# Properties

 Label 1710.2.d.g.1369.7 Level $1710$ Weight $2$ Character 1710.1369 Analytic conductor $13.654$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1710.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.6544187456$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1369.7 Root $$0.965926 + 0.258819i$$ of defining polynomial Character $$\chi$$ $$=$$ 1710.1369 Dual form 1710.2.d.g.1369.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(1.41421 - 1.73205i) q^{5} +3.86370i q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+1.00000i q^{2} -1.00000 q^{4} +(1.41421 - 1.73205i) q^{5} +3.86370i q^{7} -1.00000i q^{8} +(1.73205 + 1.41421i) q^{10} -1.03528 q^{11} +3.86370i q^{13} -3.86370 q^{14} +1.00000 q^{16} -0.535898i q^{17} +1.00000 q^{19} +(-1.41421 + 1.73205i) q^{20} -1.03528i q^{22} +5.46410i q^{23} +(-1.00000 - 4.89898i) q^{25} -3.86370 q^{26} -3.86370i q^{28} +4.62158 q^{29} -10.9282 q^{31} +1.00000i q^{32} +0.535898 q^{34} +(6.69213 + 5.46410i) q^{35} -1.79315i q^{37} +1.00000i q^{38} +(-1.73205 - 1.41421i) q^{40} -1.79315 q^{41} +6.69213i q^{43} +1.03528 q^{44} -5.46410 q^{46} -2.53590i q^{47} -7.92820 q^{49} +(4.89898 - 1.00000i) q^{50} -3.86370i q^{52} +6.00000i q^{53} +(-1.46410 + 1.79315i) q^{55} +3.86370 q^{56} +4.62158i q^{58} +6.96953 q^{59} -2.00000 q^{61} -10.9282i q^{62} -1.00000 q^{64} +(6.69213 + 5.46410i) q^{65} +13.3843i q^{67} +0.535898i q^{68} +(-5.46410 + 6.69213i) q^{70} -4.14110 q^{71} +3.58630i q^{73} +1.79315 q^{74} -1.00000 q^{76} -4.00000i q^{77} +4.00000 q^{79} +(1.41421 - 1.73205i) q^{80} -1.79315i q^{82} +16.3923i q^{83} +(-0.928203 - 0.757875i) q^{85} -6.69213 q^{86} +1.03528i q^{88} -3.86370 q^{89} -14.9282 q^{91} -5.46410i q^{92} +2.53590 q^{94} +(1.41421 - 1.73205i) q^{95} +2.55103i q^{97} -7.92820i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 8 q^{4} + O(q^{10})$$ $$8 q - 8 q^{4} + 8 q^{16} + 8 q^{19} - 8 q^{25} - 32 q^{31} + 32 q^{34} - 16 q^{46} - 8 q^{49} + 16 q^{55} - 16 q^{61} - 8 q^{64} - 16 q^{70} - 8 q^{76} + 32 q^{79} + 48 q^{85} - 64 q^{91} + 48 q^{94} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$1027$$ $$1351$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ 1.41421 1.73205i 0.632456 0.774597i
$$6$$ 0 0
$$7$$ 3.86370i 1.46034i 0.683264 + 0.730171i $$0.260560\pi$$
−0.683264 + 0.730171i $$0.739440\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 1.73205 + 1.41421i 0.547723 + 0.447214i
$$11$$ −1.03528 −0.312148 −0.156074 0.987745i $$-0.549884\pi$$
−0.156074 + 0.987745i $$0.549884\pi$$
$$12$$ 0 0
$$13$$ 3.86370i 1.07160i 0.844345 + 0.535799i $$0.179990\pi$$
−0.844345 + 0.535799i $$0.820010\pi$$
$$14$$ −3.86370 −1.03262
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 0.535898i 0.129974i −0.997886 0.0649872i $$-0.979299\pi$$
0.997886 0.0649872i $$-0.0207007\pi$$
$$18$$ 0 0
$$19$$ 1.00000 0.229416
$$20$$ −1.41421 + 1.73205i −0.316228 + 0.387298i
$$21$$ 0 0
$$22$$ 1.03528i 0.220722i
$$23$$ 5.46410i 1.13934i 0.821872 + 0.569672i $$0.192930\pi$$
−0.821872 + 0.569672i $$0.807070\pi$$
$$24$$ 0 0
$$25$$ −1.00000 4.89898i −0.200000 0.979796i
$$26$$ −3.86370 −0.757735
$$27$$ 0 0
$$28$$ 3.86370i 0.730171i
$$29$$ 4.62158 0.858206 0.429103 0.903256i $$-0.358830\pi$$
0.429103 + 0.903256i $$0.358830\pi$$
$$30$$ 0 0
$$31$$ −10.9282 −1.96276 −0.981382 0.192068i $$-0.938481\pi$$
−0.981382 + 0.192068i $$0.938481\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 0.535898 0.0919058
$$35$$ 6.69213 + 5.46410i 1.13118 + 0.923602i
$$36$$ 0 0
$$37$$ 1.79315i 0.294792i −0.989078 0.147396i $$-0.952911\pi$$
0.989078 0.147396i $$-0.0470892\pi$$
$$38$$ 1.00000i 0.162221i
$$39$$ 0 0
$$40$$ −1.73205 1.41421i −0.273861 0.223607i
$$41$$ −1.79315 −0.280043 −0.140022 0.990148i $$-0.544717\pi$$
−0.140022 + 0.990148i $$0.544717\pi$$
$$42$$ 0 0
$$43$$ 6.69213i 1.02054i 0.860014 + 0.510270i $$0.170455\pi$$
−0.860014 + 0.510270i $$0.829545\pi$$
$$44$$ 1.03528 0.156074
$$45$$ 0 0
$$46$$ −5.46410 −0.805638
