# Properties

 Label 1560.2.l.f.1249.10 Level $1560$ Weight $2$ Character 1560.1249 Analytic conductor $12.457$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1560.l (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.4566627153$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ Defining polynomial: $$x^{10} + 13x^{8} + 56x^{6} + 97x^{4} + 61x^{2} + 4$$ x^10 + 13*x^8 + 56*x^6 + 97*x^4 + 61*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1249.10 Root $$-1.28447i$$ of defining polynomial Character $$\chi$$ $$=$$ 1560.1249 Dual form 1560.2.l.f.1249.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{3} +(2.23081 + 0.153266i) q^{5} +3.71215i q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{3} +(2.23081 + 0.153266i) q^{5} +3.71215i q^{7} -1.00000 q^{9} +3.31842 q^{11} +1.00000i q^{13} +(-0.153266 + 2.23081i) q^{15} -1.55706i q^{17} +5.33709 q^{19} -3.71215 q^{21} +0.442940i q^{23} +(4.95302 + 0.683813i) q^{25} -1.00000i q^{27} -2.56894 q^{29} +0.613062 q^{31} +3.31842i q^{33} +(-0.568944 + 8.28109i) q^{35} +0.257322i q^{37} -1.00000 q^{39} -10.6114 q^{41} +12.6935i q^{43} +(-2.23081 - 0.153266i) q^{45} -7.44442i q^{47} -6.78003 q^{49} +1.55706 q^{51} -5.39521i q^{53} +(7.40275 + 0.508599i) q^{55} +5.33709i q^{57} +13.1358 q^{59} -5.27452 q^{61} -3.71215i q^{63} +(-0.153266 + 2.23081i) q^{65} -10.5384i q^{67} -0.442940 q^{69} +0.311845 q^{71} +9.46841i q^{73} +(-0.683813 + 4.95302i) q^{75} +12.3184i q^{77} -16.1871 q^{79} +1.00000 q^{81} +11.7546i q^{83} +(0.238644 - 3.47350i) q^{85} -2.56894i q^{87} +4.58762 q^{89} -3.71215 q^{91} +0.613062i q^{93} +(11.9060 + 0.817993i) q^{95} -10.8500i q^{97} -3.31842 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10 q + 2 q^{5} - 10 q^{9}+O(q^{10})$$ 10 * q + 2 * q^5 - 10 * q^9 $$10 q + 2 q^{5} - 10 q^{9} + 10 q^{11} - 12 q^{19} + 2 q^{21} + 6 q^{25} - 4 q^{29} + 16 q^{35} - 10 q^{39} - 2 q^{41} - 2 q^{45} - 4 q^{49} + 14 q^{51} + 10 q^{55} - 40 q^{59} - 38 q^{61} - 6 q^{69} + 26 q^{71} - 4 q^{75} - 14 q^{79} + 10 q^{81} + 24 q^{85} - 18 q^{89} + 2 q^{91} + 32 q^{95} - 10 q^{99}+O(q^{100})$$ 10 * q + 2 * q^5 - 10 * q^9 + 10 * q^11 - 12 * q^19 + 2 * q^21 + 6 * q^25 - 4 * q^29 + 16 * q^35 - 10 * q^39 - 2 * q^41 - 2 * q^45 - 4 * q^49 + 14 * q^51 + 10 * q^55 - 40 * q^59 - 38 * q^61 - 6 * q^69 + 26 * q^71 - 4 * q^75 - 14 * q^79 + 10 * q^81 + 24 * q^85 - 18 * q^89 + 2 * q^91 + 32 * q^95 - 10 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$$.

 $$n$$ $$391$$ $$521$$ $$781$$ $$937$$ $$1081$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ 1.00000i 0.577350i
$$4$$ 0 0
$$5$$ 2.23081 + 0.153266i 0.997648 + 0.0685425i
$$6$$ 0 0
$$7$$ 3.71215i 1.40306i 0.712640 + 0.701530i $$0.247499\pi$$
−0.712640 + 0.701530i $$0.752501\pi$$
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ 3.31842 1.00054 0.500270 0.865869i $$-0.333234\pi$$
0.500270 + 0.865869i $$0.333234\pi$$
$$12$$ 0 0
$$13$$ 1.00000i 0.277350i
$$14$$ 0 0
$$15$$ −0.153266 + 2.23081i −0.0395730 + 0.575992i
$$16$$ 0 0
$$17$$ 1.55706i 0.377642i −0.982011 0.188821i $$-0.939533\pi$$
0.982011 0.188821i $$-0.0604667\pi$$
$$18$$ 0 0
$$19$$ 5.33709 1.22441 0.612207 0.790698i $$-0.290282\pi$$
0.612207 + 0.790698i $$0.290282\pi$$
$$20$$ 0 0
$$21$$ −3.71215 −0.810057
$$22$$ 0 0
$$23$$ 0.442940i 0.0923594i 0.998933 + 0.0461797i $$0.0147047\pi$$
−0.998933 + 0.0461797i $$0.985295\pi$$
$$24$$ 0 0
$$25$$ 4.95302 + 0.683813i 0.990604 + 0.136763i
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ −2.56894 −0.477041 −0.238521 0.971137i $$-0.576662\pi$$
−0.238521 + 0.971137i $$0.576662\pi$$
$$30$$ 0 0
$$31$$ 0.613062 0.110109 0.0550546 0.998483i $$-0.482467\pi$$
0.0550546 + 0.998483i $$0.482467\pi$$
$$32$$ 0 0
$$33$$ 3.31842i 0.577662i
$$34$$ 0 0
