# Properties

 Label 1008.2.cz.a.367.1 Level $1008$ Weight $2$ Character 1008.367 Analytic conductor $8.049$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1008.cz (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.04892052375$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 367.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1008.367 Dual form 1008.2.cz.a.607.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-3.00000 + 1.73205i) q^{11} +(-1.50000 + 0.866025i) q^{13} +(1.50000 + 0.866025i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-1.50000 - 4.33013i) q^{21} +(3.00000 + 1.73205i) q^{23} +(-2.50000 - 4.33013i) q^{25} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +1.00000 q^{31} +(3.00000 - 5.19615i) q^{33} +(-3.50000 - 6.06218i) q^{37} +(1.50000 - 2.59808i) q^{39} +(-1.50000 + 0.866025i) q^{41} +(1.50000 + 0.866025i) q^{43} -9.00000 q^{47} +(-6.50000 - 2.59808i) q^{49} -3.00000 q^{51} +(4.50000 - 7.79423i) q^{53} +(7.50000 + 4.33013i) q^{57} -15.0000 q^{59} -1.73205i q^{61} +(6.00000 + 5.19615i) q^{63} -15.5885i q^{67} -6.00000 q^{69} -10.3923i q^{71} +(1.50000 + 0.866025i) q^{73} +(7.50000 + 4.33013i) q^{75} +(-3.00000 - 8.66025i) q^{77} -1.73205i q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{83} -5.19615i q^{87} +(1.50000 - 0.866025i) q^{89} +(-1.50000 - 4.33013i) q^{91} +(-1.50000 + 0.866025i) q^{93} +(-1.50000 - 0.866025i) q^{97} +10.3923i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 3 q^{3} - q^{7} + 3 q^{9} + O(q^{10})$$ $$2 q - 3 q^{3} - q^{7} + 3 q^{9} - 6 q^{11} - 3 q^{13} + 3 q^{17} - 5 q^{19} - 3 q^{21} + 6 q^{23} - 5 q^{25} - 3 q^{29} + 2 q^{31} + 6 q^{33} - 7 q^{37} + 3 q^{39} - 3 q^{41} + 3 q^{43} - 18 q^{47} - 13 q^{49} - 6 q^{51} + 9 q^{53} + 15 q^{57} - 30 q^{59} + 12 q^{63} - 12 q^{69} + 3 q^{73} + 15 q^{75} - 6 q^{77} - 9 q^{81} - 9 q^{83} + 3 q^{89} - 3 q^{91} - 3 q^{93} - 3 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$577$$ $$757$$ $$785$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.50000 + 0.866025i −0.866025 + 0.500000i
$$4$$ 0 0
$$5$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$6$$ 0 0
$$7$$ −0.500000 + 2.59808i −0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ 1.50000 2.59808i 0.500000 0.866025i
$$10$$ 0 0
$$11$$ −3.00000 + 1.73205i −0.904534 + 0.522233i −0.878668 0.477432i $$-0.841568\pi$$
−0.0258656 + 0.999665i $$0.508234\pi$$
$$12$$ 0 0
$$13$$ −1.50000 + 0.866025i −0.416025 + 0.240192i −0.693375 0.720577i $$-0.743877\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.50000 + 0.866025i 0.363803 + 0.210042i 0.670748 0.741685i $$-0.265973\pi$$
−0.306944 + 0.951727i $$0.599307\pi$$
$$18$$ 0 0
$$19$$ −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i $$-0.972237\pi$$
0.422659 0.906289i $$-0.361097\pi$$
$$20$$ 0 0
$$21$$ −1.50000 4.33013i −0.327327 0.944911i
$$22$$ 0 0
$$23$$ 3.00000 + 1.73205i 0.625543 + 0.361158i 0.779024 0.626994i $$-0.215715\pi$$
−0.153481 + 0.988152i $$0.549048\pi$$
$$24$$ 0 0
$$25$$ −2.50000 4.33013i −0.500000 0.866025i
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ 0 0
$$29$$ −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i $$-0.923185\pi$$
0.692480 + 0.721437i $$0.256518\pi$$
$$30$$ 0 0
$$31$$ 1.00000 0.179605 0.0898027 0.995960i $$-0.471376\pi$$
0.0898027 + 0.995960i $$0.471376\pi$$
$$32$$ 0 0
$$33$$ 3.00000 5.19615i 0.522233 0.904534i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i $$-0.971514\pi$$
0.420602 0.907245i $$-0.361819\pi$$
$$38$$ 0 0
$$39$$ 1.50000 2.59808i 0.240192 0.416025i
$$40$$ 0 0
$$41$$ −1.50000 + 0.866025i −0.234261 + 0.135250i −0.612536 0.790443i $$-0.709851\pi$$
0.378275 + 0.925693i $$0.376517\pi$$
$$42$$ 0 0
$$43$$ 1.50000 + 0.866025i 0.228748 + 0.132068i 0.609994 0.792406i $$-0.291172\pi$$
−0.381246 + 0.924473i $$0.624505\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −9.00000 −1.31278 −0.656392 0.754420i $$-0.727918\pi$$
