# Properties

 Label 140.2.e.a.29.1 Level $140$ Weight $2$ Character 140.29 Analytic conductor $1.118$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 140.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

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

## Embedding invariants

 Embedding label 29.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 140.29 Dual form 140.2.e.a.29.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.00000i q^{3} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{7} -6.00000 q^{9} +O(q^{10})$$ $$q-3.00000i q^{3} +(-2.00000 - 1.00000i) q^{5} +1.00000i q^{7} -6.00000 q^{9} +3.00000 q^{11} -1.00000i q^{13} +(-3.00000 + 6.00000i) q^{15} -5.00000i q^{17} +8.00000 q^{19} +3.00000 q^{21} -2.00000i q^{23} +(3.00000 + 4.00000i) q^{25} +9.00000i q^{27} +1.00000 q^{29} -2.00000 q^{31} -9.00000i q^{33} +(1.00000 - 2.00000i) q^{35} +10.0000i q^{37} -3.00000 q^{39} -6.00000 q^{41} +4.00000i q^{43} +(12.0000 + 6.00000i) q^{45} +11.0000i q^{47} -1.00000 q^{49} -15.0000 q^{51} -6.00000i q^{53} +(-6.00000 - 3.00000i) q^{55} -24.0000i q^{57} +10.0000 q^{59} -6.00000i q^{63} +(-1.00000 + 2.00000i) q^{65} -10.0000i q^{67} -6.00000 q^{69} +10.0000i q^{73} +(12.0000 - 9.00000i) q^{75} +3.00000i q^{77} +7.00000 q^{79} +9.00000 q^{81} -12.0000i q^{83} +(-5.00000 + 10.0000i) q^{85} -3.00000i q^{87} -8.00000 q^{89} +1.00000 q^{91} +6.00000i q^{93} +(-16.0000 - 8.00000i) q^{95} +3.00000i q^{97} -18.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 4 q^{5} - 12 q^{9}+O(q^{10})$$ 2 * q - 4 * q^5 - 12 * q^9 $$2 q - 4 q^{5} - 12 q^{9} + 6 q^{11} - 6 q^{15} + 16 q^{19} + 6 q^{21} + 6 q^{25} + 2 q^{29} - 4 q^{31} + 2 q^{35} - 6 q^{39} - 12 q^{41} + 24 q^{45} - 2 q^{49} - 30 q^{51} - 12 q^{55} + 20 q^{59} - 2 q^{65} - 12 q^{69} + 24 q^{75} + 14 q^{79} + 18 q^{81} - 10 q^{85} - 16 q^{89} + 2 q^{91} - 32 q^{95} - 36 q^{99}+O(q^{100})$$ 2 * q - 4 * q^5 - 12 * q^9 + 6 * q^11 - 6 * q^15 + 16 * q^19 + 6 * q^21 + 6 * q^25 + 2 * q^29 - 4 * q^31 + 2 * q^35 - 6 * q^39 - 12 * q^41 + 24 * q^45 - 2 * q^49 - 30 * q^51 - 12 * q^55 + 20 * q^59 - 2 * q^65 - 12 * q^69 + 24 * q^75 + 14 * q^79 + 18 * q^81 - 10 * q^85 - 16 * q^89 + 2 * q^91 - 32 * q^95 - 36 * q^99

## Character values

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

 $$n$$ $$57$$ $$71$$ $$101$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$3$$ 3.00000i 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$4$$ 0 0
$$5$$ −2.00000 1.00000i −0.894427 0.447214i
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ −6.00000 −2.00000
$$10$$ 0 0
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 0 0
$$13$$ 1.00000i 0.277350i −0.990338 0.138675i $$-0.955716\pi$$
0.990338 0.138675i $$-0.0442844\pi$$
$$14$$ 0 0
$$15$$ −3.00000 + 6.00000i −0.774597 + 1.54919i
$$16$$ 0 0
$$17$$ 5.00000i 1.21268i −0.795206 0.606339i $$-0.792637\pi$$
0.795206 0.606339i $$-0.207363\pi$$
$$18$$ 0 0
$$19$$ 8.00000 1.83533 0.917663 0.397360i $$-0.130073\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 0 0
$$21$$ 3.00000 0.654654
$$22$$ 0 0
$$23$$ 2.00000i 0.417029i −0.978019 0.208514i $$-0.933137\pi$$
0.978019 0.208514i $$-0.0668628\pi$$
$$24$$ 0 0
$$25$$ 3.00000 + 4.00000i 0.600000 + 0.800000i
$$26$$ 0 0
$$27$$ 9.00000i 1.73205i
$$28$$ 0 0
$$29$$ 1.00000 0.185695 0.0928477 0.995680i $$-0.470403\pi$$
0.0928477 + 0.995680i $$0.470403\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ 0 0
$$33$$ 9.00000i 1.56670i
$$34$$ 0 0
$$35$$ 1.00000 2.00000i 0.169031 0.338062i
$$36$$ 0 0