$$47$$ 2.53590i 0.369899i −0.982748 0.184949i $$-0.940788\pi$$
0.982748 0.184949i $$-0.0592121\pi$$
$$48$$ 0 0
$$49$$ −7.92820 −1.13260
$$50$$ 4.89898 1.00000i 0.692820 0.141421i
$$51$$ 0 0
$$52$$ 3.86370i 0.535799i
$$53$$ 6.00000i 0.824163i 0.911147 + 0.412082i $$0.135198\pi$$
−0.911147 + 0.412082i $$0.864802\pi$$
$$54$$ 0 0
$$55$$ −1.46410 + 1.79315i −0.197419 + 0.241788i
$$56$$ 3.86370 0.516309
$$57$$ 0 0
$$58$$ 4.62158i 0.606843i
$$59$$ 6.96953 0.907356 0.453678 0.891166i $$-0.350112\pi$$
0.453678 + 0.891166i $$0.350112\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 10.9282i 1.38788i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 6.69213 + 5.46410i 0.830057 + 0.677738i
$$66$$ 0 0
$$67$$ 13.3843i 1.63515i 0.575824 + 0.817574i $$0.304681\pi$$
−0.575824 + 0.817574i $$0.695319\pi$$
$$68$$ 0.535898i 0.0649872i
$$69$$ 0 0
$$70$$ −5.46410 + 6.69213i −0.653085 + 0.799863i
$$71$$ −4.14110 −0.491459 −0.245729 0.969338i $$-0.579027\pi$$
−0.245729 + 0.969338i $$0.579027\pi$$
$$72$$ 0 0
$$73$$ 3.58630i 0.419745i 0.977729 + 0.209872i $$0.0673049\pi$$
−0.977729 + 0.209872i $$0.932695\pi$$
$$74$$ 1.79315 0.208450
$$75$$ 0 0
$$76$$ −1.00000 −0.114708
$$77$$ 4.00000i 0.455842i
$$78$$ 0 0
$$79$$ 4.00000 0.450035 0.225018 0.974355i $$-0.427756\pi$$
0.225018 + 0.974355i $$0.427756\pi$$
$$80$$ 1.41421 1.73205i 0.158114 0.193649i
$$81$$ 0 0
$$82$$ 1.79315i 0.198020i
$$83$$ 16.3923i 1.79929i 0.436623 + 0.899645i $$0.356174\pi$$
−0.436623 + 0.899645i $$0.643826\pi$$
$$84$$ 0 0
$$85$$ −0.928203 0.757875i −0.100678 0.0822031i
$$86$$ −6.69213 −0.721631
$$87$$ 0 0
$$88$$ 1.03528i 0.110361i
$$89$$ −3.86370 −0.409552 −0.204776 0.978809i $$-0.565647\pi$$
−0.204776 + 0.978809i $$0.565647\pi$$
$$90$$ 0 0
$$91$$ −14.9282 −1.56490
$$92$$ 5.46410i 0.569672i
$$93$$ 0 0
$$94$$ 2.53590 0.261558
$$95$$ 1.41421 1.73205i 0.145095 0.177705i
$$96$$ 0 0
$$97$$ 2.55103i 0.259017i 0.991578 + 0.129509i $$0.0413400\pi$$
−0.991578 + 0.129509i $$0.958660\pi$$
$$98$$ 7.92820i 0.800869i
$$99$$ 0 0
$$100$$ 1.00000 + 4.89898i 0.100000 + 0.489898i
$$101$$ 10.5558 1.05034 0.525172 0.850996i $$-0.324001\pi$$
0.525172 + 0.850996i $$0.324001\pi$$
$$102$$ 0 0
$$103$$ 4.89898i 0.482711i −0.970437 0.241355i $$-0.922408\pi$$
0.970437 0.241355i $$-0.0775919\pi$$
$$104$$ 3.86370 0.378867
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 2.92820i 0.283080i 0.989933 + 0.141540i $$0.0452054\pi$$
−0.989933 + 0.141540i $$0.954795\pi$$
$$108$$ 0 0
$$109$$ −8.92820 −0.855167 −0.427583 0.903976i $$-0.640635\pi$$
−0.427583 + 0.903976i $$0.640635\pi$$
$$110$$ −1.79315 1.46410i −0.170970 0.139597i
$$111$$ 0 0
$$112$$ 3.86370i 0.365086i
$$113$$ 6.00000i 0.564433i 0.959351 + 0.282216i $$0.0910696\pi$$
−0.959351 + 0.282216i $$0.908930\pi$$
$$114$$ 0 0
$$115$$ 9.46410 + 7.72741i 0.882532 + 0.720584i
$$116$$ −4.62158 −0.429103
$$117$$ 0 0
$$118$$ 6.96953i 0.641597i
$$119$$ 2.07055 0.189807
$$120$$ 0 0
$$121$$ −9.92820 −0.902564
$$122$$ 2.00000i 0.181071i
$$123$$ 0 0
$$124$$ 10.9282 0.981382
$$125$$ −9.89949 5.19615i −0.885438 0.464758i
$$126$$ 0 0
$$127$$ 8.48528i 0.752947i 0.926427 + 0.376473i $$0.122863\pi$$
−0.926427 + 0.376473i $$0.877137\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ −5.46410 + 6.69213i −0.479233 + 0.586939i
$$131$$ −3.10583 −0.271357 −0.135679 0.990753i $$-0.543322\pi$$
−0.135679 + 0.990753i $$0.543322\pi$$
$$132$$ 0 0
$$133$$ 3.86370i 0.335026i
$$134$$ −13.3843 −1.15622
$$135$$ 0 0
$$136$$ −0.535898 −0.0459529
$$137$$ 0.535898i 0.0457849i −0.999738 0.0228924i $$-0.992712\pi$$
0.999738 0.0228924i $$-0.00728753\pi$$
$$138$$ 0 0
$$139$$ −6.92820 −0.587643 −0.293821 0.955860i $$-0.594927\pi$$
−0.293821 + 0.955860i $$0.594927\pi$$
$$140$$ −6.69213 5.46410i −0.565588 0.461801i
$$141$$ 0 0
$$142$$ 4.14110i 0.347514i
$$143$$ 4.00000i 0.334497i
$$144$$ 0 0
$$145$$ 6.53590 8.00481i 0.542777 0.664763i
$$146$$ −3.58630 −0.296804
$$147$$ 0 0
$$148$$ 1.79315i 0.147396i
$$149$$ 20.3538 1.66745 0.833724 0.552182i $$-0.186205\pi$$
