# Properties

 Label 672.2.h.b.575.3 Level $672$ Weight $2$ Character 672.575 Analytic conductor $5.366$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 672.h (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.36594701583$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 575.3 Root $$-0.707107 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 672.575 Dual form 672.2.h.b.575.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.41421 - 1.00000i) q^{3} -4.24264i q^{5} +1.00000i q^{7} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$$ $$q+(1.41421 - 1.00000i) q^{3} -4.24264i q^{5} +1.00000i q^{7} +(1.00000 - 2.82843i) q^{9} +4.24264 q^{11} -2.00000 q^{13} +(-4.24264 - 6.00000i) q^{15} +7.07107i q^{17} -4.00000i q^{19} +(1.00000 + 1.41421i) q^{21} +1.41421 q^{23} -13.0000 q^{25} +(-1.41421 - 5.00000i) q^{27} -2.82843i q^{29} -2.00000i q^{31} +(6.00000 - 4.24264i) q^{33} +4.24264 q^{35} -4.00000 q^{37} +(-2.82843 + 2.00000i) q^{39} -1.41421i q^{41} +8.00000i q^{43} +(-12.0000 - 4.24264i) q^{45} -2.82843 q^{47} -1.00000 q^{49} +(7.07107 + 10.0000i) q^{51} +5.65685i q^{53} -18.0000i q^{55} +(-4.00000 - 5.65685i) q^{57} +11.3137 q^{59} -2.00000 q^{61} +(2.82843 + 1.00000i) q^{63} +8.48528i q^{65} +8.00000i q^{67} +(2.00000 - 1.41421i) q^{69} +12.7279 q^{71} +14.0000 q^{73} +(-18.3848 + 13.0000i) q^{75} +4.24264i q^{77} +4.00000i q^{79} +(-7.00000 - 5.65685i) q^{81} +2.82843 q^{83} +30.0000 q^{85} +(-2.82843 - 4.00000i) q^{87} -9.89949i q^{89} -2.00000i q^{91} +(-2.00000 - 2.82843i) q^{93} -16.9706 q^{95} -10.0000 q^{97} +(4.24264 - 12.0000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 4q^{9} + O(q^{10})$$ $$4q + 4q^{9} - 8q^{13} + 4q^{21} - 52q^{25} + 24q^{33} - 16q^{37} - 48q^{45} - 4q^{49} - 16q^{57} - 8q^{61} + 8q^{69} + 56q^{73} - 28q^{81} + 120q^{85} - 8q^{93} - 40q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$421$$ $$449$$ $$577$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ 1.41421 1.00000i 0.816497 0.577350i
$$4$$ 0 0
$$5$$ 4.24264i 1.89737i −0.316228 0.948683i $$-0.602416\pi$$
0.316228 0.948683i $$-0.397584\pi$$
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ 1.00000 2.82843i 0.333333 0.942809i
$$10$$ 0 0
$$11$$ 4.24264 1.27920 0.639602 0.768706i $$-0.279099\pi$$
0.639602 + 0.768706i $$0.279099\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ −4.24264 6.00000i −1.09545 1.54919i
$$16$$ 0 0
$$17$$ 7.07107i 1.71499i 0.514496 + 0.857493i $$0.327979\pi$$
−0.514496 + 0.857493i $$0.672021\pi$$
$$18$$ 0 0
$$19$$ 4.00000i 0.917663i −0.888523 0.458831i $$-0.848268\pi$$
0.888523 0.458831i $$-0.151732\pi$$
$$20$$ 0 0
$$21$$ 1.00000 + 1.41421i 0.218218 + 0.308607i
$$22$$ 0 0
$$23$$ 1.41421 0.294884 0.147442 0.989071i $$-0.452896\pi$$
0.147442 + 0.989071i $$0.452896\pi$$
$$24$$ 0 0
$$25$$ −13.0000 −2.60000
$$26$$ 0 0
$$27$$ −1.41421 5.00000i −0.272166 0.962250i
$$28$$ 0 0
$$29$$ 2.82843i 0.525226i −0.964901 0.262613i $$-0.915416\pi$$
0.964901 0.262613i $$-0.0845842\pi$$
$$30$$ 0 0
$$31$$ 2.00000i 0.359211i −0.983739 0.179605i $$-0.942518\pi$$
0.983739 0.179605i $$-0.0574821\pi$$
$$32$$ 0 0
$$33$$ 6.00000 4.24264i 1.04447 0.738549i
$$34$$ 0 0
