# Properties

 Label 1900.2.i.g.501.3 Level $1900$ Weight $2$ Character 1900.501 Analytic conductor $15.172$ Analytic rank $0$ Dimension $20$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1900 = 2^{2} \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1900.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.1715763840$$ Analytic rank: $$0$$ Dimension: $$20$$ Relative dimension: $$10$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ Defining polynomial: $$x^{20} + 20 x^{18} + 261 x^{16} + 1994 x^{14} + 11074 x^{12} + 39211 x^{10} + 99376 x^{8} + 134299 x^{6} + 124617 x^{4} + 24768 x^{2} + 4096$$ x^20 + 20*x^18 + 261*x^16 + 1994*x^14 + 11074*x^12 + 39211*x^10 + 99376*x^8 + 134299*x^6 + 124617*x^4 + 24768*x^2 + 4096 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 380) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 501.3 Root $$1.00667 - 1.74361i$$ of defining polynomial Character $$\chi$$ $$=$$ 1900.501 Dual form 1900.2.i.g.201.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.00667 - 1.74361i) q^{3} -1.34403 q^{7} +(-0.526784 + 0.912416i) q^{9} +O(q^{10})$$ $$q+(-1.00667 - 1.74361i) q^{3} -1.34403 q^{7} +(-0.526784 + 0.912416i) q^{9} +5.25594 q^{11} +(-1.21773 + 2.10918i) q^{13} +(0.679914 + 1.17765i) q^{17} +(-2.89815 + 3.25587i) q^{19} +(1.35300 + 2.34346i) q^{21} +(-4.07329 + 7.05514i) q^{23} -3.91884 q^{27} +(1.03597 - 1.79435i) q^{29} -0.513207 q^{31} +(-5.29102 - 9.16431i) q^{33} -5.57175 q^{37} +4.90344 q^{39} +(2.70353 + 4.68265i) q^{41} +(6.36221 + 11.0197i) q^{43} +(-1.63266 + 2.82785i) q^{47} -5.19359 q^{49} +(1.36890 - 2.37101i) q^{51} +(5.88276 - 10.1892i) q^{53} +(8.59447 + 1.77564i) q^{57} +(-0.0175979 - 0.0304805i) q^{59} +(0.518372 - 0.897846i) q^{61} +(0.708011 - 1.22631i) q^{63} +(-0.383377 + 0.664028i) q^{67} +16.4019 q^{69} +(5.68450 + 9.84583i) q^{71} +(1.07635 + 1.86429i) q^{73} -7.06413 q^{77} +(6.48576 + 11.2337i) q^{79} +(5.52535 + 9.57019i) q^{81} +4.20304 q^{83} -4.17153 q^{87} +(3.65426 - 6.32937i) q^{89} +(1.63667 - 2.83479i) q^{91} +(0.516632 + 0.894833i) q^{93} +(0.416683 + 0.721716i) q^{97} +(-2.76875 + 4.79561i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20 q - 10 q^{9}+O(q^{10})$$ 20 * q - 10 * q^9 $$20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99}+O(q^{100})$$ 20 * q - 10 * q^9 - 14 * q^19 - 8 * q^21 + 16 * q^29 + 8 * q^31 + 8 * q^39 + 26 * q^41 + 44 * q^49 + 26 * q^51 - 4 * q^59 + 2 * q^61 - 48 * q^69 - 2 * q^71 + 16 * q^79 + 26 * q^81 + 40 * q^89 - 4 * q^91 + 20 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$951$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.00667 1.74361i −0.581203 1.00667i −0.995337 0.0964577i $$-0.969249\pi$$
0.414134 0.910216i $$-0.364085\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −1.34403 −0.507994 −0.253997 0.967205i $$-0.581745\pi$$
−0.253997 + 0.967205i $$0.581745\pi$$
$$8$$ 0 0
$$9$$ −0.526784 + 0.912416i −0.175595 + 0.304139i
$$10$$ 0 0
$$11$$ 5.25594 1.58473 0.792363 0.610050i $$-0.208851\pi$$
0.792363 + 0.610050i $$0.208851\pi$$
$$12$$ 0 0
$$13$$ −1.21773 + 2.10918i −0.337738 + 0.584980i −0.984007 0.178130i $$-0.942995\pi$$
0.646269 + 0.763110i $$0.276329\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0.679914 + 1.17765i 0.164903 + 0.285621i 0.936621 0.350344i $$-0.113935\pi$$
−0.771718 + 0.635965i $$0.780602\pi$$
$$18$$ 0 0
$$19$$ −2.89815 + 3.25587i −0.664882 + 0.746949i
$$20$$ 0 0
$$21$$ 1.35300 + 2.34346i 0.295248 + 0.511384i
$$22$$ 0 0
$$23$$ −4.07329 + 7.05514i −0.849339 + 1.47110i 0.0324603 + 0.999473i $$0.489666\pi$$
−0.881799 + 0.471625i $$0.843668\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −3.91884 −0.754182
$$28$$ 0 0
$$29$$ 1.03597 1.79435i 0.192375 0.333203i −0.753662 0.657262i $$-0.771714\pi$$
0.946037 + 0.324059i $$0.105048\pi$$
$$30$$ 0 0
$$31$$ −0.513207 −0.0921747 −0.0460873 0.998937i $$-0.514675\pi$$
−0.0460873 + 0.998937i $$0.514675\pi$$
$$32$$ 0 0
$$33$$ −5.29102 9.16431i −0.921048 1.59530i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −5.57175 −0.915991 −0.457995 0.888955i $$-0.651432\pi$$
