Properties

 Label 912.2.cc.c.401.2 Level $912$ Weight $2$ Character 912.401 Analytic conductor $7.282$ Analytic rank $0$ Dimension $18$ CM no Inner twists $2$

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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 401.2 Root $$0.0786547 - 1.73026i$$ of defining polynomial Character $$\chi$$ $$=$$ 912.401 Dual form 912.2.cc.c.257.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.517874 + 1.65282i) q^{3} +(-0.258510 - 0.710252i) q^{5} +(-0.777943 - 1.34744i) q^{7} +(-2.46361 - 1.71190i) q^{9} +O(q^{10})$$ $$q+(-0.517874 + 1.65282i) q^{3} +(-0.258510 - 0.710252i) q^{5} +(-0.777943 - 1.34744i) q^{7} +(-2.46361 - 1.71190i) q^{9} +(-0.832399 - 0.480586i) q^{11} +(0.416982 + 0.496940i) q^{13} +(1.30779 - 0.0594499i) q^{15} +(6.73013 + 1.18670i) q^{17} +(4.14364 - 1.35288i) q^{19} +(2.62994 - 0.587996i) q^{21} +(-0.400647 + 1.10077i) q^{23} +(3.39259 - 2.84672i) q^{25} +(4.10530 - 3.18535i) q^{27} +(1.39666 + 7.92086i) q^{29} +(2.63927 - 1.52379i) q^{31} +(1.22540 - 1.12692i) q^{33} +(-0.755913 + 0.900862i) q^{35} +4.12648i q^{37} +(-1.03729 + 0.431843i) q^{39} +(-4.09755 - 3.43825i) q^{41} +(7.34330 - 2.67274i) q^{43} +(-0.579012 + 2.19233i) q^{45} +(3.11004 - 0.548383i) q^{47} +(2.28961 - 3.96572i) q^{49} +(-5.44676 + 10.5091i) q^{51} +(-13.6276 - 4.96002i) q^{53} +(-0.126153 + 0.715449i) q^{55} +(0.0901766 + 7.54930i) q^{57} +(-2.02192 + 11.4669i) q^{59} +(10.1813 + 3.70568i) q^{61} +(-0.390129 + 4.65133i) q^{63} +(0.245158 - 0.424626i) q^{65} +(9.19012 - 1.62047i) q^{67} +(-1.61189 - 1.23226i) q^{69} +(-0.0322101 + 0.0117235i) q^{71} +(-3.04446 - 2.55461i) q^{73} +(2.94818 + 7.08158i) q^{75} +1.49547i q^{77} +(0.893115 - 1.06437i) q^{79} +(3.13878 + 8.43493i) q^{81} +(10.4856 - 6.05389i) q^{83} +(-0.896950 - 5.08686i) q^{85} +(-13.8150 - 1.79358i) q^{87} +(4.68075 - 3.92762i) q^{89} +(0.345207 - 0.948448i) q^{91} +(1.15173 + 5.15137i) q^{93} +(-2.03206 - 2.59329i) q^{95} +(9.54804 + 1.68358i) q^{97} +(1.22799 + 2.60896i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$18q - 3q^{3} - 3q^{9} + O(q^{10})$$ $$18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100})$$

Character values

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

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

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
$$3$$ −0.517874 + 1.65282i −0.298995 + 0.954255i
$$4$$ 0 0
$$5$$ −0.258510 0.710252i −0.115609 0.317634i 0.868370 0.495917i $$-0.165168\pi$$
−0.983979 + 0.178283i $$0.942946\pi$$
$$6$$ 0 0
$$7$$ −0.777943 1.34744i −0.294035 0.509283i 0.680725 0.732539i $$-0.261665\pi$$
−0.974760 + 0.223256i $$0.928331\pi$$
$$8$$ 0 0
$$9$$ −2.46361 1.71190i −0.821204 0.570634i
$$10$$ 0 0
$$11$$ −0.832399 0.480586i −0.250978 0.144902i 0.369234 0.929336i $$-0.379620\pi$$
−0.620212 + 0.784434i $$0.712953\pi$$
$$12$$ 0 0
$$13$$ 0.416982 + 0.496940i 0.115650 + 0.137826i 0.820763 0.571268i $$-0.193548\pi$$
−0.705113 + 0.709095i $$0.749104\pi$$
$$14$$ 0 0
$$15$$ 1.30779 0.0594499i 0.337671 0.0153499i
$$16$$ 0 0
$$17$$ 6.73013 + 1.18670i 1.63230 + 0.287818i 0.913328 0.407226i $$-0.133504\pi$$
0.718968 + 0.695043i $$0.244615\pi$$
$$18$$ 0 0
$$19$$ 4.14364 1.35288i 0.950615 0.310371i
$$20$$ 0 0
$$21$$ 2.62994 0.587996i 0.573901 0.128311i
$$22$$ 0 0
$$23$$ −0.400647 + 1.10077i −0.0835407 + 0.229526i −0.974429 0.224697i $$-0.927861\pi$$
0.890888 + 0.454223i $$0.150083\pi$$
$$24$$ 0 0
$$25$$ 3.39259 2.84672i 0.678519 0.569345i
$$26$$ 0 0
$$27$$ 4.10530 3.18535i 0.790066 0.613022i
$$28$$ 0 0
$$29$$ 1.39666 + 7.92086i 0.259354 + 1.47087i 0.784645 + 0.619945i $$0.212845\pi$$
−0.525292 + 0.850922i $$0.676044\pi$$
$$30$$ 0 0
$$31$$ 2.63927 1.52379i 0.474028 0.273680i −0.243897 0.969801i $$-0.578426\pi$$
0.717924 + 0.696121i $$0.245092\pi$$
$$32$$ 0 0
$$33$$ 1.22540 1.12692i 0.213314 0.196172i
$$34$$ 0 0
$$35$$ −0.755913 + 0.900862i −0.127773 + 0.152273i
$$36$$ 0 0
$$37$$ 4.12648i 0.678389i 0.940716 + 0.339195i $$0.110154\pi$$
−0.940716 + 0.339195i $$0.889846\pi$$
$$38$$ 0 0
$$39$$ −1.03729 + 0.431843i −0.166100 + 0.0691502i
$$40$$ 0 0
$$41$$ −4.09755 3.43825i −0.639929 0.536964i 0.264067 0.964504i $$-0.414936\pi$$
−0.903996 + 0.427540i $$0.859380\pi$$
$$42$$ 0 0
$$43$$ 7.34330 2.67274i 1.11984 0.407589i 0.285248 0.958454i $$-0.407924\pi$$
0.834595 + 0.550865i $$0.185702\pi$$
$$44$$ 0 0
$$45$$ −0.579012 + 2.19233i −0.0863139 + 0.326813i
$$46$$ 0 0
