# Properties

 Label 1280.2.o.o.383.1 Level $1280$ Weight $2$ Character 1280.383 Analytic conductor $10.221$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1280.o (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.2208514587$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 160) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 383.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1280.383 Dual form 1280.2.o.o.127.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(2.00000 + 2.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-2.00000 - 2.00000i) q^{7} +5.00000i q^{9} +O(q^{10})$$ $$q+(2.00000 + 2.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-2.00000 - 2.00000i) q^{7} +5.00000i q^{9} +(1.00000 - 1.00000i) q^{13} +(-6.00000 + 2.00000i) q^{15} +(-5.00000 + 5.00000i) q^{17} +4.00000i q^{19} -8.00000i q^{21} +(-2.00000 + 2.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(-4.00000 + 4.00000i) q^{27} -4.00000 q^{29} +4.00000i q^{31} +(6.00000 - 2.00000i) q^{35} +(-1.00000 - 1.00000i) q^{37} +4.00000 q^{39} +(6.00000 + 6.00000i) q^{43} +(-10.0000 - 5.00000i) q^{45} +(-2.00000 - 2.00000i) q^{47} +1.00000i q^{49} -20.0000 q^{51} +(-7.00000 + 7.00000i) q^{53} +(-8.00000 + 8.00000i) q^{57} -4.00000i q^{59} -4.00000i q^{61} +(10.0000 - 10.0000i) q^{63} +(1.00000 + 3.00000i) q^{65} +(10.0000 - 10.0000i) q^{67} -8.00000 q^{69} +12.0000i q^{71} +(3.00000 + 3.00000i) q^{73} +(2.00000 - 14.0000i) q^{75} +16.0000 q^{79} -1.00000 q^{81} +(-2.00000 - 2.00000i) q^{83} +(-5.00000 - 15.0000i) q^{85} +(-8.00000 - 8.00000i) q^{87} -4.00000 q^{91} +(-8.00000 + 8.00000i) q^{93} +(-8.00000 - 4.00000i) q^{95} +(-3.00000 + 3.00000i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 4q^{3} - 2q^{5} - 4q^{7} + O(q^{10})$$ $$2q + 4q^{3} - 2q^{5} - 4q^{7} + 2q^{13} - 12q^{15} - 10q^{17} - 4q^{23} - 6q^{25} - 8q^{27} - 8q^{29} + 12q^{35} - 2q^{37} + 8q^{39} + 12q^{43} - 20q^{45} - 4q^{47} - 40q^{51} - 14q^{53} - 16q^{57} + 20q^{63} + 2q^{65} + 20q^{67} - 16q^{69} + 6q^{73} + 4q^{75} + 32q^{79} - 2q^{81} - 4q^{83} - 10q^{85} - 16q^{87} - 8q^{91} - 16q^{93} - 16q^{95} - 6q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$261$$ $$511$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 2.00000 + 2.00000i 1.15470 + 1.15470i 0.985599 + 0.169102i $$0.0540867\pi$$
0.169102 + 0.985599i $$0.445913\pi$$
$$4$$ 0 0
$$5$$ −1.00000 + 2.00000i −0.447214 + 0.894427i
$$6$$ 0 0
$$7$$ −2.00000 2.00000i −0.755929 0.755929i 0.219650 0.975579i $$-0.429509\pi$$
−0.975579 + 0.219650i $$0.929509\pi$$
$$8$$ 0 0
$$9$$ 5.00000i 1.66667i
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 1.00000 1.00000i 0.277350 0.277350i −0.554700 0.832050i $$-0.687167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ 0 0
$$15$$ −6.00000 + 2.00000i −1.54919 + 0.516398i
$$16$$ 0 0
$$17$$ −5.00000 + 5.00000i −1.21268 + 1.21268i −0.242536 + 0.970143i $$0.577979\pi$$
−0.970143 + 0.242536i $$0.922021\pi$$
$$18$$ 0 0
$$19$$ 4.00000i 0.917663i 0.888523 + 0.458831i $$0.151732\pi$$
−0.888523 + 0.458831i $$0.848268\pi$$
$$20$$ 0 0
$$21$$ 8.00000i 1.74574i
$$22$$ 0 0
$$23$$ −2.00000 + 2.00000i −0.417029 + 0.417029i −0.884178 0.467150i $$-0.845281\pi$$
0.467150 + 0.884178i $$0.345281\pi$$
$$24$$ 0 0
$$25$$ −3.00000 4.00000i −0.600000 0.800000i
$$26$$ 0 0
$$27$$ −4.00000 + 4.00000i −0.769800 + 0.769800i
$$28$$ 0 0
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ 4.00000i 0.718421i 0.933257 + 0.359211i $$0.116954\pi$$
−0.933257 + 0.359211i $$0.883046\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 6.00000 2.00000i 1.01419 0.338062i
$$36$$ 0 0
$$37$$ −1.00000 1.00000i −0.164399 0.164399i 0.620113 0.784512i $$-0.287087\pi$$
−0.784512 + 0.620113i $$0.787087\pi$$
$$38$$ 0 0
$$39$$ 4.00000 0.640513
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 6.00000 + 6.00000i 0.914991 + 0.914991i 0.996660 0.0816682i $$-0.0260248\pi$$