$$35$$ −0.568944 + 8.28109i −0.0961692 + 1.39976i
$$36$$ 0 0
$$37$$ 0.257322i 0.0423034i 0.999776 + 0.0211517i $$0.00673331\pi$$
−0.999776 + 0.0211517i $$0.993267\pi$$
$$38$$ 0 0
$$39$$ −1.00000 −0.160128
$$40$$ 0 0
$$41$$ −10.6114 −1.65722 −0.828611 0.559826i $$-0.810868\pi$$
−0.828611 + 0.559826i $$0.810868\pi$$
$$42$$ 0 0
$$43$$ 12.6935i 1.93574i 0.251450 + 0.967870i $$0.419093\pi$$
−0.251450 + 0.967870i $$0.580907\pi$$
$$44$$ 0 0
$$45$$ −2.23081 0.153266i −0.332549 0.0228475i
$$46$$ 0 0
$$47$$ 7.44442i 1.08588i −0.839771 0.542940i $$-0.817311\pi$$
0.839771 0.542940i $$-0.182689\pi$$
$$48$$ 0 0
$$49$$ −6.78003 −0.968576
$$50$$ 0 0
$$51$$ 1.55706 0.218032
$$52$$ 0 0
$$53$$ 5.39521i 0.741089i −0.928815 0.370545i $$-0.879171\pi$$
0.928815 0.370545i $$-0.120829\pi$$
$$54$$ 0 0
$$55$$ 7.40275 + 0.508599i 0.998187 + 0.0685795i
$$56$$ 0 0
$$57$$ 5.33709i 0.706915i
$$58$$ 0 0
$$59$$ 13.1358 1.71014 0.855068 0.518516i $$-0.173515\pi$$
0.855068 + 0.518516i $$0.173515\pi$$
$$60$$ 0 0
$$61$$ −5.27452 −0.675333 −0.337667 0.941266i $$-0.609638\pi$$
−0.337667 + 0.941266i $$0.609638\pi$$
$$62$$ 0 0
$$63$$ 3.71215i 0.467687i
$$64$$ 0 0
$$65$$ −0.153266 + 2.23081i −0.0190103 + 0.276698i
$$66$$ 0 0
$$67$$ 10.5384i 1.28747i −0.765248 0.643736i $$-0.777383\pi$$
0.765248 0.643736i $$-0.222617\pi$$
$$68$$ 0 0
$$69$$ −0.442940 −0.0533237
$$70$$ 0 0
$$71$$ 0.311845 0.0370092 0.0185046 0.999829i $$-0.494109\pi$$
0.0185046 + 0.999829i $$0.494109\pi$$
$$72$$ 0 0
$$73$$ 9.46841i 1.10819i 0.832452 + 0.554097i $$0.186936\pi$$
−0.832452 + 0.554097i $$0.813064\pi$$
$$74$$ 0 0
$$75$$ −0.683813 + 4.95302i −0.0789599 + 0.571925i
$$76$$ 0 0
$$77$$ 12.3184i 1.40382i
$$78$$ 0 0
$$79$$ −16.1871 −1.82119 −0.910597 0.413295i $$-0.864378\pi$$
−0.910597 + 0.413295i $$0.864378\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 11.7546i 1.29023i 0.764084 + 0.645117i $$0.223191\pi$$
−0.764084 + 0.645117i $$0.776809\pi$$
$$84$$ 0 0
$$85$$ 0.238644 3.47350i 0.0258845 0.376754i
$$86$$ 0 0
$$87$$ 2.56894i 0.275420i
$$88$$ 0 0
$$89$$ 4.58762 0.486287 0.243144 0.969990i $$-0.421821\pi$$
0.243144 + 0.969990i $$0.421821\pi$$
$$90$$ 0 0
$$91$$ −3.71215 −0.389139
$$92$$ 0 0
$$93$$ 0.613062i 0.0635716i
$$94$$ 0 0
$$95$$ 11.9060 + 0.817993i 1.22153 + 0.0839243i
$$96$$ 0 0
$$97$$ 10.8500i 1.10165i −0.834619 0.550827i $$-0.814312\pi$$
0.834619 0.550827i $$-0.185688\pi$$
$$98$$ 0 0
$$99$$ −3.31842 −0.333513
$$100$$ 0 0
$$101$$ 1.68306 0.167471 0.0837356 0.996488i $$-0.473315\pi$$
0.0837356 + 0.996488i $$0.473315\pi$$
$$102$$ 0 0
$$103$$ 1.78535i 0.175916i 0.996124 + 0.0879578i $$0.0280341\pi$$
−0.996124 + 0.0879578i $$0.971966\pi$$
$$104$$ 0 0
$$105$$ −8.28109 0.568944i −0.808152 0.0555233i
$$106$$ 0 0
$$107$$ 1.11943i 0.108220i −0.998535 0.0541098i $$-0.982768\pi$$
0.998535 0.0541098i $$-0.0172321\pi$$
$$108$$ 0 0
$$109$$ 0.914914 0.0876329 0.0438164 0.999040i $$-0.486048\pi$$
0.0438164 + 0.999040i $$0.486048\pi$$
$$110$$ 0 0
$$111$$ −0.257322 −0.0244239
$$112$$ 0 0
$$113$$ 2.41386i 0.227077i 0.993534 + 0.113538i $$0.0362185\pi$$
−0.993534 + 0.113538i $$0.963782\pi$$
$$114$$ 0 0
$$115$$ −0.0678875 + 0.988115i −0.00633054 + 0.0921422i
$$116$$ 0 0
$$117$$ 1.00000i 0.0924500i
$$118$$ 0 0
$$119$$ 5.78003 0.529855
$$120$$ 0 0
$$121$$ 0.0118848 0.00108043
$$122$$ 0 0
$$123$$ 10.6114i 0.956797i
$$124$$ 0 0
$$125$$ 10.9444 + 2.28458i 0.978900 + 0.204339i
$$126$$ 0 0
$$127$$ 14.0418i 1.24601i 0.782218 + 0.623005i $$0.214088\pi$$
−0.782218 + 0.623005i $$0.785912\pi$$
$$128$$ 0 0
$$129$$ −12.6935 −1.11760
$$130$$ 0 0
$$131$$ 13.7650 1.20265 0.601327 0.799003i $$-0.294639\pi$$
0.601327 + 0.799003i $$0.294639\pi$$
$$132$$ 0 0
$$133$$ 19.8121i 1.71792i
$$134$$ 0 0
$$135$$ 0.153266 2.23081i 0.0131910 0.191997i
