# Properties

 Label 768.2.j.a.193.2 Level $768$ Weight $2$ Character 768.193 Analytic conductor $6.133$ Analytic rank $1$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$768 = 2^{8} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 768.j (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.13251087523$$ Analytic rank: $$1$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 193.2 Root $$-0.707107 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 768.193 Dual form 768.2.j.a.577.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 - 0.707107i) q^{3} +(-2.00000 - 2.00000i) q^{5} +4.24264i q^{7} -1.00000i q^{9} +O(q^{10})$$ $$q+(0.707107 - 0.707107i) q^{3} +(-2.00000 - 2.00000i) q^{5} +4.24264i q^{7} -1.00000i q^{9} +(-2.82843 - 2.82843i) q^{11} +(-3.00000 + 3.00000i) q^{13} -2.82843 q^{15} -6.00000 q^{17} +(1.41421 - 1.41421i) q^{19} +(3.00000 + 3.00000i) q^{21} -2.82843i q^{23} +3.00000i q^{25} +(-0.707107 - 0.707107i) q^{27} +(-4.00000 + 4.00000i) q^{29} -4.24264 q^{31} -4.00000 q^{33} +(8.48528 - 8.48528i) q^{35} +(-3.00000 - 3.00000i) q^{37} +4.24264i q^{39} +10.0000i q^{41} +(4.24264 + 4.24264i) q^{43} +(-2.00000 + 2.00000i) q^{45} +2.82843 q^{47} -11.0000 q^{49} +(-4.24264 + 4.24264i) q^{51} +(-4.00000 - 4.00000i) q^{53} +11.3137i q^{55} -2.00000i q^{57} +(-3.00000 + 3.00000i) q^{61} +4.24264 q^{63} +12.0000 q^{65} +(-2.82843 + 2.82843i) q^{67} +(-2.00000 - 2.00000i) q^{69} +2.82843i q^{71} -16.0000i q^{73} +(2.12132 + 2.12132i) q^{75} +(12.0000 - 12.0000i) q^{77} +4.24264 q^{79} -1.00000 q^{81} +(11.3137 - 11.3137i) q^{83} +(12.0000 + 12.0000i) q^{85} +5.65685i q^{87} +14.0000i q^{89} +(-12.7279 - 12.7279i) q^{91} +(-3.00000 + 3.00000i) q^{93} -5.65685 q^{95} -4.00000 q^{97} +(-2.82843 + 2.82843i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 8q^{5} + O(q^{10})$$ $$4q - 8q^{5} - 12q^{13} - 24q^{17} + 12q^{21} - 16q^{29} - 16q^{33} - 12q^{37} - 8q^{45} - 44q^{49} - 16q^{53} - 12q^{61} + 48q^{65} - 8q^{69} + 48q^{77} - 4q^{81} + 48q^{85} - 12q^{93} - 16q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$511$$ $$517$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{4}\right)$$

## 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
$$3$$ 0.707107 0.707107i 0.408248 0.408248i
$$4$$ 0 0
$$5$$ −2.00000 2.00000i −0.894427 0.894427i 0.100509 0.994936i $$-0.467953\pi$$
−0.994936 + 0.100509i $$0.967953\pi$$
$$6$$ 0 0
$$7$$ 4.24264i 1.60357i 0.597614 + 0.801784i $$0.296115\pi$$
−0.597614 + 0.801784i $$0.703885\pi$$
$$8$$ 0 0
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ −2.82843 2.82843i −0.852803 0.852803i 0.137675 0.990478i $$-0.456037\pi$$
−0.990478 + 0.137675i $$0.956037\pi$$
$$12$$ 0 0
$$13$$ −3.00000 + 3.00000i −0.832050 + 0.832050i −0.987797 0.155747i $$-0.950222\pi$$
0.155747 + 0.987797i $$0.450222\pi$$
$$14$$ 0 0
$$15$$ −2.82843 −0.730297
$$16$$ 0 0
$$17$$ −6.00000 −1.45521 −0.727607 0.685994i $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ 1.41421 1.41421i 0.324443 0.324443i −0.526026 0.850469i $$-0.676318\pi$$
0.850469 + 0.526026i $$0.176318\pi$$
$$20$$ 0 0
$$21$$ 3.00000 + 3.00000i 0.654654 + 0.654654i
$$22$$ 0 0
$$23$$ 2.82843i 0.589768i −0.955533 0.294884i $$-0.904719\pi$$
0.955533 0.294884i $$-0.0952810\pi$$
$$24$$ 0 0
$$25$$ 3.00000i 0.600000i
$$26$$ 0 0
$$27$$ −0.707107 0.707107i −0.136083 0.136083i
$$28$$ 0 0
$$29$$ −4.00000 + 4.00000i −0.742781 + 0.742781i −0.973112 0.230331i $$-0.926019\pi$$
0.230331 + 0.973112i $$0.426019\pi$$
$$30$$ 0 0
$$31$$ −4.24264 −0.762001 −0.381000 0.924575i $$-0.624420\pi$$
−0.381000 + 0.924575i $$0.624420\pi$$
$$32$$ 0 0
$$33$$ −4.00000 −0.696311
$$34$$ 0 0
$$35$$ 8.48528 8.48528i 1.43427 1.43427i
$$36$$ 0 0
$$37$$ −3.00000 3.00000i −0.493197 0.493197i 0.416115 0.909312i $$-0.363391\pi$$
−0.909312 + 0.416115i $$0.863391\pi$$
$$38$$ 0 0
$$39$$ 4.24264i 0.679366i
$$40$$ 0 0
$$41$$ 10.0000i 1.56174i 0.624695 + 0.780869i $$0.285223\pi$$