−0.656392 + 0.754420i $$0.727918\pi$$
$$48$$ 0 0
$$49$$ −6.50000 2.59808i −0.928571 0.371154i
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 0 0
$$53$$ 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i $$-0.621227\pi$$
0.989828 0.142269i $$-0.0454398\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 7.50000 + 4.33013i 0.993399 + 0.573539i
$$58$$ 0 0
$$59$$ −15.0000 −1.95283 −0.976417 0.215894i $$-0.930733\pi$$
−0.976417 + 0.215894i $$0.930733\pi$$
$$60$$ 0 0
$$61$$ 1.73205i 0.221766i −0.993833 0.110883i $$-0.964632\pi$$
0.993833 0.110883i $$-0.0353679\pi$$
$$62$$ 0 0
$$63$$ 6.00000 + 5.19615i 0.755929 + 0.654654i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 15.5885i 1.90443i −0.305424 0.952217i $$-0.598798\pi$$
0.305424 0.952217i $$-0.401202\pi$$
$$68$$ 0 0
$$69$$ −6.00000 −0.722315
$$70$$ 0 0
$$71$$ 10.3923i 1.23334i −0.787222 0.616670i $$-0.788481\pi$$
0.787222 0.616670i $$-0.211519\pi$$
$$72$$ 0 0
$$73$$ 1.50000 + 0.866025i 0.175562 + 0.101361i 0.585206 0.810885i $$-0.301014\pi$$
−0.409644 + 0.912245i $$0.634347\pi$$
$$74$$ 0 0
$$75$$ 7.50000 + 4.33013i 0.866025 + 0.500000i
$$76$$ 0 0
$$77$$ −3.00000 8.66025i −0.341882 0.986928i
$$78$$ 0 0
$$79$$ 1.73205i 0.194871i −0.995242 0.0974355i $$-0.968936\pi$$
0.995242 0.0974355i $$-0.0310640\pi$$
$$80$$ 0 0
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ 0 0
$$83$$ −4.50000 + 7.79423i −0.493939 + 0.855528i −0.999976 0.00698436i $$-0.997777\pi$$
0.506036 + 0.862512i $$0.331110\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 5.19615i 0.557086i
$$88$$ 0 0
$$89$$ 1.50000 0.866025i 0.159000 0.0917985i −0.418389 0.908268i $$-0.637405\pi$$
0.577389 + 0.816469i $$0.304072\pi$$
$$90$$ 0 0
$$91$$ −1.50000 4.33013i −0.157243 0.453921i
$$92$$ 0 0
$$93$$ −1.50000 + 0.866025i −0.155543 + 0.0898027i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.50000 0.866025i −0.152302 0.0879316i 0.421912 0.906637i $$-0.361359\pi$$
−0.574214 + 0.818705i $$0.694692\pi$$
$$98$$ 0 0
$$99$$ 10.3923i 1.04447i
$$100$$ 0 0
$$101$$ −12.0000 + 6.92820i −1.19404 + 0.689382i −0.959221 0.282656i $$-0.908784\pi$$
−0.234823 + 0.972038i $$0.575451\pi$$
$$102$$ 0 0
$$103$$ 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i $$-0.704379\pi$$
0.992990 + 0.118199i $$0.0377120\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.50000 + 0.866025i −0.145010 + 0.0837218i −0.570750 0.821124i $$-0.693347\pi$$
0.425739 + 0.904846i $$0.360014\pi$$
$$108$$ 0 0
$$109$$ −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i $$0.343277\pi$$
−0.999512 + 0.0312328i $$0.990057\pi$$
$$110$$ 0 0
$$111$$ 10.5000 + 6.06218i 0.996616 + 0.575396i
$$112$$ 0 0
$$113$$ 4.50000 + 7.79423i 0.423324 + 0.733219i 0.996262 0.0863794i $$-0.0275297\pi$$
−0.572938 + 0.819599i $$0.694196\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 5.19615i 0.480384i
$$118$$ 0 0
$$119$$ −3.00000 + 3.46410i −0.275010 + 0.317554i
$$120$$ 0 0
$$121$$ 0.500000 0.866025i 0.0454545 0.0787296i
$$122$$ 0 0
$$123$$ 1.50000 2.59808i 0.135250 0.234261i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 10.3923i 0.922168i −0.887357 0.461084i $$-0.847461\pi$$
0.887357 0.461084i $$-0.152539\pi$$
$$128$$ 0 0
$$129$$ −3.00000 −0.264135
$$130$$ 0 0
$$131$$ −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i $$0.342311\pi$$
−0.999602 + 0.0281993i $$0.991023\pi$$
$$132$$ 0 0
$$133$$ 12.5000 4.33013i 1.08389 0.375470i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i $$0.112540\pi$$
−0.169226 + 0.985577i $$0.554127\pi$$
$$138$$ 0 0
$$139$$ 2.50000 + 4.33013i 0.212047 + 0.367277i 0.952355 0.304991i $$-0.0986536\pi$$
−0.740308 + 0.672268i $$0.765320\pi$$
$$140$$ 0 0
$$141$$ 13.5000 7.79423i 1.13691 0.656392i
$$142$$ 0 0
$$143$$ 3.00000 5.19615i 0.250873 0.434524i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 12.0000 1.73205i 0.989743 0.142857i