$$37$$ 10.0000i 1.64399i 0.569495 + 0.821995i $$0.307139\pi$$
−0.569495 + 0.821995i $$0.692861\pi$$
$$38$$ 0 0
$$39$$ −3.00000 −0.480384
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 4.00000i 0.609994i 0.952353 + 0.304997i $$0.0986555\pi$$
−0.952353 + 0.304997i $$0.901344\pi$$
$$44$$ 0 0
$$45$$ 12.0000 + 6.00000i 1.78885 + 0.894427i
$$46$$ 0 0
$$47$$ 11.0000i 1.60451i 0.596978 + 0.802257i $$0.296368\pi$$
−0.596978 + 0.802257i $$0.703632\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ −15.0000 −2.10042
$$52$$ 0 0
$$53$$ 6.00000i 0.824163i −0.911147 0.412082i $$-0.864802\pi$$
0.911147 0.412082i $$-0.135198\pi$$
$$54$$ 0 0
$$55$$ −6.00000 3.00000i −0.809040 0.404520i
$$56$$ 0 0
$$57$$ 24.0000i 3.17888i
$$58$$ 0 0
$$59$$ 10.0000 1.30189 0.650945 0.759125i $$-0.274373\pi$$
0.650945 + 0.759125i $$0.274373\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 0 0
$$63$$ 6.00000i 0.755929i
$$64$$ 0 0
$$65$$ −1.00000 + 2.00000i −0.124035 + 0.248069i
$$66$$ 0 0
$$67$$ 10.0000i 1.22169i −0.791748 0.610847i $$-0.790829\pi$$
0.791748 0.610847i $$-0.209171\pi$$
$$68$$ 0 0
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 10.0000i 1.17041i 0.810885 + 0.585206i $$0.198986\pi$$
−0.810885 + 0.585206i $$0.801014\pi$$
$$74$$ 0 0
$$75$$ 12.0000 9.00000i 1.38564 1.03923i
$$76$$ 0 0
$$77$$ 3.00000i 0.341882i
$$78$$ 0 0
$$79$$ 7.00000 0.787562 0.393781 0.919204i $$-0.371167\pi$$
0.393781 + 0.919204i $$0.371167\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 12.0000i 1.31717i −0.752506 0.658586i $$-0.771155\pi$$
0.752506 0.658586i $$-0.228845\pi$$
$$84$$ 0 0
$$85$$ −5.00000 + 10.0000i −0.542326 + 1.08465i
$$86$$ 0 0
$$87$$ 3.00000i 0.321634i
$$88$$ 0 0
$$89$$ −8.00000 −0.847998 −0.423999 0.905663i $$-0.639374\pi$$
−0.423999 + 0.905663i $$0.639374\pi$$
$$90$$ 0 0
$$91$$ 1.00000 0.104828
$$92$$ 0 0
$$93$$ 6.00000i 0.622171i
$$94$$ 0 0
$$95$$ −16.0000 8.00000i −1.64157 0.820783i
$$96$$ 0 0
$$97$$ 3.00000i 0.304604i 0.988334 + 0.152302i $$0.0486686\pi$$
−0.988334 + 0.152302i $$0.951331\pi$$
$$98$$ 0 0
$$99$$ −18.0000 −1.80907
$$100$$ 0 0
$$101$$ −12.0000 −1.19404 −0.597022 0.802225i $$-0.703650\pi$$
−0.597022 + 0.802225i $$0.703650\pi$$
$$102$$ 0 0
$$103$$ 5.00000i 0.492665i 0.969185 + 0.246332i $$0.0792255\pi$$
−0.969185 + 0.246332i $$0.920775\pi$$
$$104$$ 0 0
$$105$$ −6.00000 3.00000i −0.585540 0.292770i
$$106$$ 0 0
$$107$$ 8.00000i 0.773389i 0.922208 + 0.386695i $$0.126383\pi$$
−0.922208 + 0.386695i $$0.873617\pi$$
$$108$$ 0 0
$$109$$ 7.00000 0.670478 0.335239 0.942133i $$-0.391183\pi$$
0.335239 + 0.942133i $$0.391183\pi$$
$$110$$ 0 0
$$111$$ 30.0000 2.84747
$$112$$ 0 0
$$113$$ 10.0000i 0.940721i 0.882474 + 0.470360i $$0.155876\pi$$
−0.882474 + 0.470360i $$0.844124\pi$$
$$114$$ 0 0
$$115$$ −2.00000 + 4.00000i −0.186501 + 0.373002i
$$116$$ 0 0
$$117$$ 6.00000i 0.554700i
$$118$$ 0 0
$$119$$ 5.00000 0.458349
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 0 0
$$123$$ 18.0000i 1.62301i
$$124$$ 0 0
$$125$$ −2.00000 11.0000i −0.178885 0.983870i
$$126$$ 0 0
$$127$$ 2.00000i 0.177471i −0.996055 0.0887357i $$-0.971717\pi$$
0.996055 0.0887357i $$-0.0282826\pi$$
$$128$$ 0 0
$$129$$ 12.0000 1.05654
$$130$$ 0 0
$$131$$ 2.00000 0.174741 0.0873704 0.996176i $$-0.472154\pi$$
0.0873704 + 0.996176i $$0.472154\pi$$
$$132$$ 0 0
$$133$$ 8.00000i 0.693688i
$$134$$ 0 0
$$135$$ 9.00000 18.0000i 0.774597 1.54919i
$$136$$ 0 0
$$137$$ 4.00000i 0.341743i 0.985293 + 0.170872i $$0.0546583\pi$$
−0.985293 + 0.170872i $$0.945342\pi$$
$$138$$ 0 0
$$139$$ −10.0000 −0.848189 −0.424094 0.905618i $$-0.639408\pi$$
