# Properties

 Label 140.2.q.b.9.2 Level $140$ Weight $2$ Character 140.9 Analytic conductor $1.118$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 140.q (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.11790562830$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-19})$$ Defining polynomial: $$x^{4} - x^{3} - 4 x^{2} - 5 x + 25$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 9.2 Root $$2.13746 + 0.656712i$$ of defining polynomial Character $$\chi$$ $$=$$ 140.9 Dual form 140.2.q.b.109.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.50000 - 0.866025i) q^{3} +(-0.500000 + 2.17945i) q^{5} +(2.63746 - 0.209313i) q^{7} +O(q^{10})$$ $$q+(1.50000 - 0.866025i) q^{3} +(-0.500000 + 2.17945i) q^{5} +(2.63746 - 0.209313i) q^{7} +(-1.13746 - 1.97014i) q^{11} -6.09095i q^{13} +(1.13746 + 3.70219i) q^{15} +(-4.13746 + 2.38876i) q^{17} +(-2.13746 + 3.70219i) q^{19} +(3.77492 - 2.59808i) q^{21} +(-0.774917 - 0.447399i) q^{23} +(-4.50000 - 2.17945i) q^{25} +5.19615i q^{27} +3.27492 q^{29} +(2.13746 + 3.70219i) q^{31} +(-3.41238 - 1.97014i) q^{33} +(-0.862541 + 5.85286i) q^{35} +(-4.86254 - 2.80739i) q^{37} +(-5.27492 - 9.13642i) q^{39} -11.2749 q^{41} -6.50958i q^{43} +(1.86254 + 1.07534i) q^{47} +(6.91238 - 1.10411i) q^{49} +(-4.13746 + 7.16629i) q^{51} +(6.41238 - 3.70219i) q^{53} +(4.86254 - 1.49397i) q^{55} +7.40437i q^{57} +(2.13746 + 3.70219i) q^{59} +(-0.774917 + 1.34220i) q^{61} +(13.2749 + 3.04547i) q^{65} +(12.0498 - 6.95698i) q^{67} -1.54983 q^{69} +10.5498 q^{71} +(1.86254 - 1.07534i) q^{73} +(-8.63746 + 0.627940i) q^{75} +(-3.41238 - 4.95807i) q^{77} +(-0.137459 + 0.238085i) q^{79} +(4.50000 + 7.79423i) q^{81} +5.67232i q^{83} +(-3.13746 - 10.2118i) q^{85} +(4.91238 - 2.83616i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(-1.27492 - 16.0646i) q^{91} +(6.41238 + 3.70219i) q^{93} +(-7.00000 - 6.50958i) q^{95} +6.92820i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + O(q^{10})$$ $$4 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 3 q^{11} - 3 q^{15} - 9 q^{17} - q^{19} + 12 q^{23} - 18 q^{25} - 2 q^{29} + q^{31} + 9 q^{33} - 11 q^{35} - 27 q^{37} - 6 q^{39} - 30 q^{41} + 15 q^{47} + 5 q^{49} - 9 q^{51} + 3 q^{53} + 27 q^{55} + q^{59} + 12 q^{61} + 38 q^{65} + 18 q^{67} + 24 q^{69} + 12 q^{71} + 15 q^{73} - 27 q^{75} + 9 q^{77} + 7 q^{79} + 18 q^{81} - 5 q^{85} - 3 q^{87} - 14 q^{89} + 10 q^{91} + 3 q^{93} - 28 q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$$.

 $$n$$ $$57$$ $$71$$ $$101$$ $$\chi(n)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$3$$ 1.50000 0.866025i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ 0 0
$$5$$ −0.500000 + 2.17945i −0.223607 + 0.974679i
$$6$$ 0 0
$$7$$ 2.63746 0.209313i 0.996866 0.0791130i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.13746 1.97014i −0.342957 0.594018i 0.642024 0.766685i $$-0.278095\pi$$
−0.984980 + 0.172666i $$0.944762\pi$$
$$12$$ 0 0
$$13$$ 6.09095i 1.68933i −0.535299 0.844663i $$-0.679801\pi$$
0.535299 0.844663i $$-0.320199\pi$$
$$14$$ 0 0
$$15$$ 1.13746 + 3.70219i 0.293691 + 0.955901i
$$16$$ 0 0
$$17$$ −4.13746 + 2.38876i −1.00348 + 0.579360i −0.909276 0.416193i $$-0.863364\pi$$
−0.0942047 + 0.995553i $$0.530031\pi$$
$$18$$ 0 0
$$19$$ −2.13746 + 3.70219i −0.490367 + 0.849340i −0.999939 0.0110882i $$-0.996470\pi$$
0.509572 + 0.860428i $$0.329804\pi$$
$$20$$ 0 0
$$21$$ 3.77492 2.59808i 0.823754 0.566947i
$$22$$ 0 0
$$23$$ −0.774917 0.447399i −0.161581 0.0932891i 0.417029 0.908893i $$-0.363071\pi$$
−0.578610 + 0.815604i $$0.696405\pi$$
$$24$$ 0 0
$$25$$ −4.50000 2.17945i −0.900000 0.435890i
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ 0 0
$$29$$ 3.27492 0.608137 0.304068 0.952650i $$-0.401655\pi$$
0.304068 + 0.952650i $$0.401655\pi$$
$$30$$ 0 0
$$31$$ 2.13746 + 3.70219i 0.383899 + 0.664932i 0.991616 0.129221i $$-0.0412478\pi$$
−0.607717 + 0.794154i $$0.707914\pi$$
$$32$$ 0 0
$$33$$ −3.41238 1.97014i −0.594018 0.342957i
$$34$$ 0 0
$$35$$ −0.862541 + 5.85286i −0.145796 + 0.989315i
$$36$$ 0 0
$$37$$ −4.86254 2.80739i −0.799397 0.461532i 0.0438633 0.999038i $$-0.486033\pi$$
−0.843260 + 0.537506i $$0.819367\pi$$
$$38$$ 0 0
$$39$$ −5.27492 9.13642i −0.844663 1.46300i
