Properties

 Label 560.2.g.e.449.4 Level $560$ Weight $2$ Character 560.449 Analytic conductor $4.472$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 560.g (of order $$2$$, degree $$1$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$4.47162251319$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ x^4 + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 70) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 449.4 Root $$1.22474 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 560.449 Dual form 560.2.g.e.449.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q+2.44949i q^{3} +(2.22474 + 0.224745i) q^{5} -1.00000i q^{7} -3.00000 q^{9} +O(q^{10})$$ $$q+2.44949i q^{3} +(2.22474 + 0.224745i) q^{5} -1.00000i q^{7} -3.00000 q^{9} +4.89898 q^{11} +4.44949i q^{13} +(-0.550510 + 5.44949i) q^{15} -2.00000i q^{17} +1.55051 q^{19} +2.44949 q^{21} -2.89898i q^{23} +(4.89898 + 1.00000i) q^{25} -6.89898 q^{29} -8.89898 q^{31} +12.0000i q^{33} +(0.224745 - 2.22474i) q^{35} -2.00000i q^{37} -10.8990 q^{39} -1.10102 q^{41} +0.898979i q^{43} +(-6.67423 - 0.674235i) q^{45} +8.89898i q^{47} -1.00000 q^{49} +4.89898 q^{51} -10.8990i q^{53} +(10.8990 + 1.10102i) q^{55} +3.79796i q^{57} -1.55051 q^{59} +3.55051 q^{61} +3.00000i q^{63} +(-1.00000 + 9.89898i) q^{65} -8.00000i q^{67} +7.10102 q^{69} +1.10102 q^{71} +2.89898i q^{73} +(-2.44949 + 12.0000i) q^{75} -4.89898i q^{77} +6.89898 q^{79} -9.00000 q^{81} +2.44949i q^{83} +(0.449490 - 4.44949i) q^{85} -16.8990i q^{87} +10.0000 q^{89} +4.44949 q^{91} -21.7980i q^{93} +(3.44949 + 0.348469i) q^{95} -15.7980i q^{97} -14.6969 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{5} - 12 q^{9}+O(q^{10})$$ 4 * q + 4 * q^5 - 12 * q^9 $$4 q + 4 q^{5} - 12 q^{9} - 12 q^{15} + 16 q^{19} - 8 q^{29} - 16 q^{31} - 4 q^{35} - 24 q^{39} - 24 q^{41} - 12 q^{45} - 4 q^{49} + 24 q^{55} - 16 q^{59} + 24 q^{61} - 4 q^{65} + 48 q^{69} + 24 q^{71} + 8 q^{79} - 36 q^{81} - 8 q^{85} + 40 q^{89} + 8 q^{91} + 4 q^{95}+O(q^{100})$$ 4 * q + 4 * q^5 - 12 * q^9 - 12 * q^15 + 16 * q^19 - 8 * q^29 - 16 * q^31 - 4 * q^35 - 24 * q^39 - 24 * q^41 - 12 * q^45 - 4 * q^49 + 24 * q^55 - 16 * q^59 + 24 * q^61 - 4 * q^65 + 48 * q^69 + 24 * q^71 + 8 * q^79 - 36 * q^81 - 8 * q^85 + 40 * q^89 + 8 * q^91 + 4 * q^95

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$351$$ $$421$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 2.44949i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$4$$ 0 0
$$5$$ 2.22474 + 0.224745i 0.994936 + 0.100509i
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ −3.00000 −1.00000
$$10$$ 0 0
$$11$$ 4.89898 1.47710 0.738549 0.674200i $$-0.235511\pi$$
0.738549 + 0.674200i $$0.235511\pi$$
$$12$$ 0 0
$$13$$ 4.44949i 1.23407i 0.786937 + 0.617033i $$0.211666\pi$$
−0.786937 + 0.617033i $$0.788334\pi$$
$$14$$ 0 0
$$15$$ −0.550510 + 5.44949i −0.142141 + 1.40705i
$$16$$ 0 0
$$17$$ 2.00000i 0.485071i −0.970143 0.242536i $$-0.922021\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ 0 0
$$19$$ 1.55051 0.355711 0.177856 0.984057i $$-0.443084\pi$$
0.177856 + 0.984057i $$0.443084\pi$$
$$20$$ 0 0
$$21$$ 2.44949 0.534522
$$22$$ 0 0
$$23$$ 2.89898i 0.604479i −0.953232 0.302240i $$-0.902266\pi$$
0.953232 0.302240i $$-0.0977342\pi$$
$$24$$ 0 0
$$25$$ 4.89898 + 1.00000i 0.979796 + 0.200000i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −6.89898 −1.28111 −0.640554 0.767913i $$-0.721295\pi$$
−0.640554 + 0.767913i $$0.721295\pi$$
$$30$$ 0 0
$$31$$ −8.89898 −1.59830 −0.799152 0.601129i $$-0.794718\pi$$
−0.799152 + 0.601129i $$0.794718\pi$$
$$32$$ 0 0
$$33$$ 12.0000i 2.08893i
$$34$$ 0 0
$$35$$ 0.224745 2.22474i 0.0379888 0.376051i