$$35$$ 4.24264 0.717137
$$36$$ 0 0
$$37$$ −4.00000 −0.657596 −0.328798 0.944400i $$-0.606644\pi$$
−0.328798 + 0.944400i $$0.606644\pi$$
$$38$$ 0 0
$$39$$ −2.82843 + 2.00000i −0.452911 + 0.320256i
$$40$$ 0 0
$$41$$ 1.41421i 0.220863i −0.993884 0.110432i $$-0.964777\pi$$
0.993884 0.110432i $$-0.0352233\pi$$
$$42$$ 0 0
$$43$$ 8.00000i 1.21999i 0.792406 + 0.609994i $$0.208828\pi$$
−0.792406 + 0.609994i $$0.791172\pi$$
$$44$$ 0 0
$$45$$ −12.0000 4.24264i −1.78885 0.632456i
$$46$$ 0 0
$$47$$ −2.82843 −0.412568 −0.206284 0.978492i $$-0.566137\pi$$
−0.206284 + 0.978492i $$0.566137\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 7.07107 + 10.0000i 0.990148 + 1.40028i
$$52$$ 0 0
$$53$$ 5.65685i 0.777029i 0.921443 + 0.388514i $$0.127012\pi$$
−0.921443 + 0.388514i $$0.872988\pi$$
$$54$$ 0 0
$$55$$ 18.0000i 2.42712i
$$56$$ 0 0
$$57$$ −4.00000 5.65685i −0.529813 0.749269i
$$58$$ 0 0
$$59$$ 11.3137 1.47292 0.736460 0.676481i $$-0.236496\pi$$
0.736460 + 0.676481i $$0.236496\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −0.256074 −0.128037 0.991769i $$-0.540868\pi$$
−0.128037 + 0.991769i $$0.540868\pi$$
$$62$$ 0 0
$$63$$ 2.82843 + 1.00000i 0.356348 + 0.125988i
$$64$$ 0 0
$$65$$ 8.48528i 1.05247i
$$66$$ 0 0
$$67$$ 8.00000i 0.977356i 0.872464 + 0.488678i $$0.162521\pi$$
−0.872464 + 0.488678i $$0.837479\pi$$
$$68$$ 0 0
$$69$$ 2.00000 1.41421i 0.240772 0.170251i
$$70$$ 0 0
$$71$$ 12.7279 1.51053 0.755263 0.655422i $$-0.227509\pi$$
0.755263 + 0.655422i $$0.227509\pi$$
$$72$$ 0 0
$$73$$ 14.0000 1.63858 0.819288 0.573382i $$-0.194369\pi$$
0.819288 + 0.573382i $$0.194369\pi$$
$$74$$ 0 0
$$75$$ −18.3848 + 13.0000i −2.12289 + 1.50111i
$$76$$ 0 0
$$77$$ 4.24264i 0.483494i
$$78$$ 0 0
$$79$$ 4.00000i 0.450035i 0.974355 + 0.225018i $$0.0722440\pi$$
−0.974355 + 0.225018i $$0.927756\pi$$
$$80$$ 0 0
$$81$$ −7.00000 5.65685i −0.777778 0.628539i
$$82$$ 0 0
$$83$$ 2.82843 0.310460 0.155230 0.987878i $$-0.450388\pi$$
0.155230 + 0.987878i $$0.450388\pi$$
$$84$$ 0 0
$$85$$ 30.0000 3.25396
$$86$$ 0 0
$$87$$ −2.82843 4.00000i −0.303239 0.428845i
$$88$$ 0 0
$$89$$ 9.89949i 1.04934i −0.851304 0.524672i $$-0.824188\pi$$
0.851304 0.524672i $$-0.175812\pi$$
$$90$$ 0 0
$$91$$ 2.00000i 0.209657i
$$92$$ 0 0
$$93$$ −2.00000 2.82843i −0.207390 0.293294i
$$94$$ 0 0
$$95$$ −16.9706 −1.74114
$$96$$ 0 0
$$97$$ −10.0000 −1.01535 −0.507673 0.861550i $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ 4.24264 12.0000i 0.426401 1.20605i
$$100$$ 0 0
$$101$$ 4.24264i 0.422159i −0.977469 0.211079i $$-0.932302\pi$$
0.977469 0.211079i $$-0.0676978\pi$$
$$102$$ 0 0
$$103$$ 6.00000i 0.591198i −0.955312 0.295599i $$-0.904481\pi$$
0.955312 0.295599i $$-0.0955191\pi$$
$$104$$ 0 0
$$105$$ 6.00000 4.24264i 0.585540 0.414039i
$$106$$ 0 0
$$107$$ 1.41421 0.136717 0.0683586 0.997661i $$-0.478224\pi$$
0.0683586 + 0.997661i $$0.478224\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 0 0
$$111$$ −5.65685 + 4.00000i −0.536925 + 0.379663i
$$112$$ 0 0
$$113$$ 11.3137i 1.06430i 0.846649 + 0.532152i $$0.178617\pi$$
−0.846649 + 0.532152i $$0.821383\pi$$
$$114$$ 0 0
$$115$$ 6.00000i 0.559503i
$$116$$ 0 0
$$117$$ −2.00000 + 5.65685i −0.184900 + 0.522976i