$$47$$ 3.11004 0.548383i 0.453646 0.0799899i 0.0578432 0.998326i $$-0.481578\pi$$
0.395802 + 0.918336i $$0.370467\pi$$
$$48$$ 0 0
$$49$$ 2.28961 3.96572i 0.327087 0.566531i
$$50$$ 0 0
$$51$$ −5.44676 + 10.5091i −0.762699 + 1.47157i
$$52$$ 0 0
$$53$$ −13.6276 4.96002i −1.87189 0.681312i −0.966462 0.256809i $$-0.917329\pi$$
−0.905427 0.424503i $$-0.860449\pi$$
$$54$$ 0 0
$$55$$ −0.126153 + 0.715449i −0.0170105 + 0.0964711i
$$56$$ 0 0
$$57$$ 0.0901766 + 7.54930i 0.0119442 + 0.999929i
$$58$$ 0 0
$$59$$ −2.02192 + 11.4669i −0.263231 + 1.49286i 0.510793 + 0.859704i $$0.329352\pi$$
−0.774024 + 0.633156i $$0.781759\pi$$
$$60$$ 0 0
$$61$$ 10.1813 + 3.70568i 1.30358 + 0.474464i 0.898161 0.439667i $$-0.144903\pi$$
0.405419 + 0.914131i $$0.367126\pi$$
$$62$$ 0 0
$$63$$ −0.390129 + 4.65133i −0.0491517 + 0.586012i
$$64$$ 0 0
$$65$$ 0.245158 0.424626i 0.0304081 0.0526684i
$$66$$ 0 0
$$67$$ 9.19012 1.62047i 1.12275 0.197972i 0.418703 0.908123i $$-0.362485\pi$$
0.704049 + 0.710151i $$0.251374\pi$$
$$68$$ 0 0
$$69$$ −1.61189 1.23226i −0.194048 0.148346i
$$70$$ 0 0
$$71$$ −0.0322101 + 0.0117235i −0.00382263 + 0.00139132i −0.343931 0.938995i $$-0.611759\pi$$
0.340108 + 0.940386i $$0.389536\pi$$
$$72$$ 0 0
$$73$$ −3.04446 2.55461i −0.356327 0.298994i 0.446998 0.894535i $$-0.352493\pi$$
−0.803325 + 0.595541i $$0.796938\pi$$
$$74$$ 0 0
$$75$$ 2.94818 + 7.08158i 0.340426 + 0.817711i
$$76$$ 0 0
$$77$$ 1.49547i 0.170425i
$$78$$ 0 0
$$79$$ 0.893115 1.06437i 0.100483 0.119751i −0.713459 0.700697i $$-0.752873\pi$$
0.813943 + 0.580945i $$0.197317\pi$$
$$80$$ 0 0
$$81$$ 3.13878 + 8.43493i 0.348753 + 0.937215i
$$82$$ 0 0
$$83$$ 10.4856 6.05389i 1.15095 0.664500i 0.201830 0.979421i $$-0.435311\pi$$
0.949118 + 0.314920i $$0.101978\pi$$
$$84$$ 0 0
$$85$$ −0.896950 5.08686i −0.0972879 0.551747i
$$86$$ 0 0
$$87$$ −13.8150 1.79358i −1.48113 0.192292i
$$88$$ 0 0
$$89$$ 4.68075 3.92762i 0.496159 0.416327i −0.360069 0.932926i $$-0.617247\pi$$
0.856227 + 0.516599i $$0.172802\pi$$
$$90$$ 0 0
$$91$$ 0.345207 0.948448i 0.0361875 0.0994243i
$$92$$ 0 0
$$93$$ 1.15173 + 5.15137i 0.119429 + 0.534172i
$$94$$ 0 0
$$95$$ −2.03206 2.59329i −0.208485 0.266066i
$$96$$ 0 0
$$97$$ 9.54804 + 1.68358i 0.969457 + 0.170941i 0.635885 0.771784i $$-0.280635\pi$$
0.333571 + 0.942725i $$0.391746\pi$$
$$98$$ 0 0
$$99$$ 1.22799 + 2.60896i 0.123418 + 0.262211i
$$100$$ 0 0
$$101$$ 12.0945 + 14.4137i 1.20345 + 1.43422i 0.871130 + 0.491053i $$0.163388\pi$$
0.332323 + 0.943166i $$0.392168\pi$$
$$102$$ 0 0
$$103$$ −9.92876 5.73237i −0.978310 0.564828i −0.0765505 0.997066i $$-0.524391\pi$$
−0.901759 + 0.432238i $$0.857724\pi$$
$$104$$ 0 0
$$105$$ −1.09749 1.71592i −0.107104 0.167457i
$$106$$ 0 0
$$107$$ 1.17826 + 2.04080i 0.113906 + 0.197292i 0.917342 0.398100i $$-0.130330\pi$$
−0.803436 + 0.595392i $$0.796997\pi$$
$$108$$ 0 0
$$109$$ −2.21678 6.09056i −0.212329 0.583370i 0.787111 0.616811i $$-0.211576\pi$$
−0.999441 + 0.0334410i $$0.989353\pi$$
$$110$$ 0 0
$$111$$ −6.82032 2.13700i −0.647356 0.202835i
$$112$$ 0 0
$$113$$ −10.0387 −0.944358 −0.472179 0.881503i $$-0.656532\pi$$
−0.472179 + 0.881503i $$0.656532\pi$$
$$114$$ 0 0
$$115$$ 0.885394 0.0825635
$$116$$ 0 0
$$117$$ −0.176570 1.93810i −0.0163239 0.179177i
$$118$$ 0 0
$$119$$ −3.63665 9.99161i −0.333371 0.915929i
$$120$$ 0 0
$$121$$ −5.03807 8.72620i −0.458007 0.793291i
$$122$$ 0 0
$$123$$ 7.80481 4.99192i 0.703736 0.450106i
$$124$$ 0 0
$$125$$ −6.17177 3.56327i −0.552020 0.318709i
$$126$$ 0 0
$$127$$ −8.95146 10.6679i −0.794313 0.946626i 0.205171 0.978726i $$-0.434225\pi$$
−0.999485 + 0.0321003i $$0.989780\pi$$
$$128$$ 0 0
$$129$$ 0.614653 + 13.5213i 0.0541172 + 1.19048i
$$130$$ 0 0
$$131$$ −10.9610 1.93273i −0.957671 0.168863i −0.327096 0.944991i $$-0.606070\pi$$
−0.630575 + 0.776128i $$0.717181\pi$$
$$132$$ 0 0
$$133$$ −5.04643 4.53083i −0.437581 0.392873i
$$134$$ 0 0
$$135$$ −3.32367 2.09235i −0.286056 0.180081i
$$136$$ 0 0
$$137$$ −1.69757 + 4.66403i −0.145033 + 0.398475i −0.990845 0.135007i $$-0.956894\pi$$
0.845812 + 0.533482i $$0.179117\pi$$
$$138$$ 0 0
$$139$$ 2.76202 2.31761i 0.234272 0.196577i −0.518093 0.855325i $$-0.673358\pi$$
0.752364 + 0.658747i $$0.228913\pi$$
$$140$$ 0 0
$$141$$ −0.704229 + 5.42432i −0.0593068 + 0.456810i
$$142$$ 0 0
$$143$$ −0.108273 0.614047i −0.00905425 0.0513492i
$$144$$ 0 0
$$145$$ 5.26475 3.03961i 0.437214 0.252426i
$$146$$ 0 0
$$147$$ 5.36888 + 5.83805i 0.442818 + 0.481514i
$$148$$ 0 0