$$36$$ 0 0
$$37$$ 2.00000i 0.328798i −0.986394 0.164399i $$-0.947432\pi$$
0.986394 0.164399i $$-0.0525685\pi$$
$$38$$ 0 0
$$39$$ −10.8990 −1.74523
$$40$$ 0 0
$$41$$ −1.10102 −0.171951 −0.0859753 0.996297i $$-0.527401\pi$$
−0.0859753 + 0.996297i $$0.527401\pi$$
$$42$$ 0 0
$$43$$ 0.898979i 0.137093i 0.997648 + 0.0685465i $$0.0218362\pi$$
−0.997648 + 0.0685465i $$0.978164\pi$$
$$44$$ 0 0
$$45$$ −6.67423 0.674235i −0.994936 0.100509i
$$46$$ 0 0
$$47$$ 8.89898i 1.29805i 0.760767 + 0.649025i $$0.224823\pi$$
−0.760767 + 0.649025i $$0.775177\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 4.89898 0.685994
$$52$$ 0 0
$$53$$ 10.8990i 1.49709i −0.663084 0.748545i $$-0.730753\pi$$
0.663084 0.748545i $$-0.269247\pi$$
$$54$$ 0 0
$$55$$ 10.8990 + 1.10102i 1.46962 + 0.148462i
$$56$$ 0 0
$$57$$ 3.79796i 0.503052i
$$58$$ 0 0
$$59$$ −1.55051 −0.201859 −0.100930 0.994894i $$-0.532182\pi$$
−0.100930 + 0.994894i $$0.532182\pi$$
$$60$$ 0 0
$$61$$ 3.55051 0.454596 0.227298 0.973825i $$-0.427011\pi$$
0.227298 + 0.973825i $$0.427011\pi$$
$$62$$ 0 0
$$63$$ 3.00000i 0.377964i
$$64$$ 0 0
$$65$$ −1.00000 + 9.89898i −0.124035 + 1.22782i
$$66$$ 0 0
$$67$$ 8.00000i 0.977356i −0.872464 0.488678i $$-0.837479\pi$$
0.872464 0.488678i $$-0.162521\pi$$
$$68$$ 0 0
$$69$$ 7.10102 0.854862
$$70$$ 0 0
$$71$$ 1.10102 0.130667 0.0653335 0.997863i $$-0.479189\pi$$
0.0653335 + 0.997863i $$0.479189\pi$$
$$72$$ 0 0
$$73$$ 2.89898i 0.339300i 0.985504 + 0.169650i $$0.0542637\pi$$
−0.985504 + 0.169650i $$0.945736\pi$$
$$74$$ 0 0
$$75$$ −2.44949 + 12.0000i −0.282843 + 1.38564i
$$76$$ 0 0
$$77$$ 4.89898i 0.558291i
$$78$$ 0 0
$$79$$ 6.89898 0.776196 0.388098 0.921618i $$-0.373132\pi$$
0.388098 + 0.921618i $$0.373132\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ 0 0
$$83$$ 2.44949i 0.268866i 0.990923 + 0.134433i $$0.0429214\pi$$
−0.990923 + 0.134433i $$0.957079\pi$$
$$84$$ 0 0
$$85$$ 0.449490 4.44949i 0.0487540 0.482615i
$$86$$ 0 0
$$87$$ 16.8990i 1.81176i
$$88$$ 0 0
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ 4.44949 0.466433
$$92$$ 0 0
$$93$$ 21.7980i 2.26034i
$$94$$ 0 0
$$95$$ 3.44949 + 0.348469i 0.353910 + 0.0357522i
$$96$$ 0 0
$$97$$ 15.7980i 1.60404i −0.597297 0.802020i $$-0.703759\pi$$
0.597297 0.802020i $$-0.296241\pi$$
$$98$$ 0 0
$$99$$ −14.6969 −1.47710
$$100$$ 0 0
$$101$$ 3.55051 0.353289 0.176644 0.984275i $$-0.443476\pi$$
0.176644 + 0.984275i $$0.443476\pi$$
$$102$$ 0 0
$$103$$ 12.8990i 1.27097i −0.772111 0.635487i $$-0.780799\pi$$
0.772111 0.635487i $$-0.219201\pi$$
$$104$$ 0 0
$$105$$ 5.44949 + 0.550510i 0.531816 + 0.0537243i
$$106$$ 0 0
$$107$$ 8.00000i 0.773389i −0.922208 0.386695i $$-0.873617\pi$$
0.922208 0.386695i $$-0.126383\pi$$
$$108$$ 0 0
$$109$$ −6.89898 −0.660802 −0.330401 0.943841i $$-0.607184\pi$$
−0.330401 + 0.943841i $$0.607184\pi$$
$$110$$ 0 0
$$111$$ 4.89898 0.464991
$$112$$ 0 0
$$113$$ 19.7980i 1.86244i 0.364464 + 0.931218i $$0.381252\pi$$
−0.364464 + 0.931218i $$0.618748\pi$$
$$114$$ 0 0
$$115$$ 0.651531 6.44949i 0.0607556 0.601418i
$$116$$ 0 0
$$117$$ 13.3485i 1.23407i
$$118$$ 0 0
$$119$$ −2.00000 −0.183340
$$120$$ 0 0
$$121$$ 13.0000 1.18182
$$122$$ 0 0
$$123$$ 2.69694i 0.243175i
$$124$$ 0 0
$$125$$ 10.6742 + 3.32577i 0.954733 + 0.297465i
$$126$$ 0 0
$$127$$ 14.8990i 1.32207i −0.750355 0.661035i $$-0.770117\pi$$
0.750355 0.661035i $$-0.229883\pi$$
$$128$$ 0 0
$$129$$ −2.20204 −0.193879
$$130$$ 0 0
$$131$$ 6.44949 0.563495 0.281747 0.959489i $$-0.409086\pi$$
0.281747 + 0.959489i $$0.409086\pi$$
$$132$$ 0 0
$$133$$ 1.55051i 0.134446i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 1.79796i 0.153610i 0.997046 + 0.0768050i $$0.0244719\pi$$