−0.457995 + 0.888955i $$0.651432\pi$$
$$38$$ 0 0
$$39$$ 4.90344 0.785179
$$40$$ 0 0
$$41$$ 2.70353 + 4.68265i 0.422220 + 0.731307i 0.996156 0.0875933i $$-0.0279176\pi$$
−0.573936 + 0.818900i $$0.694584\pi$$
$$42$$ 0 0
$$43$$ 6.36221 + 11.0197i 0.970228 + 1.68048i 0.694859 + 0.719146i $$0.255467\pi$$
0.275369 + 0.961339i $$0.411200\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −1.63266 + 2.82785i −0.238148 + 0.412485i −0.960183 0.279372i $$-0.909874\pi$$
0.722035 + 0.691857i $$0.243207\pi$$
$$48$$ 0 0
$$49$$ −5.19359 −0.741942
$$50$$ 0 0
$$51$$ 1.36890 2.37101i 0.191685 0.332008i
$$52$$ 0 0
$$53$$ 5.88276 10.1892i 0.808060 1.39960i −0.106146 0.994351i $$-0.533851\pi$$
0.914206 0.405250i $$-0.132815\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 8.59447 + 1.77564i 1.13837 + 0.235190i
$$58$$ 0 0
$$59$$ −0.0175979 0.0304805i −0.00229105 0.00396822i 0.864878 0.501983i $$-0.167396\pi$$
−0.867169 + 0.498015i $$0.834063\pi$$
$$60$$ 0 0
$$61$$ 0.518372 0.897846i 0.0663707 0.114957i −0.830930 0.556376i $$-0.812191\pi$$
0.897301 + 0.441419i $$0.145525\pi$$
$$62$$ 0 0
$$63$$ 0.708011 1.22631i 0.0892010 0.154501i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −0.383377 + 0.664028i −0.0468369 + 0.0811239i −0.888493 0.458889i $$-0.848247\pi$$
0.841657 + 0.540013i $$0.181581\pi$$
$$68$$ 0 0
$$69$$ 16.4019 1.97455
$$70$$ 0 0
$$71$$ 5.68450 + 9.84583i 0.674625 + 1.16849i 0.976578 + 0.215163i $$0.0690282\pi$$
−0.301953 + 0.953323i $$0.597638\pi$$
$$72$$ 0 0
$$73$$ 1.07635 + 1.86429i 0.125977 + 0.218199i 0.922115 0.386917i $$-0.126460\pi$$
−0.796137 + 0.605116i $$0.793127\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −7.06413 −0.805032
$$78$$ 0 0
$$79$$ 6.48576 + 11.2337i 0.729705 + 1.26389i 0.957008 + 0.290062i $$0.0936761\pi$$
−0.227302 + 0.973824i $$0.572991\pi$$
$$80$$ 0 0
$$81$$ 5.52535 + 9.57019i 0.613928 + 1.06335i
$$82$$ 0 0
$$83$$ 4.20304 0.461343 0.230672 0.973032i $$-0.425908\pi$$
0.230672 + 0.973032i $$0.425908\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −4.17153 −0.447235
$$88$$ 0 0
$$89$$ 3.65426 6.32937i 0.387351 0.670912i −0.604741 0.796422i $$-0.706723\pi$$
0.992092 + 0.125510i $$0.0400568\pi$$
$$90$$ 0 0
$$91$$ 1.63667 2.83479i 0.171569 0.297166i
$$92$$ 0 0
$$93$$ 0.516632 + 0.894833i 0.0535722 + 0.0927898i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0.416683 + 0.721716i 0.0423077 + 0.0732791i 0.886404 0.462913i $$-0.153196\pi$$
−0.844096 + 0.536192i $$0.819862\pi$$
$$98$$ 0 0
$$99$$ −2.76875 + 4.79561i −0.278269 + 0.481977i
$$100$$ 0 0
$$101$$ −7.40992 + 12.8344i −0.737315 + 1.27707i 0.216385 + 0.976308i $$0.430573\pi$$
−0.953700 + 0.300759i $$0.902760\pi$$
$$102$$ 0 0
$$103$$ −9.40773 −0.926971 −0.463486 0.886104i $$-0.653401\pi$$
−0.463486 + 0.886104i $$0.653401\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 12.8130 1.23868 0.619338 0.785124i $$-0.287401\pi$$
0.619338 + 0.785124i $$0.287401\pi$$
$$108$$ 0 0
$$109$$ −0.996875 1.72664i −0.0954833 0.165382i 0.814327 0.580406i $$-0.197106\pi$$
−0.909810 + 0.415025i $$0.863773\pi$$
$$110$$ 0 0
$$111$$ 5.60894 + 9.71497i 0.532377 + 0.922104i
$$112$$ 0 0
$$113$$ 8.34647 0.785170 0.392585 0.919716i $$-0.371581\pi$$
0.392585 + 0.919716i $$0.371581\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.28296 2.22216i −0.118610 0.205439i
$$118$$ 0 0
$$119$$ −0.913823 1.58279i −0.0837700 0.145094i
$$120$$ 0 0
$$121$$ 16.6249 1.51136
$$122$$ 0 0
$$123$$ 5.44314 9.42780i 0.490791 0.850076i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 10.2907 17.8240i 0.913153 1.58163i 0.103569 0.994622i $$-0.466974\pi$$
0.809583 0.587005i $$-0.199693\pi$$
$$128$$ 0 0
$$129$$ 12.8093 22.1864i 1.12780 1.95341i
$$130$$ 0 0
$$131$$ −5.36554 9.29339i −0.468790 0.811967i 0.530574 0.847639i $$-0.321976\pi$$
−0.999364 + 0.0356712i $$0.988643\pi$$
$$132$$ 0 0
$$133$$ 3.89519 4.37598i 0.337756 0.379446i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 8.58931 14.8771i 0.733834 1.27104i −0.221399 0.975183i $$-0.571062\pi$$