$$149$$ 12.3170 14.6788i 1.00904 1.20253i 0.0298610 0.999554i $$-0.490494\pi$$
0.979183 0.202978i $$-0.0650620\pi$$
$$150$$ 0 0
$$151$$ 19.2624i 1.56755i 0.621042 + 0.783777i $$0.286710\pi$$
−0.621042 + 0.783777i $$0.713290\pi$$
$$152$$ 0 0
$$153$$ −14.5489 14.4449i −1.17621 1.16780i
$$154$$ 0 0
$$155$$ −1.76455 1.48063i −0.141732 0.118927i
$$156$$ 0 0
$$157$$ −0.200940 + 0.0731363i −0.0160368 + 0.00583691i −0.350026 0.936740i $$-0.613827\pi$$
0.333989 + 0.942577i $$0.391605\pi$$
$$158$$ 0 0
$$159$$ 15.2554 19.9552i 1.20983 1.58255i
$$160$$ 0 0
$$161$$ 1.79490 0.316489i 0.141458 0.0249428i
$$162$$ 0 0
$$163$$ −7.51668 + 13.0193i −0.588752 + 1.01975i 0.405645 + 0.914031i $$0.367047\pi$$
−0.994396 + 0.105717i $$0.966286\pi$$
$$164$$ 0 0
$$165$$ −1.11718 0.579020i −0.0869720 0.0450767i
$$166$$ 0 0
$$167$$ 8.87982 + 3.23199i 0.687141 + 0.250099i 0.661911 0.749583i $$-0.269746\pi$$
0.0252305 + 0.999682i $$0.491968\pi$$
$$168$$ 0 0
$$169$$ 2.18435 12.3881i 0.168027 0.952929i
$$170$$ 0 0
$$171$$ −12.5243 3.76054i −0.957758 0.287575i
$$172$$ 0 0
$$173$$ 2.33529 13.2441i 0.177549 1.00693i −0.757612 0.652705i $$-0.773634\pi$$
0.935161 0.354224i $$-0.115255\pi$$
$$174$$ 0 0
$$175$$ −6.47502 2.35672i −0.489466 0.178151i
$$176$$ 0 0
$$177$$ −17.9056 9.28026i −1.34586 0.697547i
$$178$$ 0 0
$$179$$ −8.34644 + 14.4565i −0.623842 + 1.08053i 0.364921 + 0.931038i $$0.381096\pi$$
−0.988764 + 0.149488i $$0.952237\pi$$
$$180$$ 0 0
$$181$$ −10.0398 + 1.77029i −0.746251 + 0.131584i −0.533828 0.845593i $$-0.679247\pi$$
−0.212424 + 0.977178i $$0.568136\pi$$
$$182$$ 0 0
$$183$$ −11.3974 + 14.9087i −0.842523 + 1.10209i
$$184$$ 0 0
$$185$$ 2.93084 1.06674i 0.215480 0.0784281i
$$186$$ 0 0
$$187$$ −5.03184 4.22221i −0.367964 0.308759i
$$188$$ 0 0
$$189$$ −7.48576 3.05361i −0.544509 0.222118i
$$190$$ 0 0
$$191$$ 12.0667i 0.873115i −0.899676 0.436558i $$-0.856198\pi$$
0.899676 0.436558i $$-0.143802\pi$$
$$192$$ 0 0
$$193$$ −2.14990 + 2.56215i −0.154753 + 0.184427i −0.837850 0.545900i $$-0.816188\pi$$
0.683098 + 0.730327i $$0.260632\pi$$
$$194$$ 0 0
$$195$$ 0.574869 + 0.625104i 0.0411672 + 0.0447647i
$$196$$ 0 0
$$197$$ 5.15098 2.97392i 0.366992 0.211883i −0.305151 0.952304i $$-0.598707\pi$$
0.672144 + 0.740421i $$0.265374\pi$$
$$198$$ 0 0
$$199$$ −1.94088 11.0073i −0.137585 0.780286i −0.973024 0.230703i $$-0.925898\pi$$
0.835439 0.549583i $$-0.185214\pi$$
$$200$$ 0 0
$$201$$ −2.08099 + 16.0288i −0.146782 + 1.13058i
$$202$$ 0 0
$$203$$ 9.58634 8.04389i 0.672829 0.564571i
$$204$$ 0 0
$$205$$ −1.38276 + 3.79911i −0.0965764 + 0.265342i
$$206$$ 0 0
$$207$$ 2.87145 2.02600i 0.199579 0.140817i
$$208$$ 0 0
$$209$$ −4.09933 0.865240i −0.283557 0.0598499i
$$210$$ 0 0
$$211$$ 20.9377 + 3.69188i 1.44141 + 0.254159i 0.839045 0.544063i $$-0.183115\pi$$
0.602364 + 0.798222i $$0.294226\pi$$
$$212$$ 0 0
$$213$$ −0.00269607 0.0593087i −0.000184731 0.00406376i
$$214$$ 0 0
$$215$$ −3.79664 4.52466i −0.258928 0.308579i
$$216$$ 0 0
$$217$$ −4.10641 2.37084i −0.278761 0.160943i
$$218$$ 0 0
$$219$$ 5.79895 3.70898i 0.391856 0.250629i
$$220$$ 0 0
$$221$$ 2.21662 + 3.83930i 0.149106 + 0.258259i
$$222$$ 0 0
$$223$$ −4.71184 12.9457i −0.315528 0.866907i −0.991515 0.129993i $$-0.958505\pi$$
0.675987 0.736914i $$-0.263718\pi$$
$$224$$ 0 0
$$225$$ −13.2313 + 1.20544i −0.882090 + 0.0803625i
$$226$$ 0 0
$$227$$ −16.1886 −1.07448 −0.537238 0.843430i $$-0.680532\pi$$
−0.537238 + 0.843430i $$0.680532\pi$$
$$228$$ 0 0
$$229$$ −25.6462 −1.69475 −0.847374 0.530997i $$-0.821817\pi$$
−0.847374 + 0.530997i $$0.821817\pi$$
$$230$$ 0 0
$$231$$ −2.47174 0.774466i −0.162629 0.0509561i
$$232$$ 0 0
$$233$$ 3.98107 + 10.9379i 0.260808 + 0.716565i 0.999113 + 0.0420981i $$0.0134042\pi$$
−0.738305 + 0.674467i $$0.764374\pi$$
$$234$$ 0 0
$$235$$ −1.19347 2.06715i −0.0778532 0.134846i
$$236$$ 0 0
$$237$$ 1.29669 + 2.02737i 0.0842293 + 0.131692i
$$238$$ 0 0
$$239$$ 13.1831 + 7.61128i 0.852746 + 0.492333i 0.861576 0.507628i $$-0.169478\pi$$
−0.00883069 + 0.999961i $$0.502811\pi$$
$$240$$ 0 0
$$241$$ 9.76016 + 11.6317i 0.628707 + 0.749264i 0.982541 0.186044i $$-0.0595666\pi$$
−0.353834 + 0.935308i $$0.615122\pi$$
$$242$$ 0 0
$$243$$ −15.5669 + 0.819603i −0.998617 + 0.0525776i
$$244$$ 0 0
$$245$$ −3.40855 0.601019i −0.217764 0.0383977i
$$246$$ 0 0
$$247$$ 2.40012 + 1.49501i 0.152716 + 0.0951254i
$$248$$ 0 0
$$249$$ 4.57573 + 20.4660i 0.289975 + 1.29698i
$$250$$ 0 0
$$251$$ 3.71032 10.1940i 0.234193 0.643441i −0.765807 0.643071i $$-0.777660\pi$$