0.833724 + 0.552182i $$0.186205\pi$$
$$150$$ 0 0
$$151$$ 5.85641 0.476588 0.238294 0.971193i $$-0.423412\pi$$
0.238294 + 0.971193i $$0.423412\pi$$
$$152$$ 1.00000i 0.0811107i
$$153$$ 0 0
$$154$$ 4.00000 0.322329
$$155$$ −15.4548 + 18.9282i −1.24136 + 1.52035i
$$156$$ 0 0
$$157$$ 14.1421i 1.12867i 0.825547 + 0.564333i $$0.190866\pi$$
−0.825547 + 0.564333i $$0.809134\pi$$
$$158$$ 4.00000i 0.318223i
$$159$$ 0 0
$$160$$ 1.73205 + 1.41421i 0.136931 + 0.111803i
$$161$$ −21.1117 −1.66383
$$162$$ 0 0
$$163$$ 23.6627i 1.85341i −0.375796 0.926703i $$-0.622631\pi$$
0.375796 0.926703i $$-0.377369\pi$$
$$164$$ 1.79315 0.140022
$$165$$ 0 0
$$166$$ −16.3923 −1.27229
$$167$$ 10.9282i 0.845650i −0.906211 0.422825i $$-0.861039\pi$$
0.906211 0.422825i $$-0.138961\pi$$
$$168$$ 0 0
$$169$$ −1.92820 −0.148323
$$170$$ 0.757875 0.928203i 0.0581263 0.0711899i
$$171$$ 0 0
$$172$$ 6.69213i 0.510270i
$$173$$ 22.7846i 1.73228i −0.499800 0.866141i $$-0.666593\pi$$
0.499800 0.866141i $$-0.333407\pi$$
$$174$$ 0 0
$$175$$ 18.9282 3.86370i 1.43084 0.292069i
$$176$$ −1.03528 −0.0780369
$$177$$ 0 0
$$178$$ 3.86370i 0.289597i
$$179$$ −16.7675 −1.25326 −0.626631 0.779316i $$-0.715566\pi$$
−0.626631 + 0.779316i $$0.715566\pi$$
$$180$$ 0 0
$$181$$ 19.8564 1.47592 0.737958 0.674847i $$-0.235790\pi$$
0.737958 + 0.674847i $$0.235790\pi$$
$$182$$ 14.9282i 1.10655i
$$183$$ 0 0
$$184$$ 5.46410 0.402819
$$185$$ −3.10583 2.53590i −0.228345 0.186443i
$$186$$ 0 0
$$187$$ 0.554803i 0.0405712i
$$188$$ 2.53590i 0.184949i
$$189$$ 0 0
$$190$$ 1.73205 + 1.41421i 0.125656 + 0.102598i
$$191$$ 17.2480 1.24802 0.624009 0.781417i $$-0.285503\pi$$
0.624009 + 0.781417i $$0.285503\pi$$
$$192$$ 0 0
$$193$$ 8.76268i 0.630752i −0.948967 0.315376i $$-0.897869\pi$$
0.948967 0.315376i $$-0.102131\pi$$
$$194$$ −2.55103 −0.183153
$$195$$ 0 0
$$196$$ 7.92820 0.566300
$$197$$ 23.4641i 1.67175i −0.548921 0.835874i $$-0.684961\pi$$
0.548921 0.835874i $$-0.315039\pi$$
$$198$$ 0 0
$$199$$ −13.0718 −0.926635 −0.463318 0.886192i $$-0.653341\pi$$
−0.463318 + 0.886192i $$0.653341\pi$$
$$200$$ −4.89898 + 1.00000i −0.346410 + 0.0707107i
$$201$$ 0 0
$$202$$ 10.5558i 0.742706i
$$203$$ 17.8564i 1.25327i
$$204$$ 0 0
$$205$$ −2.53590 + 3.10583i −0.177115 + 0.216920i
$$206$$ 4.89898 0.341328
$$207$$ 0 0
$$208$$ 3.86370i 0.267900i
$$209$$ −1.03528 −0.0716116
$$210$$ 0 0
$$211$$ −17.8564 −1.22929 −0.614643 0.788806i $$-0.710700\pi$$
−0.614643 + 0.788806i $$0.710700\pi$$
$$212$$ 6.00000i 0.412082i
$$213$$ 0 0
$$214$$ −2.92820 −0.200168
$$215$$ 11.5911 + 9.46410i 0.790507 + 0.645446i
$$216$$ 0 0
$$217$$ 42.2233i 2.86631i
$$218$$ 8.92820i 0.604694i
$$219$$ 0 0
$$220$$ 1.46410 1.79315i 0.0987097 0.120894i
$$221$$ 2.07055 0.139280
$$222$$ 0 0
$$223$$ 10.5558i 0.706871i 0.935459 + 0.353435i $$0.114987\pi$$
−0.935459 + 0.353435i $$0.885013\pi$$
$$224$$ −3.86370 −0.258155
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ 1.85641i 0.123214i 0.998100 + 0.0616070i $$0.0196225\pi$$
−0.998100 + 0.0616070i $$0.980377\pi$$
$$228$$ 0 0
$$229$$ 3.85641 0.254839 0.127419 0.991849i $$-0.459331\pi$$
0.127419 + 0.991849i $$0.459331\pi$$
$$230$$ −7.72741 + 9.46410i −0.509530 + 0.624044i
$$231$$ 0 0
$$232$$ 4.62158i 0.303421i
$$233$$ 12.5359i 0.821254i 0.911803 + 0.410627i $$0.134690\pi$$
−0.911803 + 0.410627i $$0.865310\pi$$
$$234$$ 0 0
$$235$$ −4.39230 3.58630i −0.286522 0.233945i
$$236$$ −6.96953 −0.453678
$$237$$ 0 0
$$238$$ 2.07055i 0.134214i
$$239$$ 13.1069 0.847812 0.423906 0.905706i $$-0.360659\pi$$
0.423906 + 0.905706i $$0.360659\pi$$
$$240$$ 0 0
$$241$$ 10.0000 0.644157 0.322078 0.946713i $$-0.395619\pi$$
0.322078 + 0.946713i $$0.395619\pi$$
$$242$$ 9.92820i 0.638209i
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ −11.2122 + 13.7321i −0.716319 + 0.877309i
$$246$$ 0 0
$$247$$ 3.86370i 0.245842i
$$248$$ 10.9282i 0.693942i
$$249$$ 0 0
$$250$$ 5.19615 9.89949i 0.328634 0.626099i
$$251$$ 28.3586 1.78998 0.894990 0.446087i $$-0.147183\pi$$