−0.424094 + 0.905618i $$0.639408\pi$$
$$140$$ 0 0
$$141$$ 33.0000 2.77910
$$142$$ 0 0
$$143$$ 3.00000i 0.250873i
$$144$$ 0 0
$$145$$ −2.00000 1.00000i −0.166091 0.0830455i
$$146$$ 0 0
$$147$$ 3.00000i 0.247436i
$$148$$ 0 0
$$149$$ 6.00000 0.491539 0.245770 0.969328i $$-0.420959\pi$$
0.245770 + 0.969328i $$0.420959\pi$$
$$150$$ 0 0
$$151$$ 9.00000 0.732410 0.366205 0.930534i $$-0.380657\pi$$
0.366205 + 0.930534i $$0.380657\pi$$
$$152$$ 0 0
$$153$$ 30.0000i 2.42536i
$$154$$ 0 0
$$155$$ 4.00000 + 2.00000i 0.321288 + 0.160644i
$$156$$ 0 0
$$157$$ 18.0000i 1.43656i −0.695756 0.718278i $$-0.744931\pi$$
0.695756 0.718278i $$-0.255069\pi$$
$$158$$ 0 0
$$159$$ −18.0000 −1.42749
$$160$$ 0 0
$$161$$ 2.00000 0.157622
$$162$$ 0 0
$$163$$ 6.00000i 0.469956i −0.972001 0.234978i $$-0.924498\pi$$
0.972001 0.234978i $$-0.0755019\pi$$
$$164$$ 0 0
$$165$$ −9.00000 + 18.0000i −0.700649 + 1.40130i
$$166$$ 0 0
$$167$$ 3.00000i 0.232147i 0.993241 + 0.116073i $$0.0370308\pi$$
−0.993241 + 0.116073i $$0.962969\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ −48.0000 −3.67065
$$172$$ 0 0
$$173$$ 9.00000i 0.684257i 0.939653 + 0.342129i $$0.111148\pi$$
−0.939653 + 0.342129i $$0.888852\pi$$
$$174$$ 0 0
$$175$$ −4.00000 + 3.00000i −0.302372 + 0.226779i
$$176$$ 0 0
$$177$$ 30.0000i 2.25494i
$$178$$ 0 0
$$179$$ −4.00000 −0.298974 −0.149487 0.988764i $$-0.547762\pi$$
−0.149487 + 0.988764i $$0.547762\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 10.0000 20.0000i 0.735215 1.47043i
$$186$$ 0 0
$$187$$ 15.0000i 1.09691i
$$188$$ 0 0
$$189$$ −9.00000 −0.654654
$$190$$ 0 0
$$191$$ 7.00000 0.506502 0.253251 0.967401i $$-0.418500\pi$$
0.253251 + 0.967401i $$0.418500\pi$$
$$192$$ 0 0
$$193$$ 8.00000i 0.575853i −0.957653 0.287926i $$-0.907034\pi$$
0.957653 0.287926i $$-0.0929658\pi$$
$$194$$ 0 0
$$195$$ 6.00000 + 3.00000i 0.429669 + 0.214834i
$$196$$ 0 0
$$197$$ 10.0000i 0.712470i 0.934396 + 0.356235i $$0.115940\pi$$
−0.934396 + 0.356235i $$0.884060\pi$$
$$198$$ 0 0
$$199$$ −18.0000 −1.27599 −0.637993 0.770042i $$-0.720235\pi$$
−0.637993 + 0.770042i $$0.720235\pi$$
$$200$$ 0 0
$$201$$ −30.0000 −2.11604
$$202$$ 0 0
$$203$$ 1.00000i 0.0701862i
$$204$$ 0 0
$$205$$ 12.0000 + 6.00000i 0.838116 + 0.419058i
$$206$$ 0 0
$$207$$ 12.0000i 0.834058i
$$208$$ 0 0
$$209$$ 24.0000 1.66011
$$210$$ 0 0
$$211$$ −3.00000 −0.206529 −0.103264 0.994654i $$-0.532929\pi$$
−0.103264 + 0.994654i $$0.532929\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 4.00000 8.00000i 0.272798 0.545595i
$$216$$ 0 0
$$217$$ 2.00000i 0.135769i
$$218$$ 0 0
$$219$$ 30.0000 2.02721
$$220$$ 0 0
$$221$$ −5.00000 −0.336336
$$222$$ 0 0
$$223$$ 19.0000i 1.27233i −0.771551 0.636167i $$-0.780519\pi$$
0.771551 0.636167i $$-0.219481\pi$$
$$224$$ 0 0
$$225$$ −18.0000 24.0000i −1.20000 1.60000i
$$226$$ 0 0
$$227$$ 27.0000i 1.79205i 0.444001 + 0.896026i $$0.353559\pi$$
−0.444001 + 0.896026i $$0.646441\pi$$
$$228$$ 0 0
$$229$$ 26.0000 1.71813 0.859064 0.511868i $$-0.171046\pi$$
0.859064 + 0.511868i $$0.171046\pi$$
$$230$$ 0 0
$$231$$ 9.00000 0.592157
$$232$$ 0 0
$$233$$ 16.0000i 1.04819i −0.851658 0.524097i $$-0.824403\pi$$
0.851658 0.524097i $$-0.175597\pi$$
$$234$$ 0 0
$$235$$ 11.0000 22.0000i 0.717561 1.43512i
$$236$$ 0 0
$$237$$ 21.0000i 1.36410i
$$238$$ 0 0
$$239$$ −5.00000 −0.323423 −0.161712 0.986838i $$-0.551701\pi$$
−0.161712 + 0.986838i $$0.551701\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 2.00000 + 1.00000i 0.127775 + 0.0638877i
$$246$$ 0 0
$$247$$ 8.00000i 0.509028i
$$248$$ 0 0
$$249$$ −36.0000 −2.28141
$$250$$ 0 0
