# Properties

 Label 448.2.p.a.383.1 Level $448$ Weight $2$ Character 448.383 Analytic conductor $3.577$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$448 = 2^{6} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 448.p (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.57729801055$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 112) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 383.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 448.383 Dual form 448.2.p.a.255.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{3} +(-1.50000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 + 0.866025i) q^{11} +1.73205i q^{15} +(-4.50000 + 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(2.50000 + 0.866025i) q^{21} +(-7.50000 - 4.33013i) q^{23} +(-1.00000 - 1.73205i) q^{25} -5.00000 q^{27} +6.00000 q^{29} +(2.50000 + 4.33013i) q^{31} +(1.50000 + 0.866025i) q^{33} +(4.50000 - 0.866025i) q^{35} +(-2.50000 + 4.33013i) q^{37} +6.92820i q^{41} -3.46410i q^{43} +(-3.00000 + 1.73205i) q^{45} +(1.50000 - 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +(4.50000 + 2.59808i) q^{51} +(-4.50000 - 7.79423i) q^{53} +3.00000 q^{55} +7.00000 q^{57} +(-4.50000 - 7.79423i) q^{59} +(-7.50000 - 4.33013i) q^{61} +(1.00000 + 5.19615i) q^{63} +(4.50000 - 2.59808i) q^{67} +8.66025i q^{69} -3.46410i q^{71} +(1.50000 - 0.866025i) q^{73} +(-1.00000 + 1.73205i) q^{75} +(1.50000 - 4.33013i) q^{77} +(4.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(-3.00000 - 5.19615i) q^{87} +(-10.5000 - 6.06218i) q^{89} +(2.50000 - 4.33013i) q^{93} +(10.5000 - 6.06218i) q^{95} +6.92820i q^{97} +3.46410i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} - 3q^{5} - 4q^{7} + 2q^{9} + O(q^{10})$$ $$2q - q^{3} - 3q^{5} - 4q^{7} + 2q^{9} - 3q^{11} - 9q^{17} - 7q^{19} + 5q^{21} - 15q^{23} - 2q^{25} - 10q^{27} + 12q^{29} + 5q^{31} + 3q^{33} + 9q^{35} - 5q^{37} - 6q^{45} + 3q^{47} + 2q^{49} + 9q^{51} - 9q^{53} + 6q^{55} + 14q^{57} - 9q^{59} - 15q^{61} + 2q^{63} + 9q^{67} + 3q^{73} - 2q^{75} + 3q^{77} + 9q^{79} - q^{81} + 24q^{83} + 18q^{85} - 6q^{87} - 21q^{89} + 5q^{93} + 21q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$129$$ $$197$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$

## 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
$$3$$ −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i $$-0.259881\pi$$
−0.973494 + 0.228714i $$0.926548\pi$$
$$4$$ 0 0
$$5$$ −1.50000 0.866025i −0.670820 0.387298i 0.125567 0.992085i $$-0.459925\pi$$
−0.796387 + 0.604787i $$0.793258\pi$$
$$6$$ 0 0
$$7$$ −2.00000 + 1.73205i −0.755929 + 0.654654i
$$8$$ 0 0
$$9$$ 1.00000 1.73205i 0.333333 0.577350i
$$10$$ 0 0
$$11$$ −1.50000 + 0.866025i −0.452267 + 0.261116i −0.708787 0.705422i $$-0.750757\pi$$
0.256520 + 0.966539i $$0.417424\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 1.73205i 0.447214i
$$16$$ 0 0
$$17$$ −4.50000 + 2.59808i −1.09141 + 0.630126i −0.933952 0.357400i $$-0.883663\pi$$
−0.157459 + 0.987526i $$0.550330\pi$$
$$18$$ 0 0
$$19$$ −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i $$0.463407\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ 2.50000 + 0.866025i 0.545545 + 0.188982i
$$22$$ 0 0
$$23$$ −7.50000 4.33013i −1.56386 0.902894i −0.996861 0.0791743i $$-0.974772\pi$$
−0.566997 0.823720i $$1.30810\pi$$
$$24$$ 0 0
$$25$$ −1.00000 1.73205i −0.200000 0.346410i
$$26$$ 0 0
$$27$$ −5.00000 −0.962250
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ 2.50000 + 4.33013i 0.449013 + 0.777714i 0.998322 0.0579057i $$-0.0184423\pi$$
−0.549309 + 0.835619i $$0.685109\pi$$
$$32$$ 0 0
$$33$$ 1.50000 + 0.866025i 0.261116 + 0.150756i
$$34$$ 0 0
$$35$$ 4.50000 0.866025i 0.760639 0.146385i
$$36$$ 0 0
$$37$$ −2.50000 + 4.33013i −0.410997 + 0.711868i −0.994999 0.0998840i $$-0.968153\pi$$
0.584002 + 0.811752i $$0.301486\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 6.92820i 1.08200i 0.841021 + 0.541002i $$0.181955\pi$$
