# Properties

 Label 1280.2.f.j.129.1 Level $1280$ Weight $2$ Character 1280.129 Analytic conductor $10.221$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1280.f (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.2208514587$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.350464.1 Defining polynomial: $$x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2$$ x^6 - 2*x^5 + 2*x^4 + 2*x^3 + 4*x^2 - 4*x + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: no (minimal twist has level 640) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 129.1 Root $$1.45161 - 1.45161i$$ of defining polynomial Character $$\chi$$ $$=$$ 1280.129 Dual form 1280.2.f.j.129.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.90321 q^{3} +(-2.21432 - 0.311108i) q^{5} +3.52543i q^{7} +5.42864 q^{9} +O(q^{10})$$ $$q-2.90321 q^{3} +(-2.21432 - 0.311108i) q^{5} +3.52543i q^{7} +5.42864 q^{9} -3.80642i q^{11} +2.62222 q^{13} +(6.42864 + 0.903212i) q^{15} -5.80642i q^{17} +5.05086i q^{19} -10.2351i q^{21} -0.474572i q^{23} +(4.80642 + 1.37778i) q^{25} -7.05086 q^{27} -2.00000i q^{29} -2.75557 q^{31} +11.0509i q^{33} +(1.09679 - 7.80642i) q^{35} +7.18421 q^{37} -7.61285 q^{39} -5.18421 q^{41} -1.95407 q^{43} +(-12.0207 - 1.68889i) q^{45} +5.33185i q^{47} -5.42864 q^{49} +16.8573i q^{51} -5.37778 q^{53} +(-1.18421 + 8.42864i) q^{55} -14.6637i q^{57} +5.05086i q^{59} +12.2351i q^{61} +19.1383i q^{63} +(-5.80642 - 0.815792i) q^{65} -7.76049 q^{67} +1.37778i q^{69} +4.85728 q^{71} +6.66370i q^{73} +(-13.9541 - 4.00000i) q^{75} +13.4193 q^{77} +5.24443 q^{79} +4.18421 q^{81} -12.1476 q^{83} +(-1.80642 + 12.8573i) q^{85} +5.80642i q^{87} -12.1017 q^{89} +9.24443i q^{91} +8.00000 q^{93} +(1.57136 - 11.1842i) q^{95} -13.8064i q^{97} -20.6637i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 4 q^{3} + 6 q^{9}+O(q^{10})$$ 6 * q - 4 * q^3 + 6 * q^9 $$6 q - 4 q^{3} + 6 q^{9} + 16 q^{13} + 12 q^{15} + 2 q^{25} - 16 q^{27} - 16 q^{31} + 20 q^{35} + 16 q^{37} + 8 q^{39} - 4 q^{41} + 28 q^{43} - 32 q^{45} - 6 q^{49} - 32 q^{53} + 20 q^{55} - 8 q^{65} + 20 q^{67} - 24 q^{71} - 44 q^{75} + 32 q^{79} - 2 q^{81} - 60 q^{83} + 16 q^{85} - 20 q^{89} + 48 q^{93} + 36 q^{95}+O(q^{100})$$ 6 * q - 4 * q^3 + 6 * q^9 + 16 * q^13 + 12 * q^15 + 2 * q^25 - 16 * q^27 - 16 * q^31 + 20 * q^35 + 16 * q^37 + 8 * q^39 - 4 * q^41 + 28 * q^43 - 32 * q^45 - 6 * q^49 - 32 * q^53 + 20 * q^55 - 8 * q^65 + 20 * q^67 - 24 * q^71 - 44 * q^75 + 32 * q^79 - 2 * q^81 - 60 * q^83 + 16 * q^85 - 20 * q^89 + 48 * q^93 + 36 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$261$$ $$511$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −2.90321 −1.67617 −0.838085 0.545540i $$-0.816325\pi$$
−0.838085 + 0.545540i $$0.816325\pi$$
$$4$$ 0 0
$$5$$ −2.21432 0.311108i −0.990274 0.139132i
$$6$$ 0 0
$$7$$ 3.52543i 1.33249i 0.745735 + 0.666243i $$0.232099\pi$$
−0.745735 + 0.666243i $$0.767901\pi$$
$$8$$ 0 0
$$9$$ 5.42864 1.80955
$$10$$ 0 0
$$11$$ 3.80642i 1.14768i −0.818967 0.573840i $$-0.805453\pi$$
0.818967 0.573840i $$-0.194547\pi$$
$$12$$ 0 0
$$13$$ 2.62222 0.727272 0.363636 0.931541i $$-0.381535\pi$$
0.363636 + 0.931541i $$0.381535\pi$$
$$14$$ 0 0
$$15$$ 6.42864 + 0.903212i 1.65987 + 0.233208i
$$16$$ 0 0
$$17$$ 5.80642i 1.40826i −0.710069 0.704132i $$-0.751336\pi$$
0.710069 0.704132i $$-0.248664\pi$$
$$18$$ 0 0
$$19$$ 5.05086i 1.15875i 0.815063 + 0.579373i $$0.196702\pi$$
−0.815063 + 0.579373i $$0.803298\pi$$
$$20$$ 0 0
$$21$$ 10.2351i 2.23347i
$$22$$ 0 0
$$23$$ 0.474572i 0.0989552i −0.998775 0.0494776i $$-0.984244\pi$$
0.998775 0.0494776i $$-0.0157556\pi$$
$$24$$ 0 0
$$25$$ 4.80642 + 1.37778i 0.961285 + 0.275557i
$$26$$ 0 0
$$27$$ −7.05086 −1.35694
$$28$$ 0 0
$$29$$ 2.00000i 0.371391i −0.982607 0.185695i $$-0.940546\pi$$