$$40$$ 0 0
$$41$$ −11.2749 −1.76085 −0.880423 0.474189i $$-0.842741\pi$$
−0.880423 + 0.474189i $$0.842741\pi$$
$$42$$ 0 0
$$43$$ 6.50958i 0.992701i −0.868122 0.496351i $$-0.834673\pi$$
0.868122 0.496351i $$-0.165327\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 1.86254 + 1.07534i 0.271680 + 0.156854i 0.629651 0.776878i $$-0.283198\pi$$
−0.357971 + 0.933733i $$0.616531\pi$$
$$48$$ 0 0
$$49$$ 6.91238 1.10411i 0.987482 0.157730i
$$50$$ 0 0
$$51$$ −4.13746 + 7.16629i −0.579360 + 1.00348i
$$52$$ 0 0
$$53$$ 6.41238 3.70219i 0.880808 0.508534i 0.00988297 0.999951i $$-0.496854\pi$$
0.870925 + 0.491417i $$0.163521\pi$$
$$54$$ 0 0
$$55$$ 4.86254 1.49397i 0.655665 0.201446i
$$56$$ 0 0
$$57$$ 7.40437i 0.980733i
$$58$$ 0 0
$$59$$ 2.13746 + 3.70219i 0.278273 + 0.481984i 0.970956 0.239259i $$-0.0769045\pi$$
−0.692682 + 0.721243i $$0.743571\pi$$
$$60$$ 0 0
$$61$$ −0.774917 + 1.34220i −0.0992180 + 0.171851i −0.911361 0.411608i $$-0.864967\pi$$
0.812143 + 0.583458i $$0.198301\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 13.2749 + 3.04547i 1.64655 + 0.377745i
$$66$$ 0 0
$$67$$ 12.0498 6.95698i 1.47212 0.849930i 0.472613 0.881270i $$-0.343311\pi$$
0.999509 + 0.0313404i $$0.00997759\pi$$
$$68$$ 0 0
$$69$$ −1.54983 −0.186578
$$70$$ 0 0
$$71$$ 10.5498 1.25204 0.626018 0.779809i $$-0.284684\pi$$
0.626018 + 0.779809i $$0.284684\pi$$
$$72$$ 0 0
$$73$$ 1.86254 1.07534i 0.217994 0.125859i −0.387027 0.922068i $$-0.626498\pi$$
0.605021 + 0.796209i $$0.293165\pi$$
$$74$$ 0 0
$$75$$ −8.63746 + 0.627940i −0.997368 + 0.0725083i
$$76$$ 0 0
$$77$$ −3.41238 4.95807i −0.388876 0.565024i
$$78$$ 0 0
$$79$$ −0.137459 + 0.238085i −0.0154653 + 0.0267867i −0.873654 0.486547i $$-0.838256\pi$$
0.858189 + 0.513334i $$0.171590\pi$$
$$80$$ 0 0
$$81$$ 4.50000 + 7.79423i 0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 5.67232i 0.622618i 0.950309 + 0.311309i $$0.100767\pi$$
−0.950309 + 0.311309i $$0.899233\pi$$
$$84$$ 0 0
$$85$$ −3.13746 10.2118i −0.340305 1.10762i
$$86$$ 0 0
$$87$$ 4.91238 2.83616i 0.526662 0.304068i
$$88$$ 0 0
$$89$$ −3.50000 + 6.06218i −0.370999 + 0.642590i −0.989720 0.143022i $$-0.954318\pi$$
0.618720 + 0.785611i $$0.287651\pi$$
$$90$$ 0 0
$$91$$ −1.27492 16.0646i −0.133648 1.68403i
$$92$$ 0 0
$$93$$ 6.41238 + 3.70219i 0.664932 + 0.383899i
$$94$$ 0 0
$$95$$ −7.00000 6.50958i −0.718185 0.667868i
$$96$$ 0 0
$$97$$ 6.92820i 0.703452i 0.936103 + 0.351726i $$0.114405\pi$$
−0.936103 + 0.351726i $$0.885595\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −0.774917 1.34220i −0.0771071 0.133553i 0.824894 0.565288i $$-0.191235\pi$$
−0.902001 + 0.431735i $$0.857902\pi$$
$$102$$ 0 0
$$103$$ −2.22508 1.28465i −0.219244 0.126581i 0.386356 0.922350i $$-0.373734\pi$$
−0.605600 + 0.795769i $$0.707067\pi$$
$$104$$ 0 0
$$105$$ 3.77492 + 9.52628i 0.368394 + 0.929670i
$$106$$ 0 0
$$107$$ −12.0498 6.95698i −1.16490 0.672556i −0.212428 0.977177i $$-0.568137\pi$$
−0.952474 + 0.304621i $$0.901470\pi$$
$$108$$ 0 0
$$109$$ 1.77492 + 3.07425i 0.170006 + 0.294459i 0.938422 0.345492i $$-0.112288\pi$$
−0.768416 + 0.639951i $$0.778955\pi$$
$$110$$ 0 0
$$111$$ −9.72508 −0.923064
$$112$$ 0 0
$$113$$ 13.0192i 1.22474i 0.790572 + 0.612369i $$0.209783\pi$$
−0.790572 + 0.612369i $$0.790217\pi$$
$$114$$ 0 0
$$115$$ 1.36254 1.46519i 0.127058 0.136630i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −10.4124 + 7.16629i −0.954501 + 0.656933i
$$120$$ 0 0
$$121$$ 2.91238 5.04438i 0.264761 0.458580i
$$122$$ 0 0
$$123$$ −16.9124 + 9.76436i −1.52494 + 0.880423i
$$124$$ 0 0
$$125$$ 7.00000 8.71780i 0.626099 0.779744i
$$126$$ 0 0
$$127$$ 1.78959i 0.158801i −0.996843 0.0794004i $$-0.974699\pi$$
0.996843 0.0794004i $$-0.0253006\pi$$
$$128$$ 0 0
$$129$$ −5.63746 9.76436i −0.496351 0.859704i
$$130$$ 0 0
$$131$$ 9.13746 15.8265i 0.798343 1.38277i −0.122351 0.992487i $$-0.539043\pi$$
0.920694 0.390285i $$-0.127623\pi$$
$$132$$ 0 0
$$133$$ −4.86254 + 10.2118i −0.421636 + 0.885472i
$$134$$ 0 0
$$135$$ −11.3248 2.59808i −0.974679 0.223607i
$$136$$ 0 0
$$137$$ −7.96221 + 4.59698i −0.680258 + 0.392747i −0.799952 0.600064i $$-0.795142\pi$$
0.119695 + 0.992811i $$0.461808\pi$$
$$138$$ 0 0