1.00000 0.000369965i $$-0.000117763\pi$$
$$252$$ 0 0
$$253$$ 0.862512 0.723733i 0.0542257 0.0455007i
$$254$$ 0 0
$$255$$ 8.87216 + 1.15186i 0.555596 + 0.0721320i
$$256$$ 0 0
$$257$$ −0.00786014 0.0445771i −0.000490302 0.00278064i 0.984562 0.175038i $$-0.0560049\pi$$
−0.985052 + 0.172258i $$0.944894\pi$$
$$258$$ 0 0
$$259$$ 5.56017 3.21017i 0.345492 0.199470i
$$260$$ 0 0
$$261$$ 10.1189 21.9049i 0.626345 1.35588i
$$262$$ 0 0
$$263$$ 3.52577 4.20185i 0.217408 0.259097i −0.646307 0.763078i $$-0.723687\pi$$
0.863715 + 0.503981i $$0.168132\pi$$
$$264$$ 0 0
$$265$$ 10.9612i 0.673342i
$$266$$ 0 0
$$267$$ 4.06760 + 9.77044i 0.248933 + 0.597941i
$$268$$ 0 0
$$269$$ 1.50432 + 1.26228i 0.0917202 + 0.0769623i 0.687495 0.726189i $$-0.258710\pi$$
−0.595775 + 0.803152i $$0.703155\pi$$
$$270$$ 0 0
$$271$$ −19.8494 + 7.22458i −1.20576 + 0.438862i −0.865232 0.501371i $$-0.832829\pi$$
−0.340531 + 0.940233i $$0.610607\pi$$
$$272$$ 0 0
$$273$$ 1.38884 + 1.06174i 0.0840563 + 0.0642594i
$$274$$ 0 0
$$275$$ −4.19208 + 0.739177i −0.252792 + 0.0445741i
$$276$$ 0 0
$$277$$ −3.91899 + 6.78789i −0.235469 + 0.407845i −0.959409 0.282018i $$-0.908996\pi$$
0.723940 + 0.689863i $$0.242329\pi$$
$$278$$ 0 0
$$279$$ −9.11072 0.764161i −0.545445 0.0457491i
$$280$$ 0 0
$$281$$ −11.0064 4.00600i −0.656587 0.238978i −0.00782495 0.999969i $$-0.502491\pi$$
−0.648762 + 0.760991i $$0.724713\pi$$
$$282$$ 0 0
$$283$$ −1.21905 + 6.91356i −0.0724648 + 0.410968i 0.926899 + 0.375310i $$0.122464\pi$$
−0.999364 + 0.0356581i $$0.988647\pi$$
$$284$$ 0 0
$$285$$ 5.33859 2.01562i 0.316231 0.119395i
$$286$$ 0 0
$$287$$ −1.44517 + 8.19595i −0.0853055 + 0.483791i
$$288$$ 0 0
$$289$$ 27.9116 + 10.1590i 1.64186 + 0.597587i
$$290$$ 0 0
$$291$$ −7.72733 + 14.9093i −0.452984 + 0.873998i
$$292$$ 0 0
$$293$$ −1.29095 + 2.23599i −0.0754180 + 0.130628i −0.901268 0.433262i $$-0.857362\pi$$
0.825850 + 0.563890i $$0.190696\pi$$
$$294$$ 0 0
$$295$$ 8.66705 1.52824i 0.504615 0.0889773i
$$296$$ 0 0
$$297$$ −4.94808 + 0.678535i −0.287117 + 0.0393726i
$$298$$ 0 0
$$299$$ −0.714078 + 0.259903i −0.0412962 + 0.0150306i
$$300$$ 0 0
$$301$$ −9.31401 7.81539i −0.536851 0.450471i
$$302$$ 0 0
$$303$$ −30.0867 + 12.5256i −1.72844 + 0.719577i
$$304$$ 0 0
$$305$$ 8.18923i 0.468914i
$$306$$ 0 0
$$307$$ 1.26629 1.50910i 0.0722709 0.0861290i −0.728698 0.684836i $$-0.759874\pi$$
0.800968 + 0.598707i $$0.204318\pi$$
$$308$$ 0 0
$$309$$ 14.6164 13.4418i 0.831499 0.764677i
$$310$$ 0 0
$$311$$ −22.4909 + 12.9851i −1.27534 + 0.736320i −0.975989 0.217822i $$-0.930105\pi$$
−0.299355 + 0.954142i $$0.596771\pi$$
$$312$$ 0 0
$$313$$ −2.32842 13.2051i −0.131610 0.746398i −0.977161 0.212502i $$-0.931839\pi$$
0.845551 0.533895i $$-0.179272\pi$$
$$314$$ 0 0
$$315$$ 3.40446 0.925326i 0.191820 0.0521362i
$$316$$ 0 0
$$317$$ −23.3056 + 19.5557i −1.30897 + 1.09836i −0.320454 + 0.947264i $$0.603835\pi$$
−0.988519 + 0.151095i $$0.951720\pi$$
$$318$$ 0 0
$$319$$ 2.64407 7.26453i 0.148040 0.406736i
$$320$$ 0 0
$$321$$ −3.98326 + 0.890567i −0.222324 + 0.0497066i
$$322$$ 0 0
$$323$$ 29.4927 4.18776i 1.64102 0.233013i
$$324$$ 0 0
$$325$$ 2.82930 + 0.498882i 0.156941 + 0.0276730i
$$326$$ 0 0
$$327$$ 11.2146 0.509796i 0.620169 0.0281918i
$$328$$ 0 0
$$329$$ −3.15834 3.76397i −0.174125 0.207514i
$$330$$ 0 0
$$331$$ 9.22014 + 5.32325i 0.506785 + 0.292592i 0.731511 0.681830i $$-0.238815\pi$$
−0.224726 + 0.974422i $$0.572149\pi$$
$$332$$ 0 0
$$333$$ 7.06413 10.1660i 0.387112 0.557096i
$$334$$ 0 0
$$335$$ −3.52668 6.10839i −0.192683 0.333737i
$$336$$ 0 0
$$337$$ −2.38138 6.54278i −0.129722 0.356408i 0.857780 0.514018i $$-0.171843\pi$$
−0.987501 + 0.157610i $$0.949621\pi$$
$$338$$ 0 0
$$339$$ 5.19876 16.5921i 0.282358 0.901158i
$$340$$ 0 0
$$341$$ −2.92924 −0.158627
$$342$$ 0 0
$$343$$ −18.0159 −0.972770
$$344$$ 0 0
$$345$$ −0.458523 + 1.46340i −0.0246860 + 0.0787866i
$$346$$ 0 0
$$347$$ 9.63081 + 26.4604i 0.517009 + 1.42047i 0.873799 + 0.486287i $$0.161649\pi$$
−0.356790 + 0.934185i $$0.616129\pi$$
$$348$$ 0 0
$$349$$ 9.79155 + 16.9595i 0.524130 + 0.907819i 0.999605 + 0.0280904i $$0.00894261\pi$$
−0.475476 + 0.879729i $$0.657724\pi$$
$$350$$ 0 0
$$351$$ 3.29477 + 0.711853i 0.175862 + 0.0379959i
$$352$$ 0 0
$$353$$ −3.55050 2.04988i −0.188974 0.109104i 0.402528 0.915408i $$-0.368132\pi$$
−0.591502 + 0.806303i $$0.701465\pi$$
$$354$$ 0 0
$$355$$ 0.0166533 + 0.0198466i 0.000883864 + 0.00105335i
$$356$$ 0 0
$$357$$ 18.3976 0.836324i 0.973706 0.0442629i