−0.624695 + 0.780869i $$0.714777\pi$$
$$42$$ 0 0
$$43$$ 4.24264 + 4.24264i 0.646997 + 0.646997i 0.952266 0.305269i $$-0.0987465\pi$$
−0.305269 + 0.952266i $$0.598747\pi$$
$$44$$ 0 0
$$45$$ −2.00000 + 2.00000i −0.298142 + 0.298142i
$$46$$ 0 0
$$47$$ 2.82843 0.412568 0.206284 0.978492i $$-0.433863\pi$$
0.206284 + 0.978492i $$0.433863\pi$$
$$48$$ 0 0
$$49$$ −11.0000 −1.57143
$$50$$ 0 0
$$51$$ −4.24264 + 4.24264i −0.594089 + 0.594089i
$$52$$ 0 0
$$53$$ −4.00000 4.00000i −0.549442 0.549442i 0.376837 0.926279i $$-0.377012\pi$$
−0.926279 + 0.376837i $$0.877012\pi$$
$$54$$ 0 0
$$55$$ 11.3137i 1.52554i
$$56$$ 0 0
$$57$$ 2.00000i 0.264906i
$$58$$ 0 0
$$59$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$60$$ 0 0
$$61$$ −3.00000 + 3.00000i −0.384111 + 0.384111i −0.872581 0.488470i $$-0.837555\pi$$
0.488470 + 0.872581i $$0.337555\pi$$
$$62$$ 0 0
$$63$$ 4.24264 0.534522
$$64$$ 0 0
$$65$$ 12.0000 1.48842
$$66$$ 0 0
$$67$$ −2.82843 + 2.82843i −0.345547 + 0.345547i −0.858448 0.512901i $$-0.828571\pi$$
0.512901 + 0.858448i $$0.328571\pi$$
$$68$$ 0 0
$$69$$ −2.00000 2.00000i −0.240772 0.240772i
$$70$$ 0 0
$$71$$ 2.82843i 0.335673i 0.985815 + 0.167836i $$0.0536780\pi$$
−0.985815 + 0.167836i $$0.946322\pi$$
$$72$$ 0 0
$$73$$ 16.0000i 1.87266i −0.351123 0.936329i $$-0.614200\pi$$
0.351123 0.936329i $$-0.385800\pi$$
$$74$$ 0 0
$$75$$ 2.12132 + 2.12132i 0.244949 + 0.244949i
$$76$$ 0 0
$$77$$ 12.0000 12.0000i 1.36753 1.36753i
$$78$$ 0 0
$$79$$ 4.24264 0.477334 0.238667 0.971101i $$-0.423290\pi$$
0.238667 + 0.971101i $$0.423290\pi$$
$$80$$ 0 0
$$81$$ −1.00000 −0.111111
$$82$$ 0 0
$$83$$ 11.3137 11.3137i 1.24184 1.24184i 0.282604 0.959237i $$-0.408802\pi$$
0.959237 0.282604i $$-0.0911983\pi$$
$$84$$ 0 0
$$85$$ 12.0000 + 12.0000i 1.30158 + 1.30158i
$$86$$ 0 0
$$87$$ 5.65685i 0.606478i
$$88$$ 0 0
$$89$$ 14.0000i 1.48400i 0.670402 + 0.741999i $$0.266122\pi$$
−0.670402 + 0.741999i $$0.733878\pi$$
$$90$$ 0 0
$$91$$ −12.7279 12.7279i −1.33425 1.33425i
$$92$$ 0 0
$$93$$ −3.00000 + 3.00000i −0.311086 + 0.311086i
$$94$$ 0 0
$$95$$ −5.65685 −0.580381
$$96$$ 0 0
$$97$$ −4.00000 −0.406138 −0.203069 0.979164i $$-0.565092\pi$$
−0.203069 + 0.979164i $$0.565092\pi$$
$$98$$ 0 0
$$99$$ −2.82843 + 2.82843i −0.284268 + 0.284268i
$$100$$ 0 0
$$101$$ −8.00000 8.00000i −0.796030 0.796030i 0.186437 0.982467i $$-0.440306\pi$$
−0.982467 + 0.186437i $$0.940306\pi$$
$$102$$ 0 0
$$103$$ 18.3848i 1.81151i −0.423806 0.905753i $$-0.639306\pi$$
0.423806 0.905753i $$-0.360694\pi$$
$$104$$ 0 0
$$105$$ 12.0000i 1.17108i
$$106$$ 0 0
$$107$$ −2.82843 2.82843i −0.273434 0.273434i 0.557047 0.830481i $$-0.311934\pi$$
−0.830481 + 0.557047i $$0.811934\pi$$
$$108$$ 0 0
$$109$$ 7.00000 7.00000i 0.670478 0.670478i −0.287348 0.957826i $$-0.592774\pi$$
0.957826 + 0.287348i $$0.0927736\pi$$
$$110$$ 0 0
$$111$$ −4.24264 −0.402694
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ −5.65685 + 5.65685i −0.527504 + 0.527504i
$$116$$ 0 0
$$117$$ 3.00000 + 3.00000i 0.277350 + 0.277350i
$$118$$ 0 0
$$119$$ 25.4558i 2.33353i
$$120$$ 0 0
$$121$$ 5.00000i 0.454545i
$$122$$ 0 0
$$123$$ 7.07107 + 7.07107i 0.637577 + 0.637577i
$$124$$ 0 0
$$125$$ −4.00000 + 4.00000i −0.357771 + 0.357771i
$$126$$ 0 0
$$127$$ −4.24264 −0.376473 −0.188237 0.982124i $$-0.560277\pi$$
−0.188237 + 0.982124i $$0.560277\pi$$
$$128$$ 0 0
$$129$$ 6.00000 0.528271
$$130$$ 0 0
$$131$$ −14.1421 + 14.1421i −1.23560 + 1.23560i −0.273824 + 0.961780i $$0.588289\pi$$
−0.961780 + 0.273824i $$0.911711\pi$$
$$132$$ 0 0
$$133$$ 6.00000 + 6.00000i 0.520266 + 0.520266i
$$134$$ 0 0
$$135$$ 2.82843i 0.243432i
$$136$$ 0 0
$$137$$ 10.0000i 0.854358i −0.904167 0.427179i $$-0.859507\pi$$
0.904167 0.427179i $$-0.140493\pi$$
$$138$$ 0 0
$$139$$ 8.48528 + 8.48528i 0.719712 + 0.719712i 0.968546 0.248834i $$-0.0800474\pi$$
−0.248834 + 0.968546i $$0.580047\pi$$
$$140$$ 0 0