$$139$$ 17.0997 1.45037 0.725187 0.688551i $$-0.241753\pi$$
0.725187 + 0.688551i $$0.241753\pi$$
$$140$$ 0 0
$$141$$ 3.72508 0.313709
$$142$$ 0 0
$$143$$ −12.0000 + 6.92820i −1.00349 + 0.579365i
$$144$$ 0 0
$$145$$ −1.63746 + 7.13752i −0.135984 + 0.592738i
$$146$$ 0 0
$$147$$ 9.41238 7.64246i 0.776320 0.630339i
$$148$$ 0 0
$$149$$ 3.77492 6.53835i 0.309253 0.535642i −0.668946 0.743311i $$-0.733254\pi$$
0.978199 + 0.207669i $$0.0665876\pi$$
$$150$$ 0 0
$$151$$ 10.1375 + 17.5586i 0.824975 + 1.42890i 0.901939 + 0.431864i $$0.142144\pi$$
−0.0769640 + 0.997034i $$0.524523\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −9.13746 + 2.80739i −0.733938 + 0.225495i
$$156$$ 0 0
$$157$$ −9.41238 + 5.43424i −0.751189 + 0.433699i −0.826123 0.563489i $$-0.809459\pi$$
0.0749341 + 0.997188i $$0.476125\pi$$
$$158$$ 0 0
$$159$$ 6.41238 11.1066i 0.508534 0.880808i
$$160$$ 0 0
$$161$$ −2.13746 1.01779i −0.168455 0.0802135i
$$162$$ 0 0
$$163$$ 6.41238 + 3.70219i 0.502256 + 0.289978i 0.729645 0.683826i $$-0.239685\pi$$
−0.227389 + 0.973804i $$0.573019\pi$$
$$164$$ 0 0
$$165$$ 6.00000 6.45203i 0.467099 0.502290i
$$166$$ 0 0
$$167$$ 12.6005i 0.975058i −0.873107 0.487529i $$-0.837898\pi$$
0.873107 0.487529i $$-0.162102\pi$$
$$168$$ 0 0
$$169$$ −24.0997 −1.85382
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 16.2371 + 9.37451i 1.23449 + 0.712731i 0.967962 0.251097i $$-0.0807915\pi$$
0.266524 + 0.963828i $$0.414125\pi$$
$$174$$ 0 0
$$175$$ −12.3248 4.80630i −0.931664 0.363322i
$$176$$ 0 0
$$177$$ 6.41238 + 3.70219i 0.481984 + 0.278273i
$$178$$ 0 0
$$179$$ 0.137459 + 0.238085i 0.0102741 + 0.0177953i 0.871117 0.491076i $$-0.163396\pi$$
−0.860843 + 0.508871i $$0.830063\pi$$
$$180$$ 0 0
$$181$$ −16.7251 −1.24317 −0.621583 0.783348i $$-0.713510\pi$$
−0.621583 + 0.783348i $$0.713510\pi$$
$$182$$ 0 0
$$183$$ 2.68439i 0.198436i
$$184$$ 0 0
$$185$$ 8.54983 9.19397i 0.628596 0.675954i
$$186$$ 0 0
$$187$$ 9.41238 + 5.43424i 0.688301 + 0.397391i
$$188$$ 0 0
$$189$$ 1.08762 + 13.7046i 0.0791130 + 0.996866i
$$190$$ 0 0
$$191$$ −11.4124 + 19.7668i −0.825771 + 1.43028i 0.0755585 + 0.997141i $$0.475926\pi$$
−0.901329 + 0.433135i $$0.857407\pi$$
$$192$$ 0 0
$$193$$ −7.96221 + 4.59698i −0.573132 + 0.330898i −0.758399 0.651790i $$-0.774018\pi$$
0.185267 + 0.982688i $$0.440685\pi$$
$$194$$ 0 0
$$195$$ 22.5498 6.92820i 1.61483 0.496139i
$$196$$ 0 0
$$197$$ 26.0383i 1.85515i −0.373634 0.927576i $$-0.621888\pi$$
0.373634 0.927576i $$-0.378112\pi$$
$$198$$ 0 0
$$199$$ 4.86254 + 8.42217i 0.344696 + 0.597032i 0.985299 0.170841i $$-0.0546485\pi$$
−0.640602 + 0.767873i $$0.721315\pi$$
$$200$$ 0 0
$$201$$ 12.0498 20.8709i 0.849930 1.47212i
$$202$$ 0 0
$$203$$ 8.63746 0.685484i 0.606231 0.0481115i
$$204$$ 0 0
$$205$$ 5.63746 24.5731i 0.393737 1.71626i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 9.72508 0.672698
$$210$$ 0 0
$$211$$ −19.6495 −1.35273 −0.676364 0.736568i $$-0.736445\pi$$
−0.676364 + 0.736568i $$0.736445\pi$$
$$212$$ 0 0
$$213$$ 15.8248 9.13642i 1.08429 0.626018i
$$214$$ 0 0
$$215$$ 14.1873 + 3.25479i 0.967565 + 0.221975i
$$216$$ 0 0
$$217$$ 6.41238 + 9.31697i 0.435300 + 0.632477i
$$218$$ 0 0
$$219$$ 1.86254 3.22602i 0.125859 0.217994i
$$220$$ 0 0
$$221$$ 14.5498 + 25.2011i 0.978728 + 1.69521i
$$222$$ 0 0
$$223$$ 8.71780i 0.583787i 0.956451 + 0.291893i $$0.0942853\pi$$
−0.956451 + 0.291893i $$0.905715\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 5.58762 3.22602i 0.370864 0.214118i −0.302972 0.952999i $$-0.597979\pi$$
0.673836 + 0.738881i $$0.264646\pi$$
$$228$$ 0 0
$$229$$ −2.13746 + 3.70219i −0.141247 + 0.244647i −0.927967 0.372663i $$-0.878445\pi$$
0.786719 + 0.617311i $$0.211778\pi$$
$$230$$ 0 0
$$231$$ −9.41238 4.48190i −0.619289 0.294887i
$$232$$ 0 0
$$233$$ −16.1375 9.31697i −1.05720 0.610375i −0.132544 0.991177i $$-0.542314\pi$$
−0.924656 + 0.380802i $$0.875648\pi$$
$$234$$ 0 0
$$235$$ −3.27492 + 3.52165i −0.213632 + 0.229727i
$$236$$ 0 0
$$237$$ 0.476171i 0.0309306i
$$238$$ 0 0
$$239$$ 14.5498 0.941151 0.470575 0.882360i $$-0.344046\pi$$
0.470575 + 0.882360i $$0.344046\pi$$
$$240$$ 0 0
$$241$$ 6.41238 + 11.1066i 0.413057 + 0.715436i 0.995222 0.0976343i $$-0.0311275\pi$$