$$358$$ 0 0
$$359$$ 5.52450 + 0.974118i 0.291572 + 0.0514120i 0.317521 0.948251i $$-0.397150\pi$$
−0.0259490 + 0.999663i $$0.508261\pi$$
$$360$$ 0 0
$$361$$ 15.3395 11.2117i 0.807340 0.590087i
$$362$$ 0 0
$$363$$ 17.0319 3.80795i 0.893943 0.199865i
$$364$$ 0 0
$$365$$ −1.02739 + 2.82273i −0.0537760 + 0.147748i
$$366$$ 0 0
$$367$$ 2.28539 1.91767i 0.119296 0.100101i −0.581188 0.813769i $$-0.697412\pi$$
0.700484 + 0.713668i $$0.252967\pi$$
$$368$$ 0 0
$$369$$ 4.20882 + 15.4851i 0.219103 + 0.806123i
$$370$$ 0 0
$$371$$ 3.91814 + 22.2209i 0.203420 + 1.15365i
$$372$$ 0 0
$$373$$ −18.2415 + 10.5317i −0.944510 + 0.545313i −0.891371 0.453274i $$-0.850256\pi$$
−0.0531391 + 0.998587i $$0.516923\pi$$
$$374$$ 0 0
$$375$$ 9.08564 8.35548i 0.469180 0.431475i
$$376$$ 0 0
$$377$$ −3.35381 + 3.99691i −0.172730 + 0.205852i
$$378$$ 0 0
$$379$$ 9.54057i 0.490066i 0.969515 + 0.245033i $$0.0787988\pi$$
−0.969515 + 0.245033i $$0.921201\pi$$
$$380$$ 0 0
$$381$$ 22.2679 9.27048i 1.14082 0.474941i
$$382$$ 0 0
$$383$$ −5.96084 5.00173i −0.304584 0.255577i 0.477665 0.878542i $$-0.341483\pi$$
−0.782249 + 0.622965i $$0.785928\pi$$
$$384$$ 0 0
$$385$$ 1.06216 0.386595i 0.0541328 0.0197027i
$$386$$ 0 0
$$387$$ −22.6665 5.98640i −1.15220 0.304306i
$$388$$ 0 0
$$389$$ 9.63724 1.69931i 0.488627 0.0861582i 0.0760939 0.997101i $$-0.475755\pi$$
0.412533 + 0.910942i $$0.364644\pi$$
$$390$$ 0 0
$$391$$ −4.00269 + 6.93287i −0.202425 + 0.350610i
$$392$$ 0 0
$$393$$ 8.87089 17.1157i 0.447477 0.863373i
$$394$$ 0 0
$$395$$ −0.986853 0.359185i −0.0496539 0.0180726i
$$396$$ 0 0
$$397$$ −2.05329 + 11.6448i −0.103052 + 0.584435i 0.888929 + 0.458045i $$0.151450\pi$$
−0.991981 + 0.126390i $$0.959661\pi$$
$$398$$ 0 0
$$399$$ 10.1020 5.99443i 0.505735 0.300097i
$$400$$ 0 0
$$401$$ −3.59086 + 20.3648i −0.179319 + 1.01697i 0.753720 + 0.657195i $$0.228257\pi$$
−0.933039 + 0.359774i $$0.882854\pi$$
$$402$$ 0 0
$$403$$ 1.85776 + 0.676169i 0.0925416 + 0.0336824i
$$404$$ 0 0
$$405$$ 5.17952 4.40984i 0.257372 0.219127i
$$406$$ 0 0
$$407$$ 1.98313 3.43488i 0.0982999 0.170260i
$$408$$ 0 0
$$409$$ 3.39761 0.599090i 0.168001 0.0296231i −0.0890148 0.996030i $$-0.528372\pi$$
0.257016 + 0.966407i $$0.417261\pi$$
$$410$$ 0 0
$$411$$ −6.82966 5.22115i −0.336882 0.257540i
$$412$$ 0 0
$$413$$ 17.0238 6.19617i 0.837688 0.304893i
$$414$$ 0 0
$$415$$ −7.01043 5.88245i −0.344128 0.288758i
$$416$$ 0 0
$$417$$ 2.40021 + 5.76535i 0.117539 + 0.282331i
$$418$$ 0 0
$$419$$ 25.3156i 1.23675i −0.785884 0.618374i $$-0.787792\pi$$
0.785884 0.618374i $$-0.212208\pi$$
$$420$$ 0 0
$$421$$ 20.4536 24.3756i 0.996845 1.18799i 0.0146955 0.999892i $$-0.495322\pi$$
0.982150 0.188102i $$-0.0602334\pi$$
$$422$$ 0 0
$$423$$ −8.60071 3.97307i −0.418181 0.193178i
$$424$$ 0 0
$$425$$ 26.2108 15.1328i 1.27141 0.734049i
$$426$$ 0 0
$$427$$ −2.92728 16.6014i −0.141661 0.803400i
$$428$$ 0 0
$$429$$ 1.07098 + 0.139043i 0.0517074 + 0.00671308i
$$430$$ 0 0
$$431$$ 25.2345 21.1742i 1.21550 1.01993i 0.216455 0.976293i $$-0.430551\pi$$
0.999048 0.0436350i $$-0.0138938\pi$$
$$432$$ 0 0
$$433$$ −5.46188 + 15.0064i −0.262481 + 0.721161i 0.736517 + 0.676419i $$0.236469\pi$$
−0.998999 + 0.0447423i $$0.985753\pi$$
$$434$$ 0 0
$$435$$ 2.29744 + 10.2758i 0.110154 + 0.492688i
$$436$$ 0 0
$$437$$ −0.170932 + 5.10321i −0.00817679 + 0.244120i
$$438$$ 0 0
$$439$$ 30.5401 + 5.38505i 1.45760 + 0.257014i 0.845589 0.533835i $$-0.179250\pi$$
0.612011 + 0.790849i $$0.290361\pi$$
$$440$$ 0 0
$$441$$ −12.4296 + 5.85041i −0.591887 + 0.278591i
$$442$$ 0 0
$$443$$ −12.5287 14.9311i −0.595257 0.709400i 0.381350 0.924431i $$-0.375459\pi$$
−0.976607 + 0.215031i $$0.931015\pi$$
$$444$$ 0 0
$$445$$ −3.99962 2.30918i −0.189600 0.109466i
$$446$$ 0 0
$$447$$ 17.8827 + 27.9594i 0.845823 + 1.32244i
$$448$$ 0 0
$$449$$ 6.61607 + 11.4594i 0.312232 + 0.540801i 0.978845 0.204602i $$-0.0655901\pi$$
−0.666613 + 0.745404i $$0.732257\pi$$
$$450$$ 0 0
$$451$$ 1.75842 + 4.83122i 0.0828007 + 0.227493i
$$452$$ 0 0
$$453$$ −31.8373 9.97551i −1.49585 0.468690i
$$454$$ 0 0
$$455$$ −0.762876 −0.0357642
$$456$$ 0 0
$$457$$ −15.4038 −0.720559 −0.360279 0.932844i $$-0.617319\pi$$
−0.360279 + 0.932844i $$0.617319\pi$$
$$458$$ 0 0
$$459$$ 31.4093 16.5661i 1.46606 0.773238i
$$460$$ 0 0
$$461$$ −5.65076 15.5253i −0.263182 0.723087i −0.998948 0.0458511i $$-0.985400\pi$$
0.735766 0.677236i $$-0.236822\pi$$
$$462$$ 0 0
$$463$$ 4.69170 + 8.12625i 0.218042 + 0.377659i 0.954209 0.299140i $$-0.0966998\pi$$