$$136$$ 0 0
$$137$$ 6.50470i 0.555734i 0.960620 + 0.277867i $$0.0896275\pi$$
−0.960620 + 0.277867i $$0.910373\pi$$
$$138$$ 0 0
$$139$$ −9.78003 −0.829532 −0.414766 0.909928i $$-0.636137\pi$$
−0.414766 + 0.909928i $$0.636137\pi$$
$$140$$ 0 0
$$141$$ 7.44442 0.626933
$$142$$ 0 0
$$143$$ 3.31842i 0.277500i
$$144$$ 0 0
$$145$$ −5.73082 0.393731i −0.475919 0.0326976i
$$146$$ 0 0
$$147$$ 6.78003i 0.559208i
$$148$$ 0 0
$$149$$ 5.93148 0.485926 0.242963 0.970036i $$-0.421881\pi$$
0.242963 + 0.970036i $$0.421881\pi$$
$$150$$ 0 0
$$151$$ −0.272818 −0.0222016 −0.0111008 0.999938i $$-0.503534\pi$$
−0.0111008 + 0.999938i $$0.503534\pi$$
$$152$$ 0 0
$$153$$ 1.55706i 0.125881i
$$154$$ 0 0
$$155$$ 1.36763 + 0.0939614i 0.109850 + 0.00754716i
$$156$$ 0 0
$$157$$ 14.6561i 1.16969i −0.811146 0.584844i $$-0.801156\pi$$
0.811146 0.584844i $$-0.198844\pi$$
$$158$$ 0 0
$$159$$ 5.39521 0.427868
$$160$$ 0 0
$$161$$ −1.64426 −0.129586
$$162$$ 0 0
$$163$$ 3.48345i 0.272845i −0.990651 0.136422i $$-0.956440\pi$$
0.990651 0.136422i $$-0.0435604\pi$$
$$164$$ 0 0
$$165$$ −0.508599 + 7.40275i −0.0395944 + 0.576304i
$$166$$ 0 0
$$167$$ 4.69135i 0.363028i −0.983388 0.181514i $$-0.941900\pi$$
0.983388 0.181514i $$-0.0580998\pi$$
$$168$$ 0 0
$$169$$ −1.00000 −0.0769231
$$170$$ 0 0
$$171$$ −5.33709 −0.408138
$$172$$ 0 0
$$173$$ 3.26475i 0.248214i 0.992269 + 0.124107i $$0.0396067\pi$$
−0.992269 + 0.124107i $$0.960393\pi$$
$$174$$ 0 0
$$175$$ −2.53841 + 18.3863i −0.191886 + 1.38988i
$$176$$ 0 0
$$177$$ 13.1358i 0.987348i
$$178$$ 0 0
$$179$$ −19.7204 −1.47397 −0.736987 0.675907i $$-0.763752\pi$$
−0.736987 + 0.675907i $$0.763752\pi$$
$$180$$ 0 0
$$181$$ −22.0558 −1.63940 −0.819698 0.572796i $$-0.805859\pi$$
−0.819698 + 0.572796i $$0.805859\pi$$
$$182$$ 0 0
$$183$$ 5.27452i 0.389904i
$$184$$ 0 0
$$185$$ −0.0394386 + 0.574036i −0.00289958 + 0.0422040i
$$186$$ 0 0
$$187$$ 5.16697i 0.377846i
$$188$$ 0 0
$$189$$ 3.71215 0.270019
$$190$$ 0 0
$$191$$ 22.2729 1.61161 0.805805 0.592182i $$-0.201733\pi$$
0.805805 + 0.592182i $$0.201733\pi$$
$$192$$ 0 0
$$193$$ 15.7733i 1.13539i −0.823241 0.567693i $$-0.807836\pi$$
0.823241 0.567693i $$-0.192164\pi$$
$$194$$ 0 0
$$195$$ −2.23081 0.153266i −0.159752 0.0109756i
$$196$$ 0 0
$$197$$ 2.72871i 0.194413i 0.995264 + 0.0972063i $$0.0309907\pi$$
−0.995264 + 0.0972063i $$0.969009\pi$$
$$198$$ 0 0
$$199$$ 22.1029 1.56684 0.783418 0.621495i $$-0.213474\pi$$
0.783418 + 0.621495i $$0.213474\pi$$
$$200$$ 0 0
$$201$$ 10.5384 0.743322
$$202$$ 0 0
$$203$$ 9.53630i 0.669317i
$$204$$ 0 0
$$205$$ −23.6720 1.62636i −1.65332 0.113590i
$$206$$ 0 0
$$207$$ 0.442940i 0.0307865i
$$208$$ 0 0
$$209$$ 17.7107 1.22507
$$210$$ 0 0
$$211$$ 1.01720 0.0700268 0.0350134 0.999387i $$-0.488853\pi$$
0.0350134 + 0.999387i $$0.488853\pi$$
$$212$$ 0 0
$$213$$ 0.311845i 0.0213672i
$$214$$ 0 0
$$215$$ −1.94548 + 28.3168i −0.132680 + 1.93119i
$$216$$ 0 0
$$217$$ 2.27578i 0.154490i
$$218$$ 0 0
$$219$$ −9.46841 −0.639816
$$220$$ 0 0
$$221$$ 1.55706 0.104739
$$222$$ 0 0
$$223$$ 6.85535i 0.459068i −0.973301 0.229534i $$-0.926280\pi$$
0.973301 0.229534i $$-0.0737202\pi$$
$$224$$ 0 0
$$225$$ −4.95302 0.683813i −0.330201 0.0455875i
$$226$$ 0 0
$$227$$ 2.88224i 0.191301i −0.995415 0.0956504i $$-0.969507\pi$$
0.995415 0.0956504i $$-0.0304931\pi$$
$$228$$ 0 0
$$229$$ −14.1857 −0.937416 −0.468708 0.883353i $$-0.655280\pi$$
−0.468708 + 0.883353i $$0.655280\pi$$
$$230$$ 0 0
$$231$$ −12.3184 −0.810494
$$232$$ 0 0
$$233$$ 0.429354i 0.0281279i 0.999901 + 0.0140639i $$0.00447684\pi$$
−0.999901 + 0.0140639i $$0.995523\pi$$
$$234$$ 0 0
$$235$$ 1.14097 16.6071i 0.0744289 1.08333i
$$236$$ 0 0
$$237$$ 16.1871i 1.05147i
$$238$$ 0 0
$$239$$ −19.7255 −1.27594 −0.637969 0.770062i $$-0.720225\pi$$
−0.637969 + 0.770062i $$0.720225\pi$$