−0.0816682 + 0.996660i $$0.526025\pi$$
$$44$$ 0 0
$$45$$ −10.0000 5.00000i −1.49071 0.745356i
$$46$$ 0 0
$$47$$ −2.00000 2.00000i −0.291730 0.291730i 0.546033 0.837763i $$-0.316137\pi$$
−0.837763 + 0.546033i $$0.816137\pi$$
$$48$$ 0 0
$$49$$ 1.00000i 0.142857i
$$50$$ 0 0
$$51$$ −20.0000 −2.80056
$$52$$ 0 0
$$53$$ −7.00000 + 7.00000i −0.961524 + 0.961524i −0.999287 0.0377628i $$-0.987977\pi$$
0.0377628 + 0.999287i $$0.487977\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −8.00000 + 8.00000i −1.05963 + 1.05963i
$$58$$ 0 0
$$59$$ 4.00000i 0.520756i −0.965507 0.260378i $$-0.916153\pi$$
0.965507 0.260378i $$-0.0838471\pi$$
$$60$$ 0 0
$$61$$ 4.00000i 0.512148i −0.966657 0.256074i $$-0.917571\pi$$
0.966657 0.256074i $$-0.0824290\pi$$
$$62$$ 0 0
$$63$$ 10.0000 10.0000i 1.25988 1.25988i
$$64$$ 0 0
$$65$$ 1.00000 + 3.00000i 0.124035 + 0.372104i
$$66$$ 0 0
$$67$$ 10.0000 10.0000i 1.22169 1.22169i 0.254665 0.967029i $$-0.418035\pi$$
0.967029 0.254665i $$-0.0819652\pi$$
$$68$$ 0 0
$$69$$ −8.00000 −0.963087
$$70$$ 0 0
$$71$$ 12.0000i 1.42414i 0.702109 + 0.712069i $$0.252242\pi$$
−0.702109 + 0.712069i $$0.747758\pi$$
$$72$$ 0 0
$$73$$ 3.00000 + 3.00000i 0.351123 + 0.351123i 0.860527 0.509404i $$-0.170134\pi$$
−0.509404 + 0.860527i $$0.670134\pi$$
$$74$$ 0 0
$$75$$ 2.00000 14.0000i 0.230940 1.61658i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 16.0000 1.80014 0.900070 0.435745i $$-0.143515\pi$$
0.900070 + 0.435745i $$0.143515\pi$$
$$80$$ 0 0
$$81$$ −1.00000 −0.111111
$$82$$ 0 0
$$83$$ −2.00000 2.00000i −0.219529 0.219529i 0.588771 0.808300i $$-0.299612\pi$$
−0.808300 + 0.588771i $$0.799612\pi$$
$$84$$ 0 0
$$85$$ −5.00000 15.0000i −0.542326 1.62698i
$$86$$ 0 0
$$87$$ −8.00000 8.00000i −0.857690 0.857690i
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ −4.00000 −0.419314
$$92$$ 0 0
$$93$$ −8.00000 + 8.00000i −0.829561 + 0.829561i
$$94$$ 0 0
$$95$$ −8.00000 4.00000i −0.820783 0.410391i
$$96$$ 0 0
$$97$$ −3.00000 + 3.00000i −0.304604 + 0.304604i −0.842812 0.538208i $$-0.819101\pi$$
0.538208 + 0.842812i $$0.319101\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 6.00000i 0.597022i 0.954406 + 0.298511i $$0.0964900\pi$$
−0.954406 + 0.298511i $$0.903510\pi$$
$$102$$ 0 0
$$103$$ 6.00000 6.00000i 0.591198 0.591198i −0.346757 0.937955i $$-0.612717\pi$$
0.937955 + 0.346757i $$0.112717\pi$$
$$104$$ 0 0
$$105$$ 16.0000 + 8.00000i 1.56144 + 0.780720i
$$106$$ 0 0
$$107$$ 6.00000 6.00000i 0.580042 0.580042i −0.354873 0.934915i $$-0.615476\pi$$
0.934915 + 0.354873i $$0.115476\pi$$
$$108$$ 0 0
$$109$$ 10.0000 0.957826 0.478913 0.877862i $$-0.341031\pi$$
0.478913 + 0.877862i $$0.341031\pi$$
$$110$$ 0 0
$$111$$ 4.00000i 0.379663i
$$112$$ 0 0
$$113$$ −9.00000 9.00000i −0.846649 0.846649i 0.143065 0.989713i $$-0.454304\pi$$
−0.989713 + 0.143065i $$0.954304\pi$$
$$114$$ 0 0
$$115$$ −2.00000 6.00000i −0.186501 0.559503i
$$116$$ 0 0
$$117$$ 5.00000 + 5.00000i 0.462250 + 0.462250i
$$118$$ 0 0
$$119$$ 20.0000 1.83340
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 11.0000 2.00000i 0.983870 0.178885i
$$126$$ 0 0
$$127$$ 10.0000 + 10.0000i 0.887357 + 0.887357i 0.994268 0.106912i $$-0.0340963\pi$$
−0.106912 + 0.994268i $$0.534096\pi$$
$$128$$ 0 0
$$129$$ 24.0000i 2.11308i
$$130$$ 0 0
$$131$$ 8.00000 0.698963 0.349482 0.936943i $$-0.386358\pi$$
0.349482 + 0.936943i $$0.386358\pi$$
$$132$$ 0 0
$$133$$ 8.00000 8.00000i 0.693688 0.693688i
$$134$$ 0 0
$$135$$ −4.00000 12.0000i −0.344265 1.03280i
$$136$$ 0 0
$$137$$ −1.00000 + 1.00000i −0.0854358 + 0.0854358i −0.748533 0.663097i $$-0.769242\pi$$
0.663097 + 0.748533i $$0.269242\pi$$
$$138$$ 0 0
$$139$$ 12.0000i 1.01783i 0.860818 + 0.508913i $$0.169953\pi$$
−0.860818 + 0.508913i $$0.830047\pi$$
$$140$$ 0 0
$$141$$ 8.00000i 0.673722i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 4.00000 8.00000i 0.332182 0.664364i
$$146$$ 0 0