0.894990 + 0.446087i $$0.147183\pi$$
$$252$$ 0 0
$$253$$ 5.65685i 0.355643i
$$254$$ −8.48528 −0.532414
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 22.7846i 1.42126i −0.703563 0.710632i $$-0.748409\pi$$
0.703563 0.710632i $$-0.251591\pi$$
$$258$$ 0 0
$$259$$ 6.92820 0.430498
$$260$$ −6.69213 5.46410i −0.415028 0.338869i
$$261$$ 0 0
$$262$$ 3.10583i 0.191879i
$$263$$ 19.3205i 1.19135i 0.803224 + 0.595677i $$0.203116\pi$$
−0.803224 + 0.595677i $$0.796884\pi$$
$$264$$ 0 0
$$265$$ 10.3923 + 8.48528i 0.638394 + 0.521247i
$$266$$ −3.86370 −0.236899
$$267$$ 0 0
$$268$$ 13.3843i 0.817574i
$$269$$ −31.9449 −1.94772 −0.973858 0.227160i $$-0.927056\pi$$
−0.973858 + 0.227160i $$0.927056\pi$$
$$270$$ 0 0
$$271$$ 10.9282 0.663841 0.331921 0.943307i $$-0.392303\pi$$
0.331921 + 0.943307i $$0.392303\pi$$
$$272$$ 0.535898i 0.0324936i
$$273$$ 0 0
$$274$$ 0.535898 0.0323748
$$275$$ 1.03528 + 5.07180i 0.0624295 + 0.305841i
$$276$$ 0 0
$$277$$ 18.2832i 1.09853i −0.835647 0.549267i $$-0.814907\pi$$
0.835647 0.549267i $$-0.185093\pi$$
$$278$$ 6.92820i 0.415526i
$$279$$ 0 0
$$280$$ 5.46410 6.69213i 0.326543 0.399931i
$$281$$ 31.1870 1.86046 0.930231 0.366974i $$-0.119606\pi$$
0.930231 + 0.366974i $$0.119606\pi$$
$$282$$ 0 0
$$283$$ 5.17638i 0.307704i −0.988094 0.153852i $$-0.950832\pi$$
0.988094 0.153852i $$-0.0491679\pi$$
$$284$$ 4.14110 0.245729
$$285$$ 0 0
$$286$$ 4.00000 0.236525
$$287$$ 6.92820i 0.408959i
$$288$$ 0 0
$$289$$ 16.7128 0.983107
$$290$$ 8.00481 + 6.53590i 0.470059 + 0.383801i
$$291$$ 0 0
$$292$$ 3.58630i 0.209872i
$$293$$ 19.8564i 1.16002i −0.814608 0.580012i $$-0.803048\pi$$
0.814608 0.580012i $$-0.196952\pi$$
$$294$$ 0 0
$$295$$ 9.85641 12.0716i 0.573862 0.702835i
$$296$$ −1.79315 −0.104225
$$297$$ 0 0
$$298$$ 20.3538i 1.17906i
$$299$$ −21.1117 −1.22092
$$300$$ 0 0
$$301$$ −25.8564 −1.49034
$$302$$ 5.85641i 0.336998i
$$303$$ 0 0
$$304$$ 1.00000 0.0573539
$$305$$ −2.82843 + 3.46410i −0.161955 + 0.198354i
$$306$$ 0 0
$$307$$ 17.5254i 1.00023i 0.865960 + 0.500113i $$0.166708\pi$$
−0.865960 + 0.500113i $$0.833292\pi$$
$$308$$ 4.00000i 0.227921i
$$309$$ 0 0
$$310$$ −18.9282 15.4548i −1.07505 0.877774i
$$311$$ 1.79315 0.101680 0.0508401 0.998707i $$-0.483810\pi$$
0.0508401 + 0.998707i $$0.483810\pi$$
$$312$$ 0 0
$$313$$ 19.5959i 1.10763i 0.832641 + 0.553813i $$0.186828\pi$$
−0.832641 + 0.553813i $$0.813172\pi$$
$$314$$ −14.1421 −0.798087
$$315$$ 0 0
$$316$$ −4.00000 −0.225018
$$317$$ 14.0000i 0.786318i −0.919470 0.393159i $$-0.871382\pi$$
0.919470 0.393159i $$-0.128618\pi$$
$$318$$ 0 0
$$319$$ −4.78461 −0.267887
$$320$$ −1.41421 + 1.73205i −0.0790569 + 0.0968246i
$$321$$ 0 0
$$322$$ 21.1117i 1.17651i
$$323$$ 0.535898i 0.0298182i
$$324$$ 0 0
$$325$$ 18.9282 3.86370i 1.04995 0.214320i
$$326$$ 23.6627 1.31056
$$327$$ 0 0
$$328$$ 1.79315i 0.0990102i
$$329$$ 9.79796 0.540179
$$330$$ 0 0
$$331$$ 13.8564 0.761617 0.380808 0.924654i $$-0.375646\pi$$
0.380808 + 0.924654i $$0.375646\pi$$
$$332$$ 16.3923i 0.899645i
$$333$$ 0 0
$$334$$ 10.9282 0.597965
$$335$$ 23.1822 + 18.9282i 1.26658 + 1.03416i
$$336$$ 0 0
$$337$$ 1.03528i 0.0563951i 0.999602 + 0.0281975i $$0.00897675\pi$$
−0.999602 + 0.0281975i $$0.991023\pi$$
$$338$$ 1.92820i 0.104880i
$$339$$ 0 0
$$340$$ 0.928203 + 0.757875i 0.0503389 + 0.0411015i
$$341$$ 11.3137 0.612672
$$342$$ 0 0
$$343$$ 3.58630i 0.193642i
$$344$$ 6.69213 0.360815
$$345$$ 0 0
$$346$$ 22.7846 1.22491
$$347$$ 18.5359i 0.995059i −0.867447 0.497530i $$-0.834241\pi$$
0.867447 0.497530i $$-0.165759\pi$$
$$348$$ 0 0
$$349$$ −4.14359 −0.221801 −0.110901 0.993831i $$-0.535374\pi$$
−0.110901 + 0.993831i $$0.535374\pi$$
$$350$$ 3.86370 + 18.9282i 0.206524 + 1.01176i
$$351$$ 0 0
$$352$$ 1.03528i 0.0551804i
$$353$$ 21.3205i 1.13478i 0.823451 + 0.567388i $$0.192046\pi$$
−0.823451 + 0.567388i $$0.807954\pi$$
$$354$$ 0 0
$$355$$ −5.85641 + 7.17260i −0.310826 + 0.380682i
$$356$$ 3.86370 0.204776
$$357$$ 0 0
$$358$$ 16.7675i 0.886189i
$$359$$ 34.7733 1.83527 0.917633 0.397429i $$-0.130097\pi$$