0.982607 0.185695i $$-0.0594537\pi$$
$$30$$ 0 0
$$31$$ −2.75557 −0.494915 −0.247457 0.968899i $$-0.579595\pi$$
−0.247457 + 0.968899i $$0.579595\pi$$
$$32$$ 0 0
$$33$$ 11.0509i 1.92371i
$$34$$ 0 0
$$35$$ 1.09679 7.80642i 0.185391 1.31953i
$$36$$ 0 0
$$37$$ 7.18421 1.18108 0.590538 0.807010i $$-0.298915\pi$$
0.590538 + 0.807010i $$0.298915\pi$$
$$38$$ 0 0
$$39$$ −7.61285 −1.21903
$$40$$ 0 0
$$41$$ −5.18421 −0.809637 −0.404819 0.914397i $$-0.632665\pi$$
−0.404819 + 0.914397i $$0.632665\pi$$
$$42$$ 0 0
$$43$$ −1.95407 −0.297992 −0.148996 0.988838i $$-0.547604\pi$$
−0.148996 + 0.988838i $$0.547604\pi$$
$$44$$ 0 0
$$45$$ −12.0207 1.68889i −1.79195 0.251765i
$$46$$ 0 0
$$47$$ 5.33185i 0.777730i 0.921295 + 0.388865i $$0.127133\pi$$
−0.921295 + 0.388865i $$0.872867\pi$$
$$48$$ 0 0
$$49$$ −5.42864 −0.775520
$$50$$ 0 0
$$51$$ 16.8573i 2.36049i
$$52$$ 0 0
$$53$$ −5.37778 −0.738695 −0.369348 0.929291i $$-0.620419\pi$$
−0.369348 + 0.929291i $$0.620419\pi$$
$$54$$ 0 0
$$55$$ −1.18421 + 8.42864i −0.159679 + 1.13652i
$$56$$ 0 0
$$57$$ 14.6637i 1.94225i
$$58$$ 0 0
$$59$$ 5.05086i 0.657565i 0.944406 + 0.328783i $$0.106638\pi$$
−0.944406 + 0.328783i $$0.893362\pi$$
$$60$$ 0 0
$$61$$ 12.2351i 1.56654i 0.621682 + 0.783270i $$0.286450\pi$$
−0.621682 + 0.783270i $$0.713550\pi$$
$$62$$ 0 0
$$63$$ 19.1383i 2.41120i
$$64$$ 0 0
$$65$$ −5.80642 0.815792i −0.720198 0.101187i
$$66$$ 0 0
$$67$$ −7.76049 −0.948095 −0.474047 0.880499i $$-0.657207\pi$$
−0.474047 + 0.880499i $$0.657207\pi$$
$$68$$ 0 0
$$69$$ 1.37778i 0.165866i
$$70$$ 0 0
$$71$$ 4.85728 0.576453 0.288226 0.957562i $$-0.406934\pi$$
0.288226 + 0.957562i $$0.406934\pi$$
$$72$$ 0 0
$$73$$ 6.66370i 0.779927i 0.920830 + 0.389964i $$0.127512\pi$$
−0.920830 + 0.389964i $$0.872488\pi$$
$$74$$ 0 0
$$75$$ −13.9541 4.00000i −1.61128 0.461880i
$$76$$ 0 0
$$77$$ 13.4193 1.52927
$$78$$ 0 0
$$79$$ 5.24443 0.590045 0.295022 0.955490i $$-0.404673\pi$$
0.295022 + 0.955490i $$0.404673\pi$$
$$80$$ 0 0
$$81$$ 4.18421 0.464912
$$82$$ 0 0
$$83$$ −12.1476 −1.33338 −0.666689 0.745336i $$-0.732289\pi$$
−0.666689 + 0.745336i $$0.732289\pi$$
$$84$$ 0 0
$$85$$ −1.80642 + 12.8573i −0.195934 + 1.39457i
$$86$$ 0 0
$$87$$ 5.80642i 0.622514i
$$88$$ 0 0
$$89$$ −12.1017 −1.28278 −0.641389 0.767216i $$-0.721642\pi$$
−0.641389 + 0.767216i $$0.721642\pi$$
$$90$$ 0 0
$$91$$ 9.24443i 0.969080i
$$92$$ 0 0
$$93$$ 8.00000 0.829561
$$94$$ 0 0
$$95$$ 1.57136 11.1842i 0.161218 1.14748i
$$96$$ 0 0
$$97$$ 13.8064i 1.40183i −0.713245 0.700915i $$-0.752775\pi$$
0.713245 0.700915i $$-0.247225\pi$$
$$98$$ 0 0
$$99$$ 20.6637i 2.07678i
$$100$$ 0 0
$$101$$ 19.7146i 1.96167i 0.194836 + 0.980836i $$0.437583\pi$$
−0.194836 + 0.980836i $$0.562417\pi$$
$$102$$ 0 0
$$103$$ 3.13828i 0.309223i 0.987975 + 0.154612i $$0.0494127\pi$$
−0.987975 + 0.154612i $$0.950587\pi$$
$$104$$ 0 0
$$105$$ −3.18421 + 22.6637i −0.310747 + 2.21175i
$$106$$ 0 0
$$107$$ 5.39207 0.521272 0.260636 0.965437i $$-0.416068\pi$$
0.260636 + 0.965437i $$0.416068\pi$$
$$108$$ 0 0
$$109$$ 8.62222i 0.825858i 0.910763 + 0.412929i $$0.135494\pi$$
−0.910763 + 0.412929i $$0.864506\pi$$
$$110$$ 0 0
$$111$$ −20.8573 −1.97969
$$112$$ 0 0
$$113$$ 5.51114i 0.518444i 0.965818 + 0.259222i $$0.0834662\pi$$
−0.965818 + 0.259222i $$0.916534\pi$$
$$114$$ 0 0
$$115$$ −0.147643 + 1.05086i −0.0137678 + 0.0979927i
$$116$$ 0 0
$$117$$ 14.2351 1.31603
$$118$$ 0 0
$$119$$ 20.4701 1.87649
$$120$$ 0 0
$$121$$ −3.48886 −0.317169
$$122$$ 0 0
$$123$$ 15.0509 1.35709
$$124$$ 0 0
$$125$$ −10.2143 4.54617i −0.913597 0.406622i
$$126$$ 0 0
$$127$$ 10.2810i 0.912291i −0.889905 0.456145i $$-0.849230\pi$$
0.889905 0.456145i $$-0.150770\pi$$
$$128$$ 0 0
$$129$$ 5.67307 0.499486
$$130$$ 0 0