−0.841021 + 0.541002i $$0.818045\pi$$
$$42$$ 0 0
$$43$$ 3.46410i 0.528271i −0.964486 0.264135i $$-0.914913\pi$$
0.964486 0.264135i $$-0.0850865\pi$$
$$44$$ 0 0
$$45$$ −3.00000 + 1.73205i −0.447214 + 0.258199i
$$46$$ 0 0
$$47$$ 1.50000 2.59808i 0.218797 0.378968i −0.735643 0.677369i $$-0.763120\pi$$
0.954441 + 0.298401i $$0.0964533\pi$$
$$48$$ 0 0
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ 0 0
$$51$$ 4.50000 + 2.59808i 0.630126 + 0.363803i
$$52$$ 0 0
$$53$$ −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i $$-0.954560\pi$$
0.371706 0.928351i $$-0.378773\pi$$
$$54$$ 0 0
$$55$$ 3.00000 0.404520
$$56$$ 0 0
$$57$$ 7.00000 0.927173
$$58$$ 0 0
$$59$$ −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i $$-0.967427\pi$$
0.408919 0.912571i $$1.63409\pi$$
$$60$$ 0 0
$$61$$ −7.50000 4.33013i −0.960277 0.554416i −0.0640184 0.997949i $$-0.520392\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 0 0
$$63$$ 1.00000 + 5.19615i 0.125988 + 0.654654i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 4.50000 2.59808i 0.549762 0.317406i −0.199264 0.979946i $$-0.563855\pi$$
0.749026 + 0.662540i $$0.230522\pi$$
$$68$$ 0 0
$$69$$ 8.66025i 1.04257i
$$70$$ 0 0
$$71$$ 3.46410i 0.411113i −0.978645 0.205557i $$-0.934100\pi$$
0.978645 0.205557i $$-0.0659005\pi$$
$$72$$ 0 0
$$73$$ 1.50000 0.866025i 0.175562 0.101361i −0.409644 0.912245i $$-0.634347\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ 0 0
$$75$$ −1.00000 + 1.73205i −0.115470 + 0.200000i
$$76$$ 0 0
$$77$$ 1.50000 4.33013i 0.170941 0.493464i
$$78$$ 0 0
$$79$$ 4.50000 + 2.59808i 0.506290 + 0.292306i 0.731307 0.682048i $$-0.238911\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 9.00000 0.976187
$$86$$ 0 0
$$87$$ −3.00000 5.19615i −0.321634 0.557086i
$$88$$ 0 0
$$89$$ −10.5000 6.06218i −1.11300 0.642590i −0.173394 0.984853i $$-0.555473\pi$$
−0.939604 + 0.342263i $$0.888807\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 2.50000 4.33013i 0.259238 0.449013i
$$94$$ 0 0
$$95$$ 10.5000 6.06218i 1.07728 0.621966i
$$96$$ 0 0
$$97$$ 6.92820i 0.703452i 0.936103 + 0.351726i $$0.114405\pi$$
−0.936103 + 0.351726i $$0.885595\pi$$
$$98$$ 0 0
$$99$$ 3.46410i 0.348155i
$$100$$ 0 0
$$101$$ 4.50000 2.59808i 0.447767 0.258518i −0.259120 0.965845i $$-0.583432\pi$$
0.706887 + 0.707327i $$0.250099\pi$$
$$102$$ 0 0
$$103$$ −0.500000 + 0.866025i −0.0492665 + 0.0853320i −0.889607 0.456727i $$-0.849022\pi$$
0.840341 + 0.542059i $$0.182355\pi$$
$$104$$ 0 0
$$105$$ −3.00000 3.46410i −0.292770 0.338062i
$$106$$ 0 0
$$107$$ −4.50000 2.59808i −0.435031 0.251166i 0.266456 0.963847i $$-0.414147\pi$$
−0.701488 + 0.712681i $$0.747481\pi$$
$$108$$ 0 0
$$109$$ 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i $$0.00994332\pi$$
−0.472708 + 0.881219i $$0.656723\pi$$
$$110$$ 0 0
$$111$$ 5.00000 0.474579
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 7.50000 + 12.9904i 0.699379 + 1.21136i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 4.50000 12.9904i 0.412514 1.19083i
$$120$$ 0 0
$$121$$ −4.00000 + 6.92820i −0.363636 + 0.629837i
$$122$$ 0 0
$$123$$ 6.00000 3.46410i 0.541002 0.312348i
$$124$$ 0 0
$$125$$ 12.1244i 1.08444i
$$126$$ 0 0
$$127$$ 3.46410i 0.307389i −0.988118 0.153695i $$-0.950883\pi$$
0.988118 0.153695i $$-0.0491172\pi$$
$$128$$ 0 0
$$129$$ −3.00000 + 1.73205i −0.264135 + 0.152499i
$$130$$ 0 0
$$131$$ 10.5000 18.1865i 0.917389 1.58896i 0.114024 0.993478i $$-0.463626\pi$$
0.803365 0.595487i $$-0.203041\pi$$
$$132$$ 0 0
$$133$$ −3.50000 18.1865i −0.303488 1.57697i
$$134$$ 0 0
$$135$$ 7.50000 + 4.33013i 0.645497 + 0.372678i
$$136$$ 0 0
$$137$$ −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i $$-0.207572\pi$$
−0.922961 + 0.384893i $$0.874238\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ −3.00000 −0.252646
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −9.00000 5.19615i −0.747409 0.431517i
$$146$$ 0 0
$$147$$ −6.50000 + 2.59808i −0.536111 + 0.214286i