$$118$$ 0 0
$$119$$ −7.07107 −0.648204
$$120$$ 0 0
$$121$$ 7.00000 0.636364
$$122$$ 0 0
$$123$$ −1.41421 2.00000i −0.127515 0.180334i
$$124$$ 0 0
$$125$$ 33.9411i 3.03579i
$$126$$ 0 0
$$127$$ 12.0000i 1.06483i 0.846484 + 0.532414i $$0.178715\pi$$
−0.846484 + 0.532414i $$0.821285\pi$$
$$128$$ 0 0
$$129$$ 8.00000 + 11.3137i 0.704361 + 0.996116i
$$130$$ 0 0
$$131$$ 8.48528 0.741362 0.370681 0.928760i $$-0.379124\pi$$
0.370681 + 0.928760i $$0.379124\pi$$
$$132$$ 0 0
$$133$$ 4.00000 0.346844
$$134$$ 0 0
$$135$$ −21.2132 + 6.00000i −1.82574 + 0.516398i
$$136$$ 0 0
$$137$$ 8.48528i 0.724947i −0.931994 0.362473i $$-0.881932\pi$$
0.931994 0.362473i $$-0.118068\pi$$
$$138$$ 0 0
$$139$$ 10.0000i 0.848189i −0.905618 0.424094i $$-0.860592\pi$$
0.905618 0.424094i $$-0.139408\pi$$
$$140$$ 0 0
$$141$$ −4.00000 + 2.82843i −0.336861 + 0.238197i
$$142$$ 0 0
$$143$$ −8.48528 −0.709575
$$144$$ 0 0
$$145$$ −12.0000 −0.996546
$$146$$ 0 0
$$147$$ −1.41421 + 1.00000i −0.116642 + 0.0824786i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 24.0000i 1.95309i 0.215308 + 0.976546i $$0.430924\pi$$
−0.215308 + 0.976546i $$0.569076\pi$$
$$152$$ 0 0
$$153$$ 20.0000 + 7.07107i 1.61690 + 0.571662i
$$154$$ 0 0
$$155$$ −8.48528 −0.681554
$$156$$ 0 0
$$157$$ 14.0000 1.11732 0.558661 0.829396i $$-0.311315\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ 0 0
$$159$$ 5.65685 + 8.00000i 0.448618 + 0.634441i
$$160$$ 0 0
$$161$$ 1.41421i 0.111456i
$$162$$ 0 0
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ 0 0
$$165$$ −18.0000 25.4558i −1.40130 1.98173i
$$166$$ 0 0
$$167$$ 19.7990 1.53209 0.766046 0.642786i $$-0.222221\pi$$
0.766046 + 0.642786i $$0.222221\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ −11.3137 4.00000i −0.865181 0.305888i
$$172$$ 0 0
$$173$$ 7.07107i 0.537603i 0.963196 + 0.268802i $$0.0866276\pi$$
−0.963196 + 0.268802i $$0.913372\pi$$
$$174$$ 0 0
$$175$$ 13.0000i 0.982708i
$$176$$ 0 0
$$177$$ 16.0000 11.3137i 1.20263 0.850390i
$$178$$ 0 0
$$179$$ −15.5563 −1.16274 −0.581368 0.813641i $$-0.697482\pi$$
−0.581368 + 0.813641i $$0.697482\pi$$
$$180$$ 0 0
$$181$$ 6.00000 0.445976 0.222988 0.974821i $$-0.428419\pi$$
0.222988 + 0.974821i $$0.428419\pi$$
$$182$$ 0 0
$$183$$ −2.82843 + 2.00000i −0.209083 + 0.147844i
$$184$$ 0 0
$$185$$ 16.9706i 1.24770i
$$186$$ 0 0
$$187$$ 30.0000i 2.19382i
$$188$$ 0 0
$$189$$ 5.00000 1.41421i 0.363696 0.102869i
$$190$$ 0 0
$$191$$ −1.41421 −0.102329 −0.0511645 0.998690i $$-0.516293\pi$$
−0.0511645 + 0.998690i $$0.516293\pi$$
$$192$$ 0 0
$$193$$ −4.00000 −0.287926 −0.143963 0.989583i $$-0.545985\pi$$
−0.143963 + 0.989583i $$0.545985\pi$$
$$194$$ 0 0
$$195$$ 8.48528 + 12.0000i 0.607644 + 0.859338i
$$196$$ 0 0
$$197$$ 5.65685i 0.403034i −0.979485 0.201517i $$-0.935413\pi$$
0.979485 0.201517i $$-0.0645872\pi$$
$$198$$ 0 0
$$199$$ 8.00000i 0.567105i 0.958957 + 0.283552i $$0.0915130\pi$$
−0.958957 + 0.283552i $$0.908487\pi$$
$$200$$ 0 0
$$201$$ 8.00000 + 11.3137i 0.564276 + 0.798007i
$$202$$ 0 0
$$203$$ 2.82843 0.198517
$$204$$ 0 0
$$205$$ −6.00000 −0.419058
$$206$$ 0 0
$$207$$ 1.41421 4.00000i 0.0982946 0.278019i
$$208$$ 0 0
$$209$$ 16.9706i 1.17388i
$$210$$ 0 0
