0
$$649$$ −21.5458 25.6773i −0.845747 1.00792i
$$650$$ 0 0
$$651$$ −6.21245 + 6.09066i −0.243485 + 0.238712i
$$652$$ 0 0
$$653$$ 39.7547 + 22.9524i 1.55572 + 0.898196i 0.997658 + 0.0683980i $$0.0217888\pi$$
0.558063 + 0.829798i $$0.311545\pi$$
$$654$$ 0 0
$$655$$ −3.73239 + 21.1674i −0.145836 + 0.827080i
$$656$$ 0 0
$$657$$ −6.11664 + 15.8234i −0.238633 + 0.617330i
$$658$$ 0 0
$$659$$ 14.3577 + 12.0475i 0.559295 + 0.469304i 0.878074 0.478525i $$-0.158828\pi$$
−0.318779 + 0.947829i $$0.603273\pi$$
$$660$$ 0 0
$$661$$ 4.05073 + 11.1293i 0.157555 + 0.432879i 0.993204 0.116385i $$-0.0371306\pi$$
−0.835649 + 0.549263i $$0.814908\pi$$
$$662$$ 0 0
$$663$$ −0.759323 + 2.72562i −0.0294896 + 0.105854i
$$664$$ 0 0
$$665$$ 18.2071 + 25.3755i 0.706039 + 0.984020i
$$666$$ 0 0
$$667$$ 3.74366 0.660108i 0.144955 0.0255595i
$$668$$ 0 0
$$669$$ −1.99031 + 20.4193i −0.0769500 + 0.789456i
$$670$$ 0 0
$$671$$ 31.2703 37.2665i 1.20718 1.43866i
$$672$$ 0 0
$$673$$ −9.02264 + 5.20922i −0.347797 + 0.200801i −0.663715 0.747986i $$-0.731021\pi$$
0.315917 + 0.948787i $$0.397688\pi$$
$$674$$ 0 0
$$675$$ 31.8294 1.83445i 1.22512 0.0706082i
$$676$$ 0 0
$$677$$ 10.3670 17.9562i 0.398437 0.690112i −0.595097 0.803654i $$-0.702886\pi$$
0.993533 + 0.113542i $$0.0362196\pi$$
$$678$$ 0 0
$$679$$ −11.9858 + 32.9306i −0.459972 + 1.26376i
$$680$$ 0 0
$$681$$ −38.7009 + 9.96036i −1.48302 + 0.381682i
$$682$$ 0 0
$$683$$ 2.79983 0.107132 0.0535662 0.998564i $$-0.482941\pi$$
0.0535662 + 0.998564i $$0.482941\pi$$
$$684$$ 0 0
$$685$$ 35.9492 1.37355
$$686$$ 0 0
$$687$$ −23.5608 + 6.06377i −0.898899 + 0.231347i
$$688$$ 0 0
$$689$$ 0.319912 0.878950i 0.0121877 0.0334853i
$$690$$ 0 0
$$691$$ 4.20182 7.27776i 0.159845 0.276859i −0.774968 0.632001i $$-0.782234\pi$$
0.934813 + 0.355142i $$0.115567\pi$$
$$692$$ 0 0
$$693$$ −19.4543 35.2914i −0.739009 1.34061i
$$694$$ 0 0
$$695$$ −24.3697 + 14.0698i −0.924395 + 0.533700i
$$696$$ 0 0
$$697$$ −0.318658 + 0.379762i −0.0120700 + 0.0143845i
$$698$$ 0 0
$$699$$ 3.96361 40.6640i 0.149918 1.53805i
$$700$$ 0 0
$$701$$ 14.9472 2.63560i 0.564549 0.0995451i 0.115912 0.993259i $$-0.463021\pi$$
0.448636 + 0.893714i $$0.351910\pi$$
$$702$$ 0 0
$$703$$ −1.98376 + 26.1369i −0.0748190 + 0.985771i
$$704$$ 0 0
$$705$$ −11.9692 + 42.9640i −0.450787 + 1.61812i
$$706$$ 0 0
$$707$$ 4.21806 + 11.5890i 0.158636 + 0.435850i
$$708$$ 0 0
$$709$$ −29.3000 24.5857i −1.10039 0.923334i −0.102935 0.994688i $$-0.532823\pi$$
−0.997451 + 0.0713544i $$0.977268\pi$$
$$710$$ 0 0
$$711$$ 35.0616 + 13.5533i 1.31491 + 0.508287i
$$712$$ 0 0
$$713$$ −0.333055 + 1.88885i −0.0124730 + 0.0707380i
$$714$$ 0 0
$$715$$ 72.0647 + 41.6065i 2.69507 + 1.55600i
$$716$$ 0 0
$$717$$ −33.7074 + 33.0466i −1.25883 + 1.23415i
$$718$$ 0 0
$$719$$ −24.9620 29.7485i −0.930924 1.10943i −0.993775 0.111410i $$-0.964463\pi$$
0.0628501 0.998023i $$-0.479981\pi$$
$$720$$ 0 0
$$721$$ 2.37299i 0.0883749i