$$148$$ 0 0
$$149$$ −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i $$-0.953515\pi$$
0.620701 + 0.784047i $$0.286848\pi$$
$$150$$ 0 0
$$151$$ −10.5000 + 6.06218i −0.854478 + 0.493333i −0.862159 0.506637i $$-0.830888\pi$$
0.00768132 + 0.999970i $$0.497555\pi$$
$$152$$ 0 0
$$153$$ 10.3923i 0.840168i
$$154$$ 0 0
$$155$$ 8.66025i 0.695608i
$$156$$ 0 0
$$157$$ −13.5000 + 7.79423i −1.07742 + 0.622047i −0.930199 0.367057i $$-0.880365\pi$$
−0.147219 + 0.989104i $$0.547032\pi$$
$$158$$ 0 0
$$159$$ −4.50000 + 7.79423i −0.356873 + 0.618123i
$$160$$ 0 0
$$161$$ 22.5000 4.33013i 1.77325 0.341262i
$$162$$ 0 0
$$163$$ −10.5000 6.06218i −0.822423 0.474826i 0.0288280 0.999584i $$-0.490822\pi$$
−0.851251 + 0.524758i $$0.824156\pi$$
$$164$$ 0 0
$$165$$ −1.50000 2.59808i −0.116775 0.202260i
$$166$$ 0 0
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 7.00000 + 12.1244i 0.535303 + 0.927173i
$$172$$ 0 0
$$173$$ −7.50000 4.33013i −0.570214 0.329213i 0.187021 0.982356i $$-0.440117\pi$$
−0.757235 + 0.653143i $$0.773450\pi$$
$$174$$ 0 0
$$175$$ 5.00000 + 1.73205i 0.377964 + 0.130931i
$$176$$ 0 0
$$177$$ −4.50000 + 7.79423i −0.338241 + 0.585850i
$$178$$ 0 0
$$179$$ −13.5000 + 7.79423i −1.00904 + 0.582568i −0.910910 0.412606i $$-0.864619\pi$$
−0.0981277 + 0.995174i $$0.531285\pi$$
$$180$$ 0 0
$$181$$ 6.92820i 0.514969i 0.966282 + 0.257485i $$0.0828937\pi$$
−0.966282 + 0.257485i $$0.917106\pi$$
$$182$$ 0 0
$$183$$ 8.66025i 0.640184i
$$184$$ 0 0
$$185$$ 7.50000 4.33013i 0.551411 0.318357i
$$186$$ 0 0
$$187$$ 4.50000 7.79423i 0.329073 0.569970i
$$188$$ 0 0
$$189$$ 10.0000 8.66025i 0.727393 0.629941i
$$190$$ 0 0
$$191$$ 10.5000 + 6.06218i 0.759753 + 0.438644i 0.829207 0.558941i $$-0.188792\pi$$
−0.0694538 + 0.997585i $$0.522126\pi$$
$$192$$ 0 0
$$193$$ 2.50000 + 4.33013i 0.179954 + 0.311689i 0.941865 0.335993i $$-0.109072\pi$$
−0.761911 + 0.647682i $$0.775738\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ 0 0
$$199$$ −5.50000 9.52628i −0.389885 0.675300i 0.602549 0.798082i $$-0.294152\pi$$
−0.992434 + 0.122782i $$0.960818\pi$$
$$200$$ 0 0
$$201$$ −4.50000 2.59808i −0.317406 0.183254i
$$202$$ 0 0
$$203$$ −12.0000 + 10.3923i −0.842235 + 0.729397i
$$204$$ 0 0
$$205$$ 6.00000 10.3923i 0.419058 0.725830i
$$206$$ 0 0
$$207$$ −15.0000 + 8.66025i −1.04257 + 0.601929i
$$208$$ 0 0
$$209$$ 12.1244i 0.838659i
$$210$$ 0 0
$$211$$ 24.2487i 1.66935i 0.550743 + 0.834675i $$0.314345\pi$$
−0.550743 + 0.834675i $$0.685655\pi$$
$$212$$ 0 0
$$213$$ −3.00000 + 1.73205i −0.205557 + 0.118678i
$$214$$ 0 0
$$215$$ −3.00000 + 5.19615i −0.204598 + 0.354375i
$$216$$ 0 0
$$217$$ −12.5000 4.33013i −0.848555 0.293948i
$$218$$ 0 0
$$219$$ −1.50000 0.866025i −0.101361 0.0585206i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ 0 0
$$225$$ −4.00000 −0.266667
$$226$$ 0 0
$$227$$ −10.5000 18.1865i −0.696909 1.20708i −0.969533 0.244962i $$-0.921225\pi$$
0.272623 0.962121i $$1.58789\pi$$
$$228$$ 0 0
$$229$$ 10.5000 + 6.06218i 0.693860 + 0.400600i 0.805056 0.593198i $$-0.202135\pi$$
−0.111197 + 0.993798i $$0.535468\pi$$
$$230$$ 0 0
$$231$$ −4.50000 + 0.866025i −0.296078 + 0.0569803i
$$232$$ 0 0
$$233$$ −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i $$-0.864664\pi$$
0.812700 + 0.582683i $$0.197997\pi$$
$$234$$ 0 0
$$235$$ −4.50000 + 2.59808i −0.293548 + 0.169480i
$$236$$ 0 0
$$237$$ 5.19615i 0.337526i
$$238$$ 0 0
$$239$$ 10.3923i 0.672222i −0.941822 0.336111i $$-0.890888\pi$$
0.941822 0.336111i $$-0.109112\pi$$
$$240$$ 0 0
$$241$$ −10.5000 + 6.06218i −0.676364 + 0.390499i −0.798484 0.602016i $$-0.794364\pi$$
0.122119 + 0.992515i $$0.461031\pi$$
$$242$$ 0 0
$$243$$ −8.00000 + 13.8564i −0.513200 + 0.888889i
$$244$$ 0 0
$$245$$ −7.50000 + 9.52628i −0.479157 + 0.608612i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −6.00000 10.3923i −0.380235 0.658586i
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 15.0000 0.943042
$$254$$ 0 0
$$255$$ −4.50000 7.79423i −0.281801 0.488094i