$$251$$ 2.00000 0.126239 0.0631194 0.998006i $$-0.479895\pi$$
0.0631194 + 0.998006i $$0.479895\pi$$
$$252$$ 0 0
$$253$$ 6.00000i 0.377217i
$$254$$ 0 0
$$255$$ 30.0000 + 15.0000i 1.87867 + 0.939336i
$$256$$ 0 0
$$257$$ 6.00000i 0.374270i 0.982334 + 0.187135i $$0.0599201\pi$$
−0.982334 + 0.187135i $$0.940080\pi$$
$$258$$ 0 0
$$259$$ −10.0000 −0.621370
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ 24.0000i 1.47990i 0.672660 + 0.739952i $$0.265152\pi$$
−0.672660 + 0.739952i $$0.734848\pi$$
$$264$$ 0 0
$$265$$ −6.00000 + 12.0000i −0.368577 + 0.737154i
$$266$$ 0 0
$$267$$ 24.0000i 1.46878i
$$268$$ 0 0
$$269$$ −2.00000 −0.121942 −0.0609711 0.998140i $$-0.519420\pi$$
−0.0609711 + 0.998140i $$0.519420\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 3.00000i 0.181568i
$$274$$ 0 0
$$275$$ 9.00000 + 12.0000i 0.542720 + 0.723627i
$$276$$ 0 0
$$277$$ 14.0000i 0.841178i −0.907251 0.420589i $$-0.861823\pi$$
0.907251 0.420589i $$-0.138177\pi$$
$$278$$ 0 0
$$279$$ 12.0000 0.718421
$$280$$ 0 0
$$281$$ 15.0000 0.894825 0.447412 0.894328i $$-0.352346\pi$$
0.447412 + 0.894328i $$0.352346\pi$$
$$282$$ 0 0
$$283$$ 7.00000i 0.416107i 0.978117 + 0.208053i $$0.0667128\pi$$
−0.978117 + 0.208053i $$0.933287\pi$$
$$284$$ 0 0
$$285$$ −24.0000 + 48.0000i −1.42164 + 2.84327i
$$286$$ 0 0
$$287$$ 6.00000i 0.354169i
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 9.00000 0.527589
$$292$$ 0 0
$$293$$ 15.0000i 0.876309i −0.898900 0.438155i $$-0.855632\pi$$
0.898900 0.438155i $$-0.144368\pi$$
$$294$$ 0 0
$$295$$ −20.0000 10.0000i −1.16445 0.582223i
$$296$$ 0 0
$$297$$ 27.0000i 1.56670i
$$298$$ 0 0
$$299$$ −2.00000 −0.115663
$$300$$ 0 0
$$301$$ −4.00000 −0.230556
$$302$$ 0 0
$$303$$ 36.0000i 2.06815i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 19.0000i 1.08439i −0.840254 0.542194i $$-0.817594\pi$$
0.840254 0.542194i $$-0.182406\pi$$
$$308$$ 0 0
$$309$$ 15.0000 0.853320
$$310$$ 0 0
$$311$$ 12.0000 0.680458 0.340229 0.940343i $$-0.389495\pi$$
0.340229 + 0.940343i $$0.389495\pi$$
$$312$$ 0 0
$$313$$ 7.00000i 0.395663i 0.980236 + 0.197832i $$0.0633900\pi$$
−0.980236 + 0.197832i $$0.936610\pi$$
$$314$$ 0 0
$$315$$ −6.00000 + 12.0000i −0.338062 + 0.676123i
$$316$$ 0 0
$$317$$ 28.0000i 1.57264i 0.617822 + 0.786318i $$0.288015\pi$$
−0.617822 + 0.786318i $$0.711985\pi$$
$$318$$ 0 0
$$319$$ 3.00000 0.167968
$$320$$ 0 0
$$321$$ 24.0000 1.33955
$$322$$ 0 0
$$323$$ 40.0000i 2.22566i
$$324$$ 0 0
$$325$$ 4.00000 3.00000i 0.221880 0.166410i
$$326$$ 0 0
$$327$$ 21.0000i 1.16130i
$$328$$ 0 0
$$329$$ −11.0000 −0.606450
$$330$$ 0 0
$$331$$ 20.0000 1.09930 0.549650 0.835395i $$-0.314761\pi$$
0.549650 + 0.835395i $$0.314761\pi$$
$$332$$ 0 0
$$333$$ 60.0000i 3.28798i
$$334$$ 0 0
$$335$$ −10.0000 + 20.0000i −0.546358 + 1.09272i
$$336$$ 0 0
$$337$$ 22.0000i 1.19842i 0.800593 + 0.599208i $$0.204518\pi$$
−0.800593 + 0.599208i $$0.795482\pi$$
$$338$$ 0 0
$$339$$ 30.0000 1.62938
$$340$$ 0 0
$$341$$ −6.00000 −0.324918
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ 12.0000 + 6.00000i 0.646058 + 0.323029i
$$346$$ 0 0
$$347$$ 18.0000i 0.966291i 0.875540 + 0.483145i $$0.160506\pi$$
−0.875540 + 0.483145i $$0.839494\pi$$
$$348$$ 0 0
$$349$$ −36.0000 −1.92704 −0.963518 0.267644i $$-0.913755\pi$$
−0.963518 + 0.267644i $$0.913755\pi$$
$$350$$ 0 0
$$351$$ 9.00000 0.480384
$$352$$ 0 0
$$353$$ 9.00000i 0.479022i 0.970894 + 0.239511i $$0.0769871\pi$$
−0.970894 + 0.239511i $$0.923013\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 15.0000i 0.793884i
$$358$$ 0 0
$$359$$ −28.0000 −1.47778 −0.738892 0.673824i $$-0.764651\pi$$