$$211$$ 8.00000i 0.550743i 0.961338 + 0.275371i $$0.0888008\pi$$
−0.961338 + 0.275371i $$0.911199\pi$$
$$212$$ 0 0
$$213$$ 18.0000 12.7279i 1.23334 0.872103i
$$214$$ 0 0
$$215$$ 33.9411 2.31477
$$216$$ 0 0
$$217$$ 2.00000 0.135769
$$218$$ 0 0
$$219$$ 19.7990 14.0000i 1.33789 0.946032i
$$220$$ 0 0
$$221$$ 14.1421i 0.951303i
$$222$$ 0 0
$$223$$ 8.00000i 0.535720i 0.963458 + 0.267860i $$0.0863164\pi$$
−0.963458 + 0.267860i $$0.913684\pi$$
$$224$$ 0 0
$$225$$ −13.0000 + 36.7696i −0.866667 + 2.45130i
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ −30.0000 −1.98246 −0.991228 0.132164i $$-0.957808\pi$$
−0.991228 + 0.132164i $$0.957808\pi$$
$$230$$ 0 0
$$231$$ 4.24264 + 6.00000i 0.279145 + 0.394771i
$$232$$ 0 0
$$233$$ 19.7990i 1.29707i −0.761183 0.648537i $$-0.775381\pi$$
0.761183 0.648537i $$-0.224619\pi$$
$$234$$ 0 0
$$235$$ 12.0000i 0.782794i
$$236$$ 0 0
$$237$$ 4.00000 + 5.65685i 0.259828 + 0.367452i
$$238$$ 0 0
$$239$$ 18.3848 1.18921 0.594606 0.804017i $$-0.297308\pi$$
0.594606 + 0.804017i $$0.297308\pi$$
$$240$$ 0 0
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ −15.5563 1.00000i −0.997940 0.0641500i
$$244$$ 0 0
$$245$$ 4.24264i 0.271052i
$$246$$ 0 0
$$247$$ 8.00000i 0.509028i
$$248$$ 0 0
$$249$$ 4.00000 2.82843i 0.253490 0.179244i
$$250$$ 0 0
$$251$$ −5.65685 −0.357057 −0.178529 0.983935i $$-0.557134\pi$$
−0.178529 + 0.983935i $$0.557134\pi$$
$$252$$ 0 0
$$253$$ 6.00000 0.377217
$$254$$ 0 0
$$255$$ 42.4264 30.0000i 2.65684 1.87867i
$$256$$ 0 0
$$257$$ 1.41421i 0.0882162i −0.999027 0.0441081i $$-0.985955\pi$$
0.999027 0.0441081i $$-0.0140446\pi$$
$$258$$ 0 0
$$259$$ 4.00000i 0.248548i
$$260$$ 0 0
$$261$$ −8.00000 2.82843i −0.495188 0.175075i
$$262$$ 0 0
$$263$$ −29.6985 −1.83129 −0.915644 0.401991i $$-0.868318\pi$$
−0.915644 + 0.401991i $$0.868318\pi$$
$$264$$ 0 0
$$265$$ 24.0000 1.47431
$$266$$ 0 0
$$267$$ −9.89949 14.0000i −0.605839 0.856786i
$$268$$ 0 0
$$269$$ 15.5563i 0.948487i 0.880394 + 0.474244i $$0.157278\pi$$
−0.880394 + 0.474244i $$0.842722\pi$$
$$270$$ 0 0
$$271$$ 22.0000i 1.33640i 0.743980 + 0.668202i $$0.232936\pi$$
−0.743980 + 0.668202i $$0.767064\pi$$
$$272$$ 0 0
$$273$$ −2.00000 2.82843i −0.121046 0.171184i
$$274$$ 0 0
$$275$$ −55.1543 −3.32593
$$276$$ 0 0
$$277$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 0 0
$$279$$ −5.65685 2.00000i −0.338667 0.119737i
$$280$$ 0 0
$$281$$ 19.7990i 1.18111i 0.806998 + 0.590554i $$0.201091\pi$$
−0.806998 + 0.590554i $$0.798909\pi$$
$$282$$ 0 0
$$283$$ 20.0000i 1.18888i −0.804141 0.594438i $$-0.797374\pi$$
0.804141 0.594438i $$-0.202626\pi$$
$$284$$ 0 0
$$285$$ −24.0000 + 16.9706i −1.42164 + 1.00525i
$$286$$ 0 0
$$287$$ 1.41421 0.0834784
$$288$$ 0 0
$$289$$ −33.0000 −1.94118
$$290$$ 0 0
$$291$$ −14.1421 + 10.0000i −0.829027 + 0.586210i
$$292$$ 0 0
$$293$$ 32.5269i 1.90024i −0.311881 0.950121i $$-0.600959\pi$$
0.311881 0.950121i $$-0.399041\pi$$
$$294$$ 0 0
$$295$$ 48.0000i 2.79467i
$$296$$ 0 0
$$297$$ −6.00000 21.2132i −0.348155 1.23091i
$$298$$ 0 0
$$299$$ −2.82843 −0.163572
$$300$$ 0 0
$$301$$ −8.00000 −0.461112
$$302$$ 0 0
$$303$$ −4.24264 6.00000i −0.243733 0.344691i
$$304$$ 0 0
$$305$$ 8.48528i 0.485866i
$$306$$ 0 0