$$256$$ 0 0
$$257$$ −16.5000 9.52628i −1.02924 0.594233i −0.112474 0.993655i $$-0.535878\pi$$
−0.916767 + 0.399422i $$0.869211\pi$$
$$258$$ 0 0
$$259$$ −2.50000 12.9904i −0.155342 0.807183i
$$260$$ 0 0
$$261$$ 6.00000 10.3923i 0.371391 0.643268i
$$262$$ 0 0
$$263$$ 7.50000 4.33013i 0.462470 0.267007i −0.250612 0.968088i $$-0.580632\pi$$
0.713082 + 0.701080i $$0.247299\pi$$
$$264$$ 0 0
$$265$$ 15.5885i 0.957591i
$$266$$ 0 0
$$267$$ 12.1244i 0.741999i
$$268$$ 0 0
$$269$$ −1.50000 + 0.866025i −0.0914566 + 0.0528025i −0.545031 0.838416i $$-0.683482\pi$$
0.453574 + 0.891219i $$0.350149\pi$$
$$270$$ 0 0
$$271$$ −0.500000 + 0.866025i −0.0303728 + 0.0526073i −0.880812 0.473466i $$-0.843003\pi$$
0.850439 + 0.526073i $$0.176336\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 3.00000 + 1.73205i 0.180907 + 0.104447i
$$276$$ 0 0
$$277$$ −8.50000 14.7224i −0.510716 0.884585i −0.999923 0.0124177i $$-0.996047\pi$$
0.489207 0.872167i $$-0.337286\pi$$
$$278$$ 0 0
$$279$$ 10.0000 0.598684
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 5.50000 + 9.52628i 0.326941 + 0.566279i 0.981903 0.189383i $$-0.0606488\pi$$
−0.654962 + 0.755662i $$0.727315\pi$$
$$284$$ 0 0
$$285$$ −10.5000 6.06218i −0.621966 0.359092i
$$286$$ 0 0
$$287$$ −12.0000 13.8564i −0.708338 0.817918i
$$288$$ 0 0
$$289$$ 5.00000 8.66025i 0.294118 0.509427i
$$290$$ 0 0
$$291$$ 6.00000 3.46410i 0.351726 0.203069i
$$292$$ 0 0
$$293$$ 20.7846i 1.21425i 0.794606 + 0.607125i $$0.207677\pi$$
−0.794606 + 0.607125i $$0.792323\pi$$
$$294$$ 0 0
$$295$$ 15.5885i 0.907595i
$$296$$ 0 0
$$297$$ 7.50000 4.33013i 0.435194 0.251259i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 6.00000 + 6.92820i 0.345834 + 0.399335i
$$302$$ 0 0
$$303$$ −4.50000 2.59808i −0.258518 0.149256i
$$304$$ 0 0
$$305$$ 7.50000 + 12.9904i 0.429449 + 0.743827i
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ 1.00000 0.0568880
$$310$$ 0 0
$$311$$ 16.5000 + 28.5788i 0.935629 + 1.62056i 0.773508 + 0.633786i $$0.218500\pi$$
0.162121 + 0.986771i $$0.448167\pi$$
$$312$$ 0 0
$$313$$ 25.5000 + 14.7224i 1.44135 + 0.832161i 0.997940 0.0641600i $$-0.0204368\pi$$
0.443406 + 0.896321i $$0.353770\pi$$
$$314$$ 0 0
$$315$$ 3.00000 8.66025i 0.169031 0.487950i
$$316$$ 0 0
$$317$$ −10.5000 + 18.1865i −0.589739 + 1.02146i 0.404528 + 0.914526i $$0.367436\pi$$
−0.994266 + 0.106932i $$0.965897\pi$$
$$318$$ 0 0
$$319$$ −9.00000 + 5.19615i −0.503903 + 0.290929i
$$320$$ 0 0
$$321$$ 5.19615i 0.290021i
$$322$$ 0 0
$$323$$ 36.3731i 2.02385i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 5.50000 9.52628i 0.304151 0.526804i
$$328$$ 0 0
$$329$$ 1.50000 + 7.79423i 0.0826977 + 0.429710i
$$330$$ 0 0
$$331$$ 25.5000 + 14.7224i 1.40161 + 0.809218i 0.994558 0.104188i $$-0.0332244\pi$$
0.407049 + 0.913406i $$0.366558\pi$$
$$332$$ 0 0
$$333$$ 5.00000 + 8.66025i 0.273998 + 0.474579i
$$334$$ 0 0
$$335$$ −9.00000 −0.491723
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 0 0
$$339$$ −3.00000 5.19615i −0.162938 0.282216i
$$340$$ 0 0
$$341$$ −7.50000 4.33013i −0.406148 0.234490i
$$342$$ 0 0
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ 7.50000 12.9904i 0.403786 0.699379i
$$346$$ 0 0
$$347$$ −7.50000 + 4.33013i −0.402621 + 0.232453i −0.687614 0.726076i $$-0.741342\pi$$
0.284993 + 0.958530i $$0.408009\pi$$
$$348$$ 0 0
$$349$$ 27.7128i 1.48343i −0.670714 0.741716i $$-0.734012\pi$$
0.670714 0.741716i $$-0.265988\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −16.5000 + 9.52628i −0.878206 + 0.507033i −0.870067 0.492934i $$-0.835924\pi$$
−0.00813978 + 0.999967i $$0.502591\pi$$
$$354$$ 0 0
$$355$$ −3.00000 + 5.19615i −0.159223 + 0.275783i
$$356$$ 0 0
$$357$$ −13.5000 + 2.59808i −0.714496 + 0.137505i
$$358$$ 0 0
$$359$$ −13.5000 7.79423i −0.712503 0.411364i 0.0994843 0.995039i $$-0.468281\pi$$
−0.811987 + 0.583675i $$0.801614\pi$$
$$360$$ 0 0
$$361$$ −15.0000 25.9808i −0.789474 1.36741i
$$362$$ 0 0
$$363$$ 8.00000 0.419891