$$148$$ 0 0
$$149$$ 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i $$-0.754293\pi$$
0.962348 + 0.271821i $$0.0876260\pi$$
$$150$$ 0 0
$$151$$ 15.0000 8.66025i 1.22068 0.704761i 0.255619 0.966778i $$-0.417721\pi$$
0.965064 + 0.262016i $$0.0843873\pi$$
$$152$$ 0 0
$$153$$ 4.50000 2.59808i 0.363803 0.210042i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 12.1244i 0.967629i −0.875171 0.483814i $$-0.839251\pi$$
0.875171 0.483814i $$-0.160749\pi$$
$$158$$ 0 0
$$159$$ 15.5885i 1.23625i
$$160$$ 0 0
$$161$$ −6.00000 + 6.92820i −0.472866 + 0.546019i
$$162$$ 0 0
$$163$$ −13.5000 + 7.79423i −1.05740 + 0.610491i −0.924712 0.380667i $$-0.875695\pi$$
−0.132689 + 0.991158i $$0.542361\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 10.5000 + 18.1865i 0.812514 + 1.40732i 0.911099 + 0.412188i $$0.135235\pi$$
−0.0985846 + 0.995129i $$0.531432\pi$$
$$168$$ 0 0
$$169$$ −5.00000 + 8.66025i −0.384615 + 0.666173i
$$170$$ 0 0
$$171$$ −15.0000 −1.14708
$$172$$ 0 0
$$173$$ 19.0526i 1.44854i 0.689517 + 0.724270i $$0.257823\pi$$
−0.689517 + 0.724270i $$0.742177\pi$$
$$174$$ 0 0
$$175$$ 12.5000 4.33013i 0.944911 0.327327i
$$176$$ 0 0
$$177$$ 22.5000 12.9904i 1.69120 0.976417i
$$178$$ 0 0
$$179$$ −10.5000 6.06218i −0.784807 0.453108i 0.0533243 0.998577i $$-0.483018\pi$$
−0.838131 + 0.545469i $$0.816352\pi$$
$$180$$ 0 0
$$181$$ 13.8564i 1.02994i 0.857209 + 0.514969i $$0.172197\pi$$
−0.857209 + 0.514969i $$0.827803\pi$$
$$182$$ 0 0
$$183$$ 1.50000 + 2.59808i 0.110883 + 0.192055i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −6.00000 −0.438763
$$188$$ 0 0
$$189$$ −13.5000 2.59808i −0.981981 0.188982i
$$190$$ 0 0
$$191$$ 1.73205i 0.125327i −0.998035 0.0626634i $$-0.980041\pi$$
0.998035 0.0626634i $$-0.0199595\pi$$
$$192$$ 0 0
$$193$$ −17.0000 −1.22369 −0.611843 0.790979i $$-0.709572\pi$$
−0.611843 + 0.790979i $$0.709572\pi$$
$$194$$ 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
$$199$$ 0.500000 0.866025i 0.0354441 0.0613909i −0.847759 0.530381i $$-0.822049\pi$$
0.883203 + 0.468990i $$0.155382\pi$$
$$200$$ 0 0
$$201$$ 13.5000 + 23.3827i 0.952217 + 1.64929i
$$202$$ 0 0
$$203$$ −6.00000 5.19615i −0.421117 0.364698i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 9.00000 5.19615i 0.625543 0.361158i
$$208$$ 0 0
$$209$$ 15.0000 + 8.66025i 1.03757 + 0.599042i
$$210$$ 0 0
$$211$$ 10.5000 6.06218i 0.722850 0.417338i −0.0929509 0.995671i $$-0.529630\pi$$
0.815801 + 0.578333i $$0.196297\pi$$
$$212$$ 0 0
$$213$$ 9.00000 + 15.5885i 0.616670 + 1.06810i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −0.500000 + 2.59808i −0.0339422 + 0.176369i
$$218$$ 0 0
$$219$$ −3.00000 −0.202721
$$220$$ 0 0
$$221$$ −3.00000 −0.201802
$$222$$ 0 0
$$223$$ −2.50000 + 4.33013i −0.167412 + 0.289967i −0.937509 0.347960i $$-0.886874\pi$$
0.770097 + 0.637927i $$0.220208\pi$$
$$224$$ 0 0
$$225$$ −15.0000 −1.00000
$$226$$ 0 0
$$227$$ −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i $$-0.297043\pi$$
−0.993508 + 0.113761i $$0.963710\pi$$
$$228$$ 0 0
$$229$$ 12.0000 + 6.92820i 0.792982 + 0.457829i 0.841011 0.541017i $$-0.181961\pi$$
−0.0480291 + 0.998846i $$0.515294\pi$$
$$230$$ 0 0
$$231$$ 12.0000 + 10.3923i 0.789542 + 0.683763i
$$232$$ 0 0
$$233$$ 10.5000 + 18.1865i 0.687878 + 1.19144i 0.972523 + 0.232806i $$0.0747909\pi$$
−0.284645 + 0.958633i $$0.591876\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 1.50000 + 2.59808i 0.0974355 + 0.168763i
$$238$$ 0 0
$$239$$ −19.5000 + 11.2583i −1.26135 + 0.728241i −0.973336 0.229385i $$-0.926328\pi$$
−0.288014 + 0.957626i $$0.592995\pi$$
$$240$$ 0 0
$$241$$ −18.0000 + 10.3923i −1.15948 + 0.669427i −0.951180 0.308637i $$-0.900127\pi$$
−0.208302 + 0.978065i $$0.566794\pi$$
$$242$$ 0 0
$$243$$ 13.5000 + 7.79423i 0.866025 + 0.500000i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 7.50000 + 4.33013i 0.477214 + 0.275519i
$$248$$ 0 0