0.955233 0.295855i $$-0.0956045\pi$$
$$138$$ 0 0
$$139$$ −3.66394 + 6.34613i −0.310771 + 0.538272i −0.978530 0.206106i $$-0.933921\pi$$
0.667758 + 0.744378i $$0.267254\pi$$
$$140$$ 0 0
$$141$$ 6.57423 0.553650
$$142$$ 0 0
$$143$$ −6.40033 + 11.0857i −0.535223 + 0.927033i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 5.22825 + 9.05560i 0.431219 + 0.746893i
$$148$$ 0 0
$$149$$ 6.12292 + 10.6052i 0.501609 + 0.868812i 0.999998 + 0.00185904i $$0.000591751\pi$$
−0.498389 + 0.866953i $$0.666075\pi$$
$$150$$ 0 0
$$151$$ −11.5577 −0.940549 −0.470274 0.882520i $$-0.655845\pi$$
−0.470274 + 0.882520i $$0.655845\pi$$
$$152$$ 0 0
$$153$$ −1.43267 −0.115825
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 2.06996 + 3.58528i 0.165201 + 0.286137i 0.936727 0.350062i $$-0.113839\pi$$
−0.771526 + 0.636198i $$0.780506\pi$$
$$158$$ 0 0
$$159$$ −23.6881 −1.87859
$$160$$ 0 0
$$161$$ 5.47460 9.48229i 0.431459 0.747309i
$$162$$ 0 0
$$163$$ −9.41672 −0.737575 −0.368787 0.929514i $$-0.620227\pi$$
−0.368787 + 0.929514i $$0.620227\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −6.83551 + 11.8395i −0.528948 + 0.916164i 0.470482 + 0.882409i $$0.344080\pi$$
−0.999430 + 0.0337550i $$0.989253\pi$$
$$168$$ 0 0
$$169$$ 3.53425 + 6.12151i 0.271866 + 0.470885i
$$170$$ 0 0
$$171$$ −1.44401 4.35946i −0.110426 0.333376i
$$172$$ 0 0
$$173$$ 5.88891 + 10.1999i 0.447726 + 0.775484i 0.998238 0.0593437i $$-0.0189008\pi$$
−0.550512 + 0.834827i $$0.685567\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −0.0354307 + 0.0613678i −0.00266314 + 0.00461269i
$$178$$ 0 0
$$179$$ −16.5727 −1.23870 −0.619350 0.785115i $$-0.712604\pi$$
−0.619350 + 0.785115i $$0.712604\pi$$
$$180$$ 0 0
$$181$$ 7.19552 12.4630i 0.534839 0.926368i −0.464332 0.885661i $$-0.653706\pi$$
0.999171 0.0407069i $$-0.0129610\pi$$
$$182$$ 0 0
$$183$$ −2.08733 −0.154300
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 3.57359 + 6.18964i 0.261327 + 0.452631i
$$188$$ 0 0
$$189$$ 5.26703 0.383120
$$190$$ 0 0
$$191$$ −5.97170 −0.432097 −0.216049 0.976383i $$-0.569317\pi$$
−0.216049 + 0.976383i $$0.569317\pi$$
$$192$$ 0 0
$$193$$ −8.14331 14.1046i −0.586168 1.01527i −0.994729 0.102542i $$-0.967302\pi$$
0.408560 0.912731i $$-0.366031\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 11.5233 0.820998 0.410499 0.911861i $$-0.365355\pi$$
0.410499 + 0.911861i $$0.365355\pi$$
$$198$$ 0 0
$$199$$ −4.79943 + 8.31285i −0.340222 + 0.589283i −0.984474 0.175531i $$-0.943836\pi$$
0.644251 + 0.764814i $$0.277169\pi$$
$$200$$ 0 0
$$201$$ 1.54374 0.108887
$$202$$ 0 0
$$203$$ −1.39237 + 2.41166i −0.0977253 + 0.169265i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −4.29148 7.43307i −0.298279 0.516634i
$$208$$ 0 0
$$209$$ −15.2325 + 17.1127i −1.05366 + 1.18371i
$$210$$ 0 0
$$211$$ 7.28207 + 12.6129i 0.501318 + 0.868308i 0.999999 + 0.00152265i $$0.000484675\pi$$
−0.498681 + 0.866786i $$0.666182\pi$$
$$212$$ 0 0
$$213$$ 11.4449 19.8231i 0.784189 1.35826i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0.689764 0.0468242
$$218$$ 0 0
$$219$$ 2.16707 3.75347i 0.146437 0.253636i
$$220$$ 0 0
$$221$$ −3.31182 −0.222777
$$222$$ 0 0
$$223$$ 3.78635 + 6.55816i 0.253553 + 0.439167i 0.964501 0.264077i $$-0.0850675\pi$$
−0.710949 + 0.703244i $$0.751734\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 6.86640 0.455739 0.227869 0.973692i $$-0.426824\pi$$
0.227869 + 0.973692i $$0.426824\pi$$
$$228$$ 0 0
$$229$$ 22.1011 1.46048 0.730240 0.683191i $$-0.239408\pi$$
0.730240 + 0.683191i $$0.239408\pi$$
$$230$$ 0 0
$$231$$ 7.11127 + 12.3171i 0.467887 + 0.810404i
$$232$$ 0 0
$$233$$ −1.48844 2.57806i −0.0975111 0.168894i 0.813143 0.582064i $$-0.197755\pi$$
−0.910654 + 0.413170i $$0.864421\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 13.0581 22.6173i 0.848214 1.46915i
$$238$$ 0 0
$$239$$ −9.71289 −0.628275 −0.314137 0.949378i $$-0.601715\pi$$
−0.314137 + 0.949378i $$0.601715\pi$$
$$240$$ 0 0