−0.736168 + 0.676799i $$0.763366\pi$$
$$464$$ 0 0
$$465$$ 3.36103 2.14970i 0.155864 0.0996899i
$$466$$ 0 0
$$467$$ −18.5458 10.7074i −0.858196 0.495480i 0.00521153 0.999986i $$-0.498341\pi$$
−0.863408 + 0.504507i $$0.831674\pi$$
$$468$$ 0 0
$$469$$ −9.33287 11.1225i −0.430952 0.513588i
$$470$$ 0 0
$$471$$ −0.0168192 0.369993i −0.000774989 0.0170484i
$$472$$ 0 0
$$473$$ −7.39703 1.30430i −0.340116 0.0599716i
$$474$$ 0 0
$$475$$ 10.2064 16.3855i 0.468302 0.751820i
$$476$$ 0 0
$$477$$ 25.0820 + 35.5486i 1.14842 + 1.62766i
$$478$$ 0 0
$$479$$ −11.4165 + 31.3665i −0.521632 + 1.43317i 0.347071 + 0.937839i $$0.387176\pi$$
−0.868703 + 0.495333i $$0.835046\pi$$
$$480$$ 0 0
$$481$$ −2.05061 + 1.72067i −0.0934998 + 0.0784557i
$$482$$ 0 0
$$483$$ −0.406432 + 3.13054i −0.0184933 + 0.142444i
$$484$$ 0 0
$$485$$ −1.27250 7.21673i −0.0577815 0.327695i
$$486$$ 0 0
$$487$$ 28.9750 16.7288i 1.31298 0.758052i 0.330395 0.943843i $$-0.392818\pi$$
0.982589 + 0.185791i $$0.0594846\pi$$
$$488$$ 0 0
$$489$$ −17.6258 19.1660i −0.797066 0.866718i
$$490$$ 0 0
$$491$$ −0.635055 + 0.756829i −0.0286596 + 0.0341552i −0.780184 0.625550i $$-0.784875\pi$$
0.751524 + 0.659705i $$0.229319\pi$$
$$492$$ 0 0
$$493$$ 54.9658i 2.47554i
$$494$$ 0 0
$$495$$ 1.53557 1.54663i 0.0690188 0.0695158i
$$496$$ 0 0
$$497$$ 0.0408543 + 0.0342808i 0.00183256 + 0.00153770i
$$498$$ 0 0
$$499$$ 4.11402 1.49738i 0.184169 0.0670319i −0.248290 0.968686i $$-0.579868\pi$$
0.432458 + 0.901654i $$0.357646\pi$$
$$500$$ 0 0
$$501$$ −9.94052 + 13.0030i −0.444110 + 0.580930i
$$502$$ 0 0
$$503$$ −31.7905 + 5.60552i −1.41747 + 0.249938i −0.829301 0.558802i $$-0.811261\pi$$
−0.588167 + 0.808740i $$0.700150\pi$$
$$504$$ 0 0
$$505$$ 7.11080 12.3163i 0.316426 0.548067i
$$506$$ 0 0
$$507$$ 19.3440 + 10.0258i 0.859097 + 0.445261i
$$508$$ 0 0
$$509$$ 21.2608 + 7.73831i 0.942370 + 0.342994i 0.767101 0.641526i $$-0.221698\pi$$
0.175268 + 0.984521i $$0.443921\pi$$
$$510$$ 0 0
$$511$$ −1.07375 + 6.08956i −0.0475000 + 0.269386i
$$512$$ 0 0
$$513$$ 12.7015 18.7529i 0.560785 0.827962i
$$514$$ 0 0
$$515$$ −1.50474 + 8.53380i −0.0663067 + 0.376044i
$$516$$ 0 0
$$517$$ −2.85234 1.03817i −0.125446 0.0456585i
$$518$$ 0 0
$$519$$ 20.6807 + 10.7186i 0.907781 + 0.470493i
$$520$$ 0 0
$$521$$ 4.86213 8.42145i 0.213014 0.368950i −0.739643 0.673000i $$-0.765005\pi$$
0.952656 + 0.304049i $$0.0983388\pi$$
$$522$$ 0 0
$$523$$ −33.5671 + 5.91879i −1.46779 + 0.258810i −0.849686 0.527288i $$-0.823209\pi$$
−0.618101 + 0.786099i $$0.712098\pi$$
$$524$$ 0 0
$$525$$ 7.24847 9.48155i 0.316349 0.413809i
$$526$$ 0 0
$$527$$ 19.5709 7.12324i 0.852523 0.310293i
$$528$$ 0 0
$$529$$ 16.5678 + 13.9021i 0.720341 + 0.604438i
$$530$$ 0 0
$$531$$ 24.6114 24.7886i 1.06804 1.07573i
$$532$$ 0 0
$$533$$ 3.46992i 0.150299i
$$534$$ 0 0
$$535$$ 1.14489 1.36443i 0.0494980 0.0589894i
$$536$$ 0 0
$$537$$ −19.5715 21.2818i −0.844572 0.918376i
$$538$$ 0 0
$$539$$ −3.81174 + 2.20071i −0.164183 + 0.0947911i
$$540$$ 0 0
$$541$$ 0.180608 + 1.02428i 0.00776495 + 0.0440372i 0.988444 0.151586i $$-0.0484381\pi$$
−0.980679 + 0.195623i $$0.937327\pi$$
$$542$$ 0 0
$$543$$ 2.27338 17.5107i 0.0975603 0.751457i
$$544$$ 0 0
$$545$$ −3.75277 + 3.14895i −0.160751 + 0.134886i
$$546$$ 0 0
$$547$$ −8.86889 + 24.3671i −0.379207 + 1.04186i 0.592480 + 0.805586i $$0.298149\pi$$
−0.971686 + 0.236276i $$0.924073\pi$$
$$548$$ 0 0
$$549$$ −18.7390 26.5587i −0.799760 1.13350i
$$550$$ 0 0
$$551$$ 16.5032 + 30.9317i 0.703060 + 1.31773i
$$552$$ 0 0
$$553$$ −2.12897 0.375395i −0.0905330 0.0159634i
$$554$$ 0 0
$$555$$ 0.245319 + 5.39658i 0.0104132 + 0.229072i
$$556$$ 0 0
$$557$$ −2.42914 2.89494i −0.102926 0.122662i 0.712122 0.702055i $$-0.247734\pi$$
−0.815048 + 0.579393i $$0.803290\pi$$
$$558$$ 0 0
$$559$$ 4.39021 + 2.53469i 0.185686 + 0.107206i
$$560$$ 0 0
$$561$$ 9.58440 6.13013i 0.404654 0.258814i
$$562$$ 0 0
$$563$$ −5.99208 10.3786i −0.252536 0.437406i 0.711687 0.702496i $$-0.247931\pi$$
−0.964223 + 0.265091i $$0.914598\pi$$
$$564$$ 0 0
$$565$$ 2.59510 + 7.12998i 0.109177 + 0.299960i
$$566$$ 0 0
$$567$$ 8.92374 10.7912i 0.374762 0.453188i
$$568$$ 0 0
$$569$$ 11.2148 0.470147 0.235074 0.971978i $$-0.424467\pi$$
0.235074 + 0.971978i $$0.424467\pi$$
$$570$$ 0 0
$$571$$ −16.2525 −0.680144 −0.340072 0.940399i $$-0.610452\pi$$
−0.340072 + 0.940399i $$0.610452\pi$$
$$572$$ 0 0
$$573$$ 19.9440 + 6.24902i 0.833174 + 0.261057i
$$574$$ 0 0
$$575$$ 1.77435 + 4.87499i 0.0739956 + 0.203301i