$$249$$ 15.5885i 0.987878i
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −24.0000 13.8564i −1.49708 0.864339i −0.497085 0.867702i $$-0.665596\pi$$
−0.999994 + 0.00336324i $$0.998929\pi$$
$$258$$ 0 0
$$259$$ 17.5000 6.06218i 1.08740 0.376685i
$$260$$ 0 0
$$261$$ 4.50000 + 7.79423i 0.278543 + 0.482451i
$$262$$ 0 0
$$263$$ 27.0000 15.5885i 1.66489 0.961225i 0.694564 0.719431i $$-0.255597\pi$$
0.970328 0.241794i $$-0.0777359\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −1.50000 + 2.59808i −0.0917985 + 0.159000i
$$268$$ 0 0
$$269$$ 19.5000 + 11.2583i 1.18894 + 0.686433i 0.958065 0.286552i $$-0.0925091\pi$$
0.230871 + 0.972984i $$0.425842\pi$$
$$270$$ 0 0
$$271$$ −0.500000 0.866025i −0.0303728 0.0526073i 0.850439 0.526073i $$-0.176336\pi$$
−0.880812 + 0.473466i $$0.843003\pi$$
$$272$$ 0 0
$$273$$ 6.00000 + 5.19615i 0.363137 + 0.314485i
$$274$$ 0 0
$$275$$ 15.0000 + 8.66025i 0.904534 + 0.522233i
$$276$$ 0 0
$$277$$ 7.00000 + 12.1244i 0.420589 + 0.728482i 0.995997 0.0893846i $$-0.0284900\pi$$
−0.575408 + 0.817867i $$0.695157\pi$$
$$278$$ 0 0
$$279$$ 1.50000 2.59808i 0.0898027 0.155543i
$$280$$ 0 0
$$281$$ −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i $$-0.980988\pi$$
0.550804 + 0.834634i $$0.314321\pi$$
$$282$$ 0 0
$$283$$ −31.0000 −1.84276 −0.921379 0.388664i $$-0.872937\pi$$
−0.921379 + 0.388664i $$0.872937\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −1.50000 4.33013i −0.0885422 0.255599i
$$288$$ 0 0
$$289$$ −7.00000 12.1244i −0.411765 0.713197i
$$290$$ 0 0
$$291$$ 3.00000 0.175863
$$292$$ 0 0
$$293$$ 22.5000 12.9904i 1.31446 0.758906i 0.331632 0.943409i $$-0.392401\pi$$
0.982832 + 0.184503i $$0.0590674\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −9.00000 15.5885i −0.522233 0.904534i
$$298$$ 0 0
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ −3.00000 + 3.46410i −0.172917 + 0.199667i
$$302$$ 0 0
$$303$$ 12.0000 20.7846i 0.689382 1.19404i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 8.00000 0.456584 0.228292 0.973593i $$-0.426686\pi$$
0.228292 + 0.973593i $$0.426686\pi$$
$$308$$ 0 0
$$309$$ 13.8564i 0.788263i
$$310$$ 0 0
$$311$$ −3.00000 −0.170114 −0.0850572 0.996376i $$-0.527107\pi$$
−0.0850572 + 0.996376i $$0.527107\pi$$
$$312$$ 0 0
$$313$$ 29.4449i 1.66432i −0.554534 0.832161i $$-0.687103\pi$$
0.554534 0.832161i $$-0.312897\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −21.0000 −1.17948 −0.589739 0.807594i $$-0.700769\pi$$
−0.589739 + 0.807594i $$0.700769\pi$$
$$318$$ 0 0
$$319$$ 10.3923i 0.581857i
$$320$$ 0 0
$$321$$ 1.50000 2.59808i 0.0837218 0.145010i
$$322$$ 0 0
$$323$$ 8.66025i 0.481869i
$$324$$ 0 0
$$325$$ 7.50000 + 4.33013i 0.416025 + 0.240192i
$$326$$ 0 0
$$327$$ 19.0526i 1.05361i
$$328$$ 0 0
$$329$$ 4.50000 23.3827i 0.248093 1.28913i
$$330$$ 0 0
$$331$$ 5.19615i 0.285606i 0.989751 + 0.142803i $$0.0456116\pi$$
−0.989751 + 0.142803i $$0.954388\pi$$
$$332$$ 0 0
$$333$$ −21.0000 −1.15079
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −5.50000 9.52628i −0.299604 0.518930i 0.676441 0.736497i $$-0.263521\pi$$
−0.976045 + 0.217567i $$0.930188\pi$$
$$338$$ 0 0
$$339$$ −13.5000 7.79423i −0.733219 0.423324i
$$340$$ 0 0
$$341$$ −3.00000 + 1.73205i −0.162459 + 0.0937958i
$$342$$ 0 0
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 22.5167i 1.20876i −0.796697 0.604379i $$-0.793421\pi$$
0.796697 0.604379i $$-0.206579\pi$$
$$348$$ 0 0
$$349$$ 22.5000 + 12.9904i 1.20440 + 0.695359i 0.961530 0.274700i $$-0.0885786\pi$$
0.242867 + 0.970059i $$0.421912\pi$$
$$350$$ 0 0
$$351$$ −4.50000 7.79423i −0.240192 0.416025i
$$352$$ 0 0
$$353$$ −18.0000 + 10.3923i −0.958043 + 0.553127i −0.895570 0.444920i $$-0.853232\pi$$
−0.0624731 + 0.998047i $$0.519899\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 1.50000 7.79423i 0.0793884 0.412514i
$$358$$ 0 0
$$359$$ 10.5000 6.06218i 0.554169 0.319950i −0.196633 0.980477i $$-0.563001\pi$$