$$364$$ 0 0
$$365$$ −3.00000 −0.157027
$$366$$ 0 0
$$367$$ 0.500000 + 0.866025i 0.0260998 + 0.0452062i 0.878780 0.477227i $$-0.158358\pi$$
−0.852680 + 0.522433i $$0.825025\pi$$
$$368$$ 0 0
$$369$$ 12.0000 + 6.92820i 0.624695 + 0.360668i
$$370$$ 0 0
$$371$$ 22.5000 + 7.79423i 1.16814 + 0.404656i
$$372$$ 0 0
$$373$$ −6.50000 + 11.2583i −0.336557 + 0.582934i −0.983783 0.179364i $$-0.942596\pi$$
0.647225 + 0.762299i $$0.275929\pi$$
$$374$$ 0 0
$$375$$ 10.5000 6.06218i 0.542218 0.313050i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 10.3923i 0.533817i −0.963722 0.266908i $$-0.913998\pi$$
0.963722 0.266908i $$-0.0860021\pi$$
$$380$$ 0 0
$$381$$ −3.00000 + 1.73205i −0.153695 + 0.0887357i
$$382$$ 0 0
$$383$$ 13.5000 23.3827i 0.689818 1.19480i −0.282079 0.959391i $$-0.591024\pi$$
0.971897 0.235408i $$-0.0756427\pi$$
$$384$$ 0 0
$$385$$ −6.00000 + 5.19615i −0.305788 + 0.264820i
$$386$$ 0 0
$$387$$ −6.00000 3.46410i −0.304997 0.176090i
$$388$$ 0 0
$$389$$ −10.5000 18.1865i −0.532371 0.922094i −0.999286 0.0377914i $$-0.987968\pi$$
0.466915 0.884302i $$-0.345366\pi$$
$$390$$ 0 0
$$391$$ 45.0000 2.27575
$$392$$ 0 0
$$393$$ −21.0000 −1.05931
$$394$$ 0 0
$$395$$ −4.50000 7.79423i −0.226420 0.392170i
$$396$$ 0 0
$$397$$ 10.5000 + 6.06218i 0.526980 + 0.304252i 0.739786 0.672843i $$-0.234927\pi$$
−0.212806 + 0.977095i $$0.568260\pi$$
$$398$$ 0 0
$$399$$ −14.0000 + 12.1244i −0.700877 + 0.606977i
$$400$$ 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
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 1.73205i 0.0860663i
$$406$$ 0 0
$$407$$ 8.66025i 0.429273i
$$408$$ 0 0
$$409$$ −4.50000 + 2.59808i −0.222511 + 0.128467i −0.607112 0.794616i $$-0.707672\pi$$
0.384602 + 0.923083i $$0.374339\pi$$
$$410$$ 0 0
$$411$$ −1.50000 + 2.59808i −0.0739895 + 0.128154i
$$412$$ 0 0
$$413$$ 22.5000 + 7.79423i 1.10715 + 0.383529i
$$414$$ 0 0
$$415$$ −18.0000 10.3923i −0.883585 0.510138i
$$416$$ 0 0
$$417$$ 2.00000 + 3.46410i 0.0979404 + 0.169638i
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −10.0000 −0.487370 −0.243685 0.969854i $$-0.578356\pi$$
−0.243685 + 0.969854i $$0.578356\pi$$
$$422$$ 0 0
$$423$$ −3.00000 5.19615i −0.145865 0.252646i
$$424$$ 0 0
$$425$$ 9.00000 + 5.19615i 0.436564 + 0.252050i
$$426$$ 0 0
$$427$$ 22.5000 4.33013i 1.08885 0.209550i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 25.5000 14.7224i 1.22829 0.709155i 0.261619 0.965171i $$-0.415743\pi$$
0.966672 + 0.256017i $$0.0824102\pi$$
$$432$$ 0 0
$$433$$ 34.6410i 1.66474i −0.554220 0.832370i $$-0.686983\pi$$
0.554220 0.832370i $$-0.313017\pi$$
$$434$$ 0 0
$$435$$ 10.3923i 0.498273i
$$436$$ 0 0
$$437$$ 52.5000 30.3109i 2.51142 1.44997i
$$438$$ 0 0
$$439$$ 9.50000 16.4545i 0.453410 0.785330i −0.545185 0.838316i $$-0.683541\pi$$
0.998595 + 0.0529862i $$0.0168739\pi$$
$$440$$ 0 0
$$441$$ −11.0000 8.66025i −0.523810 0.412393i
$$442$$ 0 0
$$443$$ 19.5000 + 11.2583i 0.926473 + 0.534899i 0.885694 0.464269i $$-0.153683\pi$$
0.0407786 + 0.999168i $$0.487016\pi$$
$$444$$ 0 0
$$445$$ 10.5000 + 18.1865i 0.497748 + 0.862124i
$$446$$ 0 0
$$447$$ 9.00000 0.425685
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ −6.00000 10.3923i −0.282529 0.489355i
$$452$$ 0 0
$$453$$ 10.5000 + 6.06218i 0.493333 + 0.284826i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i $$-0.825888\pi$$
0.877483 + 0.479608i $$0.159221\pi$$
$$458$$ 0 0
$$459$$ 22.5000 12.9904i 1.05021 0.606339i
$$460$$ 0 0
$$461$$ 27.7128i 1.29071i −0.763881 0.645357i $$-0.776709\pi$$
0.763881 0.645357i $$-0.223291\pi$$
$$462$$ 0 0
$$463$$ 3.46410i 0.160990i −0.996755 0.0804952i $$-0.974350\pi$$
0.996755 0.0804952i $$-0.0256502\pi$$
$$464$$ 0 0
$$465$$ −7.50000 + 4.33013i −0.347804 + 0.200805i
$$466$$ 0 0
$$467$$ −1.50000 + 2.59808i −0.0694117 + 0.120225i −0.898642 0.438682i $$-0.855446\pi$$
0.829231 + 0.558906i $$0.188779\pi$$
$$468$$ 0 0
$$469$$ −4.50000 + 12.9904i −0.207791 + 0.599840i
$$470$$ 0 0