−0.582165 + 0.813071i $$0.697794\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −1.04983 + 15.6172i −0.0670715 + 0.997748i
$$246$$ 0 0
$$247$$ 22.5498 + 13.0192i 1.43481 + 0.828389i
$$248$$ 0 0
$$249$$ 4.91238 + 8.50848i 0.311309 + 0.539203i
$$250$$ 0 0
$$251$$ −5.45017 −0.344011 −0.172006 0.985096i $$-0.555025\pi$$
−0.172006 + 0.985096i $$0.555025\pi$$
$$252$$ 0 0
$$253$$ 2.03559i 0.127976i
$$254$$ 0 0
$$255$$ −13.5498 12.6005i −0.848524 0.789076i
$$256$$ 0 0
$$257$$ −21.4124 12.3624i −1.33567 0.771148i −0.349506 0.936934i $$-0.613650\pi$$
−0.986162 + 0.165786i $$0.946984\pi$$
$$258$$ 0 0
$$259$$ −13.4124 6.38658i −0.833404 0.396843i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 23.3248 13.4666i 1.43827 0.830383i 0.440536 0.897735i $$-0.354788\pi$$
0.997729 + 0.0673516i $$0.0214549\pi$$
$$264$$ 0 0
$$265$$ 4.86254 + 15.8265i 0.298704 + 0.972217i
$$266$$ 0 0
$$267$$ 12.1244i 0.741999i
$$268$$ 0 0
$$269$$ −14.7749 25.5909i −0.900843 1.56031i −0.826403 0.563080i $$-0.809616\pi$$
−0.0744400 0.997225i $$-0.523717\pi$$
$$270$$ 0 0
$$271$$ 6.41238 11.1066i 0.389524 0.674676i −0.602861 0.797846i $$-0.705973\pi$$
0.992386 + 0.123170i $$0.0393062\pi$$
$$272$$ 0 0
$$273$$ −15.8248 22.9928i −0.957758 1.39159i
$$274$$ 0 0
$$275$$ 0.824752 + 11.3446i 0.0497344 + 0.684108i
$$276$$ 0 0
$$277$$ −16.1375 + 9.31697i −0.969606 + 0.559802i −0.899116 0.437710i $$-0.855790\pi$$
−0.0704898 + 0.997512i $$0.522456\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ −16.9622 + 9.79314i −1.00830 + 0.582142i −0.910693 0.413084i $$-0.864452\pi$$
−0.0976056 + 0.995225i $$0.531118\pi$$
$$284$$ 0 0
$$285$$ −16.1375 3.70219i −0.955901 0.219299i
$$286$$ 0 0
$$287$$ −29.7371 + 2.35999i −1.75533 + 0.139306i
$$288$$ 0 0
$$289$$ 2.91238 5.04438i 0.171316 0.296728i
$$290$$ 0 0
$$291$$ 6.00000 + 10.3923i 0.351726 + 0.609208i
$$292$$ 0 0
$$293$$ 6.92820i 0.404750i 0.979308 + 0.202375i $$0.0648660\pi$$
−0.979308 + 0.202375i $$0.935134\pi$$
$$294$$ 0 0
$$295$$ −9.13746 + 2.80739i −0.532003 + 0.163453i
$$296$$ 0 0
$$297$$ 10.2371 5.91041i 0.594018 0.342957i
$$298$$ 0 0
$$299$$ −2.72508 + 4.71998i −0.157596 + 0.272964i
$$300$$ 0 0
$$301$$ −1.36254 17.1687i −0.0785356 0.989590i
$$302$$ 0 0
$$303$$ −2.32475 1.34220i −0.133553 0.0771071i
$$304$$ 0 0
$$305$$ −2.53779 2.35999i −0.145313 0.135133i
$$306$$ 0 0
$$307$$ 3.99782i 0.228167i 0.993471 + 0.114084i $$0.0363932\pi$$
−0.993471 + 0.114084i $$0.963607\pi$$
$$308$$ 0 0
$$309$$ −4.45017 −0.253161
$$310$$ 0 0
$$311$$ −6.41238 11.1066i −0.363612 0.629795i 0.624940 0.780673i $$-0.285123\pi$$
−0.988552 + 0.150878i $$0.951790\pi$$
$$312$$ 0 0
$$313$$ −12.5120 7.22383i −0.707223 0.408315i 0.102809 0.994701i $$-0.467217\pi$$
−0.810032 + 0.586386i $$0.800550\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 3.31271 + 1.91259i 0.186060 + 0.107422i 0.590137 0.807303i $$-0.299074\pi$$
−0.404077 + 0.914725i $$0.632407\pi$$
$$318$$ 0 0
$$319$$ −3.72508 6.45203i −0.208565 0.361244i
$$320$$ 0 0
$$321$$ −24.0997 −1.34511
$$322$$ 0 0
$$323$$ 20.4235i 1.13640i
$$324$$ 0 0
$$325$$ −13.2749 + 27.4093i −0.736360 + 1.52039i
$$326$$ 0 0
$$327$$ 5.32475 + 3.07425i 0.294459 + 0.170006i
$$328$$ 0 0
$$329$$ 5.13746 + 2.44631i 0.283237 + 0.134869i
$$330$$ 0 0
$$331$$ 2.41238 4.17836i 0.132596 0.229663i −0.792080 0.610417i $$-0.791002\pi$$
0.924677 + 0.380753i $$0.124335\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 9.13746 + 29.7405i 0.499233 + 1.62490i
$$336$$ 0 0
$$337$$ 13.0192i 0.709198i 0.935018 + 0.354599i $$0.115383\pi$$
−0.935018 + 0.354599i $$0.884617\pi$$
$$338$$ 0 0
$$339$$ 11.2749 + 19.5287i 0.612369 + 1.06065i
$$340$$ 0 0
$$341$$ 4.86254 8.42217i 0.263321 0.456086i
$$342$$ 0 0
$$343$$ 18.0000 4.35890i 0.971909 0.235358i
$$344$$ 0 0
$$345$$ 0.774917 3.37779i 0.0417201 0.181854i
$$346$$ 0 0
$$347$$ −10.5000 + 6.06218i −0.563670 + 0.325435i −0.754617 0.656165i $$-0.772177\pi$$
0.190947 + 0.981600i $$0.438844\pi$$
$$348$$ 0 0
$$349$$ 11.2749 0.603532 0.301766 0.953382i $$-0.402424\pi$$
0.301766 + 0.953382i $$0.402424\pi$$
$$350$$ 0 0
$$351$$ 31.6495 1.68933
$$352$$ 0 0
$$353$$ 18.4124 10.6304i 0.979992 0.565799i 0.0777242 0.996975i $$-0.475235\pi$$
0.902268 + 0.431176i $$0.141901\pi$$