$$141$$ 2.00000 2.00000i 0.168430 0.168430i
$$142$$ 0 0
$$143$$ 16.9706 1.41915
$$144$$ 0 0
$$145$$ 16.0000 1.32873
$$146$$ 0 0
$$147$$ −7.77817 + 7.77817i −0.641533 + 0.641533i
$$148$$ 0 0
$$149$$ −6.00000 6.00000i −0.491539 0.491539i 0.417252 0.908791i $$-0.362993\pi$$
−0.908791 + 0.417252i $$0.862993\pi$$
$$150$$ 0 0
$$151$$ 1.41421i 0.115087i 0.998343 + 0.0575435i $$0.0183268\pi$$
−0.998343 + 0.0575435i $$0.981673\pi$$
$$152$$ 0 0
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 8.48528 + 8.48528i 0.681554 + 0.681554i
$$156$$ 0 0
$$157$$ −5.00000 + 5.00000i −0.399043 + 0.399043i −0.877896 0.478852i $$-0.841053\pi$$
0.478852 + 0.877896i $$0.341053\pi$$
$$158$$ 0 0
$$159$$ −5.65685 −0.448618
$$160$$ 0 0
$$161$$ 12.0000 0.945732
$$162$$ 0 0
$$163$$ −7.07107 + 7.07107i −0.553849 + 0.553849i −0.927549 0.373701i $$-0.878089\pi$$
0.373701 + 0.927549i $$0.378089\pi$$
$$164$$ 0 0
$$165$$ 8.00000 + 8.00000i 0.622799 + 0.622799i
$$166$$ 0 0
$$167$$ 11.3137i 0.875481i −0.899101 0.437741i $$-0.855779\pi$$
0.899101 0.437741i $$-0.144221\pi$$
$$168$$ 0 0
$$169$$ 5.00000i 0.384615i
$$170$$ 0 0
$$171$$ −1.41421 1.41421i −0.108148 0.108148i
$$172$$ 0 0
$$173$$ 2.00000 2.00000i 0.152057 0.152057i −0.626979 0.779036i $$-0.715709\pi$$
0.779036 + 0.626979i $$0.215709\pi$$
$$174$$ 0 0
$$175$$ −12.7279 −0.962140
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$180$$ 0 0
$$181$$ 1.00000 + 1.00000i 0.0743294 + 0.0743294i 0.743294 0.668965i $$-0.233262\pi$$
−0.668965 + 0.743294i $$0.733262\pi$$
$$182$$ 0 0
$$183$$ 4.24264i 0.313625i
$$184$$ 0 0
$$185$$ 12.0000i 0.882258i
$$186$$ 0 0
$$187$$ 16.9706 + 16.9706i 1.24101 + 1.24101i
$$188$$ 0 0
$$189$$ 3.00000 3.00000i 0.218218 0.218218i
$$190$$ 0 0
$$191$$ 22.6274 1.63726 0.818631 0.574320i $$-0.194733\pi$$
0.818631 + 0.574320i $$0.194733\pi$$
$$192$$ 0 0
$$193$$ 18.0000 1.29567 0.647834 0.761781i $$-0.275675\pi$$
0.647834 + 0.761781i $$0.275675\pi$$
$$194$$ 0 0
$$195$$ 8.48528 8.48528i 0.607644 0.607644i
$$196$$ 0 0
$$197$$ −4.00000 4.00000i −0.284988 0.284988i 0.550106 0.835095i $$-0.314587\pi$$
−0.835095 + 0.550106i $$0.814587\pi$$
$$198$$ 0 0
$$199$$ 7.07107i 0.501255i 0.968084 + 0.250627i $$0.0806369\pi$$
−0.968084 + 0.250627i $$0.919363\pi$$
$$200$$ 0 0
$$201$$ 4.00000i 0.282138i
$$202$$ 0 0
$$203$$ −16.9706 16.9706i −1.19110 1.19110i
$$204$$ 0 0
$$205$$ 20.0000 20.0000i 1.39686 1.39686i
$$206$$ 0 0
$$207$$ −2.82843 −0.196589
$$208$$ 0 0
$$209$$ −8.00000 −0.553372
$$210$$ 0 0
$$211$$ −8.48528 + 8.48528i −0.584151 + 0.584151i −0.936041 0.351890i $$-0.885539\pi$$
0.351890 + 0.936041i $$0.385539\pi$$
$$212$$ 0 0
$$213$$ 2.00000 + 2.00000i 0.137038 + 0.137038i
$$214$$ 0 0
$$215$$ 16.9706i 1.15738i
$$216$$ 0 0
$$217$$ 18.0000i 1.22192i
$$218$$ 0 0
$$219$$ −11.3137 11.3137i −0.764510 0.764510i
$$220$$ 0 0
$$221$$ 18.0000 18.0000i 1.21081 1.21081i
$$222$$ 0 0
$$223$$ 21.2132 1.42054 0.710271 0.703929i $$-0.248573\pi$$
0.710271 + 0.703929i $$0.248573\pi$$
$$224$$ 0 0
$$225$$ 3.00000 0.200000
$$226$$ 0 0
$$227$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$228$$ 0 0
$$229$$ −11.0000 11.0000i −0.726900 0.726900i 0.243101 0.970001i $$-0.421835\pi$$
−0.970001 + 0.243101i $$0.921835\pi$$
$$230$$ 0 0
$$231$$ 16.9706i 1.11658i
$$232$$ 0 0
$$233$$ 18.0000i 1.17922i −0.807688 0.589610i $$-0.799282\pi$$
0.807688 0.589610i $$-0.200718\pi$$
$$234$$ 0 0
$$235$$ −5.65685 5.65685i −0.369012 0.369012i
$$236$$ 0 0
$$237$$ 3.00000 3.00000i 0.194871 0.194871i
$$238$$ 0 0
$$239$$ −11.3137 −0.731823 −0.365911 0.930650i $$-0.619243\pi$$
−0.365911 + 0.930650i $$0.619243\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ −0.707107 + 0.707107i −0.0453609 + 0.0453609i
$$244$$ 0 0
$$245$$ 22.0000 + 22.0000i 1.40553 + 1.40553i
$$246$$ 0 0
$$247$$ 8.48528i 0.539906i
$$248$$ 0 0
$$249$$ 16.0000i 1.01396i
$$250$$ 0 0
$$251$$ 2.82843 + 2.82843i 0.178529 + 0.178529i 0.790714 0.612185i $$-0.209709\pi$$