$$240$$ 0 0
$$241$$ 19.6598 1.26640 0.633200 0.773988i $$-0.281741\pi$$
0.633200 + 0.773988i $$0.281741\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ −15.1250 1.03915i −0.966298 0.0663886i
$$246$$ 0 0
$$247$$ 5.33709i 0.339591i
$$248$$ 0 0
$$249$$ −11.7546 −0.744917
$$250$$ 0 0
$$251$$ 23.4175 1.47810 0.739051 0.673650i $$-0.235274\pi$$
0.739051 + 0.673650i $$0.235274\pi$$
$$252$$ 0 0
$$253$$ 1.46986i 0.0924093i
$$254$$ 0 0
$$255$$ 3.47350 + 0.238644i 0.217519 + 0.0149444i
$$256$$ 0 0
$$257$$ 30.7987i 1.92117i −0.277981 0.960586i $$-0.589665\pi$$
0.277981 0.960586i $$-0.410335\pi$$
$$258$$ 0 0
$$259$$ −0.955216 −0.0593543
$$260$$ 0 0
$$261$$ 2.56894 0.159014
$$262$$ 0 0
$$263$$ 24.1471i 1.48897i −0.667638 0.744486i $$-0.732695\pi$$
0.667638 0.744486i $$-0.267305\pi$$
$$264$$ 0 0
$$265$$ 0.826900 12.0357i 0.0507961 0.739346i
$$266$$ 0 0
$$267$$ 4.58762i 0.280758i
$$268$$ 0 0
$$269$$ −12.7557 −0.777726 −0.388863 0.921295i $$-0.627132\pi$$
−0.388863 + 0.921295i $$0.627132\pi$$
$$270$$ 0 0
$$271$$ −10.4222 −0.633102 −0.316551 0.948575i $$-0.602525\pi$$
−0.316551 + 0.948575i $$0.602525\pi$$
$$272$$ 0 0
$$273$$ 3.71215i 0.224669i
$$274$$ 0 0
$$275$$ 16.4362 + 2.26918i 0.991139 + 0.136836i
$$276$$ 0 0
$$277$$ 19.9404i 1.19810i −0.800710 0.599052i $$-0.795544\pi$$
0.800710 0.599052i $$-0.204456\pi$$
$$278$$ 0 0
$$279$$ −0.613062 −0.0367031
$$280$$ 0 0
$$281$$ 28.5272 1.70179 0.850895 0.525336i $$-0.176060\pi$$
0.850895 + 0.525336i $$0.176060\pi$$
$$282$$ 0 0
$$283$$ 19.1888i 1.14066i 0.821416 + 0.570329i $$0.193184\pi$$
−0.821416 + 0.570329i $$0.806816\pi$$
$$284$$ 0 0
$$285$$ −0.817993 + 11.9060i −0.0484537 + 0.705253i
$$286$$ 0 0
$$287$$ 39.3910i 2.32518i
$$288$$ 0 0
$$289$$ 14.5756 0.857386
$$290$$ 0 0
$$291$$ 10.8500 0.636040
$$292$$ 0 0
$$293$$ 11.9828i 0.700045i −0.936741 0.350022i $$-0.886174\pi$$
0.936741 0.350022i $$-0.113826\pi$$
$$294$$ 0 0
$$295$$ 29.3035 + 2.01327i 1.70611 + 0.117217i
$$296$$ 0 0
$$297$$ 3.31842i 0.192554i
$$298$$ 0 0
$$299$$ −0.442940 −0.0256159
$$300$$ 0 0
$$301$$ −47.1201 −2.71596
$$302$$ 0 0
$$303$$ 1.68306i 0.0966895i
$$304$$ 0 0
$$305$$ −11.7664 0.808403i −0.673745 0.0462890i
$$306$$ 0 0
$$307$$ 25.0299i 1.42853i −0.699874 0.714267i $$-0.746760\pi$$
0.699874 0.714267i $$-0.253240\pi$$
$$308$$ 0 0
$$309$$ −1.78535 −0.101565
$$310$$ 0 0
$$311$$ 27.6360 1.56710 0.783548 0.621331i $$-0.213408\pi$$
0.783548 + 0.621331i $$0.213408\pi$$
$$312$$ 0 0
$$313$$ 14.5441i 0.822083i 0.911617 + 0.411042i $$0.134835\pi$$
−0.911617 + 0.411042i $$0.865165\pi$$
$$314$$ 0 0
$$315$$ 0.568944 8.28109i 0.0320564 0.466587i
$$316$$ 0 0
$$317$$ 8.00364i 0.449529i −0.974413 0.224765i $$-0.927839\pi$$
0.974413 0.224765i $$-0.0721613\pi$$
$$318$$ 0 0
$$319$$ −8.52483 −0.477299
$$320$$ 0 0
$$321$$ 1.11943 0.0624806
$$322$$ 0 0
$$323$$ 8.31017i 0.462390i
$$324$$ 0 0
$$325$$ −0.683813 + 4.95302i −0.0379311 + 0.274744i
$$326$$ 0 0
$$327$$ 0.914914i 0.0505949i
$$328$$ 0 0
$$329$$ 27.6348 1.52355
$$330$$ 0 0
$$331$$ 5.59929 0.307765 0.153882 0.988089i $$-0.450822\pi$$
0.153882 + 0.988089i $$0.450822\pi$$
$$332$$ 0 0
$$333$$ 0.257322i 0.0141011i
$$334$$ 0 0
$$335$$ 1.61518 23.5092i 0.0882465 1.28444i
$$336$$ 0 0
$$337$$ 34.5802i 1.88370i −0.336027 0.941852i $$-0.609083\pi$$
0.336027 0.941852i $$-0.390917\pi$$
$$338$$ 0 0
$$339$$ −2.41386 −0.131103
$$340$$ 0 0
$$341$$ 2.03440 0.110169
$$342$$ 0 0
$$343$$ 0.816545i 0.0440893i
$$344$$ 0 0
$$345$$ −0.988115 0.0678875i −0.0531983 0.00365494i
$$346$$ 0 0
$$347$$ 31.0537i 1.66705i −0.552482 0.833525i $$-0.686319\pi$$
0.552482 0.833525i $$-0.313681\pi$$
$$348$$ 0 0
$$349$$ −2.94804 −0.157805 −0.0789026 0.996882i $$-0.525142\pi$$
−0.0789026 + 0.996882i $$0.525142\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ 0 0