−0.997046 + 0.0768050i $$0.975528\pi$$
$$138$$ 0 0
$$139$$ 1.55051 0.131513 0.0657563 0.997836i $$-0.479054\pi$$
0.0657563 + 0.997836i $$0.479054\pi$$
$$140$$ 0 0
$$141$$ −21.7980 −1.83572
$$142$$ 0 0
$$143$$ 21.7980i 1.82284i
$$144$$ 0 0
$$145$$ −15.3485 1.55051i −1.27462 0.128763i
$$146$$ 0 0
$$147$$ 2.44949i 0.202031i
$$148$$ 0 0
$$149$$ 3.79796 0.311141 0.155570 0.987825i $$-0.450278\pi$$
0.155570 + 0.987825i $$0.450278\pi$$
$$150$$ 0 0
$$151$$ −19.5959 −1.59469 −0.797347 0.603522i $$-0.793764\pi$$
−0.797347 + 0.603522i $$0.793764\pi$$
$$152$$ 0 0
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ −19.7980 2.00000i −1.59021 0.160644i
$$156$$ 0 0
$$157$$ 3.55051i 0.283362i −0.989912 0.141681i $$-0.954749\pi$$
0.989912 0.141681i $$-0.0452507\pi$$
$$158$$ 0 0
$$159$$ 26.6969 2.11720
$$160$$ 0 0
$$161$$ −2.89898 −0.228472
$$162$$ 0 0
$$163$$ 7.10102i 0.556195i 0.960553 + 0.278097i $$0.0897038\pi$$
−0.960553 + 0.278097i $$0.910296\pi$$
$$164$$ 0 0
$$165$$ −2.69694 + 26.6969i −0.209956 + 2.07835i
$$166$$ 0 0
$$167$$ 4.89898i 0.379094i −0.981872 0.189547i $$-0.939298\pi$$
0.981872 0.189547i $$-0.0607020\pi$$
$$168$$ 0 0
$$169$$ −6.79796 −0.522920
$$170$$ 0 0
$$171$$ −4.65153 −0.355711
$$172$$ 0 0
$$173$$ 6.24745i 0.474985i −0.971389 0.237492i $$-0.923675\pi$$
0.971389 0.237492i $$-0.0763255\pi$$
$$174$$ 0 0
$$175$$ 1.00000 4.89898i 0.0755929 0.370328i
$$176$$ 0 0
$$177$$ 3.79796i 0.285472i
$$178$$ 0 0
$$179$$ 13.7980 1.03131 0.515654 0.856797i $$-0.327549\pi$$
0.515654 + 0.856797i $$0.327549\pi$$
$$180$$ 0 0
$$181$$ −10.2474 −0.761687 −0.380843 0.924640i $$-0.624366\pi$$
−0.380843 + 0.924640i $$0.624366\pi$$
$$182$$ 0 0
$$183$$ 8.69694i 0.642896i
$$184$$ 0 0
$$185$$ 0.449490 4.44949i 0.0330471 0.327133i
$$186$$ 0 0
$$187$$ 9.79796i 0.716498i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −12.6969 −0.918718 −0.459359 0.888251i $$-0.651921\pi$$
−0.459359 + 0.888251i $$0.651921\pi$$
$$192$$ 0 0
$$193$$ 21.5959i 1.55451i −0.629187 0.777254i $$-0.716612\pi$$
0.629187 0.777254i $$-0.283388\pi$$
$$194$$ 0 0
$$195$$ −24.2474 2.44949i −1.73640 0.175412i
$$196$$ 0 0
$$197$$ 18.8990i 1.34650i −0.739417 0.673248i $$-0.764899\pi$$
0.739417 0.673248i $$-0.235101\pi$$
$$198$$ 0 0
$$199$$ 16.8990 1.19794 0.598968 0.800773i $$-0.295577\pi$$
0.598968 + 0.800773i $$0.295577\pi$$
$$200$$ 0 0
$$201$$ 19.5959 1.38219
$$202$$ 0 0
$$203$$ 6.89898i 0.484213i
$$204$$ 0 0
$$205$$ −2.44949 0.247449i −0.171080 0.0172826i
$$206$$ 0 0
$$207$$ 8.69694i 0.604479i
$$208$$ 0 0
$$209$$ 7.59592 0.525421
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 0 0
$$213$$ 2.69694i 0.184791i
$$214$$ 0 0
$$215$$ −0.202041 + 2.00000i −0.0137791 + 0.136399i
$$216$$ 0 0
$$217$$ 8.89898i 0.604102i
$$218$$ 0 0
$$219$$ −7.10102 −0.479842
$$220$$ 0 0
$$221$$ 8.89898 0.598610
$$222$$ 0 0
$$223$$ 4.00000i 0.267860i 0.990991 + 0.133930i $$0.0427597\pi$$
−0.990991 + 0.133930i $$0.957240\pi$$
$$224$$ 0 0
$$225$$ −14.6969 3.00000i −0.979796 0.200000i
$$226$$ 0 0
$$227$$ 7.34847i 0.487735i 0.969809 + 0.243868i $$0.0784162\pi$$
−0.969809 + 0.243868i $$0.921584\pi$$
$$228$$ 0 0
$$229$$ 19.1464 1.26523 0.632616 0.774466i $$-0.281981\pi$$
0.632616 + 0.774466i $$0.281981\pi$$
$$230$$ 0 0
$$231$$ 12.0000 0.789542
$$232$$ 0 0
$$233$$ 29.7980i 1.95213i 0.217481 + 0.976065i $$0.430216\pi$$
−0.217481 + 0.976065i $$0.569784\pi$$
$$234$$ 0 0
$$235$$ −2.00000 + 19.7980i −0.130466 + 1.29148i
$$236$$ 0 0
$$237$$ 16.8990i 1.09771i
$$238$$ 0 0
$$239$$ −6.20204 −0.401177 −0.200588 0.979676i $$-0.564285\pi$$
−0.200588 + 0.979676i $$0.564285\pi$$
$$240$$ 0 0
$$241$$ −8.69694 −0.560219 −0.280110 0.959968i $$-0.590371\pi$$