$$241$$ 9.34287 16.1823i 0.601827 1.04239i −0.390717 0.920511i $$-0.627773\pi$$
0.992544 0.121884i $$-0.0388937\pi$$
$$242$$ 0 0
$$243$$ 5.24618 9.08665i 0.336543 0.582909i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −3.33803 10.0775i −0.212394 0.641216i
$$248$$ 0 0
$$249$$ −4.23109 7.32846i −0.268134 0.464422i
$$250$$ 0 0
$$251$$ 2.10091 3.63888i 0.132608 0.229684i −0.792073 0.610426i $$-0.790998\pi$$
0.924681 + 0.380742i $$0.124332\pi$$
$$252$$ 0 0
$$253$$ −21.4090 + 37.0814i −1.34597 + 2.33129i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −14.0842 + 24.3946i −0.878548 + 1.52169i −0.0256140 + 0.999672i $$0.508154\pi$$
−0.852934 + 0.522018i $$0.825179\pi$$
$$258$$ 0 0
$$259$$ 7.48859 0.465318
$$260$$ 0 0
$$261$$ 1.09146 + 1.89047i 0.0675599 + 0.117017i
$$262$$ 0 0
$$263$$ −1.35425 2.34563i −0.0835065 0.144637i 0.821247 0.570572i $$-0.193279\pi$$
−0.904754 + 0.425935i $$0.859945\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −14.7146 −0.900519
$$268$$ 0 0
$$269$$ −5.64101 9.77052i −0.343938 0.595719i 0.641222 0.767356i $$-0.278428\pi$$
−0.985160 + 0.171637i $$0.945094\pi$$
$$270$$ 0 0
$$271$$ −3.16690 5.48523i −0.192375 0.333204i 0.753662 0.657263i $$-0.228286\pi$$
−0.946037 + 0.324059i $$0.894952\pi$$
$$272$$ 0 0
$$273$$ −6.59035 −0.398866
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −11.1435 −0.669549 −0.334774 0.942298i $$-0.608660\pi$$
−0.334774 + 0.942298i $$0.608660\pi$$
$$278$$ 0 0
$$279$$ 0.270349 0.468258i 0.0161854 0.0280339i
$$280$$ 0 0
$$281$$ −12.9061 + 22.3541i −0.769916 + 1.33353i 0.167693 + 0.985839i $$0.446368\pi$$
−0.937608 + 0.347694i $$0.886965\pi$$
$$282$$ 0 0
$$283$$ 14.4304 + 24.9942i 0.857799 + 1.48575i 0.874024 + 0.485883i $$0.161502\pi$$
−0.0162249 + 0.999868i $$0.505165\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −3.63361 6.29360i −0.214485 0.371500i
$$288$$ 0 0
$$289$$ 7.57543 13.1210i 0.445614 0.771826i
$$290$$ 0 0
$$291$$ 0.838927 1.45306i 0.0491788 0.0851801i
$$292$$ 0 0
$$293$$ −22.7742 −1.33048 −0.665242 0.746628i $$-0.731672\pi$$
−0.665242 + 0.746628i $$0.731672\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −20.5972 −1.19517
$$298$$ 0 0
$$299$$ −9.92035 17.1825i −0.573709 0.993692i
$$300$$ 0 0
$$301$$ −8.55098 14.8107i −0.492870 0.853676i
$$302$$ 0 0
$$303$$ 29.8375 1.71412
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 8.09880 + 14.0275i 0.462223 + 0.800593i 0.999071 0.0430854i $$-0.0137187\pi$$
−0.536849 + 0.843679i $$0.680385\pi$$
$$308$$ 0 0
$$309$$ 9.47052 + 16.4034i 0.538759 + 0.933158i
$$310$$ 0 0
$$311$$ −28.3483 −1.60749 −0.803743 0.594977i $$-0.797161\pi$$
−0.803743 + 0.594977i $$0.797161\pi$$
$$312$$ 0 0
$$313$$ 1.54464 2.67539i 0.0873081 0.151222i −0.819064 0.573702i $$-0.805507\pi$$
0.906372 + 0.422480i $$0.138840\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −12.0225 + 20.8236i −0.675251 + 1.16957i 0.301144 + 0.953579i $$0.402632\pi$$
−0.976395 + 0.215991i $$0.930702\pi$$
$$318$$ 0 0
$$319$$ 5.44500 9.43101i 0.304861 0.528035i
$$320$$ 0 0
$$321$$ −12.8985 22.3408i −0.719923 1.24694i
$$322$$ 0 0
$$323$$ −5.80476 1.19928i −0.322986 0.0667298i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −2.00706 + 3.47632i −0.110990 + 0.192241i
$$328$$ 0 0
$$329$$ 2.19434 3.80071i 0.120978 0.209540i
$$330$$ 0 0
$$331$$ −20.7717 −1.14171 −0.570857 0.821049i $$-0.693389\pi$$
−0.570857 + 0.821049i $$0.693389\pi$$
$$332$$ 0 0
$$333$$ 2.93511 5.08376i 0.160843 0.278588i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −1.21324 2.10139i −0.0660892 0.114470i 0.831087 0.556142i $$-0.187719\pi$$
−0.897177 + 0.441672i $$0.854386\pi$$
$$338$$ 0 0
$$339$$ −8.40217 14.5530i −0.456343 0.790410i
$$340$$ 0 0
$$341$$ −2.69739 −0.146072
$$342$$ 0 0
$$343$$ 16.3885 0.884896
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.43664 + 2.48834i 0.0771230 + 0.133581i 0.902008 0.431720i $$-0.142093\pi$$
−0.824885 + 0.565301i $$0.808760\pi$$
$$348$$ 0 0
$$349$$ −5.89385 −0.315490 −0.157745 0.987480i $$-0.550422\pi$$
−0.157745 + 0.987480i $$0.550422\pi$$