$$147$$ −2.00000 + 2.00000i −0.164957 + 0.164957i
$$148$$ 0 0
$$149$$ 18.0000 1.47462 0.737309 0.675556i $$-0.236096\pi$$
0.737309 + 0.675556i $$0.236096\pi$$
$$150$$ 0 0
$$151$$ 12.0000i 0.976546i 0.872691 + 0.488273i $$0.162373\pi$$
−0.872691 + 0.488273i $$0.837627\pi$$
$$152$$ 0 0
$$153$$ −25.0000 25.0000i −2.02113 2.02113i
$$154$$ 0 0
$$155$$ −8.00000 4.00000i −0.642575 0.321288i
$$156$$ 0 0
$$157$$ −9.00000 9.00000i −0.718278 0.718278i 0.249974 0.968252i $$-0.419578\pi$$
−0.968252 + 0.249974i $$0.919578\pi$$
$$158$$ 0 0
$$159$$ −28.0000 −2.22054
$$160$$ 0 0
$$161$$ 8.00000 0.630488
$$162$$ 0 0
$$163$$ 2.00000 + 2.00000i 0.156652 + 0.156652i 0.781081 0.624429i $$-0.214668\pi$$
−0.624429 + 0.781081i $$0.714668\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 2.00000 + 2.00000i 0.154765 + 0.154765i 0.780242 0.625478i $$-0.215096\pi$$
−0.625478 + 0.780242i $$0.715096\pi$$
$$168$$ 0 0
$$169$$ 11.0000i 0.846154i
$$170$$ 0 0
$$171$$ −20.0000 −1.52944
$$172$$ 0 0
$$173$$ −13.0000 + 13.0000i −0.988372 + 0.988372i −0.999933 0.0115615i $$-0.996320\pi$$
0.0115615 + 0.999933i $$0.496320\pi$$
$$174$$ 0 0
$$175$$ −2.00000 + 14.0000i −0.151186 + 1.05830i
$$176$$ 0 0
$$177$$ 8.00000 8.00000i 0.601317 0.601317i
$$178$$ 0 0
$$179$$ 12.0000i 0.896922i 0.893802 + 0.448461i $$0.148028\pi$$
−0.893802 + 0.448461i $$0.851972\pi$$
$$180$$ 0 0
$$181$$ 10.0000i 0.743294i 0.928374 + 0.371647i $$0.121207\pi$$
−0.928374 + 0.371647i $$0.878793\pi$$
$$182$$ 0 0
$$183$$ 8.00000 8.00000i 0.591377 0.591377i
$$184$$ 0 0
$$185$$ 3.00000 1.00000i 0.220564 0.0735215i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 16.0000 1.16383
$$190$$ 0 0
$$191$$ 20.0000i 1.44715i 0.690246 + 0.723575i $$0.257502\pi$$
−0.690246 + 0.723575i $$0.742498\pi$$
$$192$$ 0 0
$$193$$ −5.00000 5.00000i −0.359908 0.359908i 0.503871 0.863779i $$-0.331909\pi$$
−0.863779 + 0.503871i $$0.831909\pi$$
$$194$$ 0 0
$$195$$ −4.00000 + 8.00000i −0.286446 + 0.572892i
$$196$$ 0 0
$$197$$ −5.00000 5.00000i −0.356235 0.356235i 0.506188 0.862423i $$-0.331054\pi$$
−0.862423 + 0.506188i $$0.831054\pi$$
$$198$$ 0 0
$$199$$ −24.0000 −1.70131 −0.850657 0.525720i $$-0.823796\pi$$
−0.850657 + 0.525720i $$0.823796\pi$$
$$200$$ 0 0
$$201$$ 40.0000 2.82138
$$202$$ 0 0
$$203$$ 8.00000 + 8.00000i 0.561490 + 0.561490i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −10.0000 10.0000i −0.695048 0.695048i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 16.0000 1.10149 0.550743 0.834675i $$-0.314345\pi$$
0.550743 + 0.834675i $$0.314345\pi$$
$$212$$ 0 0
$$213$$ −24.0000 + 24.0000i −1.64445 + 1.64445i
$$214$$ 0 0
$$215$$ −18.0000 + 6.00000i −1.22759 + 0.409197i
$$216$$ 0 0
$$217$$ 8.00000 8.00000i 0.543075 0.543075i
$$218$$ 0 0
$$219$$ 12.0000i 0.810885i
$$220$$ 0 0
$$221$$ 10.0000i 0.672673i
$$222$$ 0 0
$$223$$ −10.0000 + 10.0000i −0.669650 + 0.669650i −0.957635 0.287985i $$-0.907015\pi$$
0.287985 + 0.957635i $$0.407015\pi$$
$$224$$ 0 0
$$225$$ 20.0000 15.0000i 1.33333 1.00000i
$$226$$ 0 0
$$227$$ −10.0000 + 10.0000i −0.663723 + 0.663723i −0.956256 0.292532i $$-0.905502\pi$$
0.292532 + 0.956256i $$0.405502\pi$$
$$228$$ 0 0
$$229$$ 20.0000 1.32164 0.660819 0.750546i $$-0.270209\pi$$
0.660819 + 0.750546i $$0.270209\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 5.00000 + 5.00000i 0.327561 + 0.327561i 0.851658 0.524097i $$-0.175597\pi$$
−0.524097 + 0.851658i $$0.675597\pi$$
$$234$$ 0 0
$$235$$ 6.00000 2.00000i 0.391397 0.130466i
$$236$$ 0 0
$$237$$ 32.0000 + 32.0000i 2.07862 + 2.07862i
$$238$$ 0 0
$$239$$ 8.00000 0.517477 0.258738 0.965947i $$-0.416693\pi$$
0.258738 + 0.965947i $$0.416693\pi$$
$$240$$ 0 0
$$241$$ −16.0000 −1.03065 −0.515325 0.856995i $$-0.672329\pi$$
−0.515325 + 0.856995i $$0.672329\pi$$
$$242$$ 0 0
$$243$$ 10.0000 + 10.0000i 0.641500 + 0.641500i
$$244$$ 0 0
$$245$$ −2.00000 1.00000i −0.127775 0.0638877i
$$246$$ 0 0
$$247$$ 4.00000 + 4.00000i 0.254514 + 0.254514i