$$131$$ 4.66370i 0.407470i −0.979026 0.203735i $$-0.934692\pi$$
0.979026 0.203735i $$-0.0653080\pi$$
$$132$$ 0 0
$$133$$ −17.8064 −1.54401
$$134$$ 0 0
$$135$$ 15.6128 + 2.19358i 1.34374 + 0.188793i
$$136$$ 0 0
$$137$$ 11.3461i 0.969366i 0.874690 + 0.484683i $$0.161065\pi$$
−0.874690 + 0.484683i $$0.838935\pi$$
$$138$$ 0 0
$$139$$ 11.8064i 1.00141i −0.865619 0.500704i $$-0.833075\pi$$
0.865619 0.500704i $$-0.166925\pi$$
$$140$$ 0 0
$$141$$ 15.4795i 1.30361i
$$142$$ 0 0
$$143$$ 9.98126i 0.834675i
$$144$$ 0 0
$$145$$ −0.622216 + 4.42864i −0.0516722 + 0.367778i
$$146$$ 0 0
$$147$$ 15.7605 1.29990
$$148$$ 0 0
$$149$$ 5.47949i 0.448898i 0.974486 + 0.224449i $$0.0720582\pi$$
−0.974486 + 0.224449i $$0.927942\pi$$
$$150$$ 0 0
$$151$$ −23.6128 −1.92159 −0.960793 0.277266i $$-0.910572\pi$$
−0.960793 + 0.277266i $$0.910572\pi$$
$$152$$ 0 0
$$153$$ 31.5210i 2.54832i
$$154$$ 0 0
$$155$$ 6.10171 + 0.857279i 0.490101 + 0.0688583i
$$156$$ 0 0
$$157$$ −0.815792 −0.0651073 −0.0325536 0.999470i $$-0.510364\pi$$
−0.0325536 + 0.999470i $$0.510364\pi$$
$$158$$ 0 0
$$159$$ 15.6128 1.23818
$$160$$ 0 0
$$161$$ 1.67307 0.131856
$$162$$ 0 0
$$163$$ −10.9032 −0.854005 −0.427003 0.904250i $$-0.640431\pi$$
−0.427003 + 0.904250i $$0.640431\pi$$
$$164$$ 0 0
$$165$$ 3.43801 24.4701i 0.267649 1.90500i
$$166$$ 0 0
$$167$$ 6.57628i 0.508888i −0.967088 0.254444i $$-0.918108\pi$$
0.967088 0.254444i $$-0.0818925\pi$$
$$168$$ 0 0
$$169$$ −6.12399 −0.471076
$$170$$ 0 0
$$171$$ 27.4193i 2.09680i
$$172$$ 0 0
$$173$$ −10.5303 −0.800608 −0.400304 0.916382i $$-0.631095\pi$$
−0.400304 + 0.916382i $$0.631095\pi$$
$$174$$ 0 0
$$175$$ −4.85728 + 16.9447i −0.367176 + 1.28090i
$$176$$ 0 0
$$177$$ 14.6637i 1.10219i
$$178$$ 0 0
$$179$$ 6.29529i 0.470532i −0.971931 0.235266i $$-0.924404\pi$$
0.971931 0.235266i $$-0.0755961\pi$$
$$180$$ 0 0
$$181$$ 0.488863i 0.0363369i −0.999835 0.0181684i $$-0.994216\pi$$
0.999835 0.0181684i $$-0.00578351\pi$$
$$182$$ 0 0
$$183$$ 35.5210i 2.62579i
$$184$$ 0 0
$$185$$ −15.9081 2.23506i −1.16959 0.164325i
$$186$$ 0 0
$$187$$ −22.1017 −1.61624
$$188$$ 0 0
$$189$$ 24.8573i 1.80810i
$$190$$ 0 0
$$191$$ −10.4889 −0.758947 −0.379474 0.925203i $$-0.623895\pi$$
−0.379474 + 0.925203i $$0.623895\pi$$
$$192$$ 0 0
$$193$$ 13.8064i 0.993808i 0.867805 + 0.496904i $$0.165530\pi$$
−0.867805 + 0.496904i $$0.834470\pi$$
$$194$$ 0 0
$$195$$ 16.8573 + 2.36842i 1.20717 + 0.169606i
$$196$$ 0 0
$$197$$ 16.7239 1.19153 0.595765 0.803159i $$-0.296849\pi$$
0.595765 + 0.803159i $$0.296849\pi$$
$$198$$ 0 0
$$199$$ 20.8573 1.47853 0.739267 0.673413i $$-0.235172\pi$$
0.739267 + 0.673413i $$0.235172\pi$$
$$200$$ 0 0
$$201$$ 22.5303 1.58917
$$202$$ 0 0
$$203$$ 7.05086 0.494873
$$204$$ 0 0
$$205$$ 11.4795 + 1.61285i 0.801763 + 0.112646i
$$206$$ 0 0
$$207$$ 2.57628i 0.179064i
$$208$$ 0 0
$$209$$ 19.2257 1.32987
$$210$$ 0 0
$$211$$ 4.66370i 0.321063i −0.987031 0.160531i $$-0.948679\pi$$
0.987031 0.160531i $$-0.0513207\pi$$
$$212$$ 0 0
$$213$$ −14.1017 −0.966233
$$214$$ 0 0
$$215$$ 4.32693 + 0.607926i 0.295094 + 0.0414602i
$$216$$ 0 0
$$217$$ 9.71456i 0.659467i
$$218$$ 0 0
$$219$$ 19.3461i 1.30729i
$$220$$ 0 0
$$221$$ 15.2257i 1.02419i
$$222$$ 0 0
$$223$$ 26.4558i 1.77161i 0.464054 + 0.885807i $$0.346394\pi$$
−0.464054 + 0.885807i $$0.653606\pi$$
$$224$$ 0 0
$$225$$ 26.0923 + 7.47949i 1.73949 + 0.498633i
$$226$$ 0 0
$$227$$ 12.3225 0.817872 0.408936 0.912563i $$-0.365900\pi$$
0.408936 + 0.912563i $$0.365900\pi$$
$$228$$ 0 0
$$229$$ 13.2257i 0.873979i −0.899467 0.436989i $$-0.856045\pi$$
0.899467 0.436989i $$-0.143955\pi$$
$$230$$ 0 0
$$231$$ −38.9590 −2.56331
$$232$$ 0 0
$$233$$ 6.66370i 0.436554i 0.975887 + 0.218277i $$0.0700436\pi$$
−0.975887 + 0.218277i $$0.929956\pi$$
$$234$$ 0 0