$$354$$ 0 0
$$355$$ −5.27492 + 22.9928i −0.279964 + 1.22033i
$$356$$ 0 0
$$357$$ −9.41238 + 19.7668i −0.498156 + 1.04617i
$$358$$ 0 0
$$359$$ −0.687293 + 1.19043i −0.0362739 + 0.0628283i −0.883592 0.468257i $$-0.844882\pi$$
0.847318 + 0.531085i $$0.178216\pi$$
$$360$$ 0 0
$$361$$ 0.362541 + 0.627940i 0.0190811 + 0.0330495i
$$362$$ 0 0
$$363$$ 10.0888i 0.529523i
$$364$$ 0 0
$$365$$ 1.41238 + 4.59698i 0.0739271 + 0.240617i
$$366$$ 0 0
$$367$$ 12.7749 7.37560i 0.666845 0.385003i −0.128035 0.991770i $$-0.540867\pi$$
0.794880 + 0.606766i $$0.207534\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 16.1375 11.1066i 0.837815 0.576624i
$$372$$ 0 0
$$373$$ −4.86254 2.80739i −0.251773 0.145361i 0.368803 0.929508i $$-0.379768\pi$$
−0.620576 + 0.784146i $$0.713101\pi$$
$$374$$ 0 0
$$375$$ 2.95017 19.1389i 0.152346 0.988327i
$$376$$ 0 0
$$377$$ 19.9474i 1.02734i
$$378$$ 0 0
$$379$$ −23.6495 −1.21479 −0.607397 0.794399i $$-0.707786\pi$$
−0.607397 + 0.794399i $$0.707786\pi$$
$$380$$ 0 0
$$381$$ −1.54983 2.68439i −0.0794004 0.137526i
$$382$$ 0 0
$$383$$ −17.3248 10.0025i −0.885253 0.511101i −0.0128665 0.999917i $$-0.504096\pi$$
−0.872387 + 0.488816i $$0.837429\pi$$
$$384$$ 0 0
$$385$$ 12.5120 4.95807i 0.637673 0.252686i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −2.68729 4.65453i −0.136251 0.235994i 0.789824 0.613334i $$-0.210172\pi$$
−0.926075 + 0.377340i $$0.876839\pi$$
$$390$$ 0 0
$$391$$ 4.27492 0.216192
$$392$$ 0 0
$$393$$ 31.6531i 1.59669i
$$394$$ 0 0
$$395$$ −0.450166 0.418627i −0.0226503 0.0210634i
$$396$$ 0 0
$$397$$ 13.1375 + 7.58492i 0.659350 + 0.380676i 0.792029 0.610483i $$-0.209025\pi$$
−0.132679 + 0.991159i $$0.542358\pi$$
$$398$$ 0 0
$$399$$ 1.54983 + 19.5287i 0.0775888 + 0.977659i
$$400$$ 0 0
$$401$$ −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i $$-0.857199\pi$$
0.826139 + 0.563466i $$0.190532\pi$$
$$402$$ 0 0
$$403$$ 22.5498 13.0192i 1.12329 0.648530i
$$404$$ 0 0
$$405$$ −19.2371 + 5.91041i −0.955901 + 0.293691i
$$406$$ 0 0
$$407$$ 12.7732i 0.633142i
$$408$$ 0 0
$$409$$ 5.04983 + 8.74657i 0.249698 + 0.432490i 0.963442 0.267917i $$-0.0863352\pi$$
−0.713744 + 0.700407i $$0.753002\pi$$
$$410$$ 0 0
$$411$$ −7.96221 + 13.7910i −0.392747 + 0.680258i
$$412$$ 0 0
$$413$$ 6.41238 + 9.31697i 0.315532 + 0.458458i
$$414$$ 0 0
$$415$$ −12.3625 2.83616i −0.606853 0.139222i
$$416$$ 0 0
$$417$$ 25.6495 14.8087i 1.25606 0.725187i
$$418$$ 0 0
$$419$$ −17.0997 −0.835373 −0.417687 0.908591i $$-0.637159\pi$$
−0.417687 + 0.908591i $$0.637159\pi$$
$$420$$ 0 0
$$421$$ 3.27492 0.159610 0.0798048 0.996811i $$-0.474570\pi$$
0.0798048 + 0.996811i $$0.474570\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 23.8248 1.73205i 1.15567 0.0840168i
$$426$$ 0 0
$$427$$ −1.76287 + 3.70219i −0.0853114 + 0.179161i
$$428$$ 0 0
$$429$$ −12.0000 + 20.7846i −0.579365 + 1.00349i
$$430$$ 0 0
$$431$$ −9.68729 16.7789i −0.466620 0.808210i 0.532653 0.846334i $$-0.321195\pi$$
−0.999273 + 0.0381236i $$0.987862\pi$$
$$432$$ 0 0
$$433$$ 26.8756i 1.29156i −0.763525 0.645778i $$-0.776533\pi$$
0.763525 0.645778i $$-0.223467\pi$$
$$434$$ 0 0
$$435$$ 3.72508 + 12.1244i 0.178604 + 0.581318i
$$436$$ 0 0
$$437$$ 3.31271 1.91259i 0.158468 0.0914917i
$$438$$ 0 0
$$439$$ 0.587624 1.01779i 0.0280458 0.0485767i −0.851662 0.524092i $$-0.824405\pi$$
0.879708 + 0.475515i $$0.157738\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 10.5000 + 6.06218i 0.498870 + 0.288023i 0.728247 0.685315i $$-0.240335\pi$$
−0.229377 + 0.973338i $$0.573669\pi$$
$$444$$ 0 0
$$445$$ −11.4622 10.6592i −0.543361 0.505293i
$$446$$ 0 0
$$447$$ 13.0767i 0.618507i
$$448$$ 0 0
$$449$$ 25.8248 1.21875 0.609373 0.792884i $$-0.291421\pi$$
0.609373 + 0.792884i $$0.291421\pi$$
$$450$$ 0 0
$$451$$ 12.8248 + 22.2131i 0.603894 + 1.04598i
$$452$$ 0 0
$$453$$ 30.4124 + 17.5586i 1.42890 + 0.824975i
$$454$$ 0 0
$$455$$ 35.6495 + 5.25370i 1.67127 + 0.246297i
$$456$$ 0 0
$$457$$ 17.6873 + 10.2118i 0.827377 + 0.477686i 0.852954 0.521987i $$-0.174809\pi$$
−0.0255769 + 0.999673i $$0.508142\pi$$
$$458$$ 0 0
$$459$$ −12.4124 21.4989i −0.579360 1.00348i
$$460$$ 0 0
$$461$$ −14.0000 −0.652045 −0.326023 0.945362i $$-0.605709\pi$$