$$350$$ 0 0
$$351$$ 4.77211 8.26553i 0.254716 0.441181i
$$352$$ 0 0
$$353$$ −12.0238 −0.639962 −0.319981 0.947424i $$-0.603676\pi$$
−0.319981 + 0.947424i $$0.603676\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −1.83984 + 3.18670i −0.0973748 + 0.168658i
$$358$$ 0 0
$$359$$ 2.26590 + 3.92466i 0.119590 + 0.207136i 0.919605 0.392844i $$-0.128509\pi$$
−0.800015 + 0.599979i $$0.795175\pi$$
$$360$$ 0 0
$$361$$ −2.20143 18.8720i −0.115865 0.993265i
$$362$$ 0 0
$$363$$ −16.7359 28.9874i −0.878406 1.52144i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −17.2710 + 29.9143i −0.901539 + 1.56151i −0.0760429 + 0.997105i $$0.524229\pi$$
−0.825496 + 0.564407i $$0.809105\pi$$
$$368$$ 0 0
$$369$$ −5.69670 −0.296558
$$370$$ 0 0
$$371$$ −7.90659 + 13.6946i −0.410490 + 0.710989i
$$372$$ 0 0
$$373$$ 24.0801 1.24682 0.623411 0.781894i $$-0.285746\pi$$
0.623411 + 0.781894i $$0.285746\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 2.52307 + 4.37008i 0.129945 + 0.225071i
$$378$$ 0 0
$$379$$ 30.1565 1.54904 0.774518 0.632552i $$-0.217992\pi$$
0.774518 + 0.632552i $$0.217992\pi$$
$$380$$ 0 0
$$381$$ −41.4375 −2.12291
$$382$$ 0 0
$$383$$ −19.4101 33.6192i −0.991809 1.71786i −0.606522 0.795066i $$-0.707436\pi$$
−0.385286 0.922797i $$-0.625897\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −13.4060 −0.681467
$$388$$ 0 0
$$389$$ −18.6935 + 32.3781i −0.947799 + 1.64164i −0.197750 + 0.980252i $$0.563364\pi$$
−0.750048 + 0.661383i $$0.769970\pi$$
$$390$$ 0 0
$$391$$ −11.0779 −0.560236
$$392$$ 0 0
$$393$$ −10.8027 + 18.7108i −0.544924 + 0.943836i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −7.78211 13.4790i −0.390573 0.676492i 0.601952 0.798532i $$-0.294390\pi$$
−0.992525 + 0.122040i $$0.961056\pi$$
$$398$$ 0 0
$$399$$ −11.5512 2.38651i −0.578283 0.119475i
$$400$$ 0 0
$$401$$ −11.3113 19.5918i −0.564860 0.978366i −0.997063 0.0765898i $$-0.975597\pi$$
0.432203 0.901777i $$-0.357737\pi$$
$$402$$ 0 0
$$403$$ 0.624949 1.08244i 0.0311309 0.0539203i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −29.2848 −1.45159
$$408$$ 0 0
$$409$$ 18.1239 31.3915i 0.896169 1.55221i 0.0638187 0.997962i $$-0.479672\pi$$
0.832351 0.554249i $$-0.186995\pi$$
$$410$$ 0 0
$$411$$ −34.5865 −1.70603
$$412$$ 0 0
$$413$$ 0.0236521 + 0.0409666i 0.00116384 + 0.00201583i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 14.7536 0.722486
$$418$$ 0 0
$$419$$ −14.5598 −0.711293 −0.355647 0.934621i $$-0.615739\pi$$
−0.355647 + 0.934621i $$0.615739\pi$$
$$420$$ 0 0
$$421$$ −0.784161 1.35821i −0.0382177 0.0661950i 0.846284 0.532732i $$-0.178835\pi$$
−0.884502 + 0.466537i $$0.845501\pi$$
$$422$$ 0 0
$$423$$ −1.72012 2.97934i −0.0836351 0.144860i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −0.696705 + 1.20673i −0.0337159 + 0.0583977i
$$428$$ 0 0
$$429$$ 25.7722 1.24429
$$430$$ 0 0
$$431$$ 12.7303 22.0495i 0.613197 1.06209i −0.377500 0.926009i $$-0.623216\pi$$
0.990698 0.136080i $$-0.0434503\pi$$
$$432$$ 0 0
$$433$$ 8.44155 14.6212i 0.405675 0.702650i −0.588725 0.808334i $$-0.700370\pi$$
0.994400 + 0.105684i $$0.0337031\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −11.1656 33.7090i −0.534125 1.61252i
$$438$$ 0 0
$$439$$ −9.93240 17.2034i −0.474048 0.821075i 0.525511 0.850787i $$-0.323874\pi$$
−0.999558 + 0.0297121i $$0.990541\pi$$
$$440$$ 0 0
$$441$$ 2.73590 4.73872i 0.130281 0.225653i
$$442$$ 0 0
$$443$$ 2.57742 4.46422i 0.122457 0.212101i −0.798279 0.602288i $$-0.794256\pi$$
0.920736 + 0.390186i $$0.127589\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 12.3276 21.3520i 0.583074 1.00991i
$$448$$ 0 0
$$449$$ −33.2207 −1.56778 −0.783892 0.620897i $$-0.786768\pi$$
−0.783892 + 0.620897i $$0.786768\pi$$
$$450$$ 0 0
$$451$$ 14.2096 + 24.6117i 0.669103 + 1.15892i
$$452$$ 0 0
$$453$$ 11.6348 + 20.1520i 0.546650 + 0.946826i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 11.7126 0.547894 0.273947 0.961745i $$-0.411671\pi$$
0.273947 + 0.961745i $$0.411671\pi$$
$$458$$ 0 0
$$459$$ −2.66448 4.61501i −0.124367 0.215410i
$$460$$ 0 0