−0.738892 + 0.673824i $$0.764651\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ 0 0
$$363$$ 6.00000i 0.314918i
$$364$$ 0 0
$$365$$ 10.0000 20.0000i 0.523424 1.04685i
$$366$$ 0 0
$$367$$ 19.0000i 0.991792i 0.868382 + 0.495896i $$0.165160\pi$$
−0.868382 + 0.495896i $$0.834840\pi$$
$$368$$ 0 0
$$369$$ 36.0000 1.87409
$$370$$ 0 0
$$371$$ 6.00000 0.311504
$$372$$ 0 0
$$373$$ 32.0000i 1.65690i −0.560065 0.828449i $$-0.689224\pi$$
0.560065 0.828449i $$-0.310776\pi$$
$$374$$ 0 0
$$375$$ −33.0000 + 6.00000i −1.70411 + 0.309839i
$$376$$ 0 0
$$377$$ 1.00000i 0.0515026i
$$378$$ 0 0
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ 0 0
$$381$$ −6.00000 −0.307389
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 3.00000 6.00000i 0.152894 0.305788i
$$386$$ 0 0
$$387$$ 24.0000i 1.21999i
$$388$$ 0 0
$$389$$ −9.00000 −0.456318 −0.228159 0.973624i $$-0.573271\pi$$
−0.228159 + 0.973624i $$0.573271\pi$$
$$390$$ 0 0
$$391$$ −10.0000 −0.505722
$$392$$ 0 0
$$393$$ 6.00000i 0.302660i
$$394$$ 0 0
$$395$$ −14.0000 7.00000i −0.704416 0.352208i
$$396$$ 0 0
$$397$$ 17.0000i 0.853206i −0.904439 0.426603i $$-0.859710\pi$$
0.904439 0.426603i $$-0.140290\pi$$
$$398$$ 0 0
$$399$$ 24.0000 1.20150
$$400$$ 0 0
$$401$$ −27.0000 −1.34832 −0.674158 0.738587i $$-0.735493\pi$$
−0.674158 + 0.738587i $$0.735493\pi$$
$$402$$ 0 0
$$403$$ 2.00000i 0.0996271i
$$404$$ 0 0
$$405$$ −18.0000 9.00000i −0.894427 0.447214i
$$406$$ 0 0
$$407$$ 30.0000i 1.48704i
$$408$$ 0 0
$$409$$ −4.00000 −0.197787 −0.0988936 0.995098i $$-0.531530\pi$$
−0.0988936 + 0.995098i $$0.531530\pi$$
$$410$$ 0 0
$$411$$ 12.0000 0.591916
$$412$$ 0 0
$$413$$ 10.0000i 0.492068i
$$414$$ 0 0
$$415$$ −12.0000 + 24.0000i −0.589057 + 1.17811i
$$416$$ 0 0
$$417$$ 30.0000i 1.46911i
$$418$$ 0 0
$$419$$ −2.00000 −0.0977064 −0.0488532 0.998806i $$-0.515557\pi$$
−0.0488532 + 0.998806i $$0.515557\pi$$
$$420$$ 0 0
$$421$$ −23.0000 −1.12095 −0.560476 0.828171i $$-0.689382\pi$$
−0.560476 + 0.828171i $$0.689382\pi$$
$$422$$ 0 0
$$423$$ 66.0000i 3.20903i
$$424$$ 0 0
$$425$$ 20.0000 15.0000i 0.970143 0.727607i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −9.00000 −0.434524
$$430$$ 0 0
$$431$$ −37.0000 −1.78223 −0.891114 0.453780i $$-0.850075\pi$$
−0.891114 + 0.453780i $$0.850075\pi$$
$$432$$ 0 0
$$433$$ 38.0000i 1.82616i 0.407777 + 0.913082i $$0.366304\pi$$
−0.407777 + 0.913082i $$0.633696\pi$$
$$434$$ 0 0
$$435$$ −3.00000 + 6.00000i −0.143839 + 0.287678i
$$436$$ 0 0
$$437$$ 16.0000i 0.765384i
$$438$$ 0 0
$$439$$ −26.0000 −1.24091 −0.620456 0.784241i $$-0.713053\pi$$
−0.620456 + 0.784241i $$0.713053\pi$$
$$440$$ 0 0
$$441$$ 6.00000 0.285714
$$442$$ 0 0
$$443$$ 12.0000i 0.570137i −0.958507 0.285069i $$-0.907984\pi$$
0.958507 0.285069i $$-0.0920164\pi$$
$$444$$ 0 0
$$445$$ 16.0000 + 8.00000i 0.758473 + 0.379236i
$$446$$ 0 0
$$447$$ 18.0000i 0.851371i
$$448$$ 0 0
$$449$$ −11.0000 −0.519122 −0.259561 0.965727i $$-0.583578\pi$$
−0.259561 + 0.965727i $$0.583578\pi$$
$$450$$ 0 0
$$451$$ −18.0000 −0.847587
$$452$$ 0 0
$$453$$ 27.0000i 1.26857i
$$454$$ 0 0
$$455$$ −2.00000 1.00000i −0.0937614 0.0468807i
$$456$$ 0 0
$$457$$ 22.0000i 1.02912i −0.857455 0.514558i $$-0.827956\pi$$
0.857455 0.514558i $$-0.172044\pi$$
$$458$$ 0 0
$$459$$ 45.0000 2.10042
$$460$$ 0 0
$$461$$ 28.0000 1.30409 0.652045 0.758180i $$-0.273911\pi$$
0.652045 + 0.758180i $$0.273911\pi$$
$$462$$ 0 0
$$463$$ 4.00000i 0.185896i −0.995671 0.0929479i $$-0.970371\pi$$
0.995671 0.0929479i $$-0.0296290\pi$$
$$464$$ 0 0
$$465$$ 6.00000 12.0000i 0.278243 0.556487i