$$576$$ 0 0
$$577$$ −4.02000 6.96284i −0.167355 0.289867i 0.770134 0.637882i $$-0.220189\pi$$
−0.937489 + 0.348015i $$0.886856\pi$$
$$578$$ 0 0
$$579$$ −3.12138 4.88025i −0.129720 0.202816i
$$580$$ 0 0
$$581$$ −16.3145 9.41916i −0.676838 0.390772i
$$582$$ 0 0
$$583$$ 8.95984 + 10.6779i 0.371079 + 0.442234i
$$584$$ 0 0
$$585$$ −1.33089 + 0.626428i −0.0550257 + 0.0258996i
$$586$$ 0 0
$$587$$ 19.5628 + 3.44945i 0.807444 + 0.142374i 0.562108 0.827064i $$-0.309991\pi$$
0.245336 + 0.969438i $$0.421102\pi$$
$$588$$ 0 0
$$589$$ 8.87470 9.88463i 0.365676 0.407289i
$$590$$ 0 0
$$591$$ 2.24779 + 10.0537i 0.0924617 + 0.413556i
$$592$$ 0 0
$$593$$ −7.64203 + 20.9963i −0.313821 + 0.862215i 0.678056 + 0.735010i $$0.262823\pi$$
−0.991876 + 0.127205i $$0.959399\pi$$
$$594$$ 0 0
$$595$$ −6.15644 + 5.16587i −0.252390 + 0.211780i
$$596$$ 0 0
$$597$$ 19.1982 + 2.49246i 0.785729 + 0.102010i
$$598$$ 0 0
$$599$$ −2.89198 16.4012i −0.118163 0.670136i −0.985135 0.171780i $$-0.945048\pi$$
0.866972 0.498356i $$-0.166063\pi$$
$$600$$ 0 0
$$601$$ 17.9204 10.3464i 0.730990 0.422037i −0.0877940 0.996139i $$-0.527982\pi$$
0.818784 + 0.574101i $$0.194648\pi$$
$$602$$ 0 0
$$603$$ −25.4150 11.7404i −1.03498 0.478106i
$$604$$ 0 0
$$605$$ −4.89540 + 5.83411i −0.199026 + 0.237191i
$$606$$ 0 0
$$607$$ 39.3916i 1.59886i 0.600761 + 0.799428i $$0.294864\pi$$
−0.600761 + 0.799428i $$0.705136\pi$$
$$608$$ 0 0
$$609$$ 8.33058 + 20.0102i 0.337572 + 0.810854i
$$610$$ 0 0
$$611$$ 1.56934 + 1.31683i 0.0634888 + 0.0532734i
$$612$$ 0 0
$$613$$ −26.4005 + 9.60900i −1.06631 + 0.388104i −0.814794 0.579750i $$-0.803150\pi$$
−0.251512 + 0.967854i $$0.580928\pi$$
$$614$$ 0 0
$$615$$ −5.56314 4.25292i −0.224328 0.171494i
$$616$$ 0 0
$$617$$ 20.3648 3.59086i 0.819854 0.144562i 0.252038 0.967717i $$-0.418899\pi$$
0.567817 + 0.823155i $$0.307788\pi$$
$$618$$ 0 0
$$619$$ −16.8830 + 29.2423i −0.678586 + 1.17535i 0.296821 + 0.954933i $$0.404074\pi$$
−0.975407 + 0.220412i $$0.929260\pi$$
$$620$$ 0 0
$$621$$ 1.86156 + 5.79519i 0.0747019 + 0.232553i
$$622$$ 0 0
$$623$$ −8.93358 3.25156i −0.357916 0.130271i
$$624$$ 0 0
$$625$$ 2.90984 16.5025i 0.116394 0.660101i
$$626$$ 0 0
$$627$$ 3.55302 6.32736i 0.141894 0.252690i
$$628$$ 0 0
$$629$$ −4.89690 + 27.7717i −0.195252 + 1.10733i
$$630$$ 0 0
$$631$$ 35.0060 + 12.7411i 1.39357 + 0.507217i 0.926262 0.376880i $$-0.123003\pi$$
0.467304 + 0.884096i $$0.345225\pi$$
$$632$$ 0 0
$$633$$ −16.9451 + 32.6942i −0.673506 + 1.29948i
$$634$$ 0 0
$$635$$ −5.26287 + 9.11556i −0.208851 + 0.361740i
$$636$$ 0 0
$$637$$ 2.92545 0.515836i 0.115911 0.0204382i
$$638$$ 0 0
$$639$$ 0.0994226 + 0.0262583i 0.00393310 + 0.00103876i
$$640$$ 0 0
$$641$$ −7.37099 + 2.68282i −0.291137 + 0.105965i −0.483460 0.875367i $$-0.660620\pi$$
0.192323 + 0.981332i $$0.438398\pi$$
$$642$$ 0 0
$$643$$ −29.9819 25.1578i −1.18237 0.992126i −0.999960 0.00890393i $$-0.997166\pi$$
−0.182410 0.983223i $$-0.558390\pi$$
$$644$$ 0 0
$$645$$ 9.44461 3.93195i 0.371881 0.154820i
$$646$$ 0 0
$$647$$ 6.21339i 0.244274i 0.992513 + 0.122137i $$0.0389747\pi$$
−0.992513 + 0.122137i $$0.961025\pi$$
$$648$$ 0 0
$$649$$ 7.19386 8.57331i 0.282384 0.336532i
$$650$$ 0 0
$$651$$ 6.04516 5.55935i 0.236929 0.217888i
$$652$$ 0 0
$$653$$ −23.3831 + 13.5002i −0.915050 + 0.528304i −0.882053 0.471151i $$-0.843839\pi$$
−0.0329976 + 0.999455i $$0.510505\pi$$
$$654$$ 0 0
$$655$$ 1.46082 + 8.28473i 0.0570790 + 0.323711i
$$656$$ 0 0
$$657$$ 3.12714 + 11.5054i 0.122001 + 0.448868i
$$658$$ 0 0
$$659$$ −23.3482 + 19.5915i −0.909517 + 0.763176i −0.972027 0.234869i $$-0.924534\pi$$
0.0625097 + 0.998044i $$0.480090\pi$$
$$660$$ 0 0
$$661$$ −11.2133 + 30.8082i −0.436146 + 1.19830i 0.505834 + 0.862631i $$0.331185\pi$$
−0.941980 + 0.335670i $$0.891037\pi$$
$$662$$ 0 0
$$663$$ −7.49360 + 1.67540i −0.291027 + 0.0650671i
$$664$$ 0 0
$$665$$ −1.91347 + 4.75550i −0.0742013 + 0.184410i
$$666$$ 0 0
$$667$$ −9.27861 1.63607i −0.359269 0.0633489i
$$668$$ 0 0
$$669$$ 23.8370 1.08359i 0.921591 0.0418939i
$$670$$ 0 0
$$671$$ −6.69399 7.97759i −0.258419 0.307971i
$$672$$ 0 0
$$673$$ 26.7750 + 15.4586i 1.03210 + 0.595884i 0.917586 0.397537i $$-0.130135\pi$$
0.114516 + 0.993421i $$0.463468\pi$$
$$674$$ 0 0
$$675$$ 4.85980 22.4933i 0.187054 0.865766i
$$676$$ 0 0
$$677$$ −19.6720 34.0729i −0.756057 1.30953i −0.944847 0.327511i $$-0.893790\pi$$
0.188791 0.982017i $$-0.439543\pi$$
$$678$$ 0 0
$$679$$ −5.15932 14.1751i −0.197996 0.543991i
$$680$$ 0 0