0.750802 + 0.660528i $$0.229667\pi$$
$$360$$ 0 0
$$361$$ −3.00000 + 5.19615i −0.157895 + 0.273482i
$$362$$ 0 0
$$363$$ 1.73205i 0.0909091i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i $$-0.233622\pi$$
−0.951336 + 0.308155i $$0.900289\pi$$
$$368$$ 0 0
$$369$$ 5.19615i 0.270501i
$$370$$ 0 0
$$371$$ 18.0000 + 15.5885i 0.934513 + 0.809312i
$$372$$ 0 0
$$373$$ 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i $$-0.749977\pi$$
0.965945 + 0.258748i $$0.0833099\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 5.19615i 0.267615i
$$378$$ 0 0
$$379$$ 24.2487i 1.24557i 0.782392 + 0.622786i $$0.213999\pi$$
−0.782392 + 0.622786i $$0.786001\pi$$
$$380$$ 0 0
$$381$$ 9.00000 + 15.5885i 0.461084 + 0.798621i
$$382$$ 0 0
$$383$$ −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i $$0.376773\pi$$
−0.990702 + 0.136047i $$0.956560\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 4.50000 2.59808i 0.228748 0.132068i
$$388$$ 0 0
$$389$$ −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i $$-0.317499\pi$$
−0.998763 + 0.0497253i $$0.984165\pi$$
$$390$$ 0 0
$$391$$ 3.00000 + 5.19615i 0.151717 + 0.262781i
$$392$$ 0 0
$$393$$ 20.7846i 1.04844i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 13.5000 7.79423i 0.677546 0.391181i −0.121384 0.992606i $$-0.538733\pi$$
0.798930 + 0.601424i $$0.205400\pi$$
$$398$$ 0 0
$$399$$ −15.0000 + 17.3205i −0.750939 + 0.867110i
$$400$$ 0 0
$$401$$ −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i $$0.436163\pi$$
−0.948272 + 0.317460i $$0.897170\pi$$
$$402$$ 0 0
$$403$$ −1.50000 + 0.866025i −0.0747203 + 0.0431398i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 21.0000 + 12.1244i 1.04093 + 0.600982i
$$408$$ 0 0
$$409$$ 29.4449i 1.45595i 0.685601 + 0.727977i $$0.259539\pi$$
−0.685601 + 0.727977i $$0.740461\pi$$
$$410$$ 0 0
$$411$$ −27.0000 15.5885i −1.33181 0.768922i
$$412$$ 0 0
$$413$$ 7.50000 38.9711i 0.369051 1.91764i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −7.50000 4.33013i −0.367277 0.212047i
$$418$$ 0 0
$$419$$ −7.50000 12.9904i −0.366399 0.634622i 0.622601 0.782540i $$-0.286076\pi$$
−0.989000 + 0.147918i $$0.952743\pi$$
$$420$$ 0 0
$$421$$ 2.50000 4.33013i 0.121843 0.211037i −0.798652 0.601793i $$-0.794453\pi$$
0.920494 + 0.390756i $$0.127786\pi$$
$$422$$ 0 0
$$423$$ −13.5000 + 23.3827i −0.656392 + 1.13691i
$$424$$ 0 0
$$425$$ 8.66025i 0.420084i
$$426$$ 0 0
$$427$$ 4.50000 + 0.866025i 0.217770 + 0.0419099i
$$428$$ 0 0
$$429$$ 10.3923i 0.501745i
$$430$$ 0 0
$$431$$ −22.5000 12.9904i −1.08379 0.625725i −0.151871 0.988400i $$-0.548530\pi$$
−0.931915 + 0.362676i $$0.881863\pi$$
$$432$$ 0 0
$$433$$ 13.8564i 0.665896i −0.942945 0.332948i $$-0.891957\pi$$
0.942945 0.332948i $$-0.108043\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 17.3205i 0.828552i
$$438$$ 0 0
$$439$$ −25.0000 −1.19318 −0.596592 0.802544i $$-0.703479\pi$$
−0.596592 + 0.802544i $$0.703479\pi$$
$$440$$ 0 0
$$441$$ −16.5000 + 12.9904i −0.785714 + 0.618590i
$$442$$ 0 0
$$443$$ 25.9808i 1.23438i 0.786813 + 0.617192i $$0.211730\pi$$
−0.786813 + 0.617192i $$0.788270\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 10.3923i 0.491539i
$$448$$ 0 0
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ 3.00000 5.19615i 0.141264 0.244677i
$$452$$ 0 0
$$453$$ −15.0000 + 25.9808i −0.704761 + 1.22068i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.00000 −0.0467780 −0.0233890 0.999726i $$-0.507446\pi$$
−0.0233890 + 0.999726i $$0.507446\pi$$
$$458$$ 0 0
$$459$$ −4.50000 + 7.79423i −0.210042 + 0.363803i
$$460$$ 0 0
$$461$$ −19.5000 11.2583i −0.908206 0.524353i −0.0283522 0.999598i $$-0.509026\pi$$
−0.879853 + 0.475245i $$0.842359\pi$$
$$462$$ 0 0
$$463$$ −31.5000 + 18.1865i −1.46393 + 0.845200i −0.999190 0.0402476i $$-0.987185\pi$$
−0.464739 + 0.885448i $$0.653852\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 7.50000 + 12.9904i 0.347059 + 0.601123i 0.985726 0.168360i $$-0.0538472\pi$$