$$461$$ 3.68501 + 6.38263i 0.171628 + 0.297269i 0.938989 0.343947i $$-0.111764\pi$$
−0.767361 + 0.641215i $$0.778431\pi$$
$$462$$ 0 0
$$463$$ −28.8020 −1.33854 −0.669271 0.743019i $$-0.733393\pi$$
−0.669271 + 0.743019i $$0.733393\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 34.1251 1.57912 0.789561 0.613673i $$-0.210309\pi$$
0.789561 + 0.613673i $$0.210309\pi$$
$$468$$ 0 0
$$469$$ 0.515268 0.892471i 0.0237929 0.0412105i
$$470$$ 0 0
$$471$$ 4.16756 7.21842i 0.192031 0.332607i
$$472$$ 0 0
$$473$$ 33.4394 + 57.9188i 1.53755 + 2.66311i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 6.19789 + 10.7351i 0.283782 + 0.491525i
$$478$$ 0 0
$$479$$ −14.4130 + 24.9640i −0.658546 + 1.14064i 0.322446 + 0.946588i $$0.395495\pi$$
−0.980992 + 0.194048i $$0.937838\pi$$
$$480$$ 0 0
$$481$$ 6.78491 11.7518i 0.309365 0.535836i
$$482$$ 0 0
$$483$$ −22.0446 −1.00306
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 16.5796 0.751294 0.375647 0.926763i $$-0.377421\pi$$
0.375647 + 0.926763i $$0.377421\pi$$
$$488$$ 0 0
$$489$$ 9.47957 + 16.4191i 0.428681 + 0.742497i
$$490$$ 0 0
$$491$$ −4.94615 8.56698i −0.223217 0.386623i 0.732566 0.680696i $$-0.238322\pi$$
−0.955783 + 0.294073i $$0.904989\pi$$
$$492$$ 0 0
$$493$$ 2.81748 0.126893
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −7.64011 13.2331i −0.342706 0.593584i
$$498$$ 0 0
$$499$$ 15.4949 + 26.8380i 0.693649 + 1.20144i 0.970634 + 0.240561i $$0.0773315\pi$$
−0.276985 + 0.960874i $$0.589335\pi$$
$$500$$ 0 0
$$501$$ 27.5245 1.22970
$$502$$ 0 0
$$503$$ 6.43203 11.1406i 0.286790 0.496735i −0.686252 0.727364i $$-0.740745\pi$$
0.973042 + 0.230629i $$0.0740784\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 7.11568 12.3247i 0.316018 0.547360i
$$508$$ 0 0
$$509$$ 7.35312 12.7360i 0.325921 0.564512i −0.655777 0.754955i $$-0.727659\pi$$
0.981698 + 0.190442i $$0.0609922\pi$$
$$510$$ 0 0
$$511$$ −1.44664 2.50566i −0.0639957 0.110844i
$$512$$ 0 0
$$513$$ 11.3574 12.7593i 0.501442 0.563335i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −8.58118 + 14.8630i −0.377400 + 0.653676i
$$518$$ 0 0
$$519$$ 11.8564 20.5359i 0.520439 0.901427i
$$520$$ 0 0
$$521$$ 5.35528 0.234619 0.117310 0.993095i $$-0.462573\pi$$
0.117310 + 0.993095i $$0.462573\pi$$
$$522$$ 0 0
$$523$$ −7.98981 + 13.8388i −0.349370 + 0.605127i −0.986138 0.165929i $$-0.946938\pi$$
0.636768 + 0.771056i $$0.280271\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −0.348937 0.604376i −0.0151999 0.0263270i
$$528$$ 0 0
$$529$$ −21.6833 37.5566i −0.942753 1.63290i
$$530$$ 0 0
$$531$$ 0.0370812 0.00160919
$$532$$ 0 0
$$533$$ −13.1687 −0.570400
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 16.6833 + 28.8963i 0.719937 + 1.24697i
$$538$$ 0 0
$$539$$ −27.2972 −1.17577
$$540$$ 0 0
$$541$$ −17.9500 + 31.0904i −0.771732 + 1.33668i 0.164881 + 0.986313i $$0.447276\pi$$
−0.936613 + 0.350366i $$0.886057\pi$$
$$542$$ 0 0
$$543$$ −28.9742 −1.24340
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 13.0754 22.6473i 0.559064 0.968327i −0.438511 0.898726i $$-0.644494\pi$$
0.997575 0.0696011i $$-0.0221727\pi$$
$$548$$ 0 0
$$549$$ 0.546140 + 0.945942i 0.0233087 + 0.0403718i
$$550$$ 0 0
$$551$$ 2.83979 + 8.57329i 0.120979 + 0.365235i
$$552$$ 0 0
$$553$$ −8.71704 15.0983i −0.370686 0.642047i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 2.10412 3.64444i 0.0891543 0.154420i −0.818000 0.575219i $$-0.804917\pi$$
0.907154 + 0.420799i $$0.138250\pi$$
$$558$$ 0 0
$$559$$ −30.9899 −1.31073
$$560$$ 0 0
$$561$$ 7.19488 12.4619i 0.303768 0.526142i
$$562$$ 0 0
$$563$$ 40.5225 1.70782 0.853909 0.520422i $$-0.174225\pi$$
0.853909 + 0.520422i $$0.174225\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −7.42622 12.8626i −0.311872 0.540178i
$$568$$ 0 0
$$569$$ 23.9522 1.00413 0.502064 0.864831i $$-0.332574\pi$$
0.502064 + 0.864831i $$0.332574\pi$$
$$570$$ 0 0
$$571$$ −7.78949 −0.325980 −0.162990 0.986628i $$-0.552114\pi$$
−0.162990 + 0.986628i $$0.552114\pi$$
$$572$$ 0 0