−0.326023 + 0.945362i $$0.605709\pi$$
$$462$$ 0 0
$$463$$ 6.50958i 0.302526i 0.988494 + 0.151263i $$0.0483340\pi$$
−0.988494 + 0.151263i $$0.951666\pi$$
$$464$$ 0 0
$$465$$ −11.2749 + 12.1244i −0.522862 + 0.562254i
$$466$$ 0 0
$$467$$ −16.5997 9.58382i −0.768141 0.443486i 0.0640700 0.997945i $$-0.479592\pi$$
−0.832211 + 0.554459i $$0.812925\pi$$
$$468$$ 0 0
$$469$$ 30.3248 20.8709i 1.40027 0.963730i
$$470$$ 0 0
$$471$$ −9.41238 + 16.3027i −0.433699 + 0.751189i
$$472$$ 0 0
$$473$$ −12.8248 + 7.40437i −0.589683 + 0.340453i
$$474$$ 0 0
$$475$$ 17.6873 12.0014i 0.811549 0.550660i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −6.41238 11.1066i −0.292989 0.507472i 0.681526 0.731794i $$-0.261317\pi$$
−0.974515 + 0.224322i $$0.927983\pi$$
$$480$$ 0 0
$$481$$ −17.0997 + 29.6175i −0.779678 + 1.35044i
$$482$$ 0 0
$$483$$ −4.08762 + 0.324401i −0.185993 + 0.0147608i
$$484$$ 0 0
$$485$$ −15.0997 3.46410i −0.685641 0.157297i
$$486$$ 0 0
$$487$$ −28.9622 + 16.7213i −1.31240 + 0.757716i −0.982494 0.186296i $$-0.940352\pi$$
−0.329909 + 0.944013i $$0.607018\pi$$
$$488$$ 0 0
$$489$$ 12.8248 0.579955
$$490$$ 0 0
$$491$$ −13.4502 −0.606997 −0.303499 0.952832i $$-0.598155\pi$$
−0.303499 + 0.952832i $$0.598155\pi$$
$$492$$ 0 0
$$493$$ −13.5498 + 7.82300i −0.610254 + 0.352330i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 27.8248 2.20822i 1.24811 0.0990523i
$$498$$ 0 0
$$499$$ 19.6873 34.0994i 0.881324 1.52650i 0.0314548 0.999505i $$-0.489986\pi$$
0.849869 0.526993i $$-0.176681\pi$$
$$500$$ 0 0
$$501$$ −10.9124 18.9008i −0.487529 0.844425i
$$502$$ 0 0
$$503$$ 16.1797i 0.721418i −0.932678 0.360709i $$-0.882535\pi$$
0.932678 0.360709i $$-0.117465\pi$$
$$504$$ 0 0
$$505$$ 3.31271 1.01779i 0.147414 0.0452913i
$$506$$ 0 0
$$507$$ −36.1495 + 20.8709i −1.60546 + 0.926910i
$$508$$ 0 0
$$509$$ −14.7749 + 25.5909i −0.654887 + 1.13430i 0.327036 + 0.945012i $$0.393950\pi$$
−0.981922 + 0.189285i $$0.939383\pi$$
$$510$$ 0 0
$$511$$ 4.68729 3.22602i 0.207354 0.142711i
$$512$$ 0 0
$$513$$ −19.2371 11.1066i −0.849340 0.490367i
$$514$$ 0 0
$$515$$ 3.91238 4.20713i 0.172400 0.185388i
$$516$$ 0 0
$$517$$ 4.89261i 0.215177i
$$518$$ 0 0
$$519$$ 32.4743 1.42546
$$520$$ 0 0
$$521$$ 6.41238 + 11.1066i 0.280931 + 0.486587i 0.971614 0.236570i $$-0.0760234\pi$$
−0.690683 + 0.723158i $$0.742690\pi$$
$$522$$ 0 0
$$523$$ −10.1375 5.85286i −0.443280 0.255928i 0.261708 0.965147i $$-0.415714\pi$$
−0.704988 + 0.709219i $$0.749048\pi$$
$$524$$ 0 0
$$525$$ −22.6495 + 3.46410i −0.988505 + 0.151186i
$$526$$ 0 0
$$527$$ −17.6873 10.2118i −0.770471 0.444831i
$$528$$ 0 0
$$529$$ −11.0997 19.2252i −0.482594 0.835878i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 68.6750i 2.97464i
$$534$$ 0 0
$$535$$ 21.1873 22.7835i 0.916007 0.985017i
$$536$$ 0 0
$$537$$ 0.412376 + 0.238085i 0.0177953 + 0.0102741i
$$538$$ 0 0
$$539$$ −10.0378 12.3624i −0.432358 0.532488i
$$540$$ 0 0
$$541$$ 1.22508 2.12191i 0.0526704 0.0912278i −0.838488 0.544920i $$-0.816560\pi$$
0.891159 + 0.453692i $$0.149893\pi$$
$$542$$ 0 0
$$543$$ −25.0876 + 14.4843i −1.07661 + 0.621583i
$$544$$ 0 0
$$545$$ −7.58762 + 2.33122i −0.325018 + 0.0998585i
$$546$$ 0 0
$$547$$ 36.1271i 1.54468i −0.635208 0.772341i $$-0.719086\pi$$
0.635208 0.772341i $$-0.280914\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −7.00000 + 12.1244i −0.298210 + 0.516515i
$$552$$ 0 0
$$553$$ −0.312707 + 0.656712i −0.0132977 + 0.0279262i
$$554$$ 0 0
$$555$$ 4.86254 21.1953i 0.206403 0.899692i
$$556$$ 0 0
$$557$$ −4.86254 + 2.80739i −0.206032 + 0.118953i −0.599466 0.800400i $$-0.704620\pi$$
0.393434 + 0.919353i $$0.371287\pi$$
$$558$$ 0 0
$$559$$ −39.6495 −1.67700
$$560$$ 0 0
$$561$$ 18.8248 0.794782
$$562$$ 0 0
$$563$$ 10.5997 6.11972i 0.446723 0.257916i −0.259722 0.965683i $$-0.583631\pi$$
0.706445 + 0.707768i $$0.250298\pi$$
$$564$$ 0 0
$$565$$ −28.3746 6.50958i −1.19373 0.273860i
$$566$$ 0 0
$$567$$ 13.5000 + 19.6150i 0.566947 + 0.823754i
$$568$$ 0 0
$$569$$ −14.6873 + 25.4391i −0.615723 + 1.06646i 0.374534 + 0.927213i $$0.377803\pi$$
−0.990257 + 0.139251i $$0.955531\pi$$
$$570$$ 0 0
$$571$$ 0.137459 + 0.238085i 0.00575246 + 0.00996356i 0.868887 0.495010i $$-0.164836\pi$$
−0.863135 + 0.504974i $$0.831502\pi$$