$$235$$ 1.65878 11.8064i 0.108207 0.770166i
$$236$$ 0 0
$$237$$ −15.2257 −0.989015
$$238$$ 0 0
$$239$$ −22.9590 −1.48509 −0.742547 0.669794i $$-0.766382\pi$$
−0.742547 + 0.669794i $$0.766382\pi$$
$$240$$ 0 0
$$241$$ −14.0415 −0.904492 −0.452246 0.891893i $$-0.649377\pi$$
−0.452246 + 0.891893i $$0.649377\pi$$
$$242$$ 0 0
$$243$$ 9.00492 0.577666
$$244$$ 0 0
$$245$$ 12.0207 + 1.68889i 0.767977 + 0.107899i
$$246$$ 0 0
$$247$$ 13.2444i 0.842723i
$$248$$ 0 0
$$249$$ 35.2672 2.23497
$$250$$ 0 0
$$251$$ 24.9304i 1.57359i 0.617212 + 0.786797i $$0.288262\pi$$
−0.617212 + 0.786797i $$0.711738\pi$$
$$252$$ 0 0
$$253$$ −1.80642 −0.113569
$$254$$ 0 0
$$255$$ 5.24443 37.3274i 0.328419 2.33753i
$$256$$ 0 0
$$257$$ 25.7146i 1.60403i 0.597304 + 0.802015i $$0.296239\pi$$
−0.597304 + 0.802015i $$0.703761\pi$$
$$258$$ 0 0
$$259$$ 25.3274i 1.57377i
$$260$$ 0 0
$$261$$ 10.8573i 0.672049i
$$262$$ 0 0
$$263$$ 2.57628i 0.158860i −0.996840 0.0794302i $$-0.974690\pi$$
0.996840 0.0794302i $$-0.0253101\pi$$
$$264$$ 0 0
$$265$$ 11.9081 + 1.67307i 0.731511 + 0.102776i
$$266$$ 0 0
$$267$$ 35.1338 2.15016
$$268$$ 0 0
$$269$$ 25.7462i 1.56977i 0.619639 + 0.784887i $$0.287279\pi$$
−0.619639 + 0.784887i $$0.712721\pi$$
$$270$$ 0 0
$$271$$ 30.1847 1.83359 0.916795 0.399359i $$-0.130767\pi$$
0.916795 + 0.399359i $$0.130767\pi$$
$$272$$ 0 0
$$273$$ 26.8385i 1.62434i
$$274$$ 0 0
$$275$$ 5.24443 18.2953i 0.316251 1.10325i
$$276$$ 0 0
$$277$$ −10.5303 −0.632707 −0.316354 0.948641i $$-0.602459\pi$$
−0.316354 + 0.948641i $$0.602459\pi$$
$$278$$ 0 0
$$279$$ −14.9590 −0.895571
$$280$$ 0 0
$$281$$ 7.93978 0.473647 0.236824 0.971553i $$-0.423894\pi$$
0.236824 + 0.971553i $$0.423894\pi$$
$$282$$ 0 0
$$283$$ 10.9032 0.648129 0.324064 0.946035i $$-0.394951\pi$$
0.324064 + 0.946035i $$0.394951\pi$$
$$284$$ 0 0
$$285$$ −4.56199 + 32.4701i −0.270229 + 1.92336i
$$286$$ 0 0
$$287$$ 18.2766i 1.07883i
$$288$$ 0 0
$$289$$ −16.7146 −0.983209
$$290$$ 0 0
$$291$$ 40.0830i 2.34971i
$$292$$ 0 0
$$293$$ −4.42864 −0.258724 −0.129362 0.991597i $$-0.541293\pi$$
−0.129362 + 0.991597i $$0.541293\pi$$
$$294$$ 0 0
$$295$$ 1.57136 11.1842i 0.0914881 0.651170i
$$296$$ 0 0
$$297$$ 26.8385i 1.55733i
$$298$$ 0 0
$$299$$ 1.24443i 0.0719673i
$$300$$ 0 0
$$301$$ 6.88892i 0.397071i
$$302$$ 0 0
$$303$$ 57.2355i 3.28810i
$$304$$ 0 0
$$305$$ 3.80642 27.0923i 0.217955 1.55130i
$$306$$ 0 0
$$307$$ −5.27163 −0.300868 −0.150434 0.988620i $$-0.548067\pi$$
−0.150434 + 0.988620i $$0.548067\pi$$
$$308$$ 0 0
$$309$$ 9.11108i 0.518311i
$$310$$ 0 0
$$311$$ −0.387152 −0.0219534 −0.0109767 0.999940i $$-0.503494\pi$$
−0.0109767 + 0.999940i $$0.503494\pi$$
$$312$$ 0 0
$$313$$ 11.3461i 0.641322i −0.947194 0.320661i $$-0.896095\pi$$
0.947194 0.320661i $$-0.103905\pi$$
$$314$$ 0 0
$$315$$ 5.95407 42.3783i 0.335474 2.38774i
$$316$$ 0 0
$$317$$ 16.7239 0.939309 0.469655 0.882850i $$-0.344378\pi$$
0.469655 + 0.882850i $$0.344378\pi$$
$$318$$ 0 0
$$319$$ −7.61285 −0.426238
$$320$$ 0 0
$$321$$ −15.6543 −0.873740
$$322$$ 0 0
$$323$$ 29.3274 1.63182
$$324$$ 0 0
$$325$$ 12.6035 + 3.61285i 0.699115 + 0.200405i
$$326$$ 0 0
$$327$$ 25.0321i 1.38428i
$$328$$ 0 0
$$329$$ −18.7971 −1.03632
$$330$$ 0 0
$$331$$ 3.33630i 0.183379i 0.995788 + 0.0916897i $$0.0292268\pi$$
−0.995788 + 0.0916897i $$0.970773\pi$$
$$332$$ 0 0
$$333$$ 39.0005 2.13721
$$334$$ 0 0
$$335$$ 17.1842 + 2.41435i 0.938874 + 0.131910i
$$336$$ 0 0
$$337$$ 3.61285i 0.196804i 0.995147 + 0.0984022i $$0.0313732\pi$$
−0.995147 + 0.0984022i $$0.968627\pi$$
$$338$$ 0 0
$$339$$ 16.0000i 0.869001i
$$340$$ 0 0
$$341$$ 10.4889i 0.568004i
$$342$$ 0 0
$$343$$ 5.53972i 0.299117i
$$344$$ 0 0
$$345$$ 0.428639 3.05086i 0.0230772 0.164253i
$$346$$ 0 0
$$347$$ 15.7605 0.846067 0.423034 0.906114i $$-0.360965\pi$$