−0.638667 + 0.769483i $$0.720514\pi$$
$$468$$ 0 0
$$469$$ 40.5000 + 7.79423i 1.87012 + 0.359904i
$$470$$ 0 0
$$471$$ 10.5000 + 18.1865i 0.483814 + 0.837991i
$$472$$ 0 0
$$473$$ −6.00000 −0.275880
$$474$$ 0 0
$$475$$ −12.5000 + 21.6506i −0.573539 + 0.993399i
$$476$$ 0 0
$$477$$ −13.5000 23.3827i −0.618123 1.07062i
$$478$$ 0 0
$$479$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$480$$ 0 0
$$481$$ 10.5000 + 6.06218i 0.478759 + 0.276412i
$$482$$ 0 0
$$483$$ 3.00000 15.5885i 0.136505 0.709299i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 13.5000 + 7.79423i 0.611743 + 0.353190i 0.773647 0.633616i $$-0.218430\pi$$
−0.161904 + 0.986807i $$0.551764\pi$$
$$488$$ 0 0
$$489$$ 13.5000 23.3827i 0.610491 1.05740i
$$490$$ 0 0
$$491$$ −7.50000 + 4.33013i −0.338470 + 0.195416i −0.659595 0.751621i $$-0.729272\pi$$
0.321125 + 0.947037i $$0.395939\pi$$
$$492$$ 0 0
$$493$$ −4.50000 + 2.59808i −0.202670 + 0.117011i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 27.0000 + 5.19615i 1.21112 + 0.233079i
$$498$$ 0 0
$$499$$ 3.00000 + 1.73205i 0.134298 + 0.0775372i 0.565644 0.824650i $$-0.308628\pi$$
−0.431346 + 0.902187i $$0.641961\pi$$
$$500$$ 0 0
$$501$$ −31.5000 18.1865i −1.40732 0.812514i
$$502$$ 0 0
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 17.3205i 0.769231i
$$508$$ 0 0
$$509$$ −30.0000 17.3205i −1.32973 0.767718i −0.344469 0.938798i $$-0.611941\pi$$
−0.985257 + 0.171080i $$0.945274\pi$$
$$510$$ 0 0
$$511$$ −3.00000 + 3.46410i −0.132712 + 0.153243i
$$512$$ 0 0
$$513$$ 22.5000 12.9904i 0.993399 0.573539i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 27.0000 15.5885i 1.18746 0.685580i
$$518$$ 0 0
$$519$$ −16.5000 28.5788i −0.724270 1.25447i
$$520$$ 0 0
$$521$$ 19.5000 + 11.2583i 0.854311 + 0.493236i 0.862103 0.506733i $$-0.169147\pi$$
−0.00779240 + 0.999970i $$0.502480\pi$$
$$522$$ 0 0
$$523$$ −6.50000 11.2583i −0.284225 0.492292i 0.688196 0.725525i $$-0.258403\pi$$
−0.972421 + 0.233233i $$0.925070\pi$$
$$524$$ 0 0
$$525$$ −15.0000 + 17.3205i −0.654654 + 0.755929i
$$526$$ 0 0
$$527$$ 1.50000 + 0.866025i 0.0653410 + 0.0377247i
$$528$$ 0 0
$$529$$ −5.50000 9.52628i −0.239130 0.414186i
$$530$$ 0 0
$$531$$ −22.5000 + 38.9711i −0.976417 + 1.69120i
$$532$$ 0 0
$$533$$ 1.50000 2.59808i 0.0649722 0.112535i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 21.0000 0.906217
$$538$$ 0 0
$$539$$ 24.0000 3.46410i 1.03375 0.149209i
$$540$$ 0 0
$$541$$ −21.5000 37.2391i −0.924357 1.60103i −0.792592 0.609753i $$-0.791269\pi$$
−0.131765 0.991281i $$-0.542065\pi$$
$$542$$ 0 0
$$543$$ −12.0000 20.7846i −0.514969 0.891953i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 7.50000 + 4.33013i 0.320677 + 0.185143i 0.651694 0.758482i $$-0.274059\pi$$
−0.331017 + 0.943625i $$0.607392\pi$$
$$548$$ 0 0
$$549$$ −4.50000 2.59808i −0.192055 0.110883i
$$550$$ 0 0
$$551$$ 15.0000 0.639021
$$552$$ 0 0
$$553$$ 4.50000 + 0.866025i 0.191359 + 0.0368271i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 16.5000 28.5788i 0.699127 1.21092i −0.269642 0.962961i $$-0.586905\pi$$
0.968769 0.247964i $$-0.0797613\pi$$
$$558$$ 0 0
$$559$$ −3.00000 −0.126886
$$560$$ 0 0
$$561$$ 9.00000 5.19615i 0.379980 0.219382i
$$562$$ 0 0
$$563$$ 21.0000 0.885044 0.442522 0.896758i $$-0.354084\pi$$
0.442522 + 0.896758i $$0.354084\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 22.5000 7.79423i 0.944911 0.327327i
$$568$$ 0 0
$$569$$ 3.00000 0.125767 0.0628833 0.998021i $$-0.479970\pi$$
0.0628833 + 0.998021i $$0.479970\pi$$
$$570$$ 0 0
$$571$$ 39.8372i 1.66713i 0.552419 + 0.833567i $$0.313705\pi$$
−0.552419 + 0.833567i $$0.686295\pi$$
$$572$$ 0 0
$$573$$ 1.50000 + 2.59808i 0.0626634 + 0.108536i
$$574$$ 0 0
$$575$$ 17.3205i 0.722315i
$$576$$ 0 0
$$577$$ −22.5000 12.9904i −0.936687 0.540797i −0.0477669 0.998859i $$-0.515210\pi$$
−0.888920 + 0.458062i $$0.848544\pi$$