$$353$$ 1.80547i 0.0960957i 0.998845 + 0.0480478i $$0.0153000\pi$$
−0.998845 + 0.0480478i $$0.984700\pi$$
$$354$$ 0 0
$$355$$ 0.695666 + 0.0477951i 0.0369221 + 0.00253670i
$$356$$ 0 0
$$357$$ 5.78003i 0.305912i
$$358$$ 0 0
$$359$$ 9.29216 0.490422 0.245211 0.969470i $$-0.421143\pi$$
0.245211 + 0.969470i $$0.421143\pi$$
$$360$$ 0 0
$$361$$ 9.48457 0.499188
$$362$$ 0 0
$$363$$ 0.0118848i 0.000623788i
$$364$$ 0 0
$$365$$ −1.45118 + 21.1222i −0.0759583 + 1.10559i
$$366$$ 0 0
$$367$$ 18.0955i 0.944579i 0.881444 + 0.472289i $$0.156572\pi$$
−0.881444 + 0.472289i $$0.843428\pi$$
$$368$$ 0 0
$$369$$ 10.6114 0.552407
$$370$$ 0 0
$$371$$ 20.0278 1.03979
$$372$$ 0 0
$$373$$ 29.4689i 1.52584i −0.646491 0.762922i $$-0.723764\pi$$
0.646491 0.762922i $$-0.276236\pi$$
$$374$$ 0 0
$$375$$ −2.28458 + 10.9444i −0.117975 + 0.565168i
$$376$$ 0 0
$$377$$ 2.56894i 0.132307i
$$378$$ 0 0
$$379$$ 21.2489 1.09148 0.545740 0.837954i $$-0.316249\pi$$
0.545740 + 0.837954i $$0.316249\pi$$
$$380$$ 0 0
$$381$$ −14.0418 −0.719384
$$382$$ 0 0
$$383$$ 8.19163i 0.418573i −0.977854 0.209286i $$-0.932886\pi$$
0.977854 0.209286i $$-0.0671141\pi$$
$$384$$ 0 0
$$385$$ −1.88799 + 27.4801i −0.0962211 + 1.40052i
$$386$$ 0 0
$$387$$ 12.6935i 0.645247i
$$388$$ 0 0
$$389$$ 24.4557 1.23995 0.619976 0.784621i $$-0.287142\pi$$
0.619976 + 0.784621i $$0.287142\pi$$
$$390$$ 0 0
$$391$$ 0.689684 0.0348788
$$392$$ 0 0
$$393$$ 13.7650i 0.694352i
$$394$$ 0 0
$$395$$ −36.1104 2.48093i −1.81691 0.124829i
$$396$$ 0 0
$$397$$ 34.4916i 1.73108i −0.500837 0.865541i $$-0.666975\pi$$
0.500837 0.865541i $$-0.333025\pi$$
$$398$$ 0 0
$$399$$ −19.8121 −0.991844
$$400$$ 0 0
$$401$$ −16.9434 −0.846114 −0.423057 0.906103i $$-0.639043\pi$$
−0.423057 + 0.906103i $$0.639043\pi$$
$$402$$ 0 0
$$403$$ 0.613062i 0.0305388i
$$404$$ 0 0
$$405$$ 2.23081 + 0.153266i 0.110850 + 0.00761583i
$$406$$ 0 0
$$407$$ 0.853901i 0.0423263i
$$408$$ 0 0
$$409$$ 3.05299 0.150961 0.0754804 0.997147i $$-0.475951\pi$$
0.0754804 + 0.997147i $$0.475951\pi$$
$$410$$ 0 0
$$411$$ −6.50470 −0.320853
$$412$$ 0 0
$$413$$ 48.7620i 2.39942i
$$414$$ 0 0
$$415$$ −1.80158 + 26.2223i −0.0884358 + 1.28720i
$$416$$ 0 0
$$417$$ 9.78003i 0.478930i
$$418$$ 0 0
$$419$$ −20.9567 −1.02380 −0.511902 0.859044i $$-0.671059\pi$$
−0.511902 + 0.859044i $$0.671059\pi$$
$$420$$ 0 0
$$421$$ −37.4462 −1.82502 −0.912508 0.409059i $$-0.865857\pi$$
−0.912508 + 0.409059i $$0.865857\pi$$
$$422$$ 0 0
$$423$$ 7.44442i 0.361960i
$$424$$ 0 0
$$425$$ 1.06474 7.71215i 0.0516473 0.374094i
$$426$$ 0 0
$$427$$ 19.5798i 0.947533i
$$428$$ 0 0
$$429$$ −3.31842 −0.160215
$$430$$ 0 0
$$431$$ −27.2671 −1.31341 −0.656706 0.754147i $$-0.728051\pi$$
−0.656706 + 0.754147i $$0.728051\pi$$
$$432$$ 0 0
$$433$$ 12.5679i 0.603975i 0.953312 + 0.301988i $$0.0976501\pi$$
−0.953312 + 0.301988i $$0.902350\pi$$
$$434$$ 0 0
$$435$$ 0.393731 5.73082i 0.0188780 0.274772i
$$436$$ 0 0
$$437$$ 2.36401i 0.113086i
$$438$$ 0 0
$$439$$ −14.7241 −0.702742 −0.351371 0.936236i $$-0.614284\pi$$
−0.351371 + 0.936236i $$0.614284\pi$$
$$440$$ 0 0
$$441$$ 6.78003 0.322859
$$442$$ 0 0
$$443$$ 8.65996i 0.411447i 0.978610 + 0.205724i $$0.0659548\pi$$
−0.978610 + 0.205724i $$0.934045\pi$$
$$444$$ 0 0
$$445$$ 10.2341 + 0.703125i 0.485143 + 0.0333313i
$$446$$ 0 0
$$447$$ 5.93148i 0.280549i
$$448$$ 0 0
$$449$$ 21.5690 1.01791 0.508953 0.860795i $$-0.330033\pi$$
0.508953 + 0.860795i $$0.330033\pi$$
$$450$$ 0 0
$$451$$ −35.2130 −1.65812
$$452$$ 0 0
$$453$$ 0.272818i 0.0128181i
$$454$$ 0 0
$$455$$ −8.28109 0.568944i −0.388224 0.0266725i
$$456$$ 0 0
$$457$$ 0.192394i 0.00899982i 0.999990 + 0.00449991i $$0.00143237\pi$$
−0.999990 + 0.00449991i $$0.998568\pi$$
$$458$$ 0 0
$$459$$ −1.55706 −0.0726773