0.423034 + 0.906114i $$0.360965\pi$$
$$348$$ 0 0
$$349$$ 0.285442i 0.0152794i −0.999971 0.00763968i $$-0.997568\pi$$
0.999971 0.00763968i $$-0.00243181\pi$$
$$350$$ 0 0
$$351$$ −18.4889 −0.986862
$$352$$ 0 0
$$353$$ 4.38715i 0.233505i −0.993161 0.116752i $$-0.962752\pi$$
0.993161 0.116752i $$-0.0372484\pi$$
$$354$$ 0 0
$$355$$ −10.7556 1.51114i −0.570846 0.0802028i
$$356$$ 0 0
$$357$$ −59.4291 −3.14532
$$358$$ 0 0
$$359$$ −20.5906 −1.08673 −0.543364 0.839497i $$-0.682850\pi$$
−0.543364 + 0.839497i $$0.682850\pi$$
$$360$$ 0 0
$$361$$ −6.51114 −0.342691
$$362$$ 0 0
$$363$$ 10.1289 0.531630
$$364$$ 0 0
$$365$$ 2.07313 14.7556i 0.108513 0.772342i
$$366$$ 0 0
$$367$$ 16.5575i 0.864297i 0.901802 + 0.432148i $$0.142244\pi$$
−0.901802 + 0.432148i $$0.857756\pi$$
$$368$$ 0 0
$$369$$ −28.1432 −1.46508
$$370$$ 0 0
$$371$$ 18.9590i 0.984302i
$$372$$ 0 0
$$373$$ 24.8988 1.28921 0.644605 0.764516i $$-0.277022\pi$$
0.644605 + 0.764516i $$0.277022\pi$$
$$374$$ 0 0
$$375$$ 29.6543 + 13.1985i 1.53134 + 0.681568i
$$376$$ 0 0
$$377$$ 5.24443i 0.270102i
$$378$$ 0 0
$$379$$ 9.31756i 0.478611i −0.970944 0.239305i $$-0.923080\pi$$
0.970944 0.239305i $$-0.0769197\pi$$
$$380$$ 0 0
$$381$$ 29.8479i 1.52915i
$$382$$ 0 0
$$383$$ 32.5575i 1.66361i 0.555066 + 0.831806i $$0.312693\pi$$
−0.555066 + 0.831806i $$0.687307\pi$$
$$384$$ 0 0
$$385$$ −29.7146 4.17484i −1.51439 0.212770i
$$386$$ 0 0
$$387$$ −10.6079 −0.539231
$$388$$ 0 0
$$389$$ 18.9906i 0.962863i 0.876484 + 0.481432i $$0.159883\pi$$
−0.876484 + 0.481432i $$0.840117\pi$$
$$390$$ 0 0
$$391$$ −2.75557 −0.139355
$$392$$ 0 0
$$393$$ 13.5397i 0.682988i
$$394$$ 0 0
$$395$$ −11.6128 1.63158i −0.584306 0.0820939i
$$396$$ 0 0
$$397$$ −32.9906 −1.65575 −0.827876 0.560911i $$-0.810451\pi$$
−0.827876 + 0.560911i $$0.810451\pi$$
$$398$$ 0 0
$$399$$ 51.6958 2.58803
$$400$$ 0 0
$$401$$ −16.1017 −0.804081 −0.402041 0.915622i $$-0.631699\pi$$
−0.402041 + 0.915622i $$0.631699\pi$$
$$402$$ 0 0
$$403$$ −7.22570 −0.359938
$$404$$ 0 0
$$405$$ −9.26517 1.30174i −0.460390 0.0646840i
$$406$$ 0 0
$$407$$ 27.3461i 1.35550i
$$408$$ 0 0
$$409$$ −33.3876 −1.65091 −0.825456 0.564466i $$-0.809082\pi$$
−0.825456 + 0.564466i $$0.809082\pi$$
$$410$$ 0 0
$$411$$ 32.9403i 1.62482i
$$412$$ 0 0
$$413$$ −17.8064 −0.876197
$$414$$ 0 0
$$415$$ 26.8988 + 3.77923i 1.32041 + 0.185515i
$$416$$ 0 0
$$417$$ 34.2766i 1.67853i
$$418$$ 0 0
$$419$$ 27.4193i 1.33952i 0.742578 + 0.669760i $$0.233603\pi$$
−0.742578 + 0.669760i $$0.766397\pi$$
$$420$$ 0 0
$$421$$ 12.2351i 0.596301i −0.954519 0.298150i $$-0.903630\pi$$
0.954519 0.298150i $$-0.0963696\pi$$
$$422$$ 0 0
$$423$$ 28.9447i 1.40734i
$$424$$ 0 0
$$425$$ 8.00000 27.9081i 0.388057 1.35374i
$$426$$ 0 0
$$427$$ −43.1338 −2.08739
$$428$$ 0 0
$$429$$ 28.9777i 1.39906i
$$430$$ 0 0
$$431$$ −28.4701 −1.37136 −0.685679 0.727904i $$-0.740495\pi$$
−0.685679 + 0.727904i $$0.740495\pi$$
$$432$$ 0 0
$$433$$ 34.0098i 1.63441i 0.576348 + 0.817204i $$0.304477\pi$$
−0.576348 + 0.817204i $$0.695523\pi$$
$$434$$ 0 0
$$435$$ 1.80642 12.8573i 0.0866114 0.616459i
$$436$$ 0 0
$$437$$ 2.39700 0.114664
$$438$$ 0 0
$$439$$ −14.8385 −0.708205 −0.354103 0.935207i $$-0.615214\pi$$
−0.354103 + 0.935207i $$0.615214\pi$$
$$440$$ 0 0
$$441$$ −29.4701 −1.40334
$$442$$ 0 0
$$443$$ −13.0968 −0.622247 −0.311124 0.950369i $$-0.600705\pi$$
−0.311124 + 0.950369i $$0.600705\pi$$
$$444$$ 0 0
$$445$$ 26.7971 + 3.76494i 1.27030 + 0.178475i
$$446$$ 0 0
$$447$$ 15.9081i 0.752429i
$$448$$ 0 0
$$449$$ 21.3876 1.00934 0.504672 0.863311i $$-0.331613\pi$$
0.504672 + 0.863311i $$0.331613\pi$$
$$450$$ 0 0
$$451$$ 19.7333i 0.929205i
$$452$$ 0 0
$$453$$ 68.5531 3.22091
$$454$$ 0 0
$$455$$ 2.87601 20.4701i 0.134830 0.959654i
$$456$$ 0 0
$$457$$ 17.9813i 0.841128i 0.907263 + 0.420564i $$0.138168\pi$$