−0.280110 + 0.959968i $$0.590371\pi$$
$$242$$ 0 0
$$243$$ 22.0454i 1.41421i
$$244$$ 0 0
$$245$$ −2.22474 0.224745i −0.142134 0.0143584i
$$246$$ 0 0
$$247$$ 6.89898i 0.438972i
$$248$$ 0 0
$$249$$ −6.00000 −0.380235
$$250$$ 0 0
$$251$$ 6.44949 0.407088 0.203544 0.979066i $$-0.434754\pi$$
0.203544 + 0.979066i $$0.434754\pi$$
$$252$$ 0 0
$$253$$ 14.2020i 0.892875i
$$254$$ 0 0
$$255$$ 10.8990 + 1.10102i 0.682521 + 0.0689486i
$$256$$ 0 0
$$257$$ 8.69694i 0.542500i 0.962509 + 0.271250i $$0.0874370\pi$$
−0.962509 + 0.271250i $$0.912563\pi$$
$$258$$ 0 0
$$259$$ −2.00000 −0.124274
$$260$$ 0 0
$$261$$ 20.6969 1.28111
$$262$$ 0 0
$$263$$ 9.79796i 0.604168i −0.953281 0.302084i $$-0.902318\pi$$
0.953281 0.302084i $$-0.0976823\pi$$
$$264$$ 0 0
$$265$$ 2.44949 24.2474i 0.150471 1.48951i
$$266$$ 0 0
$$267$$ 24.4949i 1.49906i
$$268$$ 0 0
$$269$$ −19.1464 −1.16738 −0.583689 0.811977i $$-0.698391\pi$$
−0.583689 + 0.811977i $$0.698391\pi$$
$$270$$ 0 0
$$271$$ −12.0000 −0.728948 −0.364474 0.931214i $$-0.618751\pi$$
−0.364474 + 0.931214i $$0.618751\pi$$
$$272$$ 0 0
$$273$$ 10.8990i 0.659636i
$$274$$ 0 0
$$275$$ 24.0000 + 4.89898i 1.44725 + 0.295420i
$$276$$ 0 0
$$277$$ 14.8990i 0.895193i 0.894236 + 0.447596i $$0.147720\pi$$
−0.894236 + 0.447596i $$0.852280\pi$$
$$278$$ 0 0
$$279$$ 26.6969 1.59830
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 3.75255i 0.223066i −0.993761 0.111533i $$-0.964424\pi$$
0.993761 0.111533i $$-0.0355761\pi$$
$$284$$ 0 0
$$285$$ −0.853572 + 8.44949i −0.0505612 + 0.500505i
$$286$$ 0 0
$$287$$ 1.10102i 0.0649912i
$$288$$ 0 0
$$289$$ 13.0000 0.764706
$$290$$ 0 0
$$291$$ 38.6969 2.26845
$$292$$ 0 0
$$293$$ 18.2474i 1.06603i 0.846107 + 0.533014i $$0.178941\pi$$
−0.846107 + 0.533014i $$0.821059\pi$$
$$294$$ 0 0
$$295$$ −3.44949 0.348469i −0.200837 0.0202887i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 12.8990 0.745967
$$300$$ 0 0
$$301$$ 0.898979 0.0518163
$$302$$ 0 0
$$303$$ 8.69694i 0.499626i
$$304$$ 0 0
$$305$$ 7.89898 + 0.797959i 0.452294 + 0.0456910i
$$306$$ 0 0
$$307$$ 20.2474i 1.15558i −0.816184 0.577791i $$-0.803915\pi$$
0.816184 0.577791i $$-0.196085\pi$$
$$308$$ 0 0
$$309$$ 31.5959 1.79743
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ 21.5959i 1.22067i −0.792142 0.610337i $$-0.791034\pi$$
0.792142 0.610337i $$-0.208966\pi$$
$$314$$ 0 0
$$315$$ −0.674235 + 6.67423i −0.0379888 + 0.376051i
$$316$$ 0 0
$$317$$ 22.4949i 1.26344i 0.775197 + 0.631720i $$0.217651\pi$$
−0.775197 + 0.631720i $$0.782349\pi$$
$$318$$ 0 0
$$319$$ −33.7980 −1.89232
$$320$$ 0 0
$$321$$ 19.5959 1.09374
$$322$$ 0 0
$$323$$ 3.10102i 0.172545i
$$324$$ 0 0
$$325$$ −4.44949 + 21.7980i −0.246813 + 1.20913i
$$326$$ 0 0
$$327$$ 16.8990i 0.934516i
$$328$$ 0 0
$$329$$ 8.89898 0.490617
$$330$$ 0 0
$$331$$ 18.6969 1.02768 0.513838 0.857887i $$-0.328223\pi$$
0.513838 + 0.857887i $$0.328223\pi$$
$$332$$ 0 0
$$333$$ 6.00000i 0.328798i
$$334$$ 0 0
$$335$$ 1.79796 17.7980i 0.0982330 0.972406i
$$336$$ 0 0
$$337$$ 9.59592i 0.522723i −0.965241 0.261361i $$-0.915829\pi$$
0.965241 0.261361i $$-0.0841715\pi$$
$$338$$ 0 0
$$339$$ −48.4949 −2.63388
$$340$$ 0 0
$$341$$ −43.5959 −2.36085
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ 15.7980 + 1.59592i 0.850534 + 0.0859213i
$$346$$ 0 0
$$347$$ 28.8990i 1.55138i 0.631115 + 0.775689i $$0.282598\pi$$
−0.631115 + 0.775689i $$0.717402\pi$$
$$348$$ 0 0
$$349$$ 8.44949 0.452291 0.226145 0.974094i $$-0.427388\pi$$
0.226145 + 0.974094i $$0.427388\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 22.8990i 1.21879i 0.792867 + 0.609395i $$0.208588\pi$$
−0.792867 + 0.609395i $$0.791412\pi$$
$$354$$ 0 0