$$248$$ 0 0
$$249$$ 8.00000i 0.506979i
$$250$$ 0 0
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 20.0000 40.0000i 1.25245 2.50490i
$$256$$ 0 0
$$257$$ 7.00000 7.00000i 0.436648 0.436648i −0.454234 0.890882i $$-0.650087\pi$$
0.890882 + 0.454234i $$0.150087\pi$$
$$258$$ 0 0
$$259$$ 4.00000i 0.248548i
$$260$$ 0 0
$$261$$ 20.0000i 1.23797i
$$262$$ 0 0
$$263$$ −6.00000 + 6.00000i −0.369976 + 0.369976i −0.867468 0.497492i $$-0.834254\pi$$
0.497492 + 0.867468i $$0.334254\pi$$
$$264$$ 0 0
$$265$$ −7.00000 21.0000i −0.430007 1.29002i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −10.0000 −0.609711 −0.304855 0.952399i $$-0.598608\pi$$
−0.304855 + 0.952399i $$0.598608\pi$$
$$270$$ 0 0
$$271$$ 20.0000i 1.21491i −0.794353 0.607457i $$-0.792190\pi$$
0.794353 0.607457i $$-0.207810\pi$$
$$272$$ 0 0
$$273$$ −8.00000 8.00000i −0.484182 0.484182i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 9.00000 + 9.00000i 0.540758 + 0.540758i 0.923751 0.382993i $$-0.125107\pi$$
−0.382993 + 0.923751i $$0.625107\pi$$
$$278$$ 0 0
$$279$$ −20.0000 −1.19737
$$280$$ 0 0
$$281$$ −8.00000 −0.477240 −0.238620 0.971113i $$-0.576695\pi$$
−0.238620 + 0.971113i $$0.576695\pi$$
$$282$$ 0 0
$$283$$ −6.00000 6.00000i −0.356663 0.356663i 0.505918 0.862581i $$-0.331154\pi$$
−0.862581 + 0.505918i $$0.831154\pi$$
$$284$$ 0 0
$$285$$ −8.00000 24.0000i −0.473879 1.42164i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 33.0000i 1.94118i
$$290$$ 0 0
$$291$$ −12.0000 −0.703452
$$292$$ 0 0
$$293$$ −5.00000 + 5.00000i −0.292103 + 0.292103i −0.837911 0.545807i $$-0.816223\pi$$
0.545807 + 0.837911i $$0.316223\pi$$
$$294$$ 0 0
$$295$$ 8.00000 + 4.00000i 0.465778 + 0.232889i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 4.00000i 0.231326i
$$300$$ 0 0
$$301$$ 24.0000i 1.38334i
$$302$$ 0 0
$$303$$ −12.0000 + 12.0000i −0.689382 + 0.689382i
$$304$$ 0 0
$$305$$ 8.00000 + 4.00000i 0.458079 + 0.229039i
$$306$$ 0 0
$$307$$ 10.0000 10.0000i 0.570730 0.570730i −0.361602 0.932332i $$-0.617770\pi$$
0.932332 + 0.361602i $$0.117770\pi$$
$$308$$ 0 0
$$309$$ 24.0000 1.36531
$$310$$ 0 0
$$311$$ 28.0000i 1.58773i −0.608091 0.793867i $$-0.708065\pi$$
0.608091 0.793867i $$-0.291935\pi$$
$$312$$ 0 0
$$313$$ −15.0000 15.0000i −0.847850 0.847850i 0.142014 0.989865i $$-0.454642\pi$$
−0.989865 + 0.142014i $$0.954642\pi$$
$$314$$ 0 0
$$315$$ 10.0000 + 30.0000i 0.563436 + 1.69031i
$$316$$ 0 0
$$317$$ 11.0000 + 11.0000i 0.617822 + 0.617822i 0.944972 0.327151i $$-0.106088\pi$$
−0.327151 + 0.944972i $$0.606088\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 24.0000 1.33955
$$322$$ 0 0
$$323$$ −20.0000 20.0000i −1.11283 1.11283i
$$324$$ 0 0
$$325$$ −7.00000 1.00000i −0.388290 0.0554700i
$$326$$ 0 0
$$327$$ 20.0000 + 20.0000i 1.10600 + 1.10600i
$$328$$ 0 0
$$329$$ 8.00000i 0.441054i
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ 5.00000 5.00000i 0.273998 0.273998i
$$334$$ 0 0
$$335$$ 10.0000 + 30.0000i 0.546358 + 1.63908i
$$336$$ 0 0
$$337$$ −23.0000 + 23.0000i −1.25289 + 1.25289i −0.298471 + 0.954419i $$0.596477\pi$$
−0.954419 + 0.298471i $$0.903523\pi$$
$$338$$ 0 0
$$339$$ 36.0000i 1.95525i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −12.0000 + 12.0000i −0.647939 + 0.647939i
$$344$$ 0 0
$$345$$ 8.00000 16.0000i 0.430706 0.861411i
$$346$$ 0 0
$$347$$ 18.0000 18.0000i 0.966291 0.966291i −0.0331594 0.999450i $$-0.510557\pi$$
0.999450 + 0.0331594i $$0.0105569\pi$$
$$348$$ 0 0
$$349$$ 20.0000 1.07058 0.535288 0.844670i $$-0.320203\pi$$
0.535288 + 0.844670i $$0.320203\pi$$
$$350$$ 0 0
$$351$$ 8.00000i 0.427008i
$$352$$ 0 0
$$353$$ 9.00000 + 9.00000i 0.479022 + 0.479022i 0.904819 0.425797i $$-0.140006\pi$$
−0.425797 + 0.904819i $$0.640006\pi$$
$$354$$ 0 0
$$355$$ −24.0000 12.0000i −1.27379 0.636894i
$$356$$ 0 0
$$357$$ 40.0000 + 40.0000i 2.11702 + 2.11702i
$$358$$ 0 0
$$359$$ 16.0000 0.844448 0.422224 0.906492i $$-0.361250\pi$$