−0.612185 + 0.790714i $$0.709709\pi$$
$$252$$ 0 0
$$253$$ −8.00000 + 8.00000i −0.502956 + 0.502956i
$$254$$ 0 0
$$255$$ 16.9706 1.06274
$$256$$ 0 0
$$257$$ −14.0000 −0.873296 −0.436648 0.899632i $$-0.643834\pi$$
−0.436648 + 0.899632i $$0.643834\pi$$
$$258$$ 0 0
$$259$$ 12.7279 12.7279i 0.790875 0.790875i
$$260$$ 0 0
$$261$$ 4.00000 + 4.00000i 0.247594 + 0.247594i
$$262$$ 0 0
$$263$$ 22.6274i 1.39527i 0.716455 + 0.697633i $$0.245763\pi$$
−0.716455 + 0.697633i $$0.754237\pi$$
$$264$$ 0 0
$$265$$ 16.0000i 0.982872i
$$266$$ 0 0
$$267$$ 9.89949 + 9.89949i 0.605839 + 0.605839i
$$268$$ 0 0
$$269$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$270$$ 0 0
$$271$$ 1.41421 0.0859074 0.0429537 0.999077i $$-0.486323\pi$$
0.0429537 + 0.999077i $$0.486323\pi$$
$$272$$ 0 0
$$273$$ −18.0000 −1.08941
$$274$$ 0 0
$$275$$ 8.48528 8.48528i 0.511682 0.511682i
$$276$$ 0 0
$$277$$ −1.00000 1.00000i −0.0600842 0.0600842i 0.676426 0.736510i $$-0.263528\pi$$
−0.736510 + 0.676426i $$0.763528\pi$$
$$278$$ 0 0
$$279$$ 4.24264i 0.254000i
$$280$$ 0 0
$$281$$ 6.00000i 0.357930i 0.983855 + 0.178965i $$0.0572749\pi$$
−0.983855 + 0.178965i $$0.942725\pi$$
$$282$$ 0 0
$$283$$ 2.82843 + 2.82843i 0.168133 + 0.168133i 0.786158 0.618026i $$-0.212067\pi$$
−0.618026 + 0.786158i $$0.712067\pi$$
$$284$$ 0 0
$$285$$ −4.00000 + 4.00000i −0.236940 + 0.236940i
$$286$$ 0 0
$$287$$ −42.4264 −2.50435
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ 0 0
$$291$$ −2.82843 + 2.82843i −0.165805 + 0.165805i
$$292$$ 0 0
$$293$$ −4.00000 4.00000i −0.233682 0.233682i 0.580545 0.814228i $$-0.302839\pi$$
−0.814228 + 0.580545i $$0.802839\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 4.00000i 0.232104i
$$298$$ 0 0
$$299$$ 8.48528 + 8.48528i 0.490716 + 0.490716i
$$300$$ 0 0
$$301$$ −18.0000 + 18.0000i −1.03750 + 1.03750i
$$302$$ 0 0
$$303$$ −11.3137 −0.649956
$$304$$ 0 0
$$305$$ 12.0000 0.687118
$$306$$ 0 0
$$307$$ −2.82843 + 2.82843i −0.161427 + 0.161427i −0.783199 0.621772i $$-0.786413\pi$$
0.621772 + 0.783199i $$0.286413\pi$$
$$308$$ 0 0
$$309$$ −13.0000 13.0000i −0.739544 0.739544i
$$310$$ 0 0
$$311$$ 28.2843i 1.60385i 0.597422 + 0.801927i $$0.296192\pi$$
−0.597422 + 0.801927i $$0.703808\pi$$
$$312$$ 0 0
$$313$$ 26.0000i 1.46961i 0.678280 + 0.734803i $$0.262726\pi$$
−0.678280 + 0.734803i $$0.737274\pi$$
$$314$$ 0 0
$$315$$ −8.48528 8.48528i −0.478091 0.478091i
$$316$$ 0 0
$$317$$ −12.0000 + 12.0000i −0.673987 + 0.673987i −0.958633 0.284646i $$-0.908124\pi$$
0.284646 + 0.958633i $$0.408124\pi$$
$$318$$ 0 0
$$319$$ 22.6274 1.26689
$$320$$ 0 0
$$321$$ −4.00000 −0.223258
$$322$$ 0 0
$$323$$ −8.48528 + 8.48528i −0.472134 + 0.472134i
$$324$$ 0 0
$$325$$ −9.00000 9.00000i −0.499230 0.499230i
$$326$$ 0 0
$$327$$ 9.89949i 0.547443i
$$328$$ 0 0
$$329$$ 12.0000i 0.661581i
$$330$$ 0 0
$$331$$ −2.82843 2.82843i −0.155464 0.155464i 0.625089 0.780553i $$-0.285063\pi$$
−0.780553 + 0.625089i $$0.785063\pi$$
$$332$$ 0 0
$$333$$ −3.00000 + 3.00000i −0.164399 + 0.164399i
$$334$$ 0 0
$$335$$ 11.3137 0.618134
$$336$$ 0 0
$$337$$ −8.00000 −0.435788 −0.217894 0.975972i $$-0.569919\pi$$
−0.217894 + 0.975972i $$0.569919\pi$$
$$338$$ 0 0
$$339$$ 4.24264 4.24264i 0.230429 0.230429i
$$340$$ 0 0
$$341$$ 12.0000 + 12.0000i 0.649836 + 0.649836i
$$342$$ 0 0
$$343$$ 16.9706i 0.916324i
$$344$$ 0 0
$$345$$ 8.00000i 0.430706i
$$346$$ 0 0
$$347$$ 16.9706 + 16.9706i 0.911028 + 0.911028i 0.996353 0.0853256i $$-0.0271930\pi$$
−0.0853256 + 0.996353i $$0.527193\pi$$
$$348$$ 0 0
$$349$$ 3.00000 3.00000i 0.160586 0.160586i −0.622240 0.782826i $$-0.713777\pi$$
0.782826 + 0.622240i $$0.213777\pi$$
$$350$$ 0 0
$$351$$ 4.24264 0.226455
$$352$$ 0 0
$$353$$ −6.00000 −0.319348 −0.159674 0.987170i $$-0.551044\pi$$
−0.159674 + 0.987170i $$0.551044\pi$$
$$354$$ 0 0
$$355$$ 5.65685 5.65685i 0.300235 0.300235i
$$356$$ 0 0
$$357$$ −18.0000 18.0000i −0.952661 0.952661i
$$358$$ 0 0