0.917633 + 0.397429i $$0.130097\pi$$
$$360$$ 0 0
$$361$$ 1.00000 0.0526316
$$362$$ 19.8564i 1.04363i
$$363$$ 0 0
$$364$$ 14.9282 0.782450
$$365$$ 6.21166 + 5.07180i 0.325133 + 0.265470i
$$366$$ 0 0
$$367$$ 5.37945i 0.280805i −0.990094 0.140403i $$-0.955160\pi$$
0.990094 0.140403i $$-0.0448397\pi$$
$$368$$ 5.46410i 0.284836i
$$369$$ 0 0
$$370$$ 2.53590 3.10583i 0.131835 0.161464i
$$371$$ −23.1822 −1.20356
$$372$$ 0 0
$$373$$ 24.9754i 1.29318i 0.762840 + 0.646588i $$0.223805\pi$$
−0.762840 + 0.646588i $$0.776195\pi$$
$$374$$ −0.554803 −0.0286882
$$375$$ 0 0
$$376$$ −2.53590 −0.130779
$$377$$ 17.8564i 0.919652i
$$378$$ 0 0
$$379$$ 35.7128 1.83444 0.917222 0.398376i $$-0.130426\pi$$
0.917222 + 0.398376i $$0.130426\pi$$
$$380$$ −1.41421 + 1.73205i −0.0725476 + 0.0888523i
$$381$$ 0 0
$$382$$ 17.2480i 0.882483i
$$383$$ 22.9282i 1.17158i −0.810464 0.585788i $$-0.800785\pi$$
0.810464 0.585788i $$-0.199215\pi$$
$$384$$ 0 0
$$385$$ −6.92820 5.65685i −0.353094 0.288300i
$$386$$ 8.76268 0.446009
$$387$$ 0 0
$$388$$ 2.55103i 0.129509i
$$389$$ −19.7990 −1.00385 −0.501924 0.864912i $$-0.667374\pi$$
−0.501924 + 0.864912i $$0.667374\pi$$
$$390$$ 0 0
$$391$$ 2.92820 0.148086
$$392$$ 7.92820i 0.400435i
$$393$$ 0 0
$$394$$ 23.4641 1.18210
$$395$$ 5.65685 6.92820i 0.284627 0.348596i
$$396$$ 0 0
$$397$$ 18.2832i 0.917610i 0.888537 + 0.458805i $$0.151722\pi$$
−0.888537 + 0.458805i $$0.848278\pi$$
$$398$$ 13.0718i 0.655230i
$$399$$ 0 0
$$400$$ −1.00000 4.89898i −0.0500000 0.244949i
$$401$$ −9.52056 −0.475434 −0.237717 0.971334i $$-0.576399\pi$$
−0.237717 + 0.971334i $$0.576399\pi$$
$$402$$ 0 0
$$403$$ 42.2233i 2.10329i
$$404$$ −10.5558 −0.525172
$$405$$ 0 0
$$406$$ −17.8564 −0.886199
$$407$$ 1.85641i 0.0920187i
$$408$$ 0 0
$$409$$ 20.9282 1.03483 0.517417 0.855734i $$-0.326894\pi$$
0.517417 + 0.855734i $$0.326894\pi$$
$$410$$ −3.10583 2.53590i −0.153386 0.125239i
$$411$$ 0 0
$$412$$ 4.89898i 0.241355i
$$413$$ 26.9282i 1.32505i
$$414$$ 0 0
$$415$$ 28.3923 + 23.1822i 1.39372 + 1.13797i
$$416$$ −3.86370 −0.189434
$$417$$ 0 0
$$418$$ 1.03528i 0.0506370i
$$419$$ 29.3195 1.43235 0.716177 0.697919i $$-0.245890\pi$$
0.716177 + 0.697919i $$0.245890\pi$$
$$420$$ 0 0
$$421$$ 29.7128 1.44811 0.724057 0.689740i $$-0.242275\pi$$
0.724057 + 0.689740i $$0.242275\pi$$
$$422$$ 17.8564i 0.869236i
$$423$$ 0 0
$$424$$ 6.00000 0.291386
$$425$$ −2.62536 + 0.535898i −0.127348 + 0.0259949i
$$426$$ 0 0
$$427$$ 7.72741i 0.373955i
$$428$$ 2.92820i 0.141540i
$$429$$ 0 0
$$430$$ −9.46410 + 11.5911i −0.456400 + 0.558973i
$$431$$ 26.2137 1.26267 0.631335 0.775510i $$-0.282507\pi$$
0.631335 + 0.775510i $$0.282507\pi$$
$$432$$ 0 0
$$433$$ 10.8332i 0.520612i 0.965526 + 0.260306i $$0.0838235\pi$$
−0.965526 + 0.260306i $$0.916177\pi$$
$$434$$ 42.2233 2.02678
$$435$$ 0 0
$$436$$ 8.92820 0.427583
$$437$$ 5.46410i 0.261383i
$$438$$ 0 0
$$439$$ −20.0000 −0.954548 −0.477274 0.878755i $$-0.658375\pi$$
−0.477274 + 0.878755i $$0.658375\pi$$
$$440$$ 1.79315 + 1.46410i 0.0854851 + 0.0697983i
$$441$$ 0 0
$$442$$ 2.07055i 0.0984861i
$$443$$ 16.3923i 0.778822i 0.921064 + 0.389411i $$0.127321\pi$$
−0.921064 + 0.389411i $$0.872679\pi$$
$$444$$ 0 0
$$445$$ −5.46410 + 6.69213i −0.259023 + 0.317237i
$$446$$ −10.5558 −0.499833
$$447$$ 0 0
$$448$$ 3.86370i 0.182543i
$$449$$ −40.4302 −1.90802 −0.954009 0.299777i $$-0.903088\pi$$
−0.954009 + 0.299777i $$0.903088\pi$$
$$450$$ 0 0
$$451$$ 1.85641 0.0874148
$$452$$ 6.00000i 0.282216i
$$453$$ 0 0
$$454$$ −1.85641 −0.0871255
$$455$$ −21.1117 + 25.8564i −0.989730 + 1.21217i
$$456$$ 0 0
$$457$$ 33.9411i 1.58770i −0.608114 0.793849i $$-0.708074\pi$$
0.608114 0.793849i $$-0.291926\pi$$
$$458$$ 3.85641i 0.180198i
$$459$$ 0 0
$$460$$ −9.46410 7.72741i −0.441266 0.360292i
$$461$$ −27.5264 −1.28203 −0.641016 0.767527i $$-0.721487\pi$$
−0.641016 + 0.767527i $$0.721487\pi$$
$$462$$ 0 0
$$463$$ 19.8733i 0.923591i −0.886986 0.461796i $$-0.847205\pi$$
0.886986 0.461796i $$-0.152795\pi$$