$$578$$ 0 0
$$579$$ 25.5000 14.7224i 1.05974 0.611843i
$$580$$ 0 0
$$581$$ −18.0000 15.5885i −0.746766 0.646718i
$$582$$ 0 0
$$583$$ 31.1769i 1.29122i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 13.5000 23.3827i 0.557205 0.965107i −0.440524 0.897741i $$-0.645207\pi$$
0.997728 0.0673658i $$-0.0214594\pi$$
$$588$$ 0 0
$$589$$ −2.50000 4.33013i −0.103011 0.178420i
$$590$$ 0 0
$$591$$ −9.00000 + 5.19615i −0.370211 + 0.213741i
$$592$$ 0 0
$$593$$ 7.50000 4.33013i 0.307988 0.177817i −0.338038 0.941133i $$-0.609763\pi$$
0.646026 + 0.763316i $$0.276430\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 1.73205i 0.0708881i
$$598$$ 0 0
$$599$$ 36.3731i 1.48616i −0.669201 0.743082i $$-0.733363\pi$$
0.669201 0.743082i $$-0.266637\pi$$
$$600$$ 0 0
$$601$$ −31.5000 18.1865i −1.28491 0.741844i −0.307170 0.951655i $$-0.599382\pi$$
−0.977742 + 0.209811i $$0.932715\pi$$
$$602$$ 0 0
$$603$$ −40.5000 23.3827i −1.64929 0.952217i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i $$0.391655\pi$$
−0.983262 + 0.182199i $$0.941678\pi$$
$$608$$ 0 0
$$609$$ 13.5000 + 2.59808i 0.547048 + 0.105279i
$$610$$ 0 0
$$611$$ 13.5000 7.79423i 0.546152 0.315321i
$$612$$ 0 0
$$613$$ −17.5000 + 30.3109i −0.706818 + 1.22425i 0.259213 + 0.965820i $$0.416537\pi$$
−0.966031 + 0.258425i $$0.916796\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −13.5000 23.3827i −0.543490 0.941351i −0.998700 0.0509678i $$-0.983769\pi$$
0.455211 0.890384i $$-0.349564\pi$$
$$618$$ 0 0
$$619$$ −14.0000 24.2487i −0.562708 0.974638i −0.997259 0.0739910i $$-0.976426\pi$$
0.434551 0.900647i $$-0.356907\pi$$
$$620$$ 0 0
$$621$$ −9.00000 + 15.5885i −0.361158 + 0.625543i
$$622$$ 0 0
$$623$$ 1.50000 + 4.33013i 0.0600962 + 0.173483i
$$624$$ 0 0
$$625$$ −12.5000 + 21.6506i −0.500000 + 0.866025i
$$626$$ 0 0
$$627$$ −30.0000 −1.19808
$$628$$ 0 0
$$629$$ 12.1244i 0.483430i
$$630$$ 0 0
$$631$$ 31.1769i 1.24113i 0.784154 + 0.620567i $$0.213097\pi$$
−0.784154 + 0.620567i $$0.786903\pi$$
$$632$$ 0 0
$$633$$ −10.5000 + 18.1865i −0.417338 + 0.722850i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 12.0000 1.73205i 0.475457 0.0686264i
$$638$$ 0 0
$$639$$ −27.0000 15.5885i −1.06810 0.616670i
$$640$$ 0 0
$$641$$ −3.00000 5.19615i −0.118493 0.205236i 0.800678 0.599095i $$-0.204473\pi$$
−0.919171 + 0.393860i $$0.871140\pi$$
$$642$$ 0 0
$$643$$ 6.50000 + 11.2583i 0.256335 + 0.443985i 0.965257 0.261301i $$-0.0841516\pi$$
−0.708922 + 0.705287i $$0.750818\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −7.50000 + 12.9904i −0.294855 + 0.510705i −0.974951 0.222419i $$-0.928605\pi$$
0.680096 + 0.733123i $$0.261938\pi$$
$$648$$ 0 0
$$649$$ 45.0000 25.9808i 1.76640 1.01983i
$$650$$ 0 0
$$651$$ −1.50000 4.33013i −0.0587896 0.169711i
$$652$$ 0 0
$$653$$ −15.0000 + 25.9808i −0.586995 + 1.01671i 0.407628 + 0.913148i $$0.366356\pi$$
−0.994623 + 0.103558i $$0.966977\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 4.50000 2.59808i 0.175562 0.101361i
$$658$$ 0 0
$$659$$ 19.5000 + 11.2583i 0.759612 + 0.438562i 0.829156 0.559017i $$-0.188821\pi$$
−0.0695443 + 0.997579i $$0.522155\pi$$
$$660$$ 0 0
$$661$$ 8.66025i 0.336845i 0.985715 + 0.168422i $$0.0538673\pi$$
−0.985715 + 0.168422i $$0.946133\pi$$
$$662$$ 0 0
$$663$$ 4.50000 2.59808i 0.174766 0.100901i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −9.00000 + 5.19615i −0.348481 + 0.201196i
$$668$$ 0 0
$$669$$ 8.66025i 0.334825i
$$670$$ 0 0
$$671$$ 3.00000 + 5.19615i 0.115814 + 0.200595i
$$672$$ 0 0
$$673$$ −3.50000 + 6.06218i −0.134915 + 0.233680i −0.925565 0.378589i $$-0.876409\pi$$
0.790650 + 0.612268i $$0.209743\pi$$
$$674$$ 0 0
$$675$$ 22.5000 12.9904i 0.866025 0.500000i
$$676$$ 0 0
$$677$$ 1.73205i 0.0665681i −0.999446 0.0332841i $$-0.989403\pi$$
0.999446 0.0332841i $$-0.0105966\pi$$
$$678$$ 0 0
$$679$$ 3.00000 3.46410i 0.115129 0.132940i
$$680$$ 0 0