$$466$$ 0 0
$$467$$ 23.0000i 1.06431i −0.846646 0.532157i $$-0.821382\pi$$
0.846646 0.532157i $$-0.178618\pi$$
$$468$$ 0 0
$$469$$ 10.0000 0.461757
$$470$$ 0 0
$$471$$ −54.0000 −2.48819
$$472$$ 0 0
$$473$$ 12.0000i 0.551761i
$$474$$ 0 0
$$475$$ 24.0000 + 32.0000i 1.10120 + 1.46826i
$$476$$ 0 0
$$477$$ 36.0000i 1.64833i
$$478$$ 0 0
$$479$$ 18.0000 0.822441 0.411220 0.911536i $$-0.365103\pi$$
0.411220 + 0.911536i $$0.365103\pi$$
$$480$$ 0 0
$$481$$ 10.0000 0.455961
$$482$$ 0 0
$$483$$ 6.00000i 0.273009i
$$484$$ 0 0
$$485$$ 3.00000 6.00000i 0.136223 0.272446i
$$486$$ 0 0
$$487$$ 26.0000i 1.17817i −0.808070 0.589086i $$-0.799488\pi$$
0.808070 0.589086i $$-0.200512\pi$$
$$488$$ 0 0
$$489$$ −18.0000 −0.813988
$$490$$ 0 0
$$491$$ 33.0000 1.48927 0.744635 0.667472i $$-0.232624\pi$$
0.744635 + 0.667472i $$0.232624\pi$$
$$492$$ 0 0
$$493$$ 5.00000i 0.225189i
$$494$$ 0 0
$$495$$ 36.0000 + 18.0000i 1.61808 + 0.809040i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 29.0000 1.29822 0.649109 0.760695i $$-0.275142\pi$$
0.649109 + 0.760695i $$0.275142\pi$$
$$500$$ 0 0
$$501$$ 9.00000 0.402090
$$502$$ 0 0
$$503$$ 1.00000i 0.0445878i −0.999751 0.0222939i $$-0.992903\pi$$
0.999751 0.0222939i $$-0.00709696\pi$$
$$504$$ 0 0
$$505$$ 24.0000 + 12.0000i 1.06799 + 0.533993i
$$506$$ 0 0
$$507$$ 36.0000i 1.59882i
$$508$$ 0 0
$$509$$ −26.0000 −1.15243 −0.576215 0.817298i $$-0.695471\pi$$
−0.576215 + 0.817298i $$0.695471\pi$$
$$510$$ 0 0
$$511$$ −10.0000 −0.442374
$$512$$ 0 0
$$513$$ 72.0000i 3.17888i
$$514$$ 0 0
$$515$$ 5.00000 10.0000i 0.220326 0.440653i
$$516$$ 0 0
$$517$$ 33.0000i 1.45134i
$$518$$ 0 0
$$519$$ 27.0000 1.18517
$$520$$ 0 0
$$521$$ 12.0000 0.525730 0.262865 0.964833i $$-0.415333\pi$$
0.262865 + 0.964833i $$0.415333\pi$$
$$522$$ 0 0
$$523$$ 20.0000i 0.874539i 0.899331 + 0.437269i $$0.144054\pi$$
−0.899331 + 0.437269i $$0.855946\pi$$
$$524$$ 0 0
$$525$$ 9.00000 + 12.0000i 0.392792 + 0.523723i
$$526$$ 0 0
$$527$$ 10.0000i 0.435607i
$$528$$ 0 0
$$529$$ 19.0000 0.826087
$$530$$ 0 0
$$531$$ −60.0000 −2.60378
$$532$$ 0 0
$$533$$ 6.00000i 0.259889i
$$534$$ 0 0
$$535$$ 8.00000 16.0000i 0.345870 0.691740i
$$536$$ 0 0
$$537$$ 12.0000i 0.517838i
$$538$$ 0 0
$$539$$ −3.00000 −0.129219
$$540$$ 0 0
$$541$$ −25.0000 −1.07483 −0.537417 0.843317i $$-0.680600\pi$$
−0.537417 + 0.843317i $$0.680600\pi$$
$$542$$ 0 0
$$543$$ 30.0000i 1.28742i
$$544$$ 0 0
$$545$$ −14.0000 7.00000i −0.599694 0.299847i
$$546$$ 0 0
$$547$$ 8.00000i 0.342055i −0.985266 0.171028i $$-0.945291\pi$$
0.985266 0.171028i $$-0.0547087\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 8.00000 0.340811
$$552$$ 0 0
$$553$$ 7.00000i 0.297670i
$$554$$ 0 0
$$555$$ −60.0000 30.0000i −2.54686 1.27343i
$$556$$ 0 0
$$557$$ 20.0000i 0.847427i 0.905796 + 0.423714i $$0.139274\pi$$
−0.905796 + 0.423714i $$0.860726\pi$$
$$558$$ 0 0
$$559$$ 4.00000 0.169182
$$560$$ 0 0
$$561$$ −45.0000 −1.89990
$$562$$ 0 0
$$563$$ 16.0000i 0.674320i 0.941447 + 0.337160i $$0.109466\pi$$
−0.941447 + 0.337160i $$0.890534\pi$$
$$564$$ 0 0
$$565$$ 10.0000 20.0000i 0.420703 0.841406i
$$566$$ 0 0
$$567$$ 9.00000i 0.377964i
$$568$$ 0 0
$$569$$ −18.0000 −0.754599 −0.377300 0.926091i $$-0.623147\pi$$
−0.377300 + 0.926091i $$0.623147\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 0 0
$$573$$ 21.0000i 0.877288i
$$574$$ 0 0
$$575$$ 8.00000 6.00000i 0.333623 0.250217i
$$576$$ 0 0
$$577$$ 17.0000i 0.707719i 0.935299 + 0.353860i $$0.115131\pi$$
−0.935299 + 0.353860i $$0.884869\pi$$
$$578$$ 0 0
$$579$$ −24.0000 −0.997406
$$580$$ 0 0
$$581$$ 12.0000 0.497844