$$722$$ 0 0
$$723$$ −15.9001 + 33.2349i −0.591330 + 1.23602i
$$724$$ 0 0
$$725$$ −21.7933 + 18.2868i −0.809383 + 0.679153i
$$726$$ 0 0
$$727$$ −35.9582 13.0877i −1.33361 0.485396i −0.425818 0.904809i $$-0.640014\pi$$
−0.907796 + 0.419413i $$0.862236\pi$$
$$728$$ 0 0
$$729$$ 1.60266 26.9524i 0.0593577 0.998237i
$$730$$ 0 0
$$731$$ 2.52286 + 0.444849i 0.0933114 + 0.0164533i
$$732$$ 0 0
$$733$$ −7.71039 13.3548i −0.284790 0.493270i 0.687768 0.725930i $$-0.258590\pi$$
−0.972558 + 0.232660i $$0.925257\pi$$
$$734$$ 0 0
$$735$$ −12.5761 + 5.71344i −0.463875 + 0.210744i
$$736$$ 0 0
$$737$$ −20.8152 + 7.57610i −0.766736 + 0.279069i
$$738$$ 0 0
$$739$$ 4.98207 + 28.2547i 0.183268 + 1.03937i 0.928160 + 0.372181i $$0.121390\pi$$
−0.744892 + 0.667185i $$0.767499\pi$$
$$740$$ 0 0
$$741$$ −15.0043 + 26.0853i −0.551196 + 0.958269i
$$742$$ 0 0
$$743$$ 4.95784 + 28.1173i 0.181886 + 1.03152i 0.929892 + 0.367833i $$0.119900\pi$$
−0.748006 + 0.663691i $$0.768989\pi$$
$$744$$ 0 0
$$745$$ −16.6486 + 6.05959i −0.609957 + 0.222006i
$$746$$ 0 0
$$747$$ −27.7621 0.549693i −1.01576 0.0201122i
$$748$$ 0 0
$$749$$ −7.46397 12.9280i −0.272727 0.472378i
$$750$$ 0 0
$$751$$ −12.4716 2.19908i −0.455096 0.0802457i −0.0585987 0.998282i $$-0.518663\pi$$
−0.396497 + 0.918036i $$0.629774\pi$$
$$752$$ 0 0
$$753$$ 2.43101 + 3.54603i 0.0885908 + 0.129225i
$$754$$ 0 0
$$755$$ −8.02719 2.92166i −0.292139 0.106330i
$$756$$ 0 0
$$757$$ 38.4432 32.2577i 1.39724 1.17243i 0.434934 0.900462i $$-0.356772\pi$$
0.962308 0.271963i $$-0.0876729\pi$$
$$758$$ 0 0
$$759$$ −8.01413 3.83408i −0.290894 0.139168i
$$760$$ 0 0
$$761$$ 26.6803i 0.967159i 0.875300 + 0.483580i $$0.160664\pi$$
−0.875300 + 0.483580i $$0.839336\pi$$
$$762$$ 0 0
$$763$$ −9.80118 11.6806i −0.354826 0.422866i
$$764$$ 0 0
$$765$$ 1.32668 + 3.88250i 0.0479662 + 0.140372i
$$766$$ 0 0
$$767$$ 18.4945 + 10.6778i 0.667798 + 0.385553i
$$768$$ 0 0
$$769$$ −6.83201 + 38.7463i −0.246369 + 1.39723i 0.570924 + 0.821003i $$0.306585\pi$$
−0.817292 + 0.576223i $$0.804526\pi$$
$$770$$ 0 0
$$771$$ 1.50691 + 19.4383i 0.0542699 + 0.700054i
$$772$$ 0 0
$$773$$ −2.48012 2.08107i −0.0892039 0.0748509i 0.597095 0.802170i $$-0.296321\pi$$
−0.686299 + 0.727319i $$0.740766\pi$$
$$774$$ 0 0
$$775$$ −4.90933 13.4883i −0.176348 0.484513i
$$776$$ 0 0
$$777$$ 21.5433 + 6.00168i 0.772861 + 0.215309i
$$778$$ 0 0
$$779$$ −4.28394 + 3.07375i −0.153488 + 0.110128i
$$780$$ 0 0
$$781$$ −27.5242 + 4.85326i −0.984893 + 0.173663i
$$782$$ 0 0
$$783$$ 13.2269 + 20.1371i 0.472690 + 0.719642i
$$784$$ 0 0
$$785$$ 35.9667 42.8634i 1.28371 1.52986i
$$786$$ 0 0
$$787$$ 22.8624 13.1996i 0.814956 0.470515i −0.0337179 0.999431i $$-0.510735\pi$$
0.848674 + 0.528916i $$0.177401\pi$$
$$788$$ 0 0
$$789$$ 16.6052 + 11.8737i 0.591160 + 0.422716i
$$790$$ 0 0
$$791$$ 2.50141 4.33256i 0.0889397 0.154048i
$$792$$ 0 0
$$793$$ −10.6007 + 29.1251i −0.376440 + 1.03426i