0.422224 + 0.906492i $$0.361250\pi$$
$$360$$ 0 0
$$361$$ 3.00000 0.157895
$$362$$ 0 0
$$363$$ −22.0000 22.0000i −1.15470 1.15470i
$$364$$ 0 0
$$365$$ −9.00000 + 3.00000i −0.471082 + 0.157027i
$$366$$ 0 0
$$367$$ −22.0000 22.0000i −1.14839 1.14839i −0.986869 0.161521i $$-0.948360\pi$$
−0.161521 0.986869i $$-0.551640\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 28.0000 1.45369
$$372$$ 0 0
$$373$$ 21.0000 21.0000i 1.08734 1.08734i 0.0915371 0.995802i $$-0.470822\pi$$
0.995802 0.0915371i $$-0.0291780\pi$$
$$374$$ 0 0
$$375$$ 26.0000 + 18.0000i 1.34263 + 0.929516i
$$376$$ 0 0
$$377$$ −4.00000 + 4.00000i −0.206010 + 0.206010i
$$378$$ 0 0
$$379$$ 28.0000i 1.43826i −0.694874 0.719132i $$-0.744540\pi$$
0.694874 0.719132i $$-0.255460\pi$$
$$380$$ 0 0
$$381$$ 40.0000i 2.04926i
$$382$$ 0 0
$$383$$ 22.0000 22.0000i 1.12415 1.12415i 0.133036 0.991111i $$-0.457527\pi$$
0.991111 0.133036i $$-0.0424727\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −30.0000 + 30.0000i −1.52499 + 1.52499i
$$388$$ 0 0
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ 20.0000i 1.01144i
$$392$$ 0 0
$$393$$ 16.0000 + 16.0000i 0.807093 + 0.807093i
$$394$$ 0 0
$$395$$ −16.0000 + 32.0000i −0.805047 + 1.61009i
$$396$$ 0 0
$$397$$ 13.0000 + 13.0000i 0.652451 + 0.652451i 0.953583 0.301131i $$-0.0973643\pi$$
−0.301131 + 0.953583i $$0.597364\pi$$
$$398$$ 0 0
$$399$$ 32.0000 1.60200
$$400$$ 0 0
$$401$$ 34.0000 1.69788 0.848939 0.528490i $$-0.177242\pi$$
0.848939 + 0.528490i $$0.177242\pi$$
$$402$$ 0 0
$$403$$ 4.00000 + 4.00000i 0.199254 + 0.199254i
$$404$$ 0 0
$$405$$ 1.00000 2.00000i 0.0496904 0.0993808i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 2.00000i 0.0988936i 0.998777 + 0.0494468i $$0.0157458\pi$$
−0.998777 + 0.0494468i $$0.984254\pi$$
$$410$$ 0 0
$$411$$ −4.00000 −0.197305
$$412$$ 0 0
$$413$$ −8.00000 + 8.00000i −0.393654 + 0.393654i
$$414$$ 0 0
$$415$$ 6.00000 2.00000i 0.294528 0.0981761i
$$416$$ 0 0
$$417$$ −24.0000 + 24.0000i −1.17529 + 1.17529i
$$418$$ 0 0
$$419$$ 12.0000i 0.586238i −0.956076 0.293119i $$-0.905307\pi$$
0.956076 0.293119i $$-0.0946933\pi$$
$$420$$ 0 0
$$421$$ 20.0000i 0.974740i −0.873195 0.487370i $$-0.837956\pi$$
0.873195 0.487370i $$-0.162044\pi$$
$$422$$ 0 0
$$423$$ 10.0000 10.0000i 0.486217 0.486217i
$$424$$ 0 0
$$425$$ 35.0000 + 5.00000i 1.69775 + 0.242536i
$$426$$ 0 0
$$427$$ −8.00000 + 8.00000i −0.387147 + 0.387147i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 4.00000i 0.192673i −0.995349 0.0963366i $$-0.969287\pi$$
0.995349 0.0963366i $$-0.0307125\pi$$
$$432$$ 0 0
$$433$$ −19.0000 19.0000i −0.913082 0.913082i 0.0834318 0.996513i $$-0.473412\pi$$
−0.996513 + 0.0834318i $$0.973412\pi$$
$$434$$ 0 0
$$435$$ 24.0000 8.00000i 1.15071 0.383571i
$$436$$ 0 0
$$437$$ −8.00000 8.00000i −0.382692 0.382692i
$$438$$ 0 0
$$439$$ 16.0000 0.763638 0.381819 0.924237i $$-0.375298\pi$$
0.381819 + 0.924237i $$0.375298\pi$$
$$440$$ 0 0
$$441$$ −5.00000 −0.238095
$$442$$ 0 0
$$443$$ −22.0000 22.0000i −1.04525 1.04525i −0.998926 0.0463251i $$-0.985249\pi$$
−0.0463251 0.998926i $$-0.514751\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 36.0000 + 36.0000i 1.70274 + 1.70274i
$$448$$ 0 0
$$449$$ 26.0000i 1.22702i 0.789689 + 0.613508i $$0.210242\pi$$
−0.789689 + 0.613508i $$0.789758\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −24.0000 + 24.0000i −1.12762 + 1.12762i
$$454$$ 0 0
$$455$$ 4.00000 8.00000i 0.187523 0.375046i
$$456$$ 0 0
$$457$$ −15.0000 + 15.0000i −0.701670 + 0.701670i −0.964769 0.263099i $$-0.915256\pi$$
0.263099 + 0.964769i $$0.415256\pi$$
$$458$$ 0 0
$$459$$ 40.0000i 1.86704i
$$460$$ 0 0
$$461$$ 14.0000i 0.652045i −0.945362 0.326023i $$-0.894291\pi$$
0.945362 0.326023i $$-0.105709\pi$$
$$462$$ 0 0
$$463$$ −22.0000 + 22.0000i −1.02243 + 1.02243i −0.0226840 + 0.999743i $$0.507221\pi$$
−0.999743 + 0.0226840i $$0.992779\pi$$
$$464$$ 0 0