$$359$$ 2.82843i 0.149279i 0.997211 + 0.0746393i $$0.0237806\pi$$
−0.997211 + 0.0746393i $$0.976219\pi$$
$$360$$ 0 0
$$361$$ 15.0000i 0.789474i
$$362$$ 0 0
$$363$$ 3.53553 + 3.53553i 0.185567 + 0.185567i
$$364$$ 0 0
$$365$$ −32.0000 + 32.0000i −1.67496 + 1.67496i
$$366$$ 0 0
$$367$$ −18.3848 −0.959678 −0.479839 0.877357i $$-0.659305\pi$$
−0.479839 + 0.877357i $$0.659305\pi$$
$$368$$ 0 0
$$369$$ 10.0000 0.520579
$$370$$ 0 0
$$371$$ 16.9706 16.9706i 0.881068 0.881068i
$$372$$ 0 0
$$373$$ −13.0000 13.0000i −0.673114 0.673114i 0.285318 0.958433i $$-0.407901\pi$$
−0.958433 + 0.285318i $$0.907901\pi$$
$$374$$ 0 0
$$375$$ 5.65685i 0.292119i
$$376$$ 0 0
$$377$$ 24.0000i 1.23606i
$$378$$ 0 0
$$379$$ −26.8701 26.8701i −1.38022 1.38022i −0.844211 0.536011i $$-0.819930\pi$$
−0.536011 0.844211i $$-0.680070\pi$$
$$380$$ 0 0
$$381$$ −3.00000 + 3.00000i −0.153695 + 0.153695i
$$382$$ 0 0
$$383$$ −28.2843 −1.44526 −0.722629 0.691236i $$-0.757067\pi$$
−0.722629 + 0.691236i $$0.757067\pi$$
$$384$$ 0 0
$$385$$ −48.0000 −2.44631
$$386$$ 0 0
$$387$$ 4.24264 4.24264i 0.215666 0.215666i
$$388$$ 0 0
$$389$$ 2.00000 + 2.00000i 0.101404 + 0.101404i 0.755989 0.654585i $$-0.227156\pi$$
−0.654585 + 0.755989i $$0.727156\pi$$
$$390$$ 0 0
$$391$$ 16.9706i 0.858238i
$$392$$ 0 0
$$393$$ 20.0000i 1.00887i
$$394$$ 0 0
$$395$$ −8.48528 8.48528i −0.426941 0.426941i
$$396$$ 0 0
$$397$$ −23.0000 + 23.0000i −1.15434 + 1.15434i −0.168663 + 0.985674i $$0.553945\pi$$
−0.985674 + 0.168663i $$0.946055\pi$$
$$398$$ 0 0
$$399$$ 8.48528 0.424795
$$400$$ 0 0
$$401$$ −10.0000 −0.499376 −0.249688 0.968326i $$-0.580328\pi$$
−0.249688 + 0.968326i $$0.580328\pi$$
$$402$$ 0 0
$$403$$ 12.7279 12.7279i 0.634023 0.634023i
$$404$$ 0 0
$$405$$ 2.00000 + 2.00000i 0.0993808 + 0.0993808i
$$406$$ 0 0
$$407$$ 16.9706i 0.841200i
$$408$$ 0 0
$$409$$ 28.0000i 1.38451i −0.721653 0.692255i $$-0.756617\pi$$
0.721653 0.692255i $$-0.243383\pi$$
$$410$$ 0 0
$$411$$ −7.07107 7.07107i −0.348790 0.348790i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −45.2548 −2.22147
$$416$$ 0 0
$$417$$ 12.0000 0.587643
$$418$$ 0 0
$$419$$ −11.3137 + 11.3137i −0.552711 + 0.552711i −0.927222 0.374511i $$-0.877810\pi$$
0.374511 + 0.927222i $$0.377810\pi$$
$$420$$ 0 0
$$421$$ 25.0000 + 25.0000i 1.21843 + 1.21843i 0.968183 + 0.250242i $$0.0805102\pi$$
0.250242 + 0.968183i $$0.419490\pi$$
$$422$$ 0 0
$$423$$ 2.82843i 0.137523i
$$424$$ 0 0
$$425$$ 18.0000i 0.873128i
$$426$$ 0 0
$$427$$ −12.7279 12.7279i −0.615947 0.615947i
$$428$$ 0 0
$$429$$ 12.0000 12.0000i 0.579365 0.579365i
$$430$$ 0 0
$$431$$ 36.7696 1.77113 0.885564 0.464518i $$-0.153773\pi$$
0.885564 + 0.464518i $$0.153773\pi$$
$$432$$ 0 0
$$433$$ −8.00000 −0.384455 −0.192228 0.981350i $$-0.561571\pi$$
−0.192228 + 0.981350i $$0.561571\pi$$
$$434$$ 0 0
$$435$$ 11.3137 11.3137i 0.542451 0.542451i
$$436$$ 0 0
$$437$$ −4.00000 4.00000i −0.191346 0.191346i
$$438$$ 0 0
$$439$$ 1.41421i 0.0674967i −0.999430 0.0337484i $$-0.989256\pi$$
0.999430 0.0337484i $$-0.0107445\pi$$
$$440$$ 0 0
$$441$$ 11.0000i 0.523810i
$$442$$ 0 0
$$443$$ −16.9706 16.9706i −0.806296 0.806296i 0.177775 0.984071i $$-0.443110\pi$$
−0.984071 + 0.177775i $$0.943110\pi$$
$$444$$ 0 0
$$445$$ 28.0000 28.0000i 1.32733 1.32733i
$$446$$ 0 0
$$447$$ −8.48528 −0.401340
$$448$$ 0 0
$$449$$ −26.0000 −1.22702 −0.613508 0.789689i $$-0.710242\pi$$
−0.613508 + 0.789689i $$0.710242\pi$$
$$450$$ 0 0
$$451$$ 28.2843 28.2843i 1.33185 1.33185i
$$452$$ 0 0
$$453$$ 1.00000 + 1.00000i 0.0469841 + 0.0469841i
$$454$$ 0 0
$$455$$ 50.9117i 2.38678i
$$456$$ 0 0
$$457$$ 12.0000i 0.561336i −0.959805 0.280668i $$-0.909444\pi$$
0.959805 0.280668i $$-0.0905560\pi$$
$$458$$ 0 0
$$459$$ 4.24264 + 4.24264i 0.198030 + 0.198030i
$$460$$ 0 0
$$461$$ −6.00000 + 6.00000i −0.279448 + 0.279448i −0.832889 0.553441i $$-0.813315\pi$$
0.553441 + 0.832889i $$0.313315\pi$$
$$462$$ 0 0
$$463$$ −12.7279 −0.591517 −0.295758 0.955263i $$-0.595572\pi$$