$$471$$ 13.5000 + 7.79423i 0.622047 + 0.359139i
$$472$$ 0 0
$$473$$ 3.00000 + 5.19615i 0.137940 + 0.238919i
$$474$$ 0 0
$$475$$ 14.0000 0.642364
$$476$$ 0 0
$$477$$ −18.0000 −0.824163
$$478$$ 0 0
$$479$$ 4.50000 + 7.79423i 0.205610 + 0.356127i 0.950327 0.311253i $$-0.100749\pi$$
−0.744717 + 0.667381i $$0.767415\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ −15.0000 17.3205i −0.682524 0.788110i
$$484$$ 0 0
$$485$$ 6.00000 10.3923i 0.272446 0.471890i
$$486$$ 0 0
$$487$$ 7.50000 4.33013i 0.339857 0.196217i −0.320352 0.947299i $$-0.603801\pi$$
0.660209 + 0.751082i $$0.270468\pi$$
$$488$$ 0 0
$$489$$ 12.1244i 0.548282i
$$490$$ 0 0
$$491$$ 17.3205i 0.781664i 0.920462 + 0.390832i $$0.127813\pi$$
−0.920462 + 0.390832i $$0.872187\pi$$
$$492$$ 0 0
$$493$$ −27.0000 + 15.5885i −1.21602 + 0.702069i
$$494$$ 0 0
$$495$$ 3.00000 5.19615i 0.134840 0.233550i
$$496$$ 0 0
$$497$$ 6.00000 + 6.92820i 0.269137 + 0.310772i
$$498$$ 0 0
$$499$$ −10.5000 6.06218i −0.470045 0.271380i 0.246214 0.969216i $$-0.420813\pi$$
−0.716258 + 0.697835i $$0.754147\pi$$
$$500$$ 0 0
$$501$$ 6.00000 + 10.3923i 0.268060 + 0.464294i
$$502$$ 0 0
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ −9.00000 −0.400495
$$506$$ 0 0
$$507$$ −6.50000 11.2583i −0.288675 0.500000i
$$508$$ 0 0
$$509$$ −13.5000 7.79423i −0.598377 0.345473i 0.170026 0.985440i $$-0.445615\pi$$
−0.768403 + 0.639966i $$0.778948\pi$$
$$510$$ 0 0
$$511$$ −1.50000 + 4.33013i −0.0663561 + 0.191554i
$$512$$ 0 0
$$513$$ 17.5000 30.3109i 0.772644 1.33826i
$$514$$ 0 0
$$515$$ 1.50000 0.866025i 0.0660979 0.0381616i
$$516$$ 0 0
$$517$$ 5.19615i 0.228527i
$$518$$ 0 0
$$519$$ 8.66025i 0.380143i
$$520$$ 0 0
$$521$$ 25.5000 14.7224i 1.11718 0.645001i 0.176497 0.984301i $$-0.443523\pi$$
0.940678 + 0.339300i $$0.110190\pi$$
$$522$$ 0 0
$$523$$ −11.5000 + 19.9186i −0.502860 + 0.870979i 0.497135 + 0.867673i $$0.334385\pi$$
−0.999995 + 0.00330547i $$0.998948\pi$$
$$524$$ 0 0
$$525$$ −1.00000 5.19615i −0.0436436 0.226779i
$$526$$ 0 0
$$527$$ −22.5000 12.9904i −0.980115 0.565870i
$$528$$ 0 0
$$529$$ 26.0000 + 45.0333i 1.13043 + 1.95797i
$$530$$ 0 0
$$531$$ −18.0000 −0.781133
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 4.50000 + 7.79423i 0.194552 + 0.336974i
$$536$$ 0 0
$$537$$ 13.5000 + 7.79423i 0.582568 + 0.336346i
$$538$$ 0 0
$$539$$ 4.50000 + 11.2583i 0.193829 + 0.484931i
$$540$$ 0 0
$$541$$ 3.50000 6.06218i 0.150477 0.260633i −0.780926 0.624623i $$-0.785252\pi$$
0.931403 + 0.363990i $$0.118586\pi$$
$$542$$ 0 0
$$543$$ 6.00000 3.46410i 0.257485 0.148659i
$$544$$ 0 0
$$545$$ 19.0526i 0.816122i
$$546$$ 0 0
$$547$$ 24.2487i 1.03680i −0.855138 0.518400i $$-0.826528\pi$$
0.855138 0.518400i $$-0.173472\pi$$
$$548$$ 0 0
$$549$$ −15.0000 + 8.66025i −0.640184 + 0.369611i
$$550$$ 0 0
$$551$$ −21.0000 + 36.3731i −0.894630 + 1.54954i
$$552$$ 0 0
$$553$$ −13.5000 + 2.59808i −0.574078 + 0.110481i
$$554$$ 0 0
$$555$$ −7.50000 4.33013i −0.318357 0.183804i
$$556$$ 0 0
$$557$$ 1.50000 + 2.59808i 0.0635570 + 0.110084i 0.896053 0.443947i $$-0.146422\pi$$
−0.832496 + 0.554031i $$0.813089\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −9.00000 −0.379980
$$562$$ 0 0
$$563$$ 7.50000 + 12.9904i 0.316087 + 0.547479i 0.979668 0.200625i $$-0.0642974\pi$$
−0.663581 + 0.748105i $$0.730964\pi$$
$$564$$ 0 0
$$565$$ −9.00000 5.19615i −0.378633 0.218604i
$$566$$ 0 0
$$567$$ 2.50000 + 0.866025i 0.104990 + 0.0363696i
$$568$$ 0 0
$$569$$ −19.5000 + 33.7750i −0.817483 + 1.41592i 0.0900490 + 0.995937i $$0.471298\pi$$
−0.907532 + 0.419984i $$0.862036\pi$$
$$570$$ 0 0
$$571$$ 10.5000 6.06218i 0.439411 0.253694i −0.263937 0.964540i $$-0.585021\pi$$
0.703348 + 0.710846i $$0.251688\pi$$
$$572$$ 0 0
$$573$$ 12.1244i 0.506502i
$$574$$ 0 0
$$575$$ 17.3205i 0.722315i
$$576$$ 0 0
$$577$$ 13.5000 7.79423i 0.562012 0.324478i −0.191940 0.981407i $$-0.561478\pi$$
0.753953 + 0.656929i $$0.228145\pi$$
$$578$$ 0 0
$$579$$ 2.50000 4.33013i 0.103896 0.179954i