$$307$$ 20.0000i 1.14146i −0.821138 0.570730i $$-0.806660\pi$$
0.821138 0.570730i $$-0.193340\pi$$
$$308$$ 0 0
$$309$$ −6.00000 8.48528i −0.341328 0.482711i
$$310$$ 0 0
$$311$$ −19.7990 −1.12270 −0.561349 0.827579i $$-0.689717\pi$$
−0.561349 + 0.827579i $$0.689717\pi$$
$$312$$ 0 0
$$313$$ 2.00000 0.113047 0.0565233 0.998401i $$-0.481998\pi$$
0.0565233 + 0.998401i $$0.481998\pi$$
$$314$$ 0 0
$$315$$ 4.24264 12.0000i 0.239046 0.676123i
$$316$$ 0 0
$$317$$ 11.3137i 0.635441i 0.948184 + 0.317721i $$0.102917\pi$$
−0.948184 + 0.317721i $$0.897083\pi$$
$$318$$ 0 0
$$319$$ 12.0000i 0.671871i
$$320$$ 0 0
$$321$$ 2.00000 1.41421i 0.111629 0.0789337i
$$322$$ 0 0
$$323$$ 28.2843 1.57378
$$324$$ 0 0
$$325$$ 26.0000 1.44222
$$326$$ 0 0
$$327$$ 2.82843 2.00000i 0.156412 0.110600i
$$328$$ 0 0
$$329$$ 2.82843i 0.155936i
$$330$$ 0 0
$$331$$ 20.0000i 1.09930i −0.835395 0.549650i $$-0.814761\pi$$
0.835395 0.549650i $$-0.185239\pi$$
$$332$$ 0 0
$$333$$ −4.00000 + 11.3137i −0.219199 + 0.619987i
$$334$$ 0 0
$$335$$ 33.9411 1.85440
$$336$$ 0 0
$$337$$ −2.00000 −0.108947 −0.0544735 0.998515i $$-0.517348\pi$$
−0.0544735 + 0.998515i $$0.517348\pi$$
$$338$$ 0 0
$$339$$ 11.3137 + 16.0000i 0.614476 + 0.869001i
$$340$$ 0 0
$$341$$ 8.48528i 0.459504i
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ −6.00000 8.48528i −0.323029 0.456832i
$$346$$ 0 0
$$347$$ 7.07107 0.379595 0.189797 0.981823i $$-0.439217\pi$$
0.189797 + 0.981823i $$0.439217\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 2.82843 + 10.0000i 0.150970 + 0.533761i
$$352$$ 0 0
$$353$$ 12.7279i 0.677439i −0.940887 0.338719i $$-0.890006\pi$$
0.940887 0.338719i $$-0.109994\pi$$
$$354$$ 0 0
$$355$$ 54.0000i 2.86602i
$$356$$ 0 0
$$357$$ −10.0000 + 7.07107i −0.529256 + 0.374241i
$$358$$ 0 0
$$359$$ 18.3848 0.970311 0.485156 0.874428i $$-0.338763\pi$$
0.485156 + 0.874428i $$0.338763\pi$$
$$360$$ 0 0
$$361$$ 3.00000 0.157895
$$362$$ 0 0
$$363$$ 9.89949 7.00000i 0.519589 0.367405i
$$364$$ 0 0
$$365$$ 59.3970i 3.10898i
$$366$$ 0 0
$$367$$ 24.0000i 1.25279i 0.779506 + 0.626395i $$0.215470\pi$$
−0.779506 + 0.626395i $$0.784530\pi$$
$$368$$ 0 0
$$369$$ −4.00000 1.41421i −0.208232 0.0736210i
$$370$$ 0 0
$$371$$ −5.65685 −0.293689
$$372$$ 0 0
$$373$$ 14.0000 0.724893 0.362446 0.932005i $$-0.381942\pi$$
0.362446 + 0.932005i $$0.381942\pi$$
$$374$$ 0 0
$$375$$ 33.9411 + 48.0000i 1.75271 + 2.47871i
$$376$$ 0 0
$$377$$ 5.65685i 0.291343i
$$378$$ 0 0
$$379$$ 12.0000i 0.616399i −0.951322 0.308199i $$-0.900274\pi$$
0.951322 0.308199i $$-0.0997264\pi$$
$$380$$ 0 0
$$381$$ 12.0000 + 16.9706i 0.614779 + 0.869428i
$$382$$ 0 0
$$383$$ −33.9411 −1.73431 −0.867155 0.498038i $$-0.834054\pi$$
−0.867155 + 0.498038i $$0.834054\pi$$
$$384$$ 0 0
$$385$$ 18.0000 0.917365
$$386$$ 0 0
$$387$$ 22.6274 + 8.00000i 1.15022 + 0.406663i
$$388$$ 0 0
$$389$$ 25.4558i 1.29066i −0.763903 0.645331i $$-0.776719\pi$$
0.763903 0.645331i $$-0.223281\pi$$
$$390$$ 0 0
$$391$$ 10.0000i 0.505722i
$$392$$ 0 0
$$393$$ 12.0000 8.48528i 0.605320 0.428026i
$$394$$ 0 0
$$395$$ 16.9706 0.853882
$$396$$ 0 0
$$397$$ 2.00000 0.100377 0.0501886 0.998740i $$-0.484018\pi$$
0.0501886 + 0.998740i $$0.484018\pi$$