−0.907263 + 0.420564i $$0.861832\pi$$
$$458$$ 0 0
$$459$$ 40.9403i 1.91093i
$$460$$ 0 0
$$461$$ 10.7368i 0.500064i 0.968238 + 0.250032i $$0.0804412\pi$$
−0.968238 + 0.250032i $$0.919559\pi$$
$$462$$ 0 0
$$463$$ 9.30327i 0.432360i −0.976354 0.216180i $$-0.930640\pi$$
0.976354 0.216180i $$-0.0693598\pi$$
$$464$$ 0 0
$$465$$ −17.7146 2.48886i −0.821493 0.115418i
$$466$$ 0 0
$$467$$ 8.70964 0.403034 0.201517 0.979485i $$-0.435413\pi$$
0.201517 + 0.979485i $$0.435413\pi$$
$$468$$ 0 0
$$469$$ 27.3590i 1.26332i
$$470$$ 0 0
$$471$$ 2.36842 0.109131
$$472$$ 0 0
$$473$$ 7.43801i 0.342000i
$$474$$ 0 0
$$475$$ −6.95899 + 24.2766i −0.319300 + 1.11388i
$$476$$ 0 0
$$477$$ −29.1941 −1.33670
$$478$$ 0 0
$$479$$ −23.2257 −1.06121 −0.530605 0.847619i $$-0.678035\pi$$
−0.530605 + 0.847619i $$0.678035\pi$$
$$480$$ 0 0
$$481$$ 18.8385 0.858964
$$482$$ 0 0
$$483$$ −4.85728 −0.221014
$$484$$ 0 0
$$485$$ −4.29529 + 30.5718i −0.195039 + 1.38820i
$$486$$ 0 0
$$487$$ 32.8528i 1.48870i 0.667787 + 0.744352i $$0.267241\pi$$
−0.667787 + 0.744352i $$0.732759\pi$$
$$488$$ 0 0
$$489$$ 31.6543 1.43146
$$490$$ 0 0
$$491$$ 2.94914i 0.133093i −0.997783 0.0665465i $$-0.978802\pi$$
0.997783 0.0665465i $$-0.0211981\pi$$
$$492$$ 0 0
$$493$$ −11.6128 −0.523016
$$494$$ 0 0
$$495$$ −6.42864 + 45.7560i −0.288946 + 2.05658i
$$496$$ 0 0
$$497$$ 17.1240i 0.768116i
$$498$$ 0 0
$$499$$ 35.0321i 1.56825i −0.620601 0.784127i $$-0.713111\pi$$
0.620601 0.784127i $$-0.286889\pi$$
$$500$$ 0 0
$$501$$ 19.0923i 0.852983i
$$502$$ 0 0
$$503$$ 16.2908i 0.726373i −0.931717 0.363186i $$-0.881689\pi$$
0.931717 0.363186i $$-0.118311\pi$$
$$504$$ 0 0
$$505$$ 6.13335 43.6543i 0.272931 1.94259i
$$506$$ 0 0
$$507$$ 17.7792 0.789603
$$508$$ 0 0
$$509$$ 26.0000i 1.15243i −0.817298 0.576215i $$-0.804529\pi$$
0.817298 0.576215i $$-0.195471\pi$$
$$510$$ 0 0
$$511$$ −23.4924 −1.03924
$$512$$ 0 0
$$513$$ 35.6128i 1.57235i
$$514$$ 0 0
$$515$$ 0.976342 6.94914i 0.0430228 0.306216i
$$516$$ 0 0
$$517$$ 20.2953 0.892586
$$518$$ 0 0
$$519$$ 30.5718 1.34195
$$520$$ 0 0
$$521$$ −11.7146 −0.513224 −0.256612 0.966514i $$-0.582606\pi$$
−0.256612 + 0.966514i $$0.582606\pi$$
$$522$$ 0 0
$$523$$ −38.0370 −1.66324 −0.831622 0.555342i $$-0.812587\pi$$
−0.831622 + 0.555342i $$0.812587\pi$$
$$524$$ 0 0
$$525$$ 14.1017 49.1941i 0.615449 2.14700i
$$526$$ 0 0
$$527$$ 16.0000i 0.696971i
$$528$$ 0 0
$$529$$ 22.7748 0.990208
$$530$$ 0 0
$$531$$ 27.4193i 1.18990i
$$532$$ 0 0
$$533$$ −13.5941 −0.588826
$$534$$ 0 0
$$535$$ −11.9398 1.67752i −0.516202 0.0725254i
$$536$$ 0 0
$$537$$ 18.2766i 0.788691i
$$538$$ 0 0
$$539$$ 20.6637i 0.890049i
$$540$$ 0 0
$$541$$ 11.5111i 0.494902i 0.968900 + 0.247451i $$0.0795930\pi$$
−0.968900 + 0.247451i $$0.920407\pi$$
$$542$$ 0 0
$$543$$ 1.41927i 0.0609068i
$$544$$ 0 0
$$545$$ 2.68244 19.0923i 0.114903 0.817826i
$$546$$ 0 0
$$547$$ 30.2208 1.29215 0.646073 0.763275i $$-0.276410\pi$$
0.646073 + 0.763275i $$0.276410\pi$$
$$548$$ 0 0
$$549$$ 66.4197i 2.83473i
$$550$$ 0 0
$$551$$ 10.1017 0.430347
$$552$$ 0 0
$$553$$ 18.4889i 0.786226i
$$554$$ 0 0
$$555$$ 46.1847 + 6.48886i 1.96043 + 0.275437i
$$556$$ 0 0
$$557$$ −9.75605 −0.413377 −0.206688 0.978407i $$-0.566269\pi$$
−0.206688 + 0.978407i $$0.566269\pi$$
$$558$$ 0 0
$$559$$ −5.12399 −0.216721
$$560$$ 0 0
$$561$$ 64.1659 2.70909
$$562$$ 0 0
$$563$$ 4.50622 0.189914 0.0949572 0.995481i $$-0.469729\pi$$
0.0949572 + 0.995481i $$0.469729\pi$$
$$564$$ 0 0
$$565$$ 1.71456 12.2034i 0.0721320 0.513402i
$$566$$ 0 0
$$567$$ 14.7511i 0.619489i
$$568$$ 0 0
$$569$$ 5.30465 0.222383 0.111191 0.993799i $$-0.464533\pi$$
0.111191 + 0.993799i $$0.464533\pi$$
$$570$$ 0 0
$$571$$ 16.3970i 0.686193i 0.939300 + 0.343096i $$0.111476\pi$$