$$355$$ 2.44949 + 0.247449i 0.130005 + 0.0131332i
$$356$$ 0 0
$$357$$ 4.89898i 0.259281i
$$358$$ 0 0
$$359$$ −27.5959 −1.45646 −0.728228 0.685334i $$-0.759656\pi$$
−0.728228 + 0.685334i $$0.759656\pi$$
$$360$$ 0 0
$$361$$ −16.5959 −0.873469
$$362$$ 0 0
$$363$$ 31.8434i 1.67134i
$$364$$ 0 0
$$365$$ −0.651531 + 6.44949i −0.0341027 + 0.337582i
$$366$$ 0 0
$$367$$ 32.0000i 1.67039i 0.549957 + 0.835193i $$0.314644\pi$$
−0.549957 + 0.835193i $$0.685356\pi$$
$$368$$ 0 0
$$369$$ 3.30306 0.171951
$$370$$ 0 0
$$371$$ −10.8990 −0.565847
$$372$$ 0 0
$$373$$ 4.69694i 0.243198i −0.992579 0.121599i $$-0.961198\pi$$
0.992579 0.121599i $$-0.0388022\pi$$
$$374$$ 0 0
$$375$$ −8.14643 + 26.1464i −0.420680 + 1.35020i
$$376$$ 0 0
$$377$$ 30.6969i 1.58097i
$$378$$ 0 0
$$379$$ 30.6969 1.57680 0.788398 0.615166i $$-0.210911\pi$$
0.788398 + 0.615166i $$0.210911\pi$$
$$380$$ 0 0
$$381$$ 36.4949 1.86969
$$382$$ 0 0
$$383$$ 7.10102i 0.362845i 0.983405 + 0.181423i $$0.0580702\pi$$
−0.983405 + 0.181423i $$0.941930\pi$$
$$384$$ 0 0
$$385$$ 1.10102 10.8990i 0.0561132 0.555463i
$$386$$ 0 0
$$387$$ 2.69694i 0.137093i
$$388$$ 0 0
$$389$$ −13.1010 −0.664248 −0.332124 0.943236i $$-0.607765\pi$$
−0.332124 + 0.943236i $$0.607765\pi$$
$$390$$ 0 0
$$391$$ −5.79796 −0.293215
$$392$$ 0 0
$$393$$ 15.7980i 0.796902i
$$394$$ 0 0
$$395$$ 15.3485 + 1.55051i 0.772265 + 0.0780146i
$$396$$ 0 0
$$397$$ 2.65153i 0.133077i 0.997784 + 0.0665383i $$0.0211954\pi$$
−0.997784 + 0.0665383i $$0.978805\pi$$
$$398$$ 0 0
$$399$$ 3.79796 0.190136
$$400$$ 0 0
$$401$$ −29.3939 −1.46786 −0.733930 0.679225i $$-0.762316\pi$$
−0.733930 + 0.679225i $$0.762316\pi$$
$$402$$ 0 0
$$403$$ 39.5959i 1.97241i
$$404$$ 0 0
$$405$$ −20.0227 2.02270i −0.994936 0.100509i
$$406$$ 0 0
$$407$$ 9.79796i 0.485667i
$$408$$ 0 0
$$409$$ −34.4949 −1.70566 −0.852831 0.522186i $$-0.825117\pi$$
−0.852831 + 0.522186i $$0.825117\pi$$
$$410$$ 0 0
$$411$$ −4.40408 −0.217237
$$412$$ 0 0
$$413$$ 1.55051i 0.0762956i
$$414$$ 0 0
$$415$$ −0.550510 + 5.44949i −0.0270235 + 0.267505i
$$416$$ 0 0
$$417$$ 3.79796i 0.185987i
$$418$$ 0 0
$$419$$ −1.55051 −0.0757474 −0.0378737 0.999283i $$-0.512058\pi$$
−0.0378737 + 0.999283i $$0.512058\pi$$
$$420$$ 0 0
$$421$$ −4.20204 −0.204795 −0.102397 0.994744i $$-0.532651\pi$$
−0.102397 + 0.994744i $$0.532651\pi$$
$$422$$ 0 0
$$423$$ 26.6969i 1.29805i
$$424$$ 0 0
$$425$$ 2.00000 9.79796i 0.0970143 0.475271i
$$426$$ 0 0
$$427$$ 3.55051i 0.171821i
$$428$$ 0 0
$$429$$ −53.3939 −2.57788
$$430$$ 0 0
$$431$$ 1.79796 0.0866046 0.0433023 0.999062i $$-0.486212\pi$$
0.0433023 + 0.999062i $$0.486212\pi$$
$$432$$ 0 0
$$433$$ 0.202041i 0.00970947i −0.999988 0.00485474i $$-0.998455\pi$$
0.999988 0.00485474i $$-0.00154532\pi$$
$$434$$ 0 0
$$435$$ 3.79796 37.5959i 0.182098 1.80259i
$$436$$ 0 0
$$437$$ 4.49490i 0.215020i
$$438$$ 0 0
$$439$$ −21.3939 −1.02107 −0.510537 0.859856i $$-0.670553\pi$$
−0.510537 + 0.859856i $$0.670553\pi$$
$$440$$ 0 0
$$441$$ 3.00000 0.142857
$$442$$ 0 0
$$443$$ 9.79796i 0.465515i −0.972535 0.232758i $$-0.925225\pi$$
0.972535 0.232758i $$-0.0747749\pi$$
$$444$$ 0 0
$$445$$ 22.2474 + 2.24745i 1.05463 + 0.106539i
$$446$$ 0 0
$$447$$ 9.30306i 0.440020i
$$448$$ 0 0
$$449$$ 10.0000 0.471929 0.235965 0.971762i $$-0.424175\pi$$
0.235965 + 0.971762i $$0.424175\pi$$
$$450$$ 0 0
$$451$$ −5.39388 −0.253988
$$452$$ 0 0
$$453$$ 48.0000i 2.25524i
$$454$$ 0 0
$$455$$ 9.89898 + 1.00000i 0.464071 + 0.0468807i
$$456$$ 0 0
$$457$$ 29.5959i 1.38444i −0.721687 0.692219i $$-0.756633\pi$$
0.721687 0.692219i $$-0.243367\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 17.3485 0.807999 0.403999 0.914759i $$-0.367620\pi$$
0.403999 + 0.914759i $$0.367620\pi$$