$$398$$ 0 0
$$399$$ 5.65685 4.00000i 0.283197 0.200250i
$$400$$ 0 0
$$401$$ 8.48528i 0.423735i 0.977298 + 0.211867i $$0.0679545\pi$$
−0.977298 + 0.211867i $$0.932046\pi$$
$$402$$ 0 0
$$403$$ 4.00000i 0.199254i
$$404$$ 0 0
$$405$$ −24.0000 + 29.6985i −1.19257 + 1.47573i
$$406$$ 0 0
$$407$$ −16.9706 −0.841200
$$408$$ 0 0
$$409$$ −34.0000 −1.68119 −0.840596 0.541663i $$-0.817795\pi$$
−0.840596 + 0.541663i $$0.817795\pi$$
$$410$$ 0 0
$$411$$ −8.48528 12.0000i −0.418548 0.591916i
$$412$$ 0 0
$$413$$ 11.3137i 0.556711i
$$414$$ 0 0
$$415$$ 12.0000i 0.589057i
$$416$$ 0 0
$$417$$ −10.0000 14.1421i −0.489702 0.692543i
$$418$$ 0 0
$$419$$ −5.65685 −0.276355 −0.138178 0.990407i $$-0.544125\pi$$
−0.138178 + 0.990407i $$0.544125\pi$$
$$420$$ 0 0
$$421$$ −8.00000 −0.389896 −0.194948 0.980814i $$-0.562454\pi$$
−0.194948 + 0.980814i $$0.562454\pi$$
$$422$$ 0 0
$$423$$ −2.82843 + 8.00000i −0.137523 + 0.388973i
$$424$$ 0 0
$$425$$ 91.9239i 4.45896i
$$426$$ 0 0
$$427$$ 2.00000i 0.0967868i
$$428$$ 0 0
$$429$$ −12.0000 + 8.48528i −0.579365 + 0.409673i
$$430$$ 0 0
$$431$$ 15.5563 0.749323 0.374661 0.927162i $$-0.377759\pi$$
0.374661 + 0.927162i $$0.377759\pi$$
$$432$$ 0 0
$$433$$ 34.0000 1.63394 0.816968 0.576683i $$-0.195653\pi$$
0.816968 + 0.576683i $$0.195653\pi$$
$$434$$ 0 0
$$435$$ −16.9706 + 12.0000i −0.813676 + 0.575356i
$$436$$ 0 0
$$437$$ 5.65685i 0.270604i
$$438$$ 0 0
$$439$$ 16.0000i 0.763638i −0.924237 0.381819i $$-0.875298\pi$$
0.924237 0.381819i $$-0.124702\pi$$
$$440$$ 0 0
$$441$$ −1.00000 + 2.82843i −0.0476190 + 0.134687i
$$442$$ 0 0
$$443$$ −7.07107 −0.335957 −0.167978 0.985791i $$-0.553724\pi$$
−0.167978 + 0.985791i $$0.553724\pi$$
$$444$$ 0 0
$$445$$ −42.0000 −1.99099
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 5.65685i 0.266963i 0.991051 + 0.133482i $$0.0426157\pi$$
−0.991051 + 0.133482i $$0.957384\pi$$
$$450$$ 0 0
$$451$$ 6.00000i 0.282529i
$$452$$ 0 0
$$453$$ 24.0000 + 33.9411i 1.12762 + 1.59469i
$$454$$ 0 0
$$455$$ −8.48528 −0.397796
$$456$$ 0 0
$$457$$ −10.0000 −0.467780 −0.233890 0.972263i $$-0.575146\pi$$
−0.233890 + 0.972263i $$0.575146\pi$$
$$458$$ 0 0
$$459$$ 35.3553 10.0000i 1.65025 0.466760i
$$460$$ 0 0
$$461$$ 9.89949i 0.461065i 0.973065 + 0.230533i $$0.0740469\pi$$
−0.973065 + 0.230533i $$0.925953\pi$$
$$462$$ 0 0
$$463$$ 8.00000i 0.371792i 0.982569 + 0.185896i $$0.0595187\pi$$
−0.982569 + 0.185896i $$0.940481\pi$$
$$464$$ 0 0
$$465$$ −12.0000 + 8.48528i −0.556487 + 0.393496i
$$466$$ 0 0
$$467$$ 11.3137 0.523536 0.261768 0.965131i $$-0.415694\pi$$
0.261768 + 0.965131i $$0.415694\pi$$
$$468$$ 0 0
$$469$$ −8.00000 −0.369406
$$470$$ 0 0
$$471$$ 19.7990 14.0000i 0.912289 0.645086i
$$472$$ 0 0
$$473$$ 33.9411i 1.56061i
$$474$$ 0 0
$$475$$ 52.0000i 2.38592i
$$476$$ 0 0
$$477$$ 16.0000 + 5.65685i 0.732590 + 0.259010i
$$478$$ 0 0
$$479$$ 8.48528 0.387702 0.193851 0.981031i $$-0.437902\pi$$
0.193851 + 0.981031i $$0.437902\pi$$
$$480$$ 0 0
$$481$$ 8.00000 0.364769
$$482$$ 0 0
$$483$$ 1.41421 + 2.00000i 0.0643489 + 0.0910032i
$$484$$ 0 0
$$485$$ 42.4264i 1.92648i
$$486$$ 0 0
$$487$$ 8.00000i 0.362515i −0.983436 0.181257i $$-0.941983\pi$$
0.983436 0.181257i $$-0.0580167\pi$$