$$681$$ 8.38366 26.7568i 0.321263 1.02532i
$$682$$ 0 0
$$683$$ −12.0176 −0.459840 −0.229920 0.973210i $$-0.573846\pi$$
−0.229920 + 0.973210i $$0.573846\pi$$
$$684$$ 0 0
$$685$$ 3.75147 0.143336
$$686$$ 0 0
$$687$$ 13.2815 42.3885i 0.506720 1.61722i
$$688$$ 0 0
$$689$$ −3.21761 8.84031i −0.122581 0.336789i
$$690$$ 0 0
$$691$$ 17.5214 + 30.3479i 0.666544 + 1.15449i 0.978864 + 0.204512i $$0.0655606\pi$$
−0.312320 + 0.949977i $$0.601106\pi$$
$$692$$ 0 0
$$693$$ 2.56010 3.68427i 0.0972503 0.139954i
$$694$$ 0 0
$$695$$ −2.36010 1.36260i −0.0895237 0.0516865i
$$696$$ 0 0
$$697$$ −23.4968 28.0024i −0.890006 1.06067i
$$698$$ 0 0
$$699$$ −20.1400 + 0.915530i −0.761766 + 0.0346285i
$$700$$ 0 0
$$701$$ −2.95841 0.521647i −0.111738 0.0197023i 0.117500 0.993073i $$-0.462512\pi$$
−0.229237 + 0.973371i $$0.573623\pi$$
$$702$$ 0 0
$$703$$ 5.58262 + 17.0986i 0.210552 + 0.644887i
$$704$$ 0 0
$$705$$ 4.03468 0.902063i 0.151955 0.0339737i
$$706$$ 0 0
$$707$$ 10.0127 27.5097i 0.376567 1.03461i
$$708$$ 0 0
$$709$$ 2.36012 1.98037i 0.0886360 0.0743744i −0.597393 0.801949i $$-0.703797\pi$$
0.686029 + 0.727574i $$0.259352\pi$$
$$710$$ 0 0
$$711$$ −4.02239 + 1.09328i −0.150852 + 0.0410011i
$$712$$ 0 0
$$713$$ 0.619918 + 3.51573i 0.0232161 + 0.131665i
$$714$$ 0 0
$$715$$ −0.408138 + 0.235639i −0.0152635 + 0.00881239i
$$716$$ 0 0
$$717$$ −19.4073 + 17.8476i −0.724777 + 0.666532i
$$718$$ 0 0
$$719$$ −7.13781 + 8.50651i −0.266195 + 0.317239i −0.882540 0.470237i $$-0.844168\pi$$
0.616345 + 0.787476i $$0.288613\pi$$
$$720$$ 0 0
$$721$$ 17.8378i 0.664316i
$$722$$ 0 0
$$723$$ −24.2796 + 10.1080i −0.902969 + 0.375921i
$$724$$ 0 0
$$725$$ 27.2868 + 22.8964i 1.01341 + 0.850349i
$$726$$ 0 0
$$727$$ −13.8709 + 5.04860i −0.514444 + 0.187242i −0.586179 0.810182i $$-0.699368\pi$$
0.0717355 + 0.997424i $$0.477146\pi$$
$$728$$ 0 0
$$729$$ 6.70703 26.1537i 0.248409 0.968655i
$$730$$ 0 0
$$731$$ 52.5931 9.27357i 1.94522 0.342996i
$$732$$ 0 0
$$733$$ −18.1447 + 31.4276i −0.670191 + 1.16080i 0.307659 + 0.951497i $$0.400454\pi$$
−0.977850 + 0.209308i $$0.932879\pi$$
$$734$$ 0 0
$$735$$ 2.75857 5.32245i 0.101751 0.196322i
$$736$$ 0 0
$$737$$ −8.42862 3.06777i −0.310472 0.113003i
$$738$$ 0 0
$$739$$ 2.94942 16.7270i 0.108496 0.615312i −0.881270 0.472613i $$-0.843311\pi$$
0.989766 0.142699i $$-0.0455780\pi$$
$$740$$ 0 0
$$741$$ −3.71394 + 3.19273i −0.136435 + 0.117288i
$$742$$ 0 0
$$743$$ 4.59818 26.0776i 0.168691 0.956693i −0.776486 0.630134i $$-0.783000\pi$$
0.945177 0.326559i $$-0.105889\pi$$
$$744$$ 0 0
$$745$$ −13.6097 4.95352i −0.498620 0.181483i
$$746$$ 0 0
$$747$$ −36.1962 3.03595i −1.32435 0.111080i
$$748$$ 0 0
$$749$$ 1.83324 3.17526i 0.0669850 0.116021i
$$750$$ 0 0
$$751$$ −46.8929 + 8.26849i −1.71115 + 0.301722i −0.941566 0.336827i $$-0.890646\pi$$
−0.769581 + 0.638549i $$0.779535\pi$$
$$752$$ 0 0
$$753$$ 14.9274 + 11.4117i 0.543984 + 0.415866i
$$754$$ 0 0
$$755$$ 13.6812 4.97954i 0.497909 0.181224i
$$756$$ 0 0
$$757$$ −12.6519 10.6162i −0.459843 0.385854i 0.383230 0.923653i $$-0.374812\pi$$
−0.843073 + 0.537799i $$0.819256\pi$$
$$758$$ 0 0
$$759$$ 0.749527 + 1.80038i 0.0272061 + 0.0653496i
$$760$$ 0 0
$$761$$ 19.1974i 0.695906i 0.937512 + 0.347953i $$0.113123\pi$$
−0.937512 + 0.347953i $$0.886877\pi$$
$$762$$ 0 0
$$763$$ −6.48211 + 7.72508i −0.234668 + 0.279667i
$$764$$ 0 0
$$765$$ −6.49847 + 14.0675i −0.234953 + 0.508613i
$$766$$ 0 0
$$767$$ −6.54145 + 3.77671i −0.236198 + 0.136369i
$$768$$ 0 0
$$769$$ −5.25863 29.8231i −0.189631 1.07545i −0.919860 0.392248i $$-0.871698\pi$$
0.730229 0.683203i $$-0.239413\pi$$
$$770$$ 0 0
$$771$$ 0.0777483 + 0.0100939i 0.00280004 + 0.000363524i
$$772$$ 0 0
$$773$$ 21.9958 18.4567i 0.791134 0.663840i −0.154892 0.987931i $$-0.549503\pi$$
0.946026 + 0.324091i $$0.105058\pi$$
$$774$$ 0 0
$$775$$ 4.61619 12.6829i 0.165818 0.455582i
$$776$$ 0 0
$$777$$ 2.42635 + 10.8524i 0.0870449 + 0.389328i
$$778$$ 0 0
$$779$$ −21.6303 8.70339i −0.774985 0.311831i
$$780$$ 0 0
$$781$$ 0.0324458 + 0.00572106i 0.00116100 + 0.000204716i
$$782$$ 0 0
$$783$$ 30.9645 + 28.0687i 1.10658 + 1.00309i
$$784$$ 0 0
$$785$$ 0.103890 + 0.123812i 0.00370800 + 0.00441903i
$$786$$ 0 0
$$787$$ −22.1812 12.8063i −0.790673 0.456495i 0.0495262 0.998773i $$-0.484229\pi$$
−0.840200 + 0.542277i $$0.817562\pi$$
$$788$$ 0 0
$$789$$ 5.11899 + 8.00348i 0.182241 + 0.284932i
$$790$$ 0 0
$$791$$ 7.80951 + 13.5265i 0.277674 + 0.480946i
$$792$$ 0 0
$$793$$ 2.40391 + 6.60469i 0.0853653 + 0.234539i