$$462$$ 0 0
$$463$$ 3.59592i 0.167116i −0.996503 0.0835582i $$-0.973372\pi$$
0.996503 0.0835582i $$-0.0266285\pi$$
$$464$$ 0 0
$$465$$ 4.89898 48.4949i 0.227185 2.24890i
$$466$$ 0 0
$$467$$ 10.4495i 0.483545i 0.970333 + 0.241772i $$0.0777287\pi$$
−0.970333 + 0.241772i $$0.922271\pi$$
$$468$$ 0 0
$$469$$ −8.00000 −0.369406
$$470$$ 0 0
$$471$$ 8.69694 0.400734
$$472$$ 0 0
$$473$$ 4.40408i 0.202500i
$$474$$ 0 0
$$475$$ 7.59592 + 1.55051i 0.348525 + 0.0711423i
$$476$$ 0 0
$$477$$ 32.6969i 1.49709i
$$478$$ 0 0
$$479$$ 9.30306 0.425068 0.212534 0.977154i $$-0.431828\pi$$
0.212534 + 0.977154i $$0.431828\pi$$
$$480$$ 0 0
$$481$$ 8.89898 0.405759
$$482$$ 0 0
$$483$$ 7.10102i 0.323108i
$$484$$ 0 0
$$485$$ 3.55051 35.1464i 0.161220 1.59592i
$$486$$ 0 0
$$487$$ 7.30306i 0.330933i −0.986215 0.165467i $$-0.947087\pi$$
0.986215 0.165467i $$-0.0529130\pi$$
$$488$$ 0 0
$$489$$ −17.3939 −0.786578
$$490$$ 0 0
$$491$$ −19.5959 −0.884351 −0.442176 0.896928i $$-0.645793\pi$$
−0.442176 + 0.896928i $$0.645793\pi$$
$$492$$ 0 0
$$493$$ 13.7980i 0.621429i
$$494$$ 0 0
$$495$$ −32.6969 3.30306i −1.46962 0.148462i
$$496$$ 0 0
$$497$$ 1.10102i 0.0493875i
$$498$$ 0 0
$$499$$ 6.20204 0.277641 0.138821 0.990318i $$-0.455669\pi$$
0.138821 + 0.990318i $$0.455669\pi$$
$$500$$ 0 0
$$501$$ 12.0000 0.536120
$$502$$ 0 0
$$503$$ 4.00000i 0.178351i 0.996016 + 0.0891756i $$0.0284232\pi$$
−0.996016 + 0.0891756i $$0.971577\pi$$
$$504$$ 0 0
$$505$$ 7.89898 + 0.797959i 0.351500 + 0.0355087i
$$506$$ 0 0
$$507$$ 16.6515i 0.739520i
$$508$$ 0 0
$$509$$ 31.5505 1.39845 0.699226 0.714901i $$-0.253528\pi$$
0.699226 + 0.714901i $$0.253528\pi$$
$$510$$ 0 0
$$511$$ 2.89898 0.128243
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 2.89898 28.6969i 0.127744 1.26454i
$$516$$ 0 0
$$517$$ 43.5959i 1.91735i
$$518$$ 0 0
$$519$$ 15.3031 0.671730
$$520$$ 0 0
$$521$$ 32.6969 1.43248 0.716239 0.697855i $$-0.245862\pi$$
0.716239 + 0.697855i $$0.245862\pi$$
$$522$$ 0 0
$$523$$ 33.1464i 1.44939i 0.689069 + 0.724696i $$0.258020\pi$$
−0.689069 + 0.724696i $$0.741980\pi$$
$$524$$ 0 0
$$525$$ 12.0000 + 2.44949i 0.523723 + 0.106904i
$$526$$ 0 0
$$527$$ 17.7980i 0.775291i
$$528$$ 0 0
$$529$$ 14.5959 0.634605
$$530$$ 0 0
$$531$$ 4.65153 0.201859
$$532$$ 0 0
$$533$$ 4.89898i 0.212198i
$$534$$ 0 0
$$535$$ 1.79796 17.7980i 0.0777325 0.769473i
$$536$$ 0 0
$$537$$ 33.7980i 1.45849i
$$538$$ 0 0
$$539$$ −4.89898 −0.211014
$$540$$ 0 0
$$541$$ 9.59592 0.412561 0.206280 0.978493i $$-0.433864\pi$$
0.206280 + 0.978493i $$0.433864\pi$$
$$542$$ 0 0
$$543$$ 25.1010i 1.07719i
$$544$$ 0 0
$$545$$ −15.3485 1.55051i −0.657456 0.0664166i
$$546$$ 0 0
$$547$$ 18.6969i 0.799423i −0.916641 0.399712i $$-0.869110\pi$$
0.916641 0.399712i $$-0.130890\pi$$
$$548$$ 0 0
$$549$$ −10.6515 −0.454596
$$550$$ 0 0
$$551$$ −10.6969 −0.455705
$$552$$ 0 0
$$553$$ 6.89898i 0.293374i
$$554$$ 0 0
$$555$$ 10.8990 + 1.10102i 0.462636 + 0.0467357i
$$556$$ 0 0
$$557$$ 12.6969i 0.537987i −0.963142 0.268993i $$-0.913309\pi$$
0.963142 0.268993i $$-0.0866909\pi$$
$$558$$ 0 0
$$559$$ −4.00000 −0.169182
$$560$$ 0 0
$$561$$ 24.0000 1.01328
$$562$$ 0 0
$$563$$ 30.0454i 1.26626i 0.774044 + 0.633131i $$0.218231\pi$$
−0.774044 + 0.633131i $$0.781769\pi$$
$$564$$ 0 0
$$565$$ −4.44949 + 44.0454i −0.187191 + 1.85300i
$$566$$ 0 0
$$567$$ 9.00000i 0.377964i
$$568$$ 0 0
$$569$$ −33.7980 −1.41688 −0.708442 0.705769i $$-0.750602\pi$$
−0.708442 + 0.705769i $$0.750602\pi$$
$$570$$ 0 0
$$571$$ 11.1010 0.464563 0.232282 0.972649i $$-0.425381\pi$$
0.232282 + 0.972649i $$0.425381\pi$$
$$572$$ 0 0
$$573$$ 31.1010i 1.29926i
$$574$$ 0 0
$$575$$ 2.89898 14.2020i 0.120896 0.592266i
$$576$$ 0 0