$$465$$ −8.00000 24.0000i −0.370991 1.11297i
$$466$$ 0 0
$$467$$ −2.00000 + 2.00000i −0.0925490 + 0.0925490i −0.751865 0.659317i $$-0.770846\pi$$
0.659317 + 0.751865i $$0.270846\pi$$
$$468$$ 0 0
$$469$$ −40.0000 −1.84703
$$470$$ 0 0
$$471$$ 36.0000i 1.65879i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 16.0000 12.0000i 0.734130 0.550598i
$$476$$ 0 0
$$477$$ −35.0000 35.0000i −1.60254 1.60254i
$$478$$ 0 0
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ 0 0
$$481$$ −2.00000 −0.0911922
$$482$$ 0 0
$$483$$ 16.0000 + 16.0000i 0.728025 + 0.728025i
$$484$$ 0 0
$$485$$ −3.00000 9.00000i −0.136223 0.408669i
$$486$$ 0 0
$$487$$ 6.00000 + 6.00000i 0.271886 + 0.271886i 0.829859 0.557973i $$-0.188421\pi$$
−0.557973 + 0.829859i $$0.688421\pi$$
$$488$$ 0 0
$$489$$ 8.00000i 0.361773i
$$490$$ 0 0
$$491$$ 16.0000 0.722070 0.361035 0.932552i $$-0.382424\pi$$
0.361035 + 0.932552i $$0.382424\pi$$
$$492$$ 0 0
$$493$$ 20.0000 20.0000i 0.900755 0.900755i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 24.0000 24.0000i 1.07655 1.07655i
$$498$$ 0 0
$$499$$ 4.00000i 0.179065i 0.995984 + 0.0895323i $$0.0285372\pi$$
−0.995984 + 0.0895323i $$0.971463\pi$$
$$500$$ 0 0
$$501$$ 8.00000i 0.357414i
$$502$$ 0 0
$$503$$ −10.0000 + 10.0000i −0.445878 + 0.445878i −0.893982 0.448104i $$-0.852100\pi$$
0.448104 + 0.893982i $$0.352100\pi$$
$$504$$ 0 0
$$505$$ −12.0000 6.00000i −0.533993 0.266996i
$$506$$ 0 0
$$507$$ −22.0000 + 22.0000i −0.977054 + 0.977054i
$$508$$ 0 0
$$509$$ 36.0000 1.59567 0.797836 0.602875i $$-0.205978\pi$$
0.797836 + 0.602875i $$0.205978\pi$$
$$510$$ 0 0
$$511$$ 12.0000i 0.530849i
$$512$$ 0 0
$$513$$ −16.0000 16.0000i −0.706417 0.706417i
$$514$$ 0 0
$$515$$ 6.00000 + 18.0000i 0.264392 + 0.793175i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −52.0000 −2.28255
$$520$$ 0 0
$$521$$ −6.00000 −0.262865 −0.131432 0.991325i $$-0.541958\pi$$
−0.131432 + 0.991325i $$0.541958\pi$$
$$522$$ 0 0
$$523$$ −14.0000 14.0000i −0.612177 0.612177i 0.331336 0.943513i $$-0.392501\pi$$
−0.943513 + 0.331336i $$0.892501\pi$$
$$524$$ 0 0
$$525$$ −32.0000 + 24.0000i −1.39659 + 1.04745i
$$526$$ 0 0
$$527$$ −20.0000 20.0000i −0.871214 0.871214i
$$528$$ 0 0
$$529$$ 15.0000i 0.652174i
$$530$$ 0 0
$$531$$ 20.0000 0.867926
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 6.00000 + 18.0000i 0.259403 + 0.778208i
$$536$$ 0 0
$$537$$ −24.0000 + 24.0000i −1.03568 + 1.03568i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 30.0000i 1.28980i −0.764267 0.644900i $$-0.776899\pi$$
0.764267 0.644900i $$-0.223101\pi$$
$$542$$ 0 0
$$543$$ −20.0000 + 20.0000i −0.858282 + 0.858282i
$$544$$ 0 0
$$545$$ −10.0000 + 20.0000i −0.428353 + 0.856706i
$$546$$ 0 0
$$547$$ 6.00000 6.00000i 0.256541 0.256541i −0.567104 0.823646i $$-0.691936\pi$$
0.823646 + 0.567104i $$0.191936\pi$$
$$548$$ 0 0
$$549$$ 20.0000 0.853579
$$550$$ 0 0
$$551$$ 16.0000i 0.681623i
$$552$$ 0 0
$$553$$ −32.0000 32.0000i −1.36078 1.36078i
$$554$$ 0 0
$$555$$ 8.00000 + 4.00000i 0.339581 + 0.169791i
$$556$$ 0 0
$$557$$ −15.0000 15.0000i −0.635570 0.635570i 0.313889 0.949460i $$-0.398368\pi$$
−0.949460 + 0.313889i $$0.898368\pi$$
$$558$$ 0 0
$$559$$ 12.0000 0.507546
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −6.00000 6.00000i −0.252870 0.252870i 0.569276 0.822146i $$-0.307223\pi$$
−0.822146 + 0.569276i $$0.807223\pi$$
$$564$$ 0 0
$$565$$ 27.0000 9.00000i 1.13590 0.378633i
$$566$$ 0 0
$$567$$ 2.00000 + 2.00000i 0.0839921 + 0.0839921i
$$568$$ 0 0
$$569$$ 2.00000i 0.0838444i −0.999121 0.0419222i $$-0.986652\pi$$
0.999121 0.0419222i $$-0.0133482\pi$$
$$570$$ 0 0
$$571$$ 16.0000 0.669579 0.334790 0.942293i $$-0.391335\pi$$
0.334790 + 0.942293i $$0.391335\pi$$
$$572$$ 0 0
$$573$$ −40.0000 + 40.0000i −1.67102 + 1.67102i
$$574$$ 0 0
$$575$$ 14.0000 + 2.00000i 0.583840 + 0.0834058i
$$576$$ 0 0
$$577$$ 15.0000 15.0000i 0.624458 0.624458i −0.322210 0.946668i $$-0.604426\pi$$