$$582$$ 0 0
$$583$$ 18.0000i 0.745484i
$$584$$ 0 0
$$585$$ 6.00000 12.0000i 0.248069 0.496139i
$$586$$ 0 0
$$587$$ 28.0000i 1.15568i 0.816149 + 0.577842i $$0.196105\pi$$
−0.816149 + 0.577842i $$0.803895\pi$$
$$588$$ 0 0
$$589$$ −16.0000 −0.659269
$$590$$ 0 0
$$591$$ 30.0000 1.23404
$$592$$ 0 0
$$593$$ 3.00000i 0.123195i 0.998101 + 0.0615976i $$0.0196196\pi$$
−0.998101 + 0.0615976i $$0.980380\pi$$
$$594$$ 0 0
$$595$$ −10.0000 5.00000i −0.409960 0.204980i
$$596$$ 0 0
$$597$$ 54.0000i 2.21007i
$$598$$ 0 0
$$599$$ 21.0000 0.858037 0.429018 0.903296i $$-0.358860\pi$$
0.429018 + 0.903296i $$0.358860\pi$$
$$600$$ 0 0
$$601$$ 8.00000 0.326327 0.163163 0.986599i $$-0.447830\pi$$
0.163163 + 0.986599i $$0.447830\pi$$
$$602$$ 0 0
$$603$$ 60.0000i 2.44339i
$$604$$ 0 0
$$605$$ 4.00000 + 2.00000i 0.162623 + 0.0813116i
$$606$$ 0 0
$$607$$ 5.00000i 0.202944i 0.994838 + 0.101472i $$0.0323552\pi$$
−0.994838 + 0.101472i $$0.967645\pi$$
$$608$$ 0 0
$$609$$ 3.00000 0.121566
$$610$$ 0 0
$$611$$ 11.0000 0.445012
$$612$$ 0 0
$$613$$ 12.0000i 0.484675i 0.970192 + 0.242338i $$0.0779142\pi$$
−0.970192 + 0.242338i $$0.922086\pi$$
$$614$$ 0 0
$$615$$ 18.0000 36.0000i 0.725830 1.45166i
$$616$$ 0 0
$$617$$ 34.0000i 1.36879i −0.729112 0.684394i $$-0.760067\pi$$
0.729112 0.684394i $$-0.239933\pi$$
$$618$$ 0 0
$$619$$ 2.00000 0.0803868 0.0401934 0.999192i $$-0.487203\pi$$
0.0401934 + 0.999192i $$0.487203\pi$$
$$620$$ 0 0
$$621$$ 18.0000 0.722315
$$622$$ 0 0
$$623$$ 8.00000i 0.320513i
$$624$$ 0 0
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ 0 0
$$627$$ 72.0000i 2.87540i
$$628$$ 0 0
$$629$$ 50.0000 1.99363
$$630$$ 0 0
$$631$$ 15.0000 0.597141 0.298570 0.954388i $$-0.403490\pi$$
0.298570 + 0.954388i $$0.403490\pi$$
$$632$$ 0 0
$$633$$ 9.00000i 0.357718i
$$634$$ 0 0
$$635$$ −2.00000 + 4.00000i −0.0793676 + 0.158735i
$$636$$ 0 0
$$637$$ 1.00000i 0.0396214i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −26.0000 −1.02694 −0.513469 0.858108i $$-0.671640\pi$$
−0.513469 + 0.858108i $$0.671640\pi$$
$$642$$ 0 0
$$643$$ 5.00000i 0.197181i 0.995128 + 0.0985904i $$0.0314334\pi$$
−0.995128 + 0.0985904i $$0.968567\pi$$
$$644$$ 0 0
$$645$$ −24.0000 12.0000i −0.944999 0.472500i
$$646$$ 0 0
$$647$$ 24.0000i 0.943537i −0.881722 0.471769i $$-0.843616\pi$$
0.881722 0.471769i $$-0.156384\pi$$
$$648$$ 0 0
$$649$$ 30.0000 1.17760
$$650$$ 0 0
$$651$$ −6.00000 −0.235159
$$652$$ 0 0
$$653$$ 36.0000i 1.40879i −0.709809 0.704394i $$-0.751219\pi$$
0.709809 0.704394i $$-0.248781\pi$$
$$654$$ 0 0
$$655$$ −4.00000 2.00000i −0.156293 0.0781465i
$$656$$ 0 0
$$657$$ 60.0000i 2.34082i
$$658$$ 0 0
$$659$$ −39.0000 −1.51922 −0.759612 0.650376i $$-0.774611\pi$$
−0.759612 + 0.650376i $$0.774611\pi$$
$$660$$ 0 0
$$661$$ 28.0000 1.08907 0.544537 0.838737i $$-0.316705\pi$$
0.544537 + 0.838737i $$0.316705\pi$$
$$662$$ 0 0
$$663$$ 15.0000i 0.582552i
$$664$$ 0 0
$$665$$ 8.00000 16.0000i 0.310227 0.620453i
$$666$$ 0 0
$$667$$ 2.00000i 0.0774403i
$$668$$ 0 0
$$669$$ −57.0000 −2.20375
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 16.0000i 0.616755i 0.951264 + 0.308377i $$0.0997859\pi$$
−0.951264 + 0.308377i $$0.900214\pi$$
$$674$$ 0 0
$$675$$ −36.0000 + 27.0000i −1.38564 + 1.03923i
$$676$$ 0 0
$$677$$ 11.0000i 0.422764i −0.977403 0.211382i $$-0.932204\pi$$
0.977403 0.211382i $$-0.0677965\pi$$
$$678$$ 0 0
$$679$$ −3.00000 −0.115129
$$680$$ 0 0
$$681$$ 81.0000 3.10393
$$682$$ 0 0
$$683$$ 40.0000i 1.53056i −0.643699 0.765279i $$-0.722601\pi$$
0.643699 0.765279i $$-0.277399\pi$$
$$684$$ 0 0