$$464$$ 4.62158 0.214551
$$465$$ 0 0
$$466$$ −12.5359 −0.580714
$$467$$ 2.53590i 0.117347i −0.998277 0.0586737i $$-0.981313\pi$$
0.998277 0.0586737i $$-0.0186871\pi$$
$$468$$ 0 0
$$469$$ −51.7128 −2.38788
$$470$$ 3.58630 4.39230i 0.165424 0.202602i
$$471$$ 0 0
$$472$$ 6.96953i 0.320799i
$$473$$ 6.92820i 0.318559i
$$474$$ 0 0
$$475$$ −1.00000 4.89898i −0.0458831 0.224781i
$$476$$ −2.07055 −0.0949036
$$477$$ 0 0
$$478$$ 13.1069i 0.599494i
$$479$$ 16.6932 0.762730 0.381365 0.924425i $$-0.375454\pi$$
0.381365 + 0.924425i $$0.375454\pi$$
$$480$$ 0 0
$$481$$ 6.92820 0.315899
$$482$$ 10.0000i 0.455488i
$$483$$ 0 0
$$484$$ 9.92820 0.451282
$$485$$ 4.41851 + 3.60770i 0.200634 + 0.163817i
$$486$$ 0 0
$$487$$ 3.38323i 0.153309i −0.997058 0.0766544i $$-0.975576\pi$$
0.997058 0.0766544i $$-0.0244238\pi$$
$$488$$ 2.00000i 0.0905357i
$$489$$ 0 0
$$490$$ −13.7321 11.2122i −0.620351 0.506514i
$$491$$ −18.5606 −0.837630 −0.418815 0.908072i $$-0.637554\pi$$
−0.418815 + 0.908072i $$0.637554\pi$$
$$492$$ 0 0
$$493$$ 2.47670i 0.111545i
$$494$$ −3.86370 −0.173836
$$495$$ 0 0
$$496$$ −10.9282 −0.490691
$$497$$ 16.0000i 0.717698i
$$498$$ 0 0
$$499$$ −25.8564 −1.15749 −0.578746 0.815508i $$-0.696458\pi$$
−0.578746 + 0.815508i $$0.696458\pi$$
$$500$$ 9.89949 + 5.19615i 0.442719 + 0.232379i
$$501$$ 0 0
$$502$$ 28.3586i 1.26571i
$$503$$ 11.3205i 0.504757i −0.967629 0.252378i $$-0.918787\pi$$
0.967629 0.252378i $$-0.0812127\pi$$
$$504$$ 0 0
$$505$$ 14.9282 18.2832i 0.664296 0.813594i
$$506$$ 5.65685 0.251478
$$507$$ 0 0
$$508$$ 8.48528i 0.376473i
$$509$$ −37.0470 −1.64208 −0.821039 0.570873i $$-0.806605\pi$$
−0.821039 + 0.570873i $$0.806605\pi$$
$$510$$ 0 0
$$511$$ −13.8564 −0.612971
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 22.7846 1.00499
$$515$$ −8.48528 6.92820i −0.373906 0.305293i
$$516$$ 0 0
$$517$$ 2.62536i 0.115463i
$$518$$ 6.92820i 0.304408i
$$519$$ 0 0
$$520$$ 5.46410 6.69213i 0.239617 0.293469i
$$521$$ −9.52056 −0.417103 −0.208552 0.978011i $$-0.566875\pi$$
−0.208552 + 0.978011i $$0.566875\pi$$
$$522$$ 0 0
$$523$$ 26.7685i 1.17051i −0.810851 0.585253i $$-0.800995\pi$$
0.810851 0.585253i $$-0.199005\pi$$
$$524$$ 3.10583 0.135679
$$525$$ 0 0
$$526$$ −19.3205 −0.842414
$$527$$ 5.85641i 0.255109i
$$528$$ 0 0
$$529$$ −6.85641 −0.298105
$$530$$ −8.48528 + 10.3923i −0.368577 + 0.451413i
$$531$$ 0 0
$$532$$ 3.86370i 0.167513i
$$533$$ 6.92820i 0.300094i
$$534$$ 0 0
$$535$$ 5.07180 + 4.14110i 0.219273 + 0.179036i
$$536$$ 13.3843 0.578112
$$537$$ 0 0
$$538$$ 31.9449i 1.37724i
$$539$$ 8.20788 0.353538
$$540$$ 0 0
$$541$$ 26.0000 1.11783 0.558914 0.829226i $$-0.311218\pi$$
0.558914 + 0.829226i $$0.311218\pi$$
$$542$$ 10.9282i 0.469407i
$$543$$ 0 0
$$544$$ 0.535898 0.0229765
$$545$$ −12.6264 + 15.4641i −0.540855 + 0.662409i
$$546$$ 0 0
$$547$$ 10.3528i 0.442652i −0.975200 0.221326i $$-0.928961\pi$$
0.975200 0.221326i $$-0.0710385\pi$$
$$548$$ 0.535898i 0.0228924i
$$549$$ 0 0
$$550$$ −5.07180 + 1.03528i −0.216262 + 0.0441443i
$$551$$ 4.62158 0.196886
$$552$$ 0 0
$$553$$ 15.4548i 0.657206i
$$554$$ 18.2832 0.776780
$$555$$ 0 0
$$556$$ 6.92820 0.293821
$$557$$ 31.4641i 1.33318i −0.745426 0.666588i $$-0.767754\pi$$
0.745426 0.666588i $$-0.232246\pi$$
$$558$$ 0 0
$$559$$ −25.8564 −1.09361
$$560$$ 6.69213 + 5.46410i 0.282794 + 0.230900i
$$561$$ 0 0
$$562$$ 31.1870i 1.31555i
$$563$$ 25.8564i 1.08972i 0.838528 + 0.544859i $$0.183417\pi$$
−0.838528 + 0.544859i $$0.816583\pi$$
$$564$$ 0 0
$$565$$ 10.3923 + 8.48528i 0.437208 + 0.356978i
$$566$$ 5.17638 0.217580
$$567$$ 0 0
$$568$$ 4.14110i 0.173757i
$$569$$ 44.0165 1.84527 0.922634 0.385678i $$-0.126032\pi$$
0.922634 + 0.385678i $$0.126032\pi$$
$$570$$ 0 0
$$571$$ 14.9282 0.624726 0.312363 0.949963i $$-0.398880\pi$$
0.312363 + 0.949963i $$0.398880\pi$$
$$572$$ 4.00000i 0.167248i
$$573$$ 0 0
$$574$$ 6.92820 0.289178
$$575$$ 26.7685 5.46410i 1.11632 0.227869i
$$576$$ 0 0
$$577$$ 5.65685i 0.235498i 0.993043 + 0.117749i $$0.0375678\pi$$