$$460$$ 0 0
$$461$$ −12.0821 −0.562720 −0.281360 0.959602i $$-0.590785\pi$$
−0.281360 + 0.959602i $$0.590785\pi$$
$$462$$ 0 0
$$463$$ 25.7245i 1.19552i 0.801676 + 0.597759i $$0.203942\pi$$
−0.801676 + 0.597759i $$0.796058\pi$$
$$464$$ 0 0
$$465$$ −0.0939614 + 1.36763i −0.00435736 + 0.0634221i
$$466$$ 0 0
$$467$$ 18.4317i 0.852918i −0.904507 0.426459i $$-0.859761\pi$$
0.904507 0.426459i $$-0.140239\pi$$
$$468$$ 0 0
$$469$$ 39.1201 1.80640
$$470$$ 0 0
$$471$$ 14.6561 0.675319
$$472$$ 0 0
$$473$$ 42.1223i 1.93679i
$$474$$ 0 0
$$475$$ 26.4347 + 3.64957i 1.21291 + 0.167454i
$$476$$ 0 0
$$477$$ 5.39521i 0.247030i
$$478$$ 0 0
$$479$$ −25.5826 −1.16890 −0.584450 0.811430i $$-0.698690\pi$$
−0.584450 + 0.811430i $$0.698690\pi$$
$$480$$ 0 0
$$481$$ −0.257322 −0.0117329
$$482$$ 0 0
$$483$$ 1.64426i 0.0748164i
$$484$$ 0 0
$$485$$ 1.66294 24.2044i 0.0755101 1.09906i
$$486$$ 0 0
$$487$$ 30.1997i 1.36848i 0.729258 + 0.684239i $$0.239866\pi$$
−0.729258 + 0.684239i $$0.760134\pi$$
$$488$$ 0 0
$$489$$ 3.48345 0.157527
$$490$$ 0 0
$$491$$ −10.7256 −0.484039 −0.242020 0.970271i $$-0.577810\pi$$
−0.242020 + 0.970271i $$0.577810\pi$$
$$492$$ 0 0
$$493$$ 4.00000i 0.180151i
$$494$$ 0 0
$$495$$ −7.40275 0.508599i −0.332729 0.0228598i
$$496$$ 0 0
$$497$$ 1.15761i 0.0519260i
$$498$$ 0 0
$$499$$ −7.01044 −0.313830 −0.156915 0.987612i $$-0.550155\pi$$
−0.156915 + 0.987612i $$0.550155\pi$$
$$500$$ 0 0
$$501$$ 4.69135 0.209594
$$502$$ 0 0
$$503$$ 32.2604i 1.43842i −0.694793 0.719210i $$-0.744504\pi$$
0.694793 0.719210i $$-0.255496\pi$$
$$504$$ 0 0
$$505$$ 3.75459 + 0.257956i 0.167077 + 0.0114789i
$$506$$ 0 0
$$507$$ 1.00000i 0.0444116i
$$508$$ 0 0
$$509$$ −17.3631 −0.769604 −0.384802 0.922999i $$-0.625730\pi$$
−0.384802 + 0.922999i $$0.625730\pi$$
$$510$$ 0 0
$$511$$ −35.1481 −1.55486
$$512$$ 0 0
$$513$$ 5.33709i 0.235638i
$$514$$ 0 0
$$515$$ −0.273632 + 3.98277i −0.0120577 + 0.175502i
$$516$$ 0 0
$$517$$ 24.7037i 1.08647i
$$518$$ 0 0
$$519$$ −3.26475 −0.143307
$$520$$ 0 0
$$521$$ 27.6513 1.21142 0.605712 0.795684i $$-0.292888\pi$$
0.605712 + 0.795684i $$0.292888\pi$$
$$522$$ 0 0
$$523$$ 7.49745i 0.327840i −0.986474 0.163920i $$-0.947586\pi$$
0.986474 0.163920i $$-0.0524140\pi$$
$$524$$ 0 0
$$525$$ −18.3863 2.53841i −0.802445 0.110785i
$$526$$ 0 0
$$527$$ 0.954575i 0.0415819i
$$528$$ 0 0
$$529$$ 22.8038 0.991470
$$530$$ 0 0
$$531$$ −13.1358 −0.570045
$$532$$ 0 0
$$533$$ 10.6114i 0.459630i
$$534$$ 0 0
$$535$$ 0.171571 2.49724i 0.00741764 0.107965i
$$536$$ 0 0
$$537$$ 19.7204i 0.850999i
$$538$$ 0 0
$$539$$ −22.4990 −0.969099
$$540$$ 0 0
$$541$$ 18.8836 0.811871 0.405936 0.913902i $$-0.366946\pi$$
0.405936 + 0.913902i $$0.366946\pi$$
$$542$$ 0 0
$$543$$ 22.0558i 0.946506i
$$544$$ 0 0
$$545$$ 2.04100 + 0.140225i 0.0874268 + 0.00600658i
$$546$$ 0 0
$$547$$ 21.3808i 0.914178i 0.889421 + 0.457089i $$0.151108\pi$$
−0.889421 + 0.457089i $$0.848892\pi$$
$$548$$ 0 0
$$549$$ 5.27452 0.225111
$$550$$ 0 0
$$551$$ −13.7107 −0.584095
$$552$$ 0 0
$$553$$ 60.0890i 2.55524i
$$554$$ 0 0
$$555$$ −0.574036 0.0394386i −0.0243665 0.00167407i
$$556$$ 0 0
$$557$$ 3.80681i 0.161300i −0.996743 0.0806498i $$-0.974300\pi$$
0.996743 0.0806498i $$-0.0256995\pi$$
$$558$$ 0 0
$$559$$ −12.6935 −0.536878
$$560$$ 0 0
$$561$$ 5.16697 0.218150
$$562$$ 0 0
$$563$$ 29.3983i 1.23899i 0.785001 + 0.619495i $$0.212662\pi$$
−0.785001 + 0.619495i $$0.787338\pi$$
$$564$$ 0 0
$$565$$ −0.369961 + 5.38486i −0.0155644 + 0.226543i
$$566$$ 0 0
$$567$$ 3.71215i 0.155896i
$$568$$ 0 0
$$569$$ −12.4014 −0.519892 −0.259946 0.965623i $$-0.583705\pi$$
−0.259946 + 0.965623i $$0.583705\pi$$
$$570$$ 0 0
$$571$$ −4.56899 −0.191206 −0.0956032 0.995420i $$-0.530478\pi$$
−0.0956032 + 0.995420i $$0.530478\pi$$
$$572$$ 0 0
$$573$$ 22.2729i 0.930463i