−0.939300 + 0.343096i $$0.888524\pi$$
$$572$$ 0 0
$$573$$ 30.4514 1.27213
$$574$$ 0 0
$$575$$ 0.653858 2.28100i 0.0272678 0.0951241i
$$576$$ 0 0
$$577$$ 39.8163i 1.65757i −0.559565 0.828786i $$-0.689032\pi$$
0.559565 0.828786i $$-0.310968\pi$$
$$578$$ 0 0
$$579$$ 40.0830i 1.66579i
$$580$$ 0 0
$$581$$ 42.8256i 1.77671i
$$582$$ 0 0
$$583$$ 20.4701i 0.847786i
$$584$$ 0 0
$$585$$ −31.5210 4.42864i −1.30323 0.183102i
$$586$$ 0 0
$$587$$ 15.1699 0.626130 0.313065 0.949732i $$-0.398644\pi$$
0.313065 + 0.949732i $$0.398644\pi$$
$$588$$ 0 0
$$589$$ 13.9180i 0.573480i
$$590$$ 0 0
$$591$$ −48.5531 −1.99721
$$592$$ 0 0
$$593$$ 8.00000i 0.328521i −0.986417 0.164260i $$-0.947476\pi$$
0.986417 0.164260i $$-0.0525237\pi$$
$$594$$ 0 0
$$595$$ −45.3274 6.36842i −1.85824 0.261080i
$$596$$ 0 0
$$597$$ −60.5531 −2.47827
$$598$$ 0 0
$$599$$ 1.83500 0.0749762 0.0374881 0.999297i $$-0.488064\pi$$
0.0374881 + 0.999297i $$0.488064\pi$$
$$600$$ 0 0
$$601$$ 36.1432 1.47431 0.737156 0.675723i $$-0.236168\pi$$
0.737156 + 0.675723i $$0.236168\pi$$
$$602$$ 0 0
$$603$$ −42.1289 −1.71562
$$604$$ 0 0
$$605$$ 7.72546 + 1.08541i 0.314084 + 0.0441283i
$$606$$ 0 0
$$607$$ 17.5353i 0.711735i 0.934536 + 0.355867i $$0.115815\pi$$
−0.934536 + 0.355867i $$0.884185\pi$$
$$608$$ 0 0
$$609$$ −20.4701 −0.829491
$$610$$ 0 0
$$611$$ 13.9813i 0.565621i
$$612$$ 0 0
$$613$$ −33.9309 −1.37046 −0.685228 0.728329i $$-0.740297\pi$$
−0.685228 + 0.728329i $$0.740297\pi$$
$$614$$ 0 0
$$615$$ −33.3274 4.68244i −1.34389 0.188814i
$$616$$ 0 0
$$617$$ 9.68598i 0.389943i −0.980809 0.194971i $$-0.937539\pi$$
0.980809 0.194971i $$-0.0624614\pi$$
$$618$$ 0 0
$$619$$ 41.4005i 1.66403i −0.554755 0.832014i $$-0.687188\pi$$
0.554755 0.832014i $$-0.312812\pi$$
$$620$$ 0 0
$$621$$ 3.34614i 0.134276i
$$622$$ 0 0
$$623$$ 42.6637i 1.70929i
$$624$$ 0 0
$$625$$ 21.2034 + 13.2444i 0.848137 + 0.529777i
$$626$$ 0 0
$$627$$ −55.8163 −2.22909
$$628$$ 0 0
$$629$$ 41.7146i 1.66327i
$$630$$ 0 0
$$631$$ 27.8163 1.10735 0.553674 0.832733i $$-0.313225\pi$$
0.553674 + 0.832733i $$0.313225\pi$$
$$632$$ 0 0
$$633$$ 13.5397i 0.538155i
$$634$$ 0 0
$$635$$ −3.19850 + 22.7654i −0.126929 + 0.903418i
$$636$$ 0 0
$$637$$ −14.2351 −0.564014
$$638$$ 0 0
$$639$$ 26.3684 1.04312
$$640$$ 0 0
$$641$$ 42.8988 1.69440 0.847200 0.531275i $$-0.178287\pi$$
0.847200 + 0.531275i $$0.178287\pi$$
$$642$$ 0 0
$$643$$ −27.9639 −1.10279 −0.551395 0.834245i $$-0.685904\pi$$
−0.551395 + 0.834245i $$0.685904\pi$$
$$644$$ 0 0
$$645$$ −12.5620 1.76494i −0.494628 0.0694943i
$$646$$ 0 0
$$647$$ 7.13828i 0.280635i 0.990107 + 0.140317i $$0.0448123\pi$$
−0.990107 + 0.140317i $$0.955188\pi$$
$$648$$ 0 0
$$649$$ 19.2257 0.754675
$$650$$ 0 0
$$651$$ 28.2034i 1.10538i
$$652$$ 0 0
$$653$$ −17.7649 −0.695196 −0.347598 0.937644i $$-0.613003\pi$$
−0.347598 + 0.937644i $$0.613003\pi$$
$$654$$ 0 0
$$655$$ −1.45091 + 10.3269i −0.0566919 + 0.403507i
$$656$$ 0 0
$$657$$ 36.1748i 1.41131i
$$658$$ 0 0
$$659$$ 20.1936i 0.786630i 0.919404 + 0.393315i $$0.128672\pi$$
−0.919404 + 0.393315i $$0.871328\pi$$
$$660$$ 0 0
$$661$$ 22.0701i 0.858426i 0.903203 + 0.429213i $$0.141209\pi$$
−0.903203 + 0.429213i $$0.858791\pi$$
$$662$$ 0 0
$$663$$ 44.2034i 1.71672i
$$664$$ 0 0
$$665$$ 39.4291 + 5.53972i 1.52900 + 0.214821i
$$666$$ 0 0
$$667$$ −0.949145 −0.0367510
$$668$$ 0 0
$$669$$ 76.8069i 2.96953i
$$670$$ 0 0
$$671$$ 46.5718 1.79789
$$672$$ 0 0
$$673$$ 26.0098i 1.00261i −0.865272 0.501303i $$-0.832854\pi$$
0.865272 0.501303i $$-0.167146\pi$$
$$674$$ 0 0
$$675$$ −33.8894 9.71456i −1.30440 0.373914i
$$676$$ 0 0
$$677$$ −7.86665 −0.302340 −0.151170 0.988508i $$-0.548304\pi$$
−0.151170 + 0.988508i $$0.548304\pi$$
$$678$$ 0 0
$$679$$ 48.6735 1.86792
$$680$$ 0 0
$$681$$ −35.7748 −1.37089
$$682$$ 0 0