−0.993043 + 0.117749i $$0.962432\pi$$
$$578$$ 16.7128i 0.695161i
$$579$$ 0 0
$$580$$ −6.53590 + 8.00481i −0.271388 + 0.332382i
$$581$$ −63.3350 −2.62758
$$582$$ 0 0
$$583$$ 6.21166i 0.257261i
$$584$$ 3.58630 0.148402
$$585$$ 0 0
$$586$$ 19.8564 0.820261
$$587$$ 24.3923i 1.00678i −0.864060 0.503389i $$-0.832086\pi$$
0.864060 0.503389i $$-0.167914\pi$$
$$588$$ 0 0
$$589$$ −10.9282 −0.450289
$$590$$ 12.0716 + 9.85641i 0.496979 + 0.405782i
$$591$$ 0 0
$$592$$ 1.79315i 0.0736980i
$$593$$ 4.53590i 0.186267i −0.995654 0.0931335i $$-0.970312\pi$$
0.995654 0.0931335i $$-0.0296883\pi$$
$$594$$ 0 0
$$595$$ 2.92820 3.58630i 0.120045 0.147024i
$$596$$ −20.3538 −0.833724
$$597$$ 0 0
$$598$$ 21.1117i 0.863320i
$$599$$ −20.5569 −0.839931 −0.419965 0.907540i $$-0.637958\pi$$
−0.419965 + 0.907540i $$0.637958\pi$$
$$600$$ 0 0
$$601$$ −18.7846 −0.766240 −0.383120 0.923699i $$-0.625150\pi$$
−0.383120 + 0.923699i $$0.625150\pi$$
$$602$$ 25.8564i 1.05383i
$$603$$ 0 0
$$604$$ −5.85641 −0.238294
$$605$$ −14.0406 + 17.1962i −0.570832 + 0.699123i
$$606$$ 0 0
$$607$$ 45.6066i 1.85111i −0.378609 0.925557i $$-0.623598\pi$$
0.378609 0.925557i $$-0.376402\pi$$
$$608$$ 1.00000i 0.0405554i
$$609$$ 0 0
$$610$$ −3.46410 2.82843i −0.140257 0.114520i
$$611$$ 9.79796 0.396383
$$612$$ 0 0
$$613$$ 5.85993i 0.236680i 0.992973 + 0.118340i $$0.0377573\pi$$
−0.992973 + 0.118340i $$0.962243\pi$$
$$614$$ −17.5254 −0.707266
$$615$$ 0 0
$$616$$ −4.00000 −0.161165
$$617$$ 28.2487i 1.13725i −0.822597 0.568625i $$-0.807476\pi$$
0.822597 0.568625i $$-0.192524\pi$$
$$618$$ 0 0
$$619$$ 34.6410 1.39234 0.696170 0.717877i $$-0.254886\pi$$
0.696170 + 0.717877i $$0.254886\pi$$
$$620$$ 15.4548 18.9282i 0.620680 0.760175i
$$621$$ 0 0
$$622$$ 1.79315i 0.0718988i
$$623$$ 14.9282i 0.598086i
$$624$$ 0 0
$$625$$ −23.0000 + 9.79796i −0.920000 + 0.391918i
$$626$$ −19.5959 −0.783210
$$627$$ 0 0
$$628$$ 14.1421i 0.564333i
$$629$$ −0.960947 −0.0383155
$$630$$ 0 0
$$631$$ 21.8564 0.870090 0.435045 0.900409i $$-0.356732\pi$$
0.435045 + 0.900409i $$0.356732\pi$$
$$632$$ 4.00000i 0.159111i
$$633$$ 0 0
$$634$$ 14.0000 0.556011
$$635$$ 14.6969 + 12.0000i 0.583230 + 0.476205i
$$636$$ 0 0
$$637$$ 30.6322i 1.21369i
$$638$$ 4.78461i 0.189425i
$$639$$ 0 0
$$640$$ −1.73205 1.41421i −0.0684653 0.0559017i
$$641$$ −17.2480 −0.681254 −0.340627 0.940199i $$-0.610639\pi$$
−0.340627 + 0.940199i $$0.610639\pi$$
$$642$$ 0 0
$$643$$ 37.0470i 1.46099i 0.682918 + 0.730495i $$0.260710\pi$$
−0.682918 + 0.730495i $$0.739290\pi$$
$$644$$ 21.1117 0.831916
$$645$$ 0 0
$$646$$ 0.535898 0.0210846
$$647$$ 13.4641i 0.529328i −0.964341 0.264664i $$-0.914739\pi$$
0.964341 0.264664i $$-0.0852611\pi$$
$$648$$ 0 0
$$649$$ −7.21539 −0.283229
$$650$$ 3.86370 + 18.9282i 0.151547 + 0.742425i
$$651$$ 0 0
$$652$$ 23.6627i 0.926703i
$$653$$ 24.2487i 0.948925i −0.880276 0.474463i $$-0.842642\pi$$
0.880276 0.474463i $$-0.157358\pi$$
$$654$$ 0 0
$$655$$ −4.39230 + 5.37945i −0.171622 + 0.210193i
$$656$$ −1.79315 −0.0700108
$$657$$ 0 0
$$658$$ 9.79796i 0.381964i
$$659$$ 20.3538 0.792871 0.396436 0.918063i $$-0.370247\pi$$
0.396436 + 0.918063i $$0.370247\pi$$
$$660$$ 0 0
$$661$$ −10.7846 −0.419473 −0.209736 0.977758i $$-0.567261\pi$$
−0.209736 + 0.977758i $$0.567261\pi$$
$$662$$ 13.8564i 0.538545i
$$663$$ 0 0
$$664$$ 16.3923 0.636145
$$665$$ 6.69213 + 5.46410i 0.259510 + 0.211889i
$$666$$ 0 0
$$667$$ 25.2528i 0.977791i
$$668$$ 10.9282i 0.422825i
$$669$$ 0 0
$$670$$ −18.9282 + 23.1822i −0.731260 + 0.895607i
$$671$$ 2.07055 0.0799328
$$672$$ 0 0
$$673$$ 27.2490i 1.05037i 0.850988 + 0.525186i $$0.176004\pi$$
−0.850988 + 0.525186i $$0.823996\pi$$
$$674$$ −1.03528 −0.0398773
$$675$$ 0 0
$$676$$ 1.92820 0.0741617
$$677$$ 36.6410i 1.40823i −0.710087 0.704114i $$-0.751344\pi$$
0.710087 0.704114i $$-0.248656\pi$$
$$678$$ 0 0
$$679$$ −9.85641 −0.378254
$$680$$ −0.757875 + 0.928203i −0.0290632 + 0.0355950i
$$681$$ 0 0
$$682$$ 11.3137i 0.433224i
$$683$$ 18.9282i 0.724268i 0.932126 + 0.362134i $$0.117952\pi$$