$$681$$ 18.0000 + 10.3923i 0.689761 + 0.398234i
$$682$$ 0 0
$$683$$ 37.5000 + 21.6506i 1.43490 + 0.828439i 0.997489 0.0708242i $$-0.0225629\pi$$
0.437409 + 0.899263i $$0.355896\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −24.0000 −0.915657
$$688$$ 0 0
$$689$$ 15.5885i 0.593873i
$$690$$ 0 0
$$691$$ −5.00000 −0.190209 −0.0951045 0.995467i $$-0.530319\pi$$
−0.0951045 + 0.995467i $$0.530319\pi$$
$$692$$ 0 0
$$693$$ −27.0000 5.19615i −1.02565 0.197386i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −3.00000 −0.113633
$$698$$ 0 0
$$699$$ −31.5000 18.1865i −1.19144 0.687878i
$$700$$ 0 0
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ 0 0
$$703$$ −17.5000 + 30.3109i −0.660025 + 1.14320i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −12.0000 34.6410i −0.451306 1.30281i
$$708$$ 0 0
$$709$$ −37.0000 −1.38956 −0.694782 0.719220i $$-0.744499\pi$$
−0.694782 + 0.719220i $$0.744499\pi$$
$$710$$ 0 0
$$711$$ −4.50000 2.59808i −0.168763 0.0974355i
$$712$$ 0 0
$$713$$ 3.00000 + 1.73205i 0.112351 + 0.0648658i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 19.5000 33.7750i 0.728241 1.26135i
$$718$$ 0 0
$$719$$ 13.5000 + 23.3827i 0.503465 + 0.872027i 0.999992 + 0.00400572i $$0.00127506\pi$$
−0.496527 + 0.868021i $$0.665392\pi$$
$$720$$ 0 0
$$721$$ 16.0000 + 13.8564i 0.595871 + 0.516040i
$$722$$ 0 0
$$723$$ 18.0000 31.1769i 0.669427 1.15948i
$$724$$ 0 0
$$725$$ 15.0000 0.557086
$$726$$ 0 0
$$727$$ 17.5000 30.3109i 0.649039 1.12417i −0.334314 0.942462i $$-0.608504\pi$$
0.983353 0.181707i $$-0.0581622\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 1.50000 + 2.59808i 0.0554795 + 0.0960933i
$$732$$ 0 0
$$733$$ 18.0000 + 10.3923i 0.664845 + 0.383849i 0.794121 0.607760i $$-0.207932\pi$$
−0.129275 + 0.991609i $$0.541265\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 27.0000 + 46.7654i 0.994558 + 1.72262i
$$738$$ 0 0
$$739$$ 13.5000 + 7.79423i 0.496606 + 0.286715i 0.727311 0.686308i $$-0.240770\pi$$
−0.230705 + 0.973024i $$0.574103\pi$$
$$740$$ 0 0
$$741$$ −15.0000 −0.551039
$$742$$ 0 0
$$743$$ 10.5000 6.06218i 0.385208 0.222400i −0.294874 0.955536i $$-0.595278\pi$$
0.680082 + 0.733136i $$0.261944\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 13.5000 + 23.3827i 0.493939 + 0.855528i
$$748$$ 0 0
$$749$$ −1.50000 4.33013i −0.0548088 0.158219i
$$750$$ 0 0
$$751$$ −15.0000 8.66025i −0.547358 0.316017i 0.200698 0.979653i $$-0.435679\pi$$
−0.748056 + 0.663636i $$0.769012\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 0 0
$$759$$ 18.0000 10.3923i 0.653359 0.377217i
$$760$$ 0 0
$$761$$ −42.0000 24.2487i −1.52250 0.879015i −0.999646 0.0265919i $$-0.991535\pi$$
−0.522852 0.852423i $$-0.675132\pi$$
$$762$$ 0 0
$$763$$ −22.0000 19.0526i −0.796453 0.689749i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 22.5000 12.9904i 0.812428 0.469055i
$$768$$ 0 0
$$769$$ 4.50000 2.59808i 0.162274 0.0936890i −0.416664 0.909061i $$-0.636801\pi$$
0.578938 + 0.815372i $$0.303467\pi$$
$$770$$ 0 0
$$771$$ 48.0000 1.72868
$$772$$ 0 0
$$773$$ −28.5000 16.4545i −1.02507 0.591827i −0.109504 0.993986i $$-0.534926\pi$$
−0.915570 + 0.402160i $$0.868260\pi$$
$$774$$ 0 0
$$775$$ −2.50000 4.33013i −0.0898027 0.155543i
$$776$$ 0 0
$$777$$ −21.0000 + 24.2487i −0.753371 + 0.869918i
$$778$$ 0 0
$$779$$ 7.50000 + 4.33013i 0.268715 + 0.155143i
$$780$$ 0 0
$$781$$ 18.0000 + 31.1769i 0.644091 + 1.11560i
$$782$$ 0 0
$$783$$ −13.5000 7.79423i −0.482451 0.278543i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 13.0000 0.463400 0.231700 0.972787i $$-0.425571\pi$$
0.231700 + 0.972787i $$0.425571\pi$$
$$788$$ 0 0
$$789$$ −27.0000 + 46.7654i −0.961225 + 1.66489i
$$790$$ 0 0
$$791$$ −22.5000 + 7.79423i −0.800008 + 0.277131i
$$792$$ 0 0
$$793$$ 1.50000 + 2.59808i 0.0532666 + 0.0922604i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 28.5000 16.4545i 1.00952 0.582848i 0.0984702 0.995140i $$-0.468605\pi$$