0.946668 + 0.322210i $$0.104426\pi$$
$$578$$ 0 0
$$579$$ 20.0000i 0.831172i
$$580$$ 0 0
$$581$$ 8.00000i 0.331896i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ −15.0000 + 5.00000i −0.620174 + 0.206725i
$$586$$ 0 0
$$587$$ −14.0000 + 14.0000i −0.577842 + 0.577842i −0.934308 0.356466i $$-0.883981\pi$$
0.356466 + 0.934308i $$0.383981\pi$$
$$588$$ 0 0
$$589$$ −16.0000 −0.659269
$$590$$ 0 0
$$591$$ 20.0000i 0.822690i
$$592$$ 0 0
$$593$$ 1.00000 + 1.00000i 0.0410651 + 0.0410651i 0.727341 0.686276i $$-0.240756\pi$$
−0.686276 + 0.727341i $$0.740756\pi$$
$$594$$ 0 0
$$595$$ −20.0000 + 40.0000i −0.819920 + 1.63984i
$$596$$ 0 0
$$597$$ −48.0000 48.0000i −1.96451 1.96451i
$$598$$ 0 0
$$599$$ 8.00000 0.326871 0.163436 0.986554i $$-0.447742\pi$$
0.163436 + 0.986554i $$0.447742\pi$$
$$600$$ 0 0
$$601$$ 8.00000 0.326327 0.163163 0.986599i $$-0.447830\pi$$
0.163163 + 0.986599i $$0.447830\pi$$
$$602$$ 0 0
$$603$$ 50.0000 + 50.0000i 2.03616 + 2.03616i
$$604$$ 0 0
$$605$$ 11.0000 22.0000i 0.447214 0.894427i
$$606$$ 0 0
$$607$$ −18.0000 18.0000i −0.730597 0.730597i 0.240141 0.970738i $$-0.422806\pi$$
−0.970738 + 0.240141i $$0.922806\pi$$
$$608$$ 0 0
$$609$$ 32.0000i 1.29671i
$$610$$ 0 0
$$611$$ −4.00000 −0.161823
$$612$$ 0 0
$$613$$ −9.00000 + 9.00000i −0.363507 + 0.363507i −0.865102 0.501596i $$-0.832747\pi$$
0.501596 + 0.865102i $$0.332747\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 29.0000 29.0000i 1.16750 1.16750i 0.184701 0.982795i $$-0.440868\pi$$
0.982795 0.184701i $$-0.0591318\pi$$
$$618$$ 0 0
$$619$$ 28.0000i 1.12542i 0.826656 + 0.562708i $$0.190240\pi$$
−0.826656 + 0.562708i $$0.809760\pi$$
$$620$$ 0 0
$$621$$ 16.0000i 0.642058i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 10.0000 0.398726
$$630$$ 0 0
$$631$$ 4.00000i 0.159237i 0.996825 + 0.0796187i $$0.0253703\pi$$
−0.996825 + 0.0796187i $$0.974630\pi$$
$$632$$ 0 0
$$633$$ 32.0000 + 32.0000i 1.27189 + 1.27189i
$$634$$ 0 0
$$635$$ −30.0000 + 10.0000i −1.19051 + 0.396838i
$$636$$ 0 0
$$637$$ 1.00000 + 1.00000i 0.0396214 + 0.0396214i
$$638$$ 0 0
$$639$$ −60.0000 −2.37356
$$640$$ 0 0
$$641$$ −48.0000 −1.89589 −0.947943 0.318440i $$-0.896841\pi$$
−0.947943 + 0.318440i $$0.896841\pi$$
$$642$$ 0 0
$$643$$ −10.0000 10.0000i −0.394362 0.394362i 0.481877 0.876239i $$-0.339955\pi$$
−0.876239 + 0.481877i $$0.839955\pi$$
$$644$$ 0 0
$$645$$ −48.0000 24.0000i −1.89000 0.944999i
$$646$$ 0 0
$$647$$ −10.0000 10.0000i −0.393141 0.393141i 0.482665 0.875805i $$-0.339669\pi$$
−0.875805 + 0.482665i $$0.839669\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 32.0000 1.25418
$$652$$ 0 0
$$653$$ −1.00000 + 1.00000i −0.0391330 + 0.0391330i −0.726403 0.687270i $$-0.758809\pi$$
0.687270 + 0.726403i $$0.258809\pi$$
$$654$$ 0 0
$$655$$ −8.00000 + 16.0000i −0.312586 + 0.625172i
$$656$$ 0 0
$$657$$ −15.0000 + 15.0000i −0.585206 + 0.585206i
$$658$$ 0 0
$$659$$ 20.0000i 0.779089i 0.921008 + 0.389545i $$0.127368\pi$$
−0.921008 + 0.389545i $$0.872632\pi$$
$$660$$ 0 0
$$661$$ 12.0000i 0.466746i −0.972387 0.233373i $$-0.925024\pi$$
0.972387 0.233373i $$-0.0749763\pi$$
$$662$$ 0 0
$$663$$ −20.0000 + 20.0000i −0.776736 + 0.776736i
$$664$$ 0 0
$$665$$ 8.00000 + 24.0000i 0.310227 + 0.930680i
$$666$$ 0 0
$$667$$ 8.00000 8.00000i 0.309761 0.309761i
$$668$$ 0 0
$$669$$ −40.0000 −1.54649
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 5.00000 + 5.00000i 0.192736 + 0.192736i 0.796877 0.604141i $$-0.206484\pi$$
−0.604141 + 0.796877i $$0.706484\pi$$
$$674$$ 0 0
$$675$$ 28.0000 + 4.00000i 1.07772 + 0.153960i
$$676$$ 0 0
$$677$$ 3.00000 + 3.00000i 0.115299 + 0.115299i 0.762402 0.647103i $$-0.224020\pi$$
−0.647103 + 0.762402i $$0.724020\pi$$
$$678$$ 0 0
$$679$$ 12.0000 0.460518
$$680$$ 0 0
$$681$$ −40.0000 −1.53280
$$682$$ 0 0
$$683$$ 22.0000 + 22.0000i 0.841807 + 0.841807i 0.989094 0.147287i $$-0.0470541\pi$$
−0.147287 + 0.989094i $$0.547054\pi$$