$$574$$ 0 0
$$575$$ −0.302888 + 2.19389i −0.0126313 + 0.0914916i
$$576$$ 0 0
$$577$$ 27.4496i 1.14274i −0.820692 0.571370i $$-0.806412\pi$$
0.820692 0.571370i $$-0.193588\pi$$
$$578$$ 0 0
$$579$$ 15.7733 0.655515
$$580$$ 0 0
$$581$$ −43.6348 −1.81028
$$582$$ 0 0
$$583$$ 17.9036i 0.741489i
$$584$$ 0 0
$$585$$ 0.153266 2.23081i 0.00633675 0.0922326i
$$586$$ 0 0
$$587$$ 19.5191i 0.805641i 0.915279 + 0.402820i $$0.131970\pi$$
−0.915279 + 0.402820i $$0.868030\pi$$
$$588$$ 0 0
$$589$$ 3.27197 0.134819
$$590$$ 0 0
$$591$$ −2.72871 −0.112244
$$592$$ 0 0
$$593$$ 14.8539i 0.609975i −0.952356 0.304987i $$-0.901348\pi$$
0.952356 0.304987i $$-0.0986523\pi$$
$$594$$ 0 0
$$595$$ 12.8942 + 0.885881i 0.528609 + 0.0363176i
$$596$$ 0 0
$$597$$ 22.1029i 0.904613i
$$598$$ 0 0
$$599$$ 42.6098 1.74099 0.870494 0.492178i $$-0.163799\pi$$
0.870494 + 0.492178i $$0.163799\pi$$
$$600$$ 0 0
$$601$$ 34.4960 1.40712 0.703561 0.710635i $$-0.251592\pi$$
0.703561 + 0.710635i $$0.251592\pi$$
$$602$$ 0 0
$$603$$ 10.5384i 0.429157i
$$604$$ 0 0
$$605$$ 0.0265126 + 0.00182153i 0.00107789 + 7.40555e-5i
$$606$$ 0 0
$$607$$ 44.0061i 1.78615i 0.449906 + 0.893076i $$0.351457\pi$$
−0.449906 + 0.893076i $$0.648543\pi$$
$$608$$ 0 0
$$609$$ 9.53630 0.386430
$$610$$ 0 0
$$611$$ 7.44442 0.301169
$$612$$ 0 0
$$613$$ 11.4907i 0.464104i 0.972703 + 0.232052i $$0.0745439\pi$$
−0.972703 + 0.232052i $$0.925456\pi$$
$$614$$ 0 0
$$615$$ 1.62636 23.6720i 0.0655812 0.954547i
$$616$$ 0 0
$$617$$ 47.2506i 1.90224i 0.308823 + 0.951120i $$0.400065\pi$$
−0.308823 + 0.951120i $$0.599935\pi$$
$$618$$ 0 0
$$619$$ −25.5964 −1.02881 −0.514403 0.857549i $$-0.671986\pi$$
−0.514403 + 0.857549i $$0.671986\pi$$
$$620$$ 0 0
$$621$$ 0.442940 0.0177746
$$622$$ 0 0
$$623$$ 17.0299i 0.682290i
$$624$$ 0 0
$$625$$ 24.0648 + 6.77388i 0.962592 + 0.270955i
$$626$$ 0 0
$$627$$ 17.7107i 0.707297i
$$628$$ 0 0
$$629$$ 0.400665 0.0159756
$$630$$ 0 0
$$631$$ 6.54777 0.260663 0.130331 0.991470i $$-0.458396\pi$$
0.130331 + 0.991470i $$0.458396\pi$$
$$632$$ 0 0
$$633$$ 1.01720i 0.0404300i
$$634$$ 0 0
$$635$$ −2.15213 + 31.3246i −0.0854046 + 1.24308i
$$636$$ 0 0
$$637$$ 6.78003i 0.268635i
$$638$$ 0 0
$$639$$ −0.311845 −0.0123364
$$640$$ 0 0
$$641$$ −0.899023 −0.0355093 −0.0177546 0.999842i $$-0.505652\pi$$
−0.0177546 + 0.999842i $$0.505652\pi$$
$$642$$ 0 0
$$643$$ 2.48862i 0.0981416i −0.998795 0.0490708i $$-0.984374\pi$$
0.998795 0.0490708i $$-0.0156260\pi$$
$$644$$ 0 0
$$645$$ −28.3168 1.94548i −1.11497 0.0766031i
$$646$$ 0 0
$$647$$ 0.773002i 0.0303898i 0.999885 + 0.0151949i $$0.00483688\pi$$
−0.999885 + 0.0151949i $$0.995163\pi$$
$$648$$ 0 0
$$649$$ 43.5901 1.71106
$$650$$ 0 0
$$651$$ −2.27578 −0.0891948
$$652$$ 0 0
$$653$$ 43.1740i 1.68953i −0.535139 0.844764i $$-0.679741\pi$$
0.535139 0.844764i $$-0.320259\pi$$
$$654$$ 0 0
$$655$$ 30.7071 + 2.10970i 1.19983 + 0.0824328i
$$656$$ 0 0
$$657$$ 9.46841i 0.369398i
$$658$$ 0 0
$$659$$ 39.3552 1.53306 0.766530 0.642208i $$-0.221981\pi$$
0.766530 + 0.642208i $$0.221981\pi$$
$$660$$ 0 0
$$661$$ −20.7673 −0.807756 −0.403878 0.914813i $$-0.632338\pi$$
−0.403878 + 0.914813i $$0.632338\pi$$
$$662$$ 0 0
$$663$$ 1.55706i 0.0604712i
$$664$$ 0 0
$$665$$ −3.03651 + 44.1970i −0.117751 + 1.71388i
$$666$$ 0 0
$$667$$ 1.13789i 0.0440592i
$$668$$ 0 0
$$669$$ 6.85535 0.265043
$$670$$ 0 0
$$671$$ −17.5031 −0.675698
$$672$$ 0 0
$$673$$ 49.6479i 1.91379i −0.290439 0.956893i $$-0.593801\pi$$
0.290439 0.956893i $$-0.406199\pi$$
$$674$$ 0 0
$$675$$ 0.683813 4.95302i 0.0263200 0.190642i
$$676$$ 0 0
$$677$$ 30.5884i 1.17561i 0.809004 + 0.587803i $$0.200007\pi$$
−0.809004 + 0.587803i $$0.799993\pi$$
$$678$$ 0 0
$$679$$ 40.2769 1.54569
$$680$$ 0 0
$$681$$ 2.88224 0.110448
$$682$$ 0 0
$$683$$ 28.9405i 1.10738i 0.832724 + 0.553688i $$0.186780\pi$$