−0.295758 + 0.955263i $$0.595572\pi$$
$$464$$ 0 0
$$465$$ 12.0000 0.556487
$$466$$ 0 0
$$467$$ −16.9706 + 16.9706i −0.785304 + 0.785304i −0.980720 0.195416i $$-0.937394\pi$$
0.195416 + 0.980720i $$0.437394\pi$$
$$468$$ 0 0
$$469$$ −12.0000 12.0000i −0.554109 0.554109i
$$470$$ 0 0
$$471$$ 7.07107i 0.325818i
$$472$$ 0 0
$$473$$ 24.0000i 1.10352i
$$474$$ 0 0
$$475$$ 4.24264 + 4.24264i 0.194666 + 0.194666i
$$476$$ 0 0
$$477$$ −4.00000 + 4.00000i −0.183147 + 0.183147i
$$478$$ 0 0
$$479$$ −25.4558 −1.16311 −0.581554 0.813508i $$-0.697555\pi$$
−0.581554 + 0.813508i $$0.697555\pi$$
$$480$$ 0 0
$$481$$ 18.0000 0.820729
$$482$$ 0 0
$$483$$ 8.48528 8.48528i 0.386094 0.386094i
$$484$$ 0 0
$$485$$ 8.00000 + 8.00000i 0.363261 + 0.363261i
$$486$$ 0 0
$$487$$ 43.8406i 1.98661i −0.115529 0.993304i $$-0.536856\pi$$
0.115529 0.993304i $$-0.463144\pi$$
$$488$$ 0 0
$$489$$ 10.0000i 0.452216i
$$490$$ 0 0
$$491$$ −5.65685 5.65685i −0.255290 0.255290i 0.567845 0.823135i $$-0.307777\pi$$
−0.823135 + 0.567845i $$0.807777\pi$$
$$492$$ 0 0
$$493$$ 24.0000 24.0000i 1.08091 1.08091i
$$494$$ 0 0
$$495$$ 11.3137 0.508513
$$496$$ 0 0
$$497$$ −12.0000 −0.538274
$$498$$ 0 0
$$499$$ 14.1421 14.1421i 0.633089 0.633089i −0.315753 0.948842i $$-0.602257\pi$$
0.948842 + 0.315753i $$0.102257\pi$$
$$500$$ 0 0
$$501$$ −8.00000 8.00000i −0.357414 0.357414i
$$502$$ 0 0
$$503$$ 14.1421i 0.630567i 0.948998 + 0.315283i $$0.102100\pi$$
−0.948998 + 0.315283i $$0.897900\pi$$
$$504$$ 0 0
$$505$$ 32.0000i 1.42398i
$$506$$ 0 0
$$507$$ −3.53553 3.53553i −0.157019 0.157019i
$$508$$ 0 0
$$509$$ −16.0000 + 16.0000i −0.709188 + 0.709188i −0.966364 0.257177i $$-0.917208\pi$$
0.257177 + 0.966364i $$0.417208\pi$$
$$510$$ 0 0
$$511$$ 67.8823 3.00293
$$512$$ 0 0
$$513$$ −2.00000 −0.0883022
$$514$$ 0 0
$$515$$ −36.7696 + 36.7696i −1.62026 + 1.62026i
$$516$$ 0 0
$$517$$ −8.00000 8.00000i −0.351840 0.351840i
$$518$$ 0 0
$$519$$ 2.82843i 0.124154i
$$520$$ 0 0
$$521$$ 22.0000i 0.963837i 0.876216 + 0.481919i $$0.160060\pi$$
−0.876216 + 0.481919i $$0.839940\pi$$
$$522$$ 0 0
$$523$$ 15.5563 + 15.5563i 0.680232 + 0.680232i 0.960052 0.279821i $$-0.0902750\pi$$
−0.279821 + 0.960052i $$0.590275\pi$$
$$524$$ 0 0
$$525$$ −9.00000 + 9.00000i −0.392792 + 0.392792i
$$526$$ 0 0
$$527$$ 25.4558 1.10887
$$528$$ 0 0
$$529$$ 15.0000 0.652174
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −30.0000 30.0000i −1.29944 1.29944i
$$534$$ 0 0
$$535$$ 11.3137i 0.489134i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 31.1127 + 31.1127i 1.34012 + 1.34012i
$$540$$ 0 0
$$541$$ −29.0000 + 29.0000i −1.24681 + 1.24681i −0.289685 + 0.957122i $$0.593551\pi$$
−0.957122 + 0.289685i $$0.906449\pi$$
$$542$$ 0 0
$$543$$ 1.41421 0.0606897
$$544$$ 0 0
$$545$$ −28.0000 −1.19939
$$546$$ 0 0
$$547$$ 24.0416 24.0416i 1.02795 1.02795i 0.0283478 0.999598i $$-0.490975\pi$$
0.999598 0.0283478i $$-0.00902459\pi$$
$$548$$ 0 0
$$549$$ 3.00000 + 3.00000i 0.128037 + 0.128037i
$$550$$ 0 0
$$551$$ 11.3137i 0.481980i
$$552$$ 0 0
$$553$$ 18.0000i 0.765438i
$$554$$ 0 0
$$555$$ 8.48528 + 8.48528i 0.360180 + 0.360180i
$$556$$ 0 0
$$557$$ 14.0000 14.0000i 0.593199 0.593199i −0.345295 0.938494i $$-0.612221\pi$$
0.938494 + 0.345295i $$0.112221\pi$$
$$558$$ 0 0
$$559$$ −25.4558 −1.07667
$$560$$ 0 0
$$561$$ 24.0000 1.01328
$$562$$ 0 0
$$563$$ −2.82843 + 2.82843i −0.119204 + 0.119204i −0.764192 0.644988i $$-0.776862\pi$$
0.644988 + 0.764192i $$0.276862\pi$$
$$564$$ 0 0
$$565$$ −12.0000 12.0000i −0.504844 0.504844i
$$566$$ 0 0
$$567$$ 4.24264i 0.178174i
$$568$$ 0 0
$$569$$ 18.0000i 0.754599i −0.926091 0.377300i $$-0.876853\pi$$
0.926091 0.377300i $$-0.123147\pi$$
$$570$$ 0 0
$$571$$ −14.1421 14.1421i −0.591830 0.591830i 0.346296 0.938125i $$-0.387439\pi$$
−0.938125 + 0.346296i $$0.887439\pi$$
$$572$$ 0 0
$$573$$ 16.0000 16.0000i 0.668410 0.668410i
$$574$$ 0 0
$$575$$ 8.48528 0.353861
$$576$$ 0 0