$$683$$ 18.2494 0.698292 0.349146 0.937068i $$-0.386472\pi$$
0.349146 + 0.937068i $$0.386472\pi$$
$$684$$ 0 0
$$685$$ 3.52987 25.1240i 0.134870 0.959938i
$$686$$ 0 0
$$687$$ 38.3970i 1.46494i
$$688$$ 0 0
$$689$$ −14.1017 −0.537232
$$690$$ 0 0
$$691$$ 25.2543i 0.960718i 0.877072 + 0.480359i $$0.159494\pi$$
−0.877072 + 0.480359i $$0.840506\pi$$
$$692$$ 0 0
$$693$$ 72.8484 2.76728
$$694$$ 0 0
$$695$$ −3.67307 + 26.1432i −0.139328 + 0.991668i
$$696$$ 0 0
$$697$$ 30.1017i 1.14018i
$$698$$ 0 0
$$699$$ 19.3461i 0.731738i
$$700$$ 0 0
$$701$$ 34.8069i 1.31464i −0.753612 0.657319i $$-0.771690\pi$$
0.753612 0.657319i $$-0.228310\pi$$
$$702$$ 0 0
$$703$$ 36.2864i 1.36857i
$$704$$ 0 0
$$705$$ −4.81579 + 34.2766i −0.181373 + 1.29093i
$$706$$ 0 0
$$707$$ −69.5022 −2.61390
$$708$$ 0 0
$$709$$ 7.51114i 0.282087i 0.990003 + 0.141043i $$0.0450457\pi$$
−0.990003 + 0.141043i $$0.954954\pi$$
$$710$$ 0 0
$$711$$ 28.4701 1.06771
$$712$$ 0 0
$$713$$ 1.30772i 0.0489744i
$$714$$ 0 0
$$715$$ −3.10525 + 22.1017i −0.116130 + 0.826557i
$$716$$ 0 0
$$717$$ 66.6548 2.48927
$$718$$ 0 0
$$719$$ −26.7556 −0.997814 −0.498907 0.866655i $$-0.666265\pi$$
−0.498907 + 0.866655i $$0.666265\pi$$
$$720$$ 0 0
$$721$$ −11.0638 −0.412036
$$722$$ 0 0
$$723$$ 40.7654 1.51608
$$724$$ 0 0
$$725$$ 2.75557 9.61285i 0.102339 0.357012i
$$726$$ 0 0
$$727$$ 25.6271i 0.950458i 0.879862 + 0.475229i $$0.157635\pi$$
−0.879862 + 0.475229i $$0.842365\pi$$
$$728$$ 0 0
$$729$$ −38.6958 −1.43318
$$730$$ 0 0
$$731$$ 11.3461i 0.419652i
$$732$$ 0 0
$$733$$ −19.6543 −0.725949 −0.362975 0.931799i $$-0.618239\pi$$
−0.362975 + 0.931799i $$0.618239\pi$$
$$734$$ 0 0
$$735$$ −34.8988 4.90321i −1.28726 0.180858i
$$736$$ 0 0
$$737$$ 29.5397i 1.08811i
$$738$$ 0 0
$$739$$ 32.5433i 1.19712i −0.801077 0.598562i $$-0.795739\pi$$
0.801077 0.598562i $$-0.204261\pi$$
$$740$$ 0 0
$$741$$ 38.4514i 1.41255i
$$742$$ 0 0
$$743$$ 23.1383i 0.848861i 0.905461 + 0.424430i $$0.139526\pi$$
−0.905461 + 0.424430i $$0.860474\pi$$
$$744$$ 0 0
$$745$$ 1.70471 12.1334i 0.0624559 0.444532i
$$746$$ 0 0
$$747$$ −65.9452 −2.41281
$$748$$ 0 0
$$749$$ 19.0094i 0.694587i
$$750$$ 0 0
$$751$$ −2.48886 −0.0908199 −0.0454099 0.998968i $$-0.514459\pi$$
−0.0454099 + 0.998968i $$0.514459\pi$$
$$752$$ 0 0
$$753$$ 72.3783i 2.63761i
$$754$$ 0 0
$$755$$ 52.2864 + 7.34614i 1.90290 + 0.267353i
$$756$$ 0 0
$$757$$ 21.2859 0.773650 0.386825 0.922153i $$-0.373572\pi$$
0.386825 + 0.922153i $$0.373572\pi$$
$$758$$ 0 0
$$759$$ 5.24443 0.190361
$$760$$ 0 0
$$761$$ −19.1240 −0.693244 −0.346622 0.938005i $$-0.612671\pi$$
−0.346622 + 0.938005i $$0.612671\pi$$
$$762$$ 0 0
$$763$$ −30.3970 −1.10045
$$764$$ 0 0
$$765$$ −9.80642 + 69.7975i −0.354552 + 2.52354i
$$766$$ 0 0
$$767$$ 13.2444i 0.478229i
$$768$$ 0 0
$$769$$ 33.9625 1.22472 0.612360 0.790579i $$-0.290220\pi$$
0.612360 + 0.790579i $$0.290220\pi$$
$$770$$ 0 0
$$771$$ 74.6548i 2.68863i
$$772$$ 0 0
$$773$$ 0.133353 0.00479638 0.00239819 0.999997i $$-0.499237\pi$$
0.00239819 + 0.999997i $$0.499237\pi$$
$$774$$ 0 0
$$775$$ −13.2444 3.79658i −0.475754 0.136377i
$$776$$ 0 0
$$777$$ 73.5308i 2.63790i
$$778$$ 0 0
$$779$$ 26.1847i 0.938164i
$$780$$ 0 0
$$781$$ 18.4889i 0.661584i
$$782$$ 0 0
$$783$$ 14.1017i 0.503954i
$$784$$ 0 0
$$785$$ 1.80642 + 0.253799i 0.0644740 + 0.00905848i
$$786$$ 0 0
$$787$$ −1.12537 −0.0401150 −0.0200575 0.999799i $$-0.506385\pi$$
−0.0200575 + 0.999799i $$0.506385\pi$$
$$788$$ 0 0
$$789$$ 7.47949i 0.266277i
$$790$$ 0 0
$$791$$ −19.4291 −0.690820
$$792$$ 0 0
$$793$$ 32.0830i 1.13930i
$$794$$ 0 0
$$795$$ −34.5718 4.85728i −1.22614 0.172270i
$$796$$ 0 0
$$797$$ 5.11108 0.181044 0.0905218 0.995894i $$-0.471147\pi$$
0.0905218 + 0.995894i $$0.471147\pi$$
$$798$$ 0 0
$$799$$ 30.9590 1.09525
$$800$$ 0