−0.832724 + 0.553688i $$0.813220\pi$$
$$684$$ 0 0
$$685$$ −0.996947 + 14.5107i −0.0380914 + 0.554427i
$$686$$ 0 0
$$687$$ 14.1857i 0.541218i
$$688$$ 0 0
$$689$$ 5.39521 0.205541
$$690$$ 0 0
$$691$$ −31.9739 −1.21635 −0.608173 0.793805i $$-0.708097\pi$$
−0.608173 + 0.793805i $$0.708097\pi$$
$$692$$ 0 0
$$693$$ 12.3184i 0.467939i
$$694$$ 0 0
$$695$$ −21.8174 1.49894i −0.827581 0.0568581i
$$696$$ 0 0
$$697$$ 16.5226i 0.625837i
$$698$$ 0 0
$$699$$ −0.429354 −0.0162396
$$700$$ 0 0
$$701$$ 4.51673 0.170595 0.0852973 0.996356i $$-0.472816\pi$$
0.0852973 + 0.996356i $$0.472816\pi$$
$$702$$ 0 0
$$703$$ 1.37335i 0.0517969i
$$704$$ 0 0
$$705$$ 16.6071 + 1.14097i 0.625459 + 0.0429716i
$$706$$ 0 0
$$707$$ 6.24778i 0.234972i
$$708$$ 0 0
$$709$$ 29.7979 1.11908 0.559542 0.828802i $$-0.310977\pi$$
0.559542 + 0.828802i $$0.310977\pi$$
$$710$$ 0 0
$$711$$ 16.1871 0.607065
$$712$$ 0 0
$$713$$ 0.271550i 0.0101696i
$$714$$ 0 0
$$715$$ −0.508599 + 7.40275i −0.0190205 + 0.276847i
$$716$$ 0 0
$$717$$ 19.7255i 0.736663i
$$718$$ 0 0
$$719$$ −41.8431 −1.56049 −0.780243 0.625477i $$-0.784904\pi$$
−0.780243 + 0.625477i $$0.784904\pi$$
$$720$$ 0 0
$$721$$ −6.62747 −0.246820
$$722$$ 0 0
$$723$$ 19.6598i 0.731157i
$$724$$ 0 0
$$725$$ −12.7240 1.75668i −0.472559 0.0652413i
$$726$$ 0 0
$$727$$ 15.4317i 0.572330i −0.958180 0.286165i $$-0.907619\pi$$
0.958180 0.286165i $$-0.0923806\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 19.7645 0.731018
$$732$$ 0 0
$$733$$ 39.1794i 1.44712i 0.690260 + 0.723561i $$0.257496\pi$$
−0.690260 + 0.723561i $$0.742504\pi$$
$$734$$ 0 0
$$735$$ 1.03915 15.1250i 0.0383295 0.557893i
$$736$$ 0 0
$$737$$ 34.9708i 1.28817i
$$738$$ 0 0
$$739$$ −32.5361 −1.19686 −0.598430 0.801175i $$-0.704209\pi$$
−0.598430 + 0.801175i $$0.704209\pi$$
$$740$$ 0 0
$$741$$ −5.33709 −0.196063
$$742$$ 0 0
$$743$$ 8.13346i 0.298388i 0.988808 + 0.149194i $$0.0476679\pi$$
−0.988808 + 0.149194i $$0.952332\pi$$
$$744$$ 0 0
$$745$$ 13.2320 + 0.909092i 0.484783 + 0.0333065i
$$746$$ 0 0
$$747$$ 11.7546i 0.430078i
$$748$$ 0 0
$$749$$ 4.15550 0.151839
$$750$$ 0 0
$$751$$ −48.9359 −1.78570 −0.892848 0.450358i $$-0.851296\pi$$
−0.892848 + 0.450358i $$0.851296\pi$$
$$752$$ 0 0
$$753$$ 23.4175i 0.853382i
$$754$$ 0 0
$$755$$ −0.608605 0.0418136i −0.0221494 0.00152175i
$$756$$ 0 0
$$757$$ 3.54775i 0.128945i 0.997919 + 0.0644726i $$0.0205365\pi$$
−0.997919 + 0.0644726i $$0.979463\pi$$
$$758$$ 0 0
$$759$$ −1.46986 −0.0533525
$$760$$ 0 0
$$761$$ 40.8645 1.48134 0.740669 0.671870i $$-0.234509\pi$$
0.740669 + 0.671870i $$0.234509\pi$$
$$762$$ 0 0
$$763$$ 3.39630i 0.122954i
$$764$$ 0 0
$$765$$ −0.238644 + 3.47350i −0.00862818 + 0.125585i
$$766$$ 0 0
$$767$$ 13.1358i 0.474306i
$$768$$ 0 0
$$769$$ 42.6263 1.53714 0.768571 0.639764i $$-0.220968\pi$$
0.768571 + 0.639764i $$0.220968\pi$$
$$770$$ 0 0
$$771$$ 30.7987 1.10919
$$772$$ 0 0
$$773$$ 36.3873i 1.30876i 0.756166 + 0.654379i $$0.227070\pi$$
−0.756166 + 0.654379i $$0.772930\pi$$
$$774$$ 0 0
$$775$$ 3.03651 + 0.419220i 0.109075 + 0.0150588i
$$776$$ 0 0
$$777$$ 0.955216i 0.0342682i
$$778$$ 0 0
$$779$$ −56.6340 −2.02912
$$780$$ 0 0
$$781$$ 1.03483 0.0370291
$$782$$ 0 0
$$783$$ 2.56894i 0.0918066i
$$784$$ 0 0
$$785$$ 2.24628 32.6951i 0.0801733 1.16694i
$$786$$ 0 0
$$787$$ 12.7280i 0.453705i −0.973929 0.226853i $$-0.927156\pi$$
0.973929 0.226853i $$-0.0728436\pi$$
$$788$$ 0 0
$$789$$ 24.1471 0.859658
$$790$$ 0 0
$$791$$ −8.96059 −0.318602
$$792$$ 0 0
$$793$$ 5.27452i 0.187304i
$$794$$ 0 0
$$795$$ 12.0357 + 0.826900i 0.426862 + 0.0293271i
$$796$$ 0 0
$$797$$ 20.3707i 0.721566i −0.932650 0.360783i $$-0.882510\pi$$
0.932650 0.360783i $$-0.117490\pi$$
$$798$$ 0 0
$$799$$ −11.5914 −0.410074
$$800$$ 0 0
$$801$$ −4.58762