$$577$$ 4.00000 0.166522 0.0832611 0.996528i $$-0.473466\pi$$
0.0832611 + 0.996528i $$0.473466\pi$$
$$578$$ 0 0
$$579$$ 12.7279 12.7279i 0.528954 0.528954i
$$580$$ 0 0
$$581$$ 48.0000 + 48.0000i 1.99138 + 1.99138i
$$582$$ 0 0
$$583$$ 22.6274i 0.937132i
$$584$$ 0 0
$$585$$ 12.0000i 0.496139i
$$586$$ 0 0
$$587$$ 16.9706 + 16.9706i 0.700450 + 0.700450i 0.964507 0.264057i $$-0.0850607\pi$$
−0.264057 + 0.964507i $$0.585061\pi$$
$$588$$ 0 0
$$589$$ −6.00000 + 6.00000i −0.247226 + 0.247226i
$$590$$ 0 0
$$591$$ −5.65685 −0.232692
$$592$$ 0 0
$$593$$ 14.0000 0.574911 0.287456 0.957794i $$-0.407191\pi$$
0.287456 + 0.957794i $$0.407191\pi$$
$$594$$ 0 0
$$595$$ −50.9117 + 50.9117i −2.08718 + 2.08718i
$$596$$ 0 0
$$597$$ 5.00000 + 5.00000i 0.204636 + 0.204636i
$$598$$ 0 0
$$599$$ 48.0833i 1.96463i −0.187239 0.982314i $$-0.559954\pi$$
0.187239 0.982314i $$-0.440046\pi$$
$$600$$ 0 0
$$601$$ 28.0000i 1.14214i 0.820900 + 0.571072i $$0.193472\pi$$
−0.820900 + 0.571072i $$0.806528\pi$$
$$602$$ 0 0
$$603$$ 2.82843 + 2.82843i 0.115182 + 0.115182i
$$604$$ 0 0
$$605$$ 10.0000 10.0000i 0.406558 0.406558i
$$606$$ 0 0
$$607$$ −4.24264 −0.172203 −0.0861017 0.996286i $$-0.527441\pi$$
−0.0861017 + 0.996286i $$0.527441\pi$$
$$608$$ 0 0
$$609$$ −24.0000 −0.972529
$$610$$ 0 0
$$611$$ −8.48528 + 8.48528i −0.343278 + 0.343278i
$$612$$ 0 0
$$613$$ 13.0000 + 13.0000i 0.525065 + 0.525065i 0.919097 0.394032i $$-0.128920\pi$$
−0.394032 + 0.919097i $$0.628920\pi$$
$$614$$ 0 0
$$615$$ 28.2843i 1.14053i
$$616$$ 0 0
$$617$$ 22.0000i 0.885687i −0.896599 0.442843i $$-0.853970\pi$$
0.896599 0.442843i $$-0.146030\pi$$
$$618$$ 0 0
$$619$$ 25.4558 + 25.4558i 1.02316 + 1.02316i 0.999725 + 0.0234313i $$0.00745910\pi$$
0.0234313 + 0.999725i $$0.492541\pi$$
$$620$$ 0 0
$$621$$ −2.00000 + 2.00000i −0.0802572 + 0.0802572i
$$622$$ 0 0
$$623$$ −59.3970 −2.37969
$$624$$ 0 0
$$625$$ 31.0000 1.24000
$$626$$ 0 0
$$627$$ −5.65685 + 5.65685i −0.225913 + 0.225913i
$$628$$ 0 0
$$629$$ 18.0000 + 18.0000i 0.717707 + 0.717707i
$$630$$ 0 0
$$631$$ 35.3553i 1.40747i −0.710461 0.703737i $$-0.751513\pi$$
0.710461 0.703737i $$-0.248487\pi$$
$$632$$ 0 0
$$633$$ 12.0000i 0.476957i
$$634$$ 0 0
$$635$$ 8.48528 + 8.48528i 0.336728 + 0.336728i
$$636$$ 0 0
$$637$$ 33.0000 33.0000i 1.30751 1.30751i
$$638$$ 0 0
$$639$$ 2.82843 0.111891
$$640$$ 0 0
$$641$$ 18.0000 0.710957 0.355479 0.934684i $$-0.384318\pi$$
0.355479 + 0.934684i $$0.384318\pi$$
$$642$$ 0 0
$$643$$ −9.89949 + 9.89949i −0.390398 + 0.390398i −0.874829 0.484431i $$-0.839027\pi$$
0.484431 + 0.874829i $$0.339027\pi$$
$$644$$ 0 0
$$645$$ −12.0000 12.0000i −0.472500 0.472500i
$$646$$ 0 0
$$647$$ 14.1421i 0.555985i 0.960583 + 0.277992i $$0.0896690\pi$$
−0.960583 + 0.277992i $$0.910331\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −12.7279 12.7279i −0.498847 0.498847i
$$652$$ 0 0
$$653$$ 6.00000 6.00000i 0.234798 0.234798i −0.579894 0.814692i $$-0.696906\pi$$
0.814692 + 0.579894i $$0.196906\pi$$
$$654$$ 0 0
$$655$$ 56.5685 2.21032
$$656$$ 0 0
$$657$$ −16.0000 −0.624219
$$658$$ 0 0
$$659$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$660$$ 0 0
$$661$$ 9.00000 + 9.00000i 0.350059 + 0.350059i 0.860132 0.510072i $$-0.170381\pi$$
−0.510072 + 0.860132i $$0.670381\pi$$
$$662$$ 0 0
$$663$$ 25.4558i 0.988623i
$$664$$ 0 0
$$665$$ 24.0000i 0.930680i
$$666$$ 0 0
$$667$$ 11.3137 + 11.3137i 0.438069 + 0.438069i
$$668$$ 0 0
$$669$$ 15.0000 15.0000i 0.579934 0.579934i
$$670$$ 0 0
$$671$$ 16.9706 0.655141
$$672$$ 0 0
$$673$$ −40.0000 −1.54189 −0.770943 0.636904i $$-0.780215\pi$$
−0.770943 + 0.636904i $$0.780215\pi$$
$$674$$ 0 0
$$675$$ 2.12132 2.12132i 0.0816497 0.0816497i
$$676$$ 0 0
$$677$$ 26.0000 + 26.0000i 0.999261 + 0.999261i 1.00000 0.000738553i $$-0.000235089\pi$$
−0.000738553 1.00000i $$0.500235\pi$$
$$678$$ 0 0
$$679$$ 16.9706i 0.651270i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −16.9706 16.9706i −0.649361 0.649361i 0.303478 0.952838i $$-0.401852\pi$$