$$685$$ 4.00000 8.00000i 0.152832 0.305664i
$$686$$ 0 0
$$687$$ 78.0000i 2.97589i
$$688$$ 0 0
$$689$$ −6.00000 −0.228582
$$690$$ 0 0
$$691$$ 40.0000 1.52167 0.760836 0.648944i $$-0.224789\pi$$
0.760836 + 0.648944i $$0.224789\pi$$
$$692$$ 0 0
$$693$$ 18.0000i 0.683763i
$$694$$ 0 0
$$695$$ 20.0000 + 10.0000i 0.758643 + 0.379322i
$$696$$ 0 0
$$697$$ 30.0000i 1.13633i
$$698$$ 0 0
$$699$$ −48.0000 −1.81553
$$700$$ 0 0
$$701$$ −25.0000 −0.944237 −0.472118 0.881535i $$-0.656511\pi$$
−0.472118 + 0.881535i $$0.656511\pi$$
$$702$$ 0 0
$$703$$ 80.0000i 3.01726i
$$704$$ 0 0
$$705$$ −66.0000 33.0000i −2.48570 1.24285i
$$706$$ 0 0
$$707$$ 12.0000i 0.451306i
$$708$$ 0 0
$$709$$ −15.0000 −0.563337 −0.281668 0.959512i $$-0.590888\pi$$
−0.281668 + 0.959512i $$0.590888\pi$$
$$710$$ 0 0
$$711$$ −42.0000 −1.57512
$$712$$ 0 0
$$713$$ 4.00000i 0.149801i
$$714$$ 0 0
$$715$$ −3.00000 + 6.00000i −0.112194 + 0.224387i
$$716$$ 0 0
$$717$$ 15.0000i 0.560185i
$$718$$ 0 0
$$719$$ −2.00000 −0.0745874 −0.0372937 0.999304i $$-0.511874\pi$$
−0.0372937 + 0.999304i $$0.511874\pi$$
$$720$$ 0 0
$$721$$ −5.00000 −0.186210
$$722$$ 0 0
$$723$$ 54.0000i 2.00828i
$$724$$ 0 0
$$725$$ 3.00000 + 4.00000i 0.111417 + 0.148556i
$$726$$ 0 0
$$727$$ 28.0000i 1.03846i 0.854634 + 0.519231i $$0.173782\pi$$
−0.854634 + 0.519231i $$0.826218\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 20.0000 0.739727
$$732$$ 0 0
$$733$$ 41.0000i 1.51437i −0.653201 0.757185i $$-0.726574\pi$$
0.653201 0.757185i $$-0.273426\pi$$
$$734$$ 0 0
$$735$$ 3.00000 6.00000i 0.110657 0.221313i
$$736$$ 0 0
$$737$$ 30.0000i 1.10506i
$$738$$ 0 0
$$739$$ 5.00000 0.183928 0.0919640 0.995762i $$-0.470686\pi$$
0.0919640 + 0.995762i $$0.470686\pi$$
$$740$$ 0 0
$$741$$ −24.0000 −0.881662
$$742$$ 0 0
$$743$$ 30.0000i 1.10059i −0.834969 0.550297i $$-0.814515\pi$$
0.834969 0.550297i $$-0.185485\pi$$
$$744$$ 0 0
$$745$$ −12.0000 6.00000i −0.439646 0.219823i
$$746$$ 0 0
$$747$$ 72.0000i 2.63434i
$$748$$ 0 0
$$749$$ −8.00000 −0.292314
$$750$$ 0 0
$$751$$ 13.0000 0.474377 0.237188 0.971464i $$-0.423774\pi$$
0.237188 + 0.971464i $$0.423774\pi$$
$$752$$ 0 0
$$753$$ 6.00000i 0.218652i
$$754$$ 0 0
$$755$$ −18.0000 9.00000i −0.655087 0.327544i
$$756$$ 0 0
$$757$$ 48.0000i 1.74459i −0.488980 0.872295i $$-0.662631\pi$$
0.488980 0.872295i $$-0.337369\pi$$
$$758$$ 0 0
$$759$$ −18.0000 −0.653359
$$760$$ 0 0
$$761$$ −38.0000 −1.37750 −0.688749 0.724999i $$-0.741840\pi$$
−0.688749 + 0.724999i $$0.741840\pi$$
$$762$$ 0 0
$$763$$ 7.00000i 0.253417i
$$764$$ 0 0
$$765$$ 30.0000 60.0000i 1.08465 2.16930i
$$766$$ 0 0
$$767$$ 10.0000i 0.361079i
$$768$$ 0 0
$$769$$ −16.0000 −0.576975 −0.288487 0.957484i $$-0.593152\pi$$
−0.288487 + 0.957484i $$0.593152\pi$$
$$770$$ 0 0
$$771$$ 18.0000 0.648254
$$772$$ 0 0
$$773$$ 27.0000i 0.971123i 0.874203 + 0.485561i $$0.161385\pi$$
−0.874203 + 0.485561i $$0.838615\pi$$
$$774$$ 0 0
$$775$$ −6.00000 8.00000i −0.215526 0.287368i
$$776$$ 0 0
$$777$$ 30.0000i 1.07624i
$$778$$ 0 0
$$779$$ −48.0000 −1.71978
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 9.00000i 0.321634i
$$784$$ 0 0
$$785$$ −18.0000 + 36.0000i −0.642448 + 1.28490i
$$786$$ 0 0
$$787$$ 3.00000i 0.106938i 0.998569 + 0.0534692i $$0.0170279\pi$$
−0.998569 + 0.0534692i $$0.982972\pi$$
$$788$$ 0 0
$$789$$ 72.0000 2.56327
$$790$$ 0 0
$$791$$ −10.0000 −0.355559
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 36.0000 + 18.0000i 1.27679 + 0.638394i
$$796$$ 0 0
$$797$$ 43.0000i 1.52314i 0.648084 + 0.761569i $$0.275571\pi$$
−0.648084 + 0.761569i $$0.724429\pi$$
$$798$$ 0 0
$$799$$ 55.0000