$$580$$ 0 0
$$581$$ −24.0000 + 20.7846i −0.995688 + 0.862291i
$$582$$ 0 0
$$583$$ 13.5000 + 7.79423i 0.559113 + 0.322804i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ −35.0000 −1.44215
$$590$$ 0 0
$$591$$ −3.00000 5.19615i −0.123404 0.213741i
$$592$$ 0 0
$$593$$ −16.5000 9.52628i −0.677574 0.391197i 0.121367 0.992608i $$-0.461272\pi$$
−0.798940 + 0.601410i $$0.794606\pi$$
$$594$$ 0 0
$$595$$ −18.0000 + 15.5885i −0.737928 + 0.639064i
$$596$$ 0 0
$$597$$ −5.50000 + 9.52628i −0.225100 + 0.389885i
$$598$$ 0 0
$$599$$ −28.5000 + 16.4545i −1.16448 + 0.672312i −0.952373 0.304935i $$-0.901365\pi$$
−0.212105 + 0.977247i $$0.568032\pi$$
$$600$$ 0 0
$$601$$ 6.92820i 0.282607i −0.989966 0.141304i $$-0.954871\pi$$
0.989966 0.141304i $$-0.0451294\pi$$
$$602$$ 0 0
$$603$$ 10.3923i 0.423207i
$$604$$ 0 0
$$605$$ 12.0000 6.92820i 0.487869 0.281672i
$$606$$ 0 0
$$607$$ −14.5000 + 25.1147i −0.588537 + 1.01938i 0.405887 + 0.913923i $$0.366962\pi$$
−0.994424 + 0.105453i $$0.966371\pi$$
$$608$$ 0 0
$$609$$ 15.0000 + 5.19615i 0.607831 + 0.210559i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 5.50000 + 9.52628i 0.222143 + 0.384763i 0.955458 0.295126i $$-0.0953615\pi$$
−0.733316 + 0.679888i $$0.762028\pi$$
$$614$$ 0 0
$$615$$ −12.0000 −0.483887
$$616$$ 0 0
$$617$$ −18.0000 −0.724653 −0.362326 0.932051i $$-0.618017\pi$$
−0.362326 + 0.932051i $$0.618017\pi$$
$$618$$ 0 0
$$619$$ 3.50000 + 6.06218i 0.140677 + 0.243659i 0.927752 0.373198i $$-0.121739\pi$$
−0.787075 + 0.616858i $$0.788405\pi$$
$$620$$ 0 0
$$621$$ 37.5000 + 21.6506i 1.50482 + 0.868810i
$$622$$ 0 0
$$623$$ 31.5000 6.06218i 1.26202 0.242876i
$$624$$ 0 0
$$625$$ 5.50000 9.52628i 0.220000 0.381051i
$$626$$ 0 0
$$627$$ −10.5000 + 6.06218i −0.419330 + 0.242100i
$$628$$ 0 0
$$629$$ 25.9808i 1.03592i
$$630$$ 0 0
$$631$$ 45.0333i 1.79275i −0.443298 0.896374i $$-0.646192\pi$$
0.443298 0.896374i $$-0.353808\pi$$
$$632$$ 0 0
$$633$$ 21.0000 12.1244i 0.834675 0.481900i
$$634$$ 0 0
$$635$$ −3.00000 + 5.19615i −0.119051 + 0.206203i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −6.00000 3.46410i −0.237356 0.137038i
$$640$$ 0 0
$$641$$ 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i $$-0.109788\pi$$
−0.763367 + 0.645966i $$0.776455\pi$$
$$642$$ 0 0
$$643$$ 4.00000 0.157745 0.0788723 0.996885i $$-0.474868\pi$$
0.0788723 + 0.996885i $$0.474868\pi$$
$$644$$ 0 0
$$645$$ 6.00000 0.236250
$$646$$ 0 0
$$647$$ −7.50000 12.9904i −0.294855 0.510705i 0.680096 0.733123i $$-0.261938\pi$$
−0.974951 + 0.222419i $$0.928605\pi$$
$$648$$ 0 0
$$649$$ 13.5000 + 7.79423i 0.529921 + 0.305950i
$$650$$ 0 0
$$651$$ 2.50000 + 12.9904i 0.0979827 + 0.509133i
$$652$$ 0 0
$$653$$ 1.50000 2.59808i 0.0586995 0.101671i −0.835182 0.549973i $$-0.814638\pi$$
0.893882 + 0.448303i $$0.147971\pi$$
$$654$$ 0 0
$$655$$ −31.5000 + 18.1865i −1.23081 + 0.710607i
$$656$$ 0 0
$$657$$ 3.46410i 0.135147i
$$658$$ 0 0
$$659$$ 24.2487i 0.944596i 0.881439 + 0.472298i $$0.156575\pi$$
−0.881439 + 0.472298i $$0.843425\pi$$
$$660$$ 0 0
$$661$$ 34.5000 19.9186i 1.34189 0.774743i 0.354809 0.934939i $$-0.384546\pi$$
0.987085 + 0.160196i $$0.0512125\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −10.5000 + 30.3109i −0.407173 + 1.17541i
$$666$$ 0 0
$$667$$ −45.0000 25.9808i −1.74241 1.00598i
$$668$$ 0 0
$$669$$ 8.00000 + 13.8564i 0.309298 + 0.535720i
$$670$$ 0 0
$$671$$ 15.0000 0.579069
$$672$$ 0 0
$$673$$ −50.0000 −1.92736 −0.963679 0.267063i $$-0.913947\pi$$
−0.963679 + 0.267063i $$0.913947\pi$$
$$674$$ 0 0
$$675$$ 5.00000 + 8.66025i 0.192450 + 0.333333i
$$676$$ 0 0
$$677$$ 34.5000 + 19.9186i 1.32594 + 0.765533i 0.984669 0.174431i $$-0.0558085\pi$$
0.341273 + 0.939964i $$0.389142\pi$$
$$678$$ 0 0
$$679$$ −12.0000 13.8564i −0.460518 0.531760i
$$680$$ 0 0
$$681$$ −10.5000 + 18.1865i −0.402361 + 0.696909i
$$682$$ 0 0
$$683$$ −37.5000 + 21.6506i −1.43490 + 0.828439i −0.997489 0.0708242i $$-0.977437\pi$$
−0.437409 + 0.899263i $$0.644104\pi$$