−0.952838 + 0.303478i $$0.901852\pi$$
$$684$$ 0 0
$$685$$ −20.0000 + 20.0000i −0.764161 + 0.764161i
$$686$$ 0 0
$$687$$ −15.5563 −0.593512
$$688$$ 0 0
$$689$$ 24.0000 0.914327
$$690$$ 0 0
$$691$$ −15.5563 + 15.5563i −0.591791 + 0.591791i −0.938115 0.346324i $$-0.887430\pi$$
0.346324 + 0.938115i $$0.387430\pi$$
$$692$$ 0 0
$$693$$ −12.0000 12.0000i −0.455842 0.455842i
$$694$$ 0 0
$$695$$ 33.9411i 1.28746i
$$696$$ 0 0
$$697$$ 60.0000i 2.27266i
$$698$$ 0 0
$$699$$ −12.7279 12.7279i −0.481414 0.481414i
$$700$$ 0 0
$$701$$ 4.00000 4.00000i 0.151078 0.151078i −0.627521 0.778599i $$-0.715931\pi$$
0.778599 + 0.627521i $$0.215931\pi$$
$$702$$ 0 0
$$703$$ −8.48528 −0.320028
$$704$$ 0 0
$$705$$ −8.00000 −0.301297
$$706$$ 0 0
$$707$$ 33.9411 33.9411i 1.27649 1.27649i
$$708$$ 0 0
$$709$$ −13.0000 13.0000i −0.488225 0.488225i 0.419521 0.907746i $$-0.362198\pi$$
−0.907746 + 0.419521i $$0.862198\pi$$
$$710$$ 0 0
$$711$$ 4.24264i 0.159111i
$$712$$ 0 0
$$713$$ 12.0000i 0.449404i
$$714$$ 0 0
$$715$$ −33.9411 33.9411i −1.26933 1.26933i
$$716$$ 0 0
$$717$$ −8.00000 + 8.00000i −0.298765 + 0.298765i
$$718$$ 0 0
$$719$$ −8.48528 −0.316448 −0.158224 0.987403i $$-0.550577\pi$$
−0.158224 + 0.987403i $$0.550577\pi$$
$$720$$ 0 0
$$721$$ 78.0000 2.90487
$$722$$ 0 0
$$723$$ −12.7279 + 12.7279i −0.473357 + 0.473357i
$$724$$ 0 0
$$725$$ −12.0000 12.0000i −0.445669 0.445669i
$$726$$ 0 0
$$727$$ 26.8701i 0.996555i 0.867018 + 0.498278i $$0.166034\pi$$
−0.867018 + 0.498278i $$0.833966\pi$$
$$728$$ 0 0
$$729$$ 1.00000i 0.0370370i
$$730$$ 0 0
$$731$$ −25.4558 25.4558i −0.941518 0.941518i
$$732$$ 0 0
$$733$$ 25.0000 25.0000i 0.923396 0.923396i −0.0738717 0.997268i $$-0.523536\pi$$
0.997268 + 0.0738717i $$0.0235355\pi$$
$$734$$ 0 0
$$735$$ 31.1127 1.14761
$$736$$ 0 0
$$737$$ 16.0000 0.589368
$$738$$ 0 0
$$739$$ −25.4558 + 25.4558i −0.936408 + 0.936408i −0.998096 0.0616872i $$-0.980352\pi$$
0.0616872 + 0.998096i $$0.480352\pi$$
$$740$$ 0 0
$$741$$ 6.00000 + 6.00000i 0.220416 + 0.220416i
$$742$$ 0 0
$$743$$ 22.6274i 0.830119i −0.909794 0.415060i $$-0.863761\pi$$
0.909794 0.415060i $$-0.136239\pi$$
$$744$$ 0 0
$$745$$ 24.0000i 0.879292i
$$746$$ 0 0
$$747$$ −11.3137 11.3137i −0.413947 0.413947i
$$748$$ 0 0
$$749$$ 12.0000 12.0000i 0.438470 0.438470i
$$750$$ 0 0
$$751$$ 12.7279 0.464448 0.232224 0.972662i $$-0.425400\pi$$
0.232224 + 0.972662i $$0.425400\pi$$
$$752$$ 0 0
$$753$$ 4.00000 0.145768
$$754$$ 0 0
$$755$$ 2.82843 2.82843i 0.102937 0.102937i
$$756$$ 0 0
$$757$$ −27.0000 27.0000i −0.981332 0.981332i 0.0184972 0.999829i $$-0.494112\pi$$
−0.999829 + 0.0184972i $$0.994112\pi$$
$$758$$ 0 0
$$759$$ 11.3137i 0.410662i
$$760$$ 0 0
$$761$$ 34.0000i 1.23250i −0.787551 0.616250i $$-0.788651\pi$$
0.787551 0.616250i $$-0.211349\pi$$
$$762$$ 0 0
$$763$$ 29.6985 + 29.6985i 1.07516 + 1.07516i
$$764$$ 0 0
$$765$$ 12.0000 12.0000i 0.433861 0.433861i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ −9.89949 + 9.89949i −0.356522 + 0.356522i
$$772$$ 0 0
$$773$$ 4.00000 + 4.00000i 0.143870 + 0.143870i 0.775373 0.631503i $$-0.217562\pi$$
−0.631503 + 0.775373i $$0.717562\pi$$
$$774$$ 0 0
$$775$$ 12.7279i 0.457200i
$$776$$ 0 0
$$777$$ 18.0000i 0.645746i
$$778$$ 0 0
$$779$$ 14.1421 + 14.1421i 0.506695 + 0.506695i
$$780$$ 0 0
$$781$$ 8.00000 8.00000i 0.286263 0.286263i
$$782$$ 0 0
$$783$$ 5.65685 0.202159
$$784$$ 0 0
$$785$$ 20.0000 0.713831
$$786$$ 0 0
$$787$$ 26.8701 26.8701i 0.957814 0.957814i −0.0413314 0.999145i $$-0.513160\pi$$
0.999145 + 0.0413314i $$0.0131599\pi$$
$$788$$ 0 0
$$789$$ 16.0000 + 16.0000i 0.569615 + 0.569615i
$$790$$ 0 0
$$791$$ 25.4558i 0.905106i
$$792$$ 0 0
$$793$$ 18.0000i 0.639199i
$$794$$ 0 0
$$795$$ 11.3137 + 11.3137i 0.401256 + 0.401256i
$$796$$ 0 0
$$797$$ 22.0000 22.0000i 0.779280 0.779280i −0.200428 0.979708i $$-0.564233\pi$$
0.979708 + 0.200428i $$0.0642334\pi$$