$$684$$ 0 0
$$685$$ −1.00000 3.00000i −0.0382080 0.114624i
$$686$$ 0 0
$$687$$ 40.0000 + 40.0000i 1.52610 + 1.52610i
$$688$$ 0 0
$$689$$ 14.0000i 0.533358i
$$690$$ 0 0
$$691$$ −32.0000 −1.21734 −0.608669 0.793424i $$-0.708296\pi$$
−0.608669 + 0.793424i $$0.708296\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −24.0000 12.0000i −0.910372 0.455186i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 20.0000i 0.756469i
$$700$$ 0 0
$$701$$ 20.0000i 0.755390i 0.925930 + 0.377695i $$0.123283\pi$$
−0.925930 + 0.377695i $$0.876717\pi$$
$$702$$ 0 0
$$703$$ 4.00000 4.00000i 0.150863 0.150863i
$$704$$ 0 0
$$705$$ 16.0000 + 8.00000i 0.602595 + 0.301297i
$$706$$ 0 0
$$707$$ 12.0000 12.0000i 0.451306 0.451306i
$$708$$ 0 0
$$709$$ 12.0000 0.450669 0.225335 0.974281i $$-0.427652\pi$$
0.225335 + 0.974281i $$0.427652\pi$$
$$710$$ 0 0
$$711$$ 80.0000i 3.00023i
$$712$$ 0 0
$$713$$ −8.00000 8.00000i −0.299602 0.299602i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 16.0000 + 16.0000i 0.597531 + 0.597531i
$$718$$ 0 0
$$719$$ 8.00000 0.298350 0.149175 0.988811i $$-0.452338\pi$$
0.149175 + 0.988811i $$0.452338\pi$$
$$720$$ 0 0
$$721$$ −24.0000 −0.893807
$$722$$ 0 0
$$723$$ −32.0000 32.0000i −1.19009 1.19009i
$$724$$ 0 0
$$725$$ 12.0000 + 16.0000i 0.445669 + 0.594225i
$$726$$ 0 0
$$727$$ −18.0000 18.0000i −0.667583 0.667583i 0.289573 0.957156i $$-0.406487\pi$$
−0.957156 + 0.289573i $$0.906487\pi$$
$$728$$ 0 0
$$729$$ 43.0000i 1.59259i
$$730$$ 0 0
$$731$$ −60.0000 −2.21918
$$732$$ 0 0
$$733$$ −21.0000 + 21.0000i −0.775653 + 0.775653i −0.979088 0.203436i $$-0.934789\pi$$
0.203436 + 0.979088i $$0.434789\pi$$
$$734$$ 0 0
$$735$$ −2.00000 6.00000i −0.0737711 0.221313i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 44.0000i 1.61857i 0.587419 + 0.809283i $$0.300144\pi$$
−0.587419 + 0.809283i $$0.699856\pi$$
$$740$$ 0 0
$$741$$ 16.0000i 0.587775i
$$742$$ 0 0
$$743$$ −30.0000 + 30.0000i −1.10059 + 1.10059i −0.106254 + 0.994339i $$0.533886\pi$$
−0.994339 + 0.106254i $$0.966114\pi$$
$$744$$ 0 0
$$745$$ −18.0000 + 36.0000i −0.659469 + 1.31894i
$$746$$ 0 0
$$747$$ 10.0000 10.0000i 0.365881 0.365881i
$$748$$ 0 0
$$749$$ −24.0000 −0.876941
$$750$$ 0 0
$$751$$ 44.0000i 1.60558i −0.596260 0.802791i $$-0.703347\pi$$
0.596260 0.802791i $$-0.296653\pi$$
$$752$$ 0 0
$$753$$ 48.0000 + 48.0000i 1.74922 + 1.74922i
$$754$$ 0 0
$$755$$ −24.0000 12.0000i −0.873449 0.436725i
$$756$$ 0 0
$$757$$ 1.00000 + 1.00000i 0.0363456 + 0.0363456i 0.725046 0.688700i $$-0.241818\pi$$
−0.688700 + 0.725046i $$0.741818\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 22.0000 0.797499 0.398750 0.917060i $$-0.369444\pi$$
0.398750 + 0.917060i $$0.369444\pi$$
$$762$$ 0 0
$$763$$ −20.0000 20.0000i −0.724049 0.724049i
$$764$$ 0 0
$$765$$ 75.0000 25.0000i 2.71163 0.903877i
$$766$$ 0 0
$$767$$ −4.00000 4.00000i −0.144432 0.144432i
$$768$$ 0 0
$$769$$ 40.0000i 1.44244i −0.692708 0.721218i $$-0.743582\pi$$
0.692708 0.721218i $$-0.256418\pi$$
$$770$$ 0 0
$$771$$ 28.0000 1.00840
$$772$$ 0 0
$$773$$ −1.00000 + 1.00000i −0.0359675 + 0.0359675i −0.724862 0.688894i $$-0.758096\pi$$
0.688894 + 0.724862i $$0.258096\pi$$
$$774$$ 0 0
$$775$$ 16.0000 12.0000i 0.574737 0.431053i
$$776$$ 0 0
$$777$$ −8.00000 + 8.00000i −0.286998 + 0.286998i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 16.0000 16.0000i 0.571793 0.571793i
$$784$$ 0 0
$$785$$ 27.0000 9.00000i 0.963671 0.321224i
$$786$$ 0 0
$$787$$ −30.0000 + 30.0000i −1.06938 + 1.06938i −0.0719783 + 0.997406i $$0.522931\pi$$
−0.997406 + 0.0719783i $$0.977069\pi$$
$$788$$ 0 0
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 36.0000i 1.28001i
$$792$$ 0 0
$$793$$ −4.00000 4.00000i −0.142044 0.142044i
$$794$$ 0 0
$$795$$ 28.0000 56.0000i 0.993058 1.98612i
$$796$$ 0 0
$$797$$ −29.0000 29.0000i −1.02723 1.02723i −0.999619 0.0276140i $$-0.991209\pi$$
−0.0276140 0.999619i $$-0.508791\pi$$
$$798$$ 0