$$488$$ 0 0
$$489$$ −4.00000 5.65685i −0.180886 0.255812i
$$490$$ 0 0
$$491$$ −18.3848 −0.829693 −0.414847 0.909891i $$-0.636165\pi$$
−0.414847 + 0.909891i $$0.636165\pi$$
$$492$$ 0 0
$$493$$ 20.0000 0.900755
$$494$$ 0 0
$$495$$ −50.9117 18.0000i −2.28831 0.809040i
$$496$$ 0 0
$$497$$ 12.7279i 0.570925i
$$498$$ 0 0
$$499$$ 36.0000i 1.61158i 0.592200 + 0.805791i $$0.298259\pi$$
−0.592200 + 0.805791i $$0.701741\pi$$
$$500$$ 0 0
$$501$$ 28.0000 19.7990i 1.25095 0.884554i
$$502$$ 0 0
$$503$$ −33.9411 −1.51336 −0.756680 0.653785i $$-0.773180\pi$$
−0.756680 + 0.653785i $$0.773180\pi$$
$$504$$ 0 0
$$505$$ −18.0000 −0.800989
$$506$$ 0 0
$$507$$ −12.7279 + 9.00000i −0.565267 + 0.399704i
$$508$$ 0 0
$$509$$ 24.0416i 1.06563i −0.846233 0.532813i $$-0.821135\pi$$
0.846233 0.532813i $$-0.178865\pi$$
$$510$$ 0 0
$$511$$ 14.0000i 0.619324i
$$512$$ 0 0
$$513$$ −20.0000 + 5.65685i −0.883022 + 0.249756i
$$514$$ 0 0
$$515$$ −25.4558 −1.12172
$$516$$ 0 0
$$517$$ −12.0000 −0.527759
$$518$$ 0 0
$$519$$ 7.07107 + 10.0000i 0.310385 + 0.438951i
$$520$$ 0 0
$$521$$ 26.8701i 1.17720i 0.808425 + 0.588599i $$0.200320\pi$$
−0.808425 + 0.588599i $$0.799680\pi$$
$$522$$ 0 0
$$523$$ 26.0000i 1.13690i 0.822718 + 0.568450i $$0.192457\pi$$
−0.822718 + 0.568450i $$0.807543\pi$$
$$524$$ 0 0
$$525$$ −13.0000 18.3848i −0.567367 0.802377i
$$526$$ 0 0
$$527$$ 14.1421 0.616041
$$528$$ 0 0
$$529$$ −21.0000 −0.913043
$$530$$ 0 0
$$531$$ 11.3137 32.0000i 0.490973 1.38868i
$$532$$ 0 0
$$533$$ 2.82843i 0.122513i
$$534$$ 0 0
$$535$$ 6.00000i 0.259403i
$$536$$ 0 0
$$537$$ −22.0000 + 15.5563i −0.949370 + 0.671306i
$$538$$ 0 0
$$539$$ −4.24264 −0.182743
$$540$$ 0 0
$$541$$ −32.0000 −1.37579 −0.687894 0.725811i $$-0.741464\pi$$
−0.687894 + 0.725811i $$0.741464\pi$$
$$542$$ 0 0
$$543$$ 8.48528 6.00000i 0.364138 0.257485i
$$544$$ 0 0
$$545$$ 8.48528i 0.363470i
$$546$$ 0 0
$$547$$ 32.0000i 1.36822i −0.729378 0.684111i $$-0.760191\pi$$
0.729378 0.684111i $$-0.239809\pi$$
$$548$$ 0 0
$$549$$ −2.00000 + 5.65685i −0.0853579 + 0.241429i
$$550$$ 0 0
$$551$$ −11.3137 −0.481980
$$552$$ 0 0
$$553$$ −4.00000 −0.170097
$$554$$ 0 0
$$555$$ 16.9706 + 24.0000i 0.720360 + 1.01874i
$$556$$ 0 0
$$557$$ 22.6274i 0.958754i 0.877609 + 0.479377i $$0.159137\pi$$
−0.877609 + 0.479377i $$0.840863\pi$$
$$558$$ 0 0
$$559$$ 16.0000i 0.676728i
$$560$$ 0 0
$$561$$ 30.0000 + 42.4264i 1.26660 + 1.79124i
$$562$$ 0 0
$$563$$ −11.3137 −0.476816 −0.238408 0.971165i $$-0.576626\pi$$
−0.238408 + 0.971165i $$0.576626\pi$$
$$564$$ 0 0
$$565$$ 48.0000 2.01938
$$566$$ 0 0
$$567$$ 5.65685 7.00000i 0.237566 0.293972i
$$568$$ 0 0
$$569$$ 19.7990i 0.830017i −0.909818 0.415008i $$-0.863779\pi$$
0.909818 0.415008i $$-0.136221\pi$$
$$570$$ 0 0
$$571$$ 32.0000i 1.33916i 0.742741 + 0.669579i $$0.233526\pi$$
−0.742741 + 0.669579i $$0.766474\pi$$
$$572$$ 0 0
$$573$$ −2.00000 + 1.41421i −0.0835512 + 0.0590796i
$$574$$ 0 0
$$575$$ −18.3848 −0.766698
$$576$$ 0 0
$$577$$ 14.0000 0.582828 0.291414 0.956597i $$-0.405874\pi$$
0.291414 + 0.956597i $$0.405874\pi$$
$$578$$ 0 0
$$579$$ −5.65685 + 4.00000i −0.235091 + 0.166234i
$$580$$ 0 0
$$581$$ 2.82843i 0.117343i
$$582$$ 0 0
$$583$$ 24.0000i 0.993978i