$$572$$ 0 0
$$573$$ 39.5336i 1.65154i
$$574$$ 0 0
$$575$$ 2.51204 + 3.70219i 0.104760 + 0.154392i
$$576$$ 0 0
$$577$$ 7.13746 4.12081i 0.297136 0.171552i −0.344019 0.938963i $$-0.611789\pi$$
0.641156 + 0.767411i $$0.278455\pi$$
$$578$$ 0 0
$$579$$ −7.96221 + 13.7910i −0.330898 + 0.573132i
$$580$$ 0 0
$$581$$ 1.18729 + 14.9605i 0.0492572 + 0.620667i
$$582$$ 0 0
$$583$$ −14.5876 8.42217i −0.604158 0.348811i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 13.9715i 0.576665i 0.957530 + 0.288333i $$0.0931009\pi$$
−0.957530 + 0.288333i $$0.906899\pi$$
$$588$$ 0 0
$$589$$ −18.2749 −0.753005
$$590$$ 0 0
$$591$$ −22.5498 39.0575i −0.927576 1.60661i
$$592$$ 0 0
$$593$$ −17.5876 10.1542i −0.722237 0.416984i 0.0933384 0.995634i $$-0.470246\pi$$
−0.815576 + 0.578651i $$0.803579\pi$$
$$594$$ 0 0
$$595$$ −10.4124 26.2764i −0.426866 1.07723i
$$596$$ 0 0
$$597$$ 14.5876 + 8.42217i 0.597032 + 0.344696i
$$598$$ 0 0
$$599$$ −1.13746 1.97014i −0.0464753 0.0804976i 0.841852 0.539709i $$-0.181466\pi$$
−0.888327 + 0.459211i $$0.848132\pi$$
$$600$$ 0 0
$$601$$ 14.0000 0.571072 0.285536 0.958368i $$-0.407828\pi$$
0.285536 + 0.958368i $$0.407828\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 9.53779 + 8.86957i 0.387766 + 0.360599i
$$606$$ 0 0
$$607$$ −27.8746 16.0934i −1.13139 0.653211i −0.187109 0.982339i $$-0.559912\pi$$
−0.944285 + 0.329128i $$0.893245\pi$$
$$608$$ 0 0
$$609$$ 12.3625 8.50848i 0.500955 0.344781i
$$610$$ 0 0
$$611$$ 6.54983 11.3446i 0.264978 0.458955i
$$612$$ 0 0
$$613$$ 32.0619 18.5109i 1.29497 0.747650i 0.315437 0.948947i $$-0.397849\pi$$
0.979530 + 0.201297i $$0.0645156\pi$$
$$614$$ 0 0
$$615$$ −12.8248 41.7419i −0.517144 1.68319i
$$616$$ 0 0
$$617$$ 3.57919i 0.144093i −0.997401 0.0720464i $$-0.977047\pi$$
0.997401 0.0720464i $$-0.0229530\pi$$
$$618$$ 0 0
$$619$$ 21.9622 + 38.0397i 0.882736 + 1.52894i 0.848287 + 0.529537i $$0.177634\pi$$
0.0344487 + 0.999406i $$0.489032\pi$$
$$620$$ 0 0
$$621$$ 2.32475 4.02659i 0.0932891 0.161581i
$$622$$ 0 0
$$623$$ −7.96221 + 16.7213i −0.318999 + 0.669926i
$$624$$ 0 0
$$625$$ 15.5000 + 19.6150i 0.620000 + 0.784602i
$$626$$ 0 0
$$627$$ 14.5876 8.42217i 0.582574 0.336349i
$$628$$ 0 0
$$629$$ 26.8248 1.06957
$$630$$ 0 0
$$631$$ 2.90033 0.115460 0.0577302 0.998332i $$-0.481614\pi$$
0.0577302 + 0.998332i $$0.481614\pi$$
$$632$$ 0 0
$$633$$ −29.4743 + 17.0170i −1.17150 + 0.676364i
$$634$$ 0 0
$$635$$ 3.90033 + 0.894797i 0.154780 + 0.0355089i
$$636$$ 0 0
$$637$$ −6.72508 42.1029i −0.266457 1.66818i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −14.0498 24.3350i −0.554935 0.961176i −0.997909 0.0646411i $$-0.979410\pi$$
0.442973 0.896535i $$-0.353924\pi$$
$$642$$ 0 0
$$643$$ 38.3353i 1.51180i 0.654689 + 0.755898i $$0.272800\pi$$
−0.654689 + 0.755898i $$0.727200\pi$$
$$644$$ 0 0
$$645$$ 24.0997 7.40437i 0.948924 0.291547i
$$646$$ 0 0
$$647$$ −0.675248 + 0.389855i −0.0265468 + 0.0153268i −0.513215 0.858260i $$-0.671546\pi$$
0.486668 + 0.873587i $$0.338212\pi$$
$$648$$ 0 0
$$649$$ 4.86254 8.42217i 0.190871 0.330599i
$$650$$ 0 0
$$651$$ 17.6873 + 8.42217i 0.693220 + 0.330091i
$$652$$ 0 0
$$653$$ 32.0619 + 18.5109i 1.25468 + 0.724389i 0.972035 0.234836i $$-0.0754554\pi$$
0.282643 + 0.959225i $$0.408789\pi$$
$$654$$ 0 0
$$655$$ 29.9244 + 27.8279i 1.16924 + 1.08733i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 25.4502 0.991398 0.495699 0.868494i $$-0.334912\pi$$
0.495699 + 0.868494i $$0.334912\pi$$
$$660$$ 0 0
$$661$$ 7.77492 + 13.4666i 0.302409 + 0.523788i 0.976681 0.214695i $$-0.0688758\pi$$
−0.674272 + 0.738483i $$0.735542\pi$$
$$662$$ 0 0
$$663$$ 43.6495 + 25.2011i 1.69521 + 0.978728i
$$664$$ 0 0
$$665$$ −19.8248 15.7035i −0.768771 0.608957i
$$666$$ 0 0
$$667$$ −2.53779 1.46519i −0.0982636 0.0567325i
$$668$$ 0 0
$$669$$ 7.54983 + 13.0767i 0.291893 + 0.505574i
$$670$$ 0 0
$$671$$ 3.52575 0.136110
$$672$$ 0 0
$$673$$ 3.57919i 0.137968i 0.997618 + 0.0689838i $$0.0219757\pi$$
−0.997618 + 0.0689838i $$0.978024\pi$$
$$674$$ 0 0
$$675$$ 11.3248 23.3827i 0.435890 0.900000i
$$676$$ 0 0
$$677$$ 21.3127 + 12.3049i 0.819114 + 0.472916i 0.850111 0.526604i $$-0.176535\pi$$
−0.0309969 + 0.999519i $$0.509868\pi$$