$$573$$ 6.01155 + 10.4123i 0.251136 + 0.434981i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 34.1385 1.42121 0.710603 0.703593i $$-0.248422\pi$$
0.710603 + 0.703593i $$0.248422\pi$$
$$578$$ 0 0
$$579$$ −16.3953 + 28.3975i −0.681366 + 1.18016i
$$580$$ 0 0
$$581$$ −5.64899 −0.234360
$$582$$ 0 0
$$583$$ 30.9195 53.5541i 1.28055 2.21798i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 11.0700 + 19.1737i 0.456906 + 0.791384i 0.998796 0.0490654i $$-0.0156243\pi$$
−0.541890 + 0.840450i $$0.682291\pi$$
$$588$$ 0 0
$$589$$ 1.48735 1.67094i 0.0612853 0.0688498i
$$590$$ 0 0
$$591$$ −11.6002 20.0921i −0.477167 0.826477i
$$592$$ 0 0
$$593$$ −20.6767 + 35.8131i −0.849089 + 1.47067i 0.0329325 + 0.999458i $$0.489515\pi$$
−0.882022 + 0.471208i $$0.843818\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 19.3258 0.790954
$$598$$ 0 0
$$599$$ −16.8243 + 29.1406i −0.687423 + 1.19065i 0.285246 + 0.958454i $$0.407925\pi$$
−0.972669 + 0.232197i $$0.925409\pi$$
$$600$$ 0 0
$$601$$ 38.4939 1.57020 0.785100 0.619369i $$-0.212611\pi$$
0.785100 + 0.619369i $$0.212611\pi$$
$$602$$ 0 0
$$603$$ −0.403913 0.699598i −0.0164486 0.0284899i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −22.1827 −0.900367 −0.450183 0.892936i $$-0.648641\pi$$
−0.450183 + 0.892936i $$0.648641\pi$$
$$608$$ 0 0
$$609$$ 5.60665 0.227193
$$610$$ 0 0
$$611$$ −3.97629 6.88714i −0.160864 0.278624i
$$612$$ 0 0
$$613$$ −2.38703 4.13445i −0.0964111 0.166989i 0.813786 0.581165i $$-0.197403\pi$$
−0.910197 + 0.414176i $$0.864070\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 8.09317 14.0178i 0.325819 0.564335i −0.655859 0.754883i $$-0.727693\pi$$
0.981678 + 0.190549i $$0.0610267\pi$$
$$618$$ 0 0
$$619$$ 13.4892 0.542176 0.271088 0.962555i $$-0.412617\pi$$
0.271088 + 0.962555i $$0.412617\pi$$
$$620$$ 0 0
$$621$$ 15.9626 27.6480i 0.640556 1.10948i
$$622$$ 0 0
$$623$$ −4.91143 + 8.50684i −0.196772 + 0.340819i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 45.1720 + 9.33268i 1.80400 + 0.372711i
$$628$$ 0 0
$$629$$ −3.78832 6.56156i −0.151050 0.261626i
$$630$$ 0 0
$$631$$ 13.2207 22.8989i 0.526308 0.911592i −0.473222 0.880943i $$-0.656909\pi$$
0.999530 0.0306488i $$-0.00975735\pi$$
$$632$$ 0 0
$$633$$ 14.6613 25.3942i 0.582735 1.00933i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.32441 10.9542i 0.250582 0.434021i
$$638$$ 0 0
$$639$$ −11.9780 −0.473842
$$640$$ 0 0
$$641$$ −4.27817 7.41000i −0.168977 0.292677i 0.769083 0.639149i $$-0.220713\pi$$
−0.938061 + 0.346471i $$0.887380\pi$$
$$642$$ 0 0
$$643$$ 14.0112 + 24.2681i 0.552548 + 0.957042i 0.998090 + 0.0617804i $$0.0196779\pi$$
−0.445541 + 0.895261i $$0.646989\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −9.57376 −0.376383 −0.188192 0.982132i $$-0.560263\pi$$
−0.188192 + 0.982132i $$0.560263\pi$$
$$648$$ 0 0
$$649$$ −0.0924936 0.160204i −0.00363069 0.00628854i
$$650$$ 0 0
$$651$$ −0.694367 1.20268i −0.0272144 0.0471367i
$$652$$ 0 0
$$653$$ 16.4168 0.642439 0.321219 0.947005i $$-0.395907\pi$$
0.321219 + 0.947005i $$0.395907\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −2.26801 −0.0884837
$$658$$ 0 0
$$659$$ −7.08162 + 12.2657i −0.275861 + 0.477805i −0.970352 0.241697i $$-0.922296\pi$$
0.694491 + 0.719501i $$0.255629\pi$$
$$660$$ 0 0
$$661$$ −18.5170 + 32.0724i −0.720229 + 1.24747i 0.240679 + 0.970605i $$0.422630\pi$$
−0.960908 + 0.276868i $$0.910704\pi$$
$$662$$ 0 0
$$663$$ 3.33392 + 5.77452i 0.129479 + 0.224264i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 8.43960 + 14.6178i 0.326783 + 0.566004i
$$668$$ 0 0
$$669$$ 7.62324 13.2038i 0.294732 0.510490i
$$670$$ 0 0
$$671$$ 2.72453 4.71903i 0.105179 0.182176i
$$672$$ 0 0
$$673$$ −42.3293 −1.63167 −0.815837 0.578282i $$-0.803723\pi$$
−0.815837 + 0.578282i $$0.803723\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −13.9856 −0.537510 −0.268755 0.963209i $$-0.586612\pi$$
−0.268755 + 0.963209i $$0.586612\pi$$
$$678$$ 0 0
$$679$$ −0.560033 0.970005i −0.0214921 0.0372254i
$$680$$ 0 0
$$681$$ −6.91222 11.9723i −0.264877 0.458780i
$$682$$ 0 0