$$684$$ 0 0
$$685$$ 5.19615i 0.198535i
$$686$$ 0 0
$$687$$ 12.1244i 0.462573i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 6.50000 11.2583i 0.247272 0.428287i −0.715496 0.698617i $$-0.753799\pi$$
0.962768 + 0.270330i $$0.0871327\pi$$
$$692$$ 0 0
$$693$$ −6.00000 6.92820i −0.227921 0.263181i
$$694$$ 0 0
$$695$$ 6.00000 + 3.46410i 0.227593 + 0.131401i
$$696$$ 0 0
$$697$$ −18.0000 31.1769i −0.681799 1.18091i
$$698$$ 0 0
$$699$$ 3.00000 0.113470
$$700$$ 0 0
$$701$$ −30.0000 −1.13308 −0.566542 0.824033i $$-0.691719\pi$$
−0.566542 + 0.824033i $$0.691719\pi$$
$$702$$ 0 0
$$703$$ −17.5000 30.3109i −0.660025 1.14320i
$$704$$ 0 0
$$705$$ 4.50000 + 2.59808i 0.169480 + 0.0978492i
$$706$$ 0 0
$$707$$ −4.50000 + 12.9904i −0.169240 + 0.488554i
$$708$$ 0 0
$$709$$ 17.5000 30.3109i 0.657226 1.13835i −0.324104 0.946021i $$-0.605063\pi$$
0.981331 0.192328i $$-0.0616038\pi$$
$$710$$ 0 0
$$711$$ 9.00000 5.19615i 0.337526 0.194871i
$$712$$ 0 0
$$713$$ 43.3013i 1.62165i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −9.00000 + 5.19615i −0.336111 + 0.194054i
$$718$$ 0 0
$$719$$ −16.5000 + 28.5788i −0.615346 + 1.06581i 0.374978 + 0.927034i $$0.377650\pi$$
−0.990324 + 0.138777i $$0.955683\pi$$
$$720$$ 0 0
$$721$$ −0.500000 2.59808i −0.0186210 0.0967574i
$$722$$ 0 0
$$723$$ 10.5000 + 6.06218i 0.390499 + 0.225455i
$$724$$ 0 0
$$725$$ −6.00000 10.3923i −0.222834 0.385961i
$$726$$ 0 0
$$727$$ −32.0000 −1.18681 −0.593407 0.804902i $$-0.702218\pi$$
−0.593407 + 0.804902i $$0.702218\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 9.00000 + 15.5885i 0.332877 + 0.576560i
$$732$$ 0 0
$$733$$ 16.5000 + 9.52628i 0.609441 + 0.351861i 0.772747 0.634714i $$-0.218882\pi$$
−0.163305 + 0.986576i $$0.552216\pi$$
$$734$$ 0 0
$$735$$ 12.0000 + 1.73205i 0.442627 + 0.0638877i
$$736$$ 0 0
$$737$$ −4.50000 + 7.79423i −0.165760 + 0.287104i
$$738$$ 0 0
$$739$$ −1.50000 + 0.866025i −0.0551784 + 0.0318573i −0.527335 0.849657i $$-0.676809\pi$$
0.472157 + 0.881514i $$0.343476\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 38.1051i 1.39794i 0.715150 + 0.698971i $$0.246358\pi$$
−0.715150 + 0.698971i $$0.753642\pi$$
$$744$$ 0 0
$$745$$ 13.5000 7.79423i 0.494602 0.285558i
$$746$$ 0 0
$$747$$ 12.0000 20.7846i 0.439057 0.760469i
$$748$$ 0 0
$$749$$ 13.5000 2.59808i 0.493279 0.0949316i
$$750$$ 0 0
$$751$$ 34.5000 + 19.9186i 1.25892 + 0.726839i 0.972865 0.231373i $$-0.0743217\pi$$
0.286058 + 0.958212i $$0.407655\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 21.0000 0.764268
$$756$$ 0 0
$$757$$ −26.0000 −0.944986 −0.472493 0.881334i $$-0.656646\pi$$
−0.472493 + 0.881334i $$0.656646\pi$$
$$758$$ 0 0
$$759$$ −7.50000 12.9904i −0.272233 0.471521i
$$760$$ 0 0
$$761$$ −4.50000 2.59808i −0.163125 0.0941802i 0.416215 0.909266i $$-0.363356\pi$$
−0.579340 + 0.815086i $$0.696690\pi$$
$$762$$ 0 0
$$763$$ −27.5000 9.52628i −0.995567 0.344874i
$$764$$ 0 0
$$765$$ 9.00000 15.5885i 0.325396 0.563602i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 6.92820i 0.249837i −0.992167 0.124919i $$-0.960133\pi$$
0.992167 0.124919i $$-0.0398670\pi$$
$$770$$ 0 0
$$771$$ 19.0526i 0.686161i
$$772$$ 0 0
$$773$$ −7.50000 + 4.33013i −0.269756 + 0.155744i −0.628777 0.777586i $$-0.716444\pi$$
0.359021 + 0.933330i $$0.383111\pi$$
$$774$$ 0 0
$$775$$ 5.00000 8.66025i 0.179605 0.311086i
$$776$$ 0 0
$$777$$ −10.0000 + 8.66025i −0.358748 + 0.310685i
$$778$$ 0 0
$$779$$ −42.0000 24.2487i −1.50481 0.868800i
$$780$$ 0 0
$$781$$ 3.00000 + 5.19615i 0.107348 + 0.185933i
$$782$$ 0 0
$$783$$ −30.0000 −1.07211
$$784$$ 0 0
$$785$$ 27.0000 0.963671
$$786$$ 0 0
$$787$$ 3.50000 + 6.06218i 0.124762 + 0.216093i 0.921640 0.388047i $$-0.126850\pi$$
−0.796878 + 0.604140i $$0.793517\pi$$
$$788$$ 0 0
$$789$$ −7.50000 4.33013i −0.267007 0.154157i
$$790$$ 0 0
$$791$$ −12.0000 + 10.3923i −0.426671 + 0.369508i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 13.5000 7.79423i 0.478796 0.276433i
$$796$$ 0 0