$$678$$ 0 0
$$679$$ 1.45017 + 18.2728i 0.0556522 + 0.701248i
$$680$$ 0 0
$$681$$ 5.58762 9.67805i 0.214118 0.370864i
$$682$$ 0 0
$$683$$ −13.5997 + 7.85177i −0.520377 + 0.300440i −0.737089 0.675796i $$-0.763800\pi$$
0.216712 + 0.976236i $$0.430467\pi$$
$$684$$ 0 0
$$685$$ −6.03779 19.6517i −0.230692 0.750854i
$$686$$ 0 0
$$687$$ 7.40437i 0.282494i
$$688$$ 0 0
$$689$$ −22.5498 39.0575i −0.859080 1.48797i
$$690$$ 0 0
$$691$$ 3.68729 6.38658i 0.140271 0.242957i −0.787327 0.616535i $$-0.788536\pi$$
0.927599 + 0.373578i $$0.121869\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −8.54983 + 37.2679i −0.324314 + 1.41365i
$$696$$ 0 0
$$697$$ 46.6495 26.9331i 1.76698 1.02016i
$$698$$ 0 0
$$699$$ −32.2749 −1.22075
$$700$$ 0 0
$$701$$ −13.8248 −0.522154 −0.261077 0.965318i $$-0.584078\pi$$
−0.261077 + 0.965318i $$0.584078\pi$$
$$702$$ 0 0
$$703$$ 20.7870 12.0014i 0.783995 0.452640i
$$704$$ 0 0
$$705$$ −1.86254 + 8.11863i −0.0701474 + 0.305765i
$$706$$ 0 0
$$707$$ −2.32475 3.37779i −0.0874313 0.127035i
$$708$$ 0 0
$$709$$ −12.7749 + 22.1268i −0.479772 + 0.830990i −0.999731 0.0232018i $$-0.992614\pi$$
0.519959 + 0.854191i $$0.325947\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 3.82518i 0.143254i
$$714$$ 0 0
$$715$$ −9.09967 29.6175i −0.340308 1.10763i
$$716$$ 0 0
$$717$$ 21.8248 12.6005i 0.815060 0.470575i
$$718$$ 0 0
$$719$$ 3.68729 6.38658i 0.137513 0.238179i −0.789042 0.614340i $$-0.789423\pi$$
0.926555 + 0.376160i $$0.122756\pi$$
$$720$$ 0 0
$$721$$ −6.13746 2.92248i −0.228571 0.108839i
$$722$$ 0 0
$$723$$ 19.2371 + 11.1066i 0.715436 + 0.413057i
$$724$$ 0 0
$$725$$ −14.7371 7.13752i −0.547323 0.265081i
$$726$$ 0 0
$$727$$ 18.6915i 0.693228i 0.938008 + 0.346614i $$0.112669\pi$$
−0.938008 + 0.346614i $$0.887331\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 15.5498 + 26.9331i 0.575131 + 0.996157i
$$732$$ 0 0
$$733$$ −28.8625 16.6638i −1.06606 0.615491i −0.138959 0.990298i $$-0.544376\pi$$
−0.927103 + 0.374807i $$0.877709\pi$$
$$734$$ 0 0
$$735$$ 11.9502 + 24.3350i 0.440788 + 0.897611i
$$736$$ 0 0
$$737$$ −27.4124 15.8265i −1.00975 0.582978i
$$738$$ 0 0
$$739$$ 15.9622 + 27.6474i 0.587179 + 1.01702i 0.994600 + 0.103784i $$0.0330950\pi$$
−0.407420 + 0.913241i $$0.633572\pi$$
$$740$$ 0 0
$$741$$ 45.0997 1.65678
$$742$$ 0 0
$$743$$ 19.5287i 0.716440i −0.933637 0.358220i $$-0.883384\pi$$
0.933637 0.358220i $$-0.116616\pi$$
$$744$$ 0 0
$$745$$ 12.3625 + 11.4964i 0.452928 + 0.421196i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −33.2371 15.8265i −1.21446 0.578289i
$$750$$ 0 0
$$751$$ 11.1375 19.2906i 0.406412 0.703926i −0.588073 0.808808i $$-0.700113\pi$$
0.994485 + 0.104882i $$0.0334466\pi$$
$$752$$ 0 0
$$753$$ −8.17525 + 4.71998i −0.297923 + 0.172006i
$$754$$ 0 0
$$755$$ −43.3368 + 13.3148i −1.57719 + 0.484575i
$$756$$ 0 0
$$757$$ 9.43996i 0.343101i −0.985175 0.171551i $$-0.945122\pi$$
0.985175 0.171551i $$-0.0548777\pi$$
$$758$$ 0 0
$$759$$ 1.76287 + 3.05338i 0.0639882 + 0.110831i
$$760$$ 0 0
$$761$$ 14.9622 25.9153i 0.542380 0.939429i −0.456387 0.889781i $$-0.650857\pi$$
0.998767 0.0496479i $$-0.0158099\pi$$
$$762$$ 0 0
$$763$$ 5.32475 + 7.73668i 0.192769 + 0.280087i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 22.5498 13.0192i 0.814227 0.470094i
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ −42.8248 −1.54230
$$772$$ 0 0
$$773$$ −23.5876 + 13.6183i −0.848388 + 0.489817i −0.860107 0.510114i $$-0.829603\pi$$
0.0117187 + 0.999931i $$0.496270\pi$$
$$774$$ 0 0
$$775$$ −1.54983 21.3183i −0.0556717 0.765777i
$$776$$ 0 0
$$777$$ −25.6495 + 2.03559i −0.920171 + 0.0730264i
$$778$$ 0 0
$$779$$ 24.0997 41.7419i 0.863460 1.49556i
$$780$$ 0 0
$$781$$ −12.0000 20.7846i −0.429394 0.743732i
$$782$$ 0 0
$$783$$ 17.0170i 0.608137i
$$784$$ 0 0
$$785$$ −7.13746 23.2309i −0.254747 0.829147i
$$786$$ 0 0
$$787$$ 1.50000 0.866025i 0.0534692 0.0308705i −0.473027 0.881048i $$-0.656839\pi$$
0.526496 + 0.850177i $$0.323505\pi$$
$$788$$ 0 0
$$789$$ 23.3248 40.3997i 0.830383 1.43827i
$$790$$ 0 0
$$791$$ 2.72508 + 34.3375i 0.0968928 + 1.22090i
$$792$$ 0 0
$$793$$ 8.17525 + 4.71998i 0.290312 + 0.167611i
$$794$$ 0 0
$$795$$ 21.0000 + 19.5287i 0.744793 + 0.692613i
$$796$$ 0 0