$$577$$ 2.49490i 0.103864i 0.998651 + 0.0519320i $$0.0165379\pi$$
−0.998651 + 0.0519320i $$0.983462\pi$$
$$578$$ 0 0
$$579$$ 52.8990 2.19841
$$580$$ 0 0
$$581$$ 2.44949 0.101622
$$582$$ 0 0
$$583$$ 53.3939i 2.21135i
$$584$$ 0 0
$$585$$ 3.00000 29.6969i 0.124035 1.22782i
$$586$$ 0 0
$$587$$ 1.14643i 0.0473182i 0.999720 + 0.0236591i $$0.00753162\pi$$
−0.999720 + 0.0236591i $$0.992468\pi$$
$$588$$ 0 0
$$589$$ −13.7980 −0.568535
$$590$$ 0 0
$$591$$ 46.2929 1.90423
$$592$$ 0 0
$$593$$ 10.8990i 0.447567i −0.974639 0.223784i $$-0.928159\pi$$
0.974639 0.223784i $$-0.0718409\pi$$
$$594$$ 0 0
$$595$$ −4.44949 0.449490i −0.182411 0.0184273i
$$596$$ 0 0
$$597$$ 41.3939i 1.69414i
$$598$$ 0 0
$$599$$ −13.1010 −0.535293 −0.267647 0.963517i $$-0.586246\pi$$
−0.267647 + 0.963517i $$0.586246\pi$$
$$600$$ 0 0
$$601$$ −39.3939 −1.60691 −0.803455 0.595366i $$-0.797007\pi$$
−0.803455 + 0.595366i $$0.797007\pi$$
$$602$$ 0 0
$$603$$ 24.0000i 0.977356i
$$604$$ 0 0
$$605$$ 28.9217 + 2.92168i 1.17583 + 0.118783i
$$606$$ 0 0
$$607$$ 33.3939i 1.35542i 0.735331 + 0.677708i $$0.237027\pi$$
−0.735331 + 0.677708i $$0.762973\pi$$
$$608$$ 0 0
$$609$$ −16.8990 −0.684781
$$610$$ 0 0
$$611$$ −39.5959 −1.60188
$$612$$ 0 0
$$613$$ 27.7980i 1.12275i −0.827562 0.561374i $$-0.810273\pi$$
0.827562 0.561374i $$-0.189727\pi$$
$$614$$ 0 0
$$615$$ 0.606123 6.00000i 0.0244412 0.241943i
$$616$$ 0 0
$$617$$ 29.5959i 1.19149i −0.803175 0.595743i $$-0.796858\pi$$
0.803175 0.595743i $$-0.203142\pi$$
$$618$$ 0 0
$$619$$ −41.5505 −1.67006 −0.835028 0.550207i $$-0.814549\pi$$
−0.835028 + 0.550207i $$0.814549\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 10.0000i 0.400642i
$$624$$ 0 0
$$625$$ 23.0000 + 9.79796i 0.920000 + 0.391918i
$$626$$ 0 0
$$627$$ 18.6061i 0.743057i
$$628$$ 0 0
$$629$$ −4.00000 −0.159490
$$630$$ 0 0
$$631$$ 42.4949 1.69170 0.845848 0.533425i $$-0.179095\pi$$
0.845848 + 0.533425i $$0.179095\pi$$
$$632$$ 0 0
$$633$$ 29.3939i 1.16830i
$$634$$ 0 0
$$635$$ 3.34847 33.1464i 0.132880 1.31538i
$$636$$ 0 0
$$637$$ 4.44949i 0.176295i
$$638$$ 0 0
$$639$$ −3.30306 −0.130667
$$640$$ 0 0
$$641$$ 25.7980 1.01896 0.509479 0.860483i $$-0.329838\pi$$
0.509479 + 0.860483i $$0.329838\pi$$
$$642$$ 0 0
$$643$$ 25.1464i 0.991678i −0.868414 0.495839i $$-0.834861\pi$$
0.868414 0.495839i $$-0.165139\pi$$
$$644$$ 0 0
$$645$$ −4.89898 0.494897i −0.192897 0.0194866i
$$646$$ 0 0
$$647$$ 46.2929i 1.81996i −0.414652 0.909980i $$-0.636097\pi$$
0.414652 0.909980i $$-0.363903\pi$$
$$648$$ 0 0
$$649$$ −7.59592 −0.298166
$$650$$ 0 0
$$651$$ −21.7980 −0.854329
$$652$$ 0 0
$$653$$ 20.2020i 0.790567i −0.918559 0.395283i $$-0.870646\pi$$
0.918559 0.395283i $$-0.129354\pi$$
$$654$$ 0 0
$$655$$ 14.3485 + 1.44949i 0.560641 + 0.0566363i
$$656$$ 0 0
$$657$$ 8.69694i 0.339300i
$$658$$ 0 0
$$659$$ 16.8990 0.658291 0.329145 0.944279i $$-0.393239\pi$$
0.329145 + 0.944279i $$0.393239\pi$$
$$660$$ 0 0
$$661$$ −40.9444 −1.59255 −0.796276 0.604933i $$-0.793200\pi$$
−0.796276 + 0.604933i $$0.793200\pi$$
$$662$$ 0 0
$$663$$ 21.7980i 0.846563i
$$664$$ 0 0
$$665$$ 0.348469 3.44949i 0.0135131 0.133765i
$$666$$ 0 0
$$667$$ 20.0000i 0.774403i
$$668$$ 0 0
$$669$$ −9.79796 −0.378811
$$670$$ 0 0
$$671$$ 17.3939 0.671483
$$672$$ 0 0
$$673$$ 17.7980i 0.686061i −0.939324 0.343030i $$-0.888547\pi$$
0.939324 0.343030i $$-0.111453\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 36.4495i 1.40087i 0.713717 + 0.700434i $$0.247010\pi$$
−0.713717 + 0.700434i $$0.752990\pi$$
$$678$$ 0 0
$$679$$ −15.7980 −0.606270
$$680$$ 0 0
$$681$$ −18.0000 −0.689761
$$682$$ 0 0
$$683$$ 3.59592i 0.137594i −0.997631 0.0687970i $$-0.978084\pi$$
0.997631 0.0687970i $$-0.0219161\pi$$