−0.932126 + 0.362134i $$0.882048\pi$$
$$684$$ 0 0
$$685$$ −0.928203 0.757875i −0.0354648 0.0289569i
$$686$$ 3.58630 0.136926
$$687$$ 0 0
$$688$$ 6.69213i 0.255135i
$$689$$ −23.1822 −0.883172
$$690$$ 0 0
$$691$$ 38.9282 1.48090 0.740449 0.672112i $$-0.234613\pi$$
0.740449 + 0.672112i $$0.234613\pi$$
$$692$$ 22.7846i 0.866141i
$$693$$ 0 0
$$694$$ 18.5359 0.703613
$$695$$ −9.79796 + 12.0000i −0.371658 + 0.455186i
$$696$$ 0 0
$$697$$ 0.960947i 0.0363985i
$$698$$ 4.14359i 0.156837i
$$699$$ 0 0
$$700$$ −18.9282 + 3.86370i −0.715419 + 0.146034i
$$701$$ 7.52433 0.284190 0.142095 0.989853i $$-0.454616\pi$$
0.142095 + 0.989853i $$0.454616\pi$$
$$702$$ 0 0
$$703$$ 1.79315i 0.0676300i
$$704$$ 1.03528 0.0390184
$$705$$ 0 0
$$706$$ −21.3205 −0.802408
$$707$$ 40.7846i 1.53386i
$$708$$ 0 0
$$709$$ 11.8564 0.445277 0.222638 0.974901i $$-0.428533\pi$$
0.222638 + 0.974901i $$0.428533\pi$$
$$710$$ −7.17260 5.85641i −0.269183 0.219787i
$$711$$ 0 0
$$712$$ 3.86370i 0.144798i
$$713$$ 59.7128i 2.23626i
$$714$$ 0 0
$$715$$ −6.92820 5.65685i −0.259100 0.211554i
$$716$$ 16.7675 0.626631
$$717$$ 0 0
$$718$$ 34.7733i 1.29773i
$$719$$ 46.6418 1.73945 0.869724 0.493539i $$-0.164297\pi$$
0.869724 + 0.493539i $$0.164297\pi$$
$$720$$ 0 0
$$721$$ 18.9282 0.704923
$$722$$ 1.00000i 0.0372161i
$$723$$ 0 0
$$724$$ −19.8564 −0.737958
$$725$$ −4.62158 22.6410i −0.171641 0.840866i
$$726$$ 0 0
$$727$$ 15.1774i 0.562899i −0.959576 0.281450i $$-0.909185\pi$$
0.959576 0.281450i $$-0.0908152\pi$$
$$728$$ 14.9282i 0.553276i
$$729$$ 0 0
$$730$$ −5.07180 + 6.21166i −0.187716 + 0.229904i
$$731$$ 3.58630 0.132644
$$732$$ 0 0
$$733$$ 21.8695i 0.807770i 0.914810 + 0.403885i $$0.132340\pi$$
−0.914810 + 0.403885i $$0.867660\pi$$
$$734$$ 5.37945 0.198559
$$735$$ 0 0
$$736$$ −5.46410 −0.201409
$$737$$ 13.8564i 0.510407i
$$738$$ 0 0
$$739$$ −23.7128 −0.872290 −0.436145 0.899876i $$-0.643657\pi$$
−0.436145 + 0.899876i $$0.643657\pi$$
$$740$$ 3.10583 + 2.53590i 0.114173 + 0.0932215i
$$741$$ 0 0
$$742$$ 23.1822i 0.851046i
$$743$$ 34.6410i 1.27086i −0.772160 0.635428i $$-0.780824\pi$$
0.772160 0.635428i $$-0.219176\pi$$
$$744$$ 0 0
$$745$$ 28.7846 35.2538i 1.05459 1.29160i
$$746$$ −24.9754 −0.914413
$$747$$ 0 0
$$748$$ 0.554803i 0.0202856i
$$749$$ −11.3137 −0.413394
$$750$$ 0 0
$$751$$ 5.85641 0.213703 0.106852 0.994275i $$-0.465923\pi$$
0.106852 + 0.994275i $$0.465923\pi$$
$$752$$ 2.53590i 0.0924747i
$$753$$ 0 0
$$754$$ −17.8564 −0.650292
$$755$$ 8.28221 10.1436i 0.301420 0.369163i
$$756$$ 0 0
$$757$$ 40.3559i 1.46676i 0.679820 + 0.733379i $$0.262058\pi$$
−0.679820 + 0.733379i $$0.737942\pi$$
$$758$$ 35.7128i 1.29715i
$$759$$ 0 0
$$760$$ −1.73205 1.41421i −0.0628281 0.0512989i
$$761$$ −23.1822 −0.840355 −0.420177 0.907442i $$-0.638032\pi$$
−0.420177 + 0.907442i $$0.638032\pi$$
$$762$$ 0 0
$$763$$ 34.4959i 1.24884i
$$764$$ −17.2480 −0.624009
$$765$$ 0 0
$$766$$ 22.9282 0.828430
$$767$$ 26.9282i 0.972321i
$$768$$ 0 0
$$769$$ −35.8564 −1.29302 −0.646508 0.762908i $$-0.723771\pi$$
−0.646508 + 0.762908i $$0.723771\pi$$
$$770$$ 5.65685 6.92820i 0.203859 0.249675i
$$771$$ 0 0
$$772$$ 8.76268i 0.315376i
$$773$$ 7.85641i 0.282575i −0.989969 0.141288i $$-0.954876\pi$$
0.989969 0.141288i $$-0.0451242\pi$$
$$774$$ 0 0
$$775$$ 10.9282 + 53.5370i 0.392553 + 1.92311i
$$776$$ 2.55103 0.0915765
$$777$$ 0 0
$$778$$ 19.7990i 0.709828i
$$779$$ −1.79315 −0.0642463
$$780$$ 0 0
$$781$$ 4.28719 0.153408
$$782$$ 2.92820i 0.104712i
$$783$$ 0 0
$$784$$ −7.92820 −0.283150
$$785$$ 24.4949 + 20.0000i 0.874260 + 0.713831i
$$786$$ 0 0
$$787$$ 7.17260i 0.255676i 0.991795 + 0.127838i $$0.0408037\pi$$
−0.991795 + 0.127838i $$0.959196\pi$$
$$788$$ 23.4641i 0.835874i
$$789$$ 0 0
$$790$$ 6.92820 + 5.65685i 0.246494 + 0.201262i
$$791$$ −23.1822 −0.824265
$$792$$ 0 0
$$793$$ 7.72741i 0.274408i
$$794$$ −18.2832 −0.648848
$$795$$ 0 0
$$796$$ 13.0718 0.463318
$$797$$ 40.6410i 1.43958i −0.694193 0.719789i $$-0.744238\pi$$
0.694193 0.719789i $$-0.255762\pi$$
$$798$$ 0