$$683$$ 11.6668 0.446416 0.223208 0.974771i $$-0.428347\pi$$
0.223208 + 0.974771i $$0.428347\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −22.2486 38.5356i −0.848835 1.47023i
$$688$$ 0 0
$$689$$ 14.3273 + 24.8156i 0.545825 + 0.945397i
$$690$$ 0 0
$$691$$ −15.7886 −0.600627 −0.300313 0.953841i $$-0.597091\pi$$
−0.300313 + 0.953841i $$0.597091\pi$$
$$692$$ 0 0
$$693$$ 3.72127 6.44542i 0.141359 0.244841i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −3.67633 + 6.36760i −0.139251 + 0.241190i
$$698$$ 0 0
$$699$$ −2.99675 + 5.19053i −0.113348 + 0.196324i
$$700$$ 0 0
$$701$$ 2.64450 + 4.58042i 0.0998816 + 0.173000i 0.911635 0.411000i $$-0.134820\pi$$
−0.811754 + 0.584000i $$0.801487\pi$$
$$702$$ 0 0
$$703$$ 16.1478 18.1409i 0.609025 0.684198i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 9.95913 17.2497i 0.374552 0.648743i
$$708$$ 0 0
$$709$$ 12.2529 21.2226i 0.460166 0.797031i −0.538803 0.842432i $$-0.681123\pi$$
0.998969 + 0.0454011i $$0.0144566\pi$$
$$710$$ 0 0
$$711$$ −13.6664 −0.512529
$$712$$ 0 0
$$713$$ 2.09044 3.62075i 0.0782875 0.135598i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 9.77771 + 16.9355i 0.365155 + 0.632467i
$$718$$ 0 0
$$719$$ −22.4239 38.8393i −0.836269 1.44846i −0.892993 0.450071i $$-0.851399\pi$$
0.0567236 0.998390i $$-0.481935\pi$$
$$720$$ 0 0
$$721$$ 12.6442 0.470896
$$722$$ 0 0
$$723$$ −37.6209 −1.39914
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −16.2453 28.1376i −0.602504 1.04357i −0.992441 0.122726i $$-0.960836\pi$$
0.389937 0.920842i $$-0.372497\pi$$
$$728$$ 0 0
$$729$$ 12.0273 0.445457
$$730$$ 0 0
$$731$$ −8.65152 + 14.9849i −0.319988 + 0.554235i
$$732$$ 0 0
$$733$$ −11.1969 −0.413568 −0.206784 0.978387i $$-0.566300\pi$$
−0.206784 + 0.978387i $$0.566300\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −2.01501 + 3.49009i −0.0742237 + 0.128559i
$$738$$ 0 0
$$739$$ −0.466361 0.807761i −0.0171554 0.0297140i 0.857320 0.514783i $$-0.172128\pi$$
−0.874476 + 0.485069i $$0.838794\pi$$
$$740$$ 0 0
$$741$$ −14.2109 + 15.9650i −0.522051 + 0.586488i
$$742$$ 0 0
$$743$$ 13.4736 + 23.3370i 0.494300 + 0.856153i 0.999978 0.00656939i $$-0.00209112\pi$$
−0.505678 + 0.862722i $$0.668758\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −2.21409 + 3.83492i −0.0810094 + 0.140312i
$$748$$ 0 0
$$749$$ −17.2210 −0.629240
$$750$$ 0 0
$$751$$ 2.33645 4.04686i 0.0852584 0.147672i −0.820243 0.572015i $$-0.806162\pi$$
0.905501 + 0.424343i $$0.139495\pi$$
$$752$$ 0 0
$$753$$ −8.45971 −0.308289
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 21.4140 + 37.0902i 0.778306 + 1.34807i 0.932918 + 0.360090i $$0.117254\pi$$
−0.154612 + 0.987975i $$0.549413\pi$$
$$758$$ 0 0
$$759$$ 86.2073 3.12913
$$760$$ 0 0
$$761$$ −16.7169 −0.605987 −0.302994 0.952993i $$-0.597986\pi$$
−0.302994 + 0.952993i $$0.597986\pi$$
$$762$$ 0 0
$$763$$ 1.33983 + 2.32065i 0.0485050 + 0.0840131i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0.0857182 0.00309511
$$768$$ 0 0
$$769$$ 7.70852 13.3516i 0.277976 0.481469i −0.692905 0.721029i $$-0.743670\pi$$
0.970882 + 0.239559i $$0.0770029\pi$$
$$770$$ 0 0
$$771$$ 56.7128 2.04246
$$772$$ 0 0
$$773$$ 16.5897 28.7343i 0.596691 1.03350i −0.396615 0.917985i $$-0.629815\pi$$
0.993306 0.115514i $$-0.0368516\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −7.53856 13.0572i −0.270444 0.468423i
$$778$$ 0 0
$$779$$ −23.0813 4.76868i −0.826975 0.170856i
$$780$$ 0 0
$$781$$ 29.8774 + 51.7491i 1.06910 + 1.85173i
$$782$$ 0 0
$$783$$ −4.05980 + 7.03179i −0.145086 + 0.251296i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −12.8318 −0.457405 −0.228702 0.973496i $$-0.573448\pi$$
−0.228702 + 0.973496i $$0.573448\pi$$
$$788$$ 0 0
$$789$$ −2.72657 + 4.72256i −0.0970685 + 0.168128i
$$790$$ 0 0
$$791$$ −11.2179 −0.398862
$$792$$ 0 0
$$793$$ 1.26248 + 2.18667i 0.0448319 + 0.0776511i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −2.28485 −0.0809336 −0.0404668 0.999181i $$-0.512885\pi$$
−0.0404668 + 0.999181i $$0.512885\pi$$
$$798$$ 0 0
$$799$$ −4.44028 −0.157086