$$684$$ 0 0
$$685$$ −0.404082 + 4.00000i −0.0154392 + 0.152832i
$$686$$ 0 0
$$687$$ 46.8990i 1.78931i
$$688$$ 0 0
$$689$$ 48.4949 1.84751
$$690$$ 0 0
$$691$$ −21.1464 −0.804448 −0.402224 0.915541i $$-0.631763\pi$$
−0.402224 + 0.915541i $$0.631763\pi$$
$$692$$ 0 0
$$693$$ 14.6969i 0.558291i
$$694$$ 0 0
$$695$$ 3.44949 + 0.348469i 0.130847 + 0.0132182i
$$696$$ 0 0
$$697$$ 2.20204i 0.0834083i
$$698$$ 0 0
$$699$$ −72.9898 −2.76073
$$700$$ 0 0
$$701$$ 11.3031 0.426911 0.213455 0.976953i $$-0.431528\pi$$
0.213455 + 0.976953i $$0.431528\pi$$
$$702$$ 0 0
$$703$$ 3.10102i 0.116957i
$$704$$ 0 0
$$705$$ −48.4949 4.89898i −1.82642 0.184506i
$$706$$ 0 0
$$707$$ 3.55051i 0.133531i
$$708$$ 0 0
$$709$$ 28.2929 1.06256 0.531280 0.847196i $$-0.321711\pi$$
0.531280 + 0.847196i $$0.321711\pi$$
$$710$$ 0 0
$$711$$ −20.6969 −0.776196
$$712$$ 0 0
$$713$$ 25.7980i 0.966141i
$$714$$ 0 0
$$715$$ −4.89898 + 48.4949i −0.183211 + 1.81361i
$$716$$ 0 0
$$717$$ 15.1918i 0.567350i
$$718$$ 0 0
$$719$$ −4.49490 −0.167631 −0.0838157 0.996481i $$-0.526711\pi$$
−0.0838157 + 0.996481i $$0.526711\pi$$
$$720$$ 0 0
$$721$$ −12.8990 −0.480383
$$722$$ 0 0
$$723$$ 21.3031i 0.792269i
$$724$$ 0 0
$$725$$ −33.7980 6.89898i −1.25522 0.256222i
$$726$$ 0 0
$$727$$ 22.6969i 0.841783i 0.907111 + 0.420891i $$0.138283\pi$$
−0.907111 + 0.420891i $$0.861717\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 1.79796 0.0664999
$$732$$ 0 0
$$733$$ 39.6413i 1.46419i 0.681205 + 0.732093i $$0.261456\pi$$
−0.681205 + 0.732093i $$0.738544\pi$$
$$734$$ 0 0
$$735$$ 0.550510 5.44949i 0.0203059 0.201007i
$$736$$ 0 0
$$737$$ 39.1918i 1.44365i
$$738$$ 0 0
$$739$$ 4.49490 0.165347 0.0826737 0.996577i $$-0.473654\pi$$
0.0826737 + 0.996577i $$0.473654\pi$$
$$740$$ 0 0
$$741$$ −16.8990 −0.620800
$$742$$ 0 0
$$743$$ 44.6969i 1.63977i 0.572527 + 0.819886i $$0.305963\pi$$
−0.572527 + 0.819886i $$0.694037\pi$$
$$744$$ 0 0
$$745$$ 8.44949 + 0.853572i 0.309565 + 0.0312725i
$$746$$ 0 0
$$747$$ 7.34847i 0.268866i
$$748$$ 0 0
$$749$$ −8.00000 −0.292314
$$750$$ 0 0
$$751$$ 41.7980 1.52523 0.762615 0.646853i $$-0.223915\pi$$
0.762615 + 0.646853i $$0.223915\pi$$
$$752$$ 0 0
$$753$$ 15.7980i 0.575710i
$$754$$ 0 0
$$755$$ −43.5959 4.40408i −1.58662 0.160281i
$$756$$ 0 0
$$757$$ 51.7980i 1.88263i 0.337531 + 0.941314i $$0.390408\pi$$
−0.337531 + 0.941314i $$0.609592\pi$$
$$758$$ 0 0
$$759$$ 34.7878 1.26272
$$760$$ 0 0
$$761$$ −21.1010 −0.764911 −0.382456 0.923974i $$-0.624922\pi$$
−0.382456 + 0.923974i $$0.624922\pi$$
$$762$$ 0 0
$$763$$ 6.89898i 0.249760i
$$764$$ 0 0
$$765$$ −1.34847 + 13.3485i −0.0487540 + 0.482615i
$$766$$ 0 0
$$767$$ 6.89898i 0.249108i
$$768$$ 0 0
$$769$$ 40.6969 1.46757 0.733785 0.679382i $$-0.237752\pi$$
0.733785 + 0.679382i $$0.237752\pi$$
$$770$$ 0 0
$$771$$ −21.3031 −0.767211
$$772$$ 0 0
$$773$$ 1.34847i 0.0485011i 0.999706 + 0.0242505i $$0.00771994\pi$$
−0.999706 + 0.0242505i $$0.992280\pi$$
$$774$$ 0 0
$$775$$ −43.5959 8.89898i −1.56601 0.319661i
$$776$$ 0 0
$$777$$ 4.89898i 0.175750i
$$778$$ 0 0
$$779$$ −1.70714 −0.0611648
$$780$$ 0 0
$$781$$ 5.39388 0.193008
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0.797959 7.89898i 0.0284804 0.281927i
$$786$$ 0 0
$$787$$ 50.4495i 1.79833i 0.437610 + 0.899165i $$0.355825\pi$$
−0.437610 + 0.899165i $$0.644175\pi$$
$$788$$ 0 0
$$789$$ 24.0000 0.854423
$$790$$ 0 0
$$791$$ 19.7980 0.703934
$$792$$ 0 0
$$793$$ 15.7980i 0.561002i
$$794$$ 0 0
$$795$$ 59.3939 + 6.00000i 2.10648 + 0.212798i
$$796$$ 0 0
$$797$$ 0.944387i 0.0334519i 0.999860 + 0.0167260i $$0.00532429\pi$$
−0.999860 + 0.0167260i $$0.994676\pi$$
$$798$$ 0 0
$$799$$ 17.7980 0.629647
$$800$$ 0 0