$$584$$ 0 0
$$585$$ 24.0000 + 8.48528i 0.992278 + 0.350823i
$$586$$ 0 0
$$587$$ −28.2843 −1.16742 −0.583708 0.811963i $$-0.698399\pi$$
−0.583708 + 0.811963i $$0.698399\pi$$
$$588$$ 0 0
$$589$$ −8.00000 −0.329634
$$590$$ 0 0
$$591$$ −5.65685 8.00000i −0.232692 0.329076i
$$592$$ 0 0
$$593$$ 1.41421i 0.0580748i 0.999578 + 0.0290374i $$0.00924419\pi$$
−0.999578 + 0.0290374i $$0.990756\pi$$
$$594$$ 0 0
$$595$$ 30.0000i 1.22988i
$$596$$ 0 0
$$597$$ 8.00000 + 11.3137i 0.327418 + 0.463039i
$$598$$ 0 0
$$599$$ −9.89949 −0.404482 −0.202241 0.979336i $$-0.564822\pi$$
−0.202241 + 0.979336i $$0.564822\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ 0 0
$$603$$ 22.6274 + 8.00000i 0.921460 + 0.325785i
$$604$$ 0 0
$$605$$ 29.6985i 1.20742i
$$606$$ 0 0
$$607$$ 24.0000i 0.974130i 0.873366 + 0.487065i $$0.161933\pi$$
−0.873366 + 0.487065i $$0.838067\pi$$
$$608$$ 0 0
$$609$$ 4.00000 2.82843i 0.162088 0.114614i
$$610$$ 0 0
$$611$$ 5.65685 0.228852
$$612$$ 0 0
$$613$$ 26.0000 1.05013 0.525065 0.851062i $$-0.324041\pi$$
0.525065 + 0.851062i $$0.324041\pi$$
$$614$$ 0 0
$$615$$ −8.48528 + 6.00000i −0.342160 + 0.241943i
$$616$$ 0 0
$$617$$ 14.1421i 0.569341i 0.958625 + 0.284670i $$0.0918842\pi$$
−0.958625 + 0.284670i $$0.908116\pi$$
$$618$$ 0 0
$$619$$ 30.0000i 1.20580i −0.797816 0.602901i $$-0.794011\pi$$
0.797816 0.602901i $$-0.205989\pi$$
$$620$$ 0 0
$$621$$ −2.00000 7.07107i −0.0802572 0.283752i
$$622$$ 0 0
$$623$$ 9.89949 0.396615
$$624$$ 0 0
$$625$$ 79.0000 3.16000
$$626$$ 0 0
$$627$$ −16.9706 24.0000i −0.677739 0.958468i
$$628$$ 0 0
$$629$$ 28.2843i 1.12777i
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 8.00000 + 11.3137i 0.317971 + 0.449680i
$$634$$ 0 0
$$635$$ 50.9117 2.02037
$$636$$ 0 0
$$637$$ 2.00000 0.0792429
$$638$$ 0 0
$$639$$ 12.7279 36.0000i 0.503509 1.42414i
$$640$$ 0 0
$$641$$ 25.4558i 1.00545i 0.864448 + 0.502723i $$0.167668\pi$$
−0.864448 + 0.502723i $$0.832332\pi$$
$$642$$ 0 0
$$643$$ 44.0000i 1.73519i 0.497271 + 0.867595i $$0.334335\pi$$
−0.497271 + 0.867595i $$0.665665\pi$$
$$644$$ 0 0
$$645$$ 48.0000 33.9411i 1.89000 1.33643i
$$646$$ 0 0
$$647$$ −2.82843 −0.111197 −0.0555985 0.998453i $$-0.517707\pi$$
−0.0555985 + 0.998453i $$0.517707\pi$$
$$648$$ 0 0
$$649$$ 48.0000 1.88416
$$650$$ 0 0
$$651$$ 2.82843 2.00000i 0.110855 0.0783862i
$$652$$ 0 0
$$653$$ 14.1421i 0.553425i 0.960953 + 0.276712i $$0.0892449\pi$$
−0.960953 + 0.276712i $$0.910755\pi$$
$$654$$ 0 0
$$655$$ 36.0000i 1.40664i
$$656$$ 0 0
$$657$$ 14.0000 39.5980i 0.546192 1.54486i
$$658$$ 0 0
$$659$$ 7.07107 0.275450 0.137725 0.990471i $$-0.456021\pi$$
0.137725 + 0.990471i $$0.456021\pi$$
$$660$$ 0 0
$$661$$ −50.0000 −1.94477 −0.972387 0.233373i $$-0.925024\pi$$
−0.972387 + 0.233373i $$0.925024\pi$$
$$662$$ 0 0
$$663$$ −14.1421 20.0000i −0.549235 0.776736i
$$664$$ 0 0
$$665$$ 16.9706i 0.658090i
$$666$$ 0 0
$$667$$ 4.00000i 0.154881i
$$668$$ 0 0
$$669$$ 8.00000 + 11.3137i 0.309298 + 0.437413i
$$670$$ 0 0
$$671$$ −8.48528 −0.327571
$$672$$ 0 0
$$673$$ −40.0000 −1.54189 −0.770943 0.636904i $$-0.780215\pi$$
−0.770943 + 0.636904i $$0.780215\pi$$
$$674$$ 0 0
$$675$$ 18.3848 + 65.0000i 0.707630 + 2.50185i
$$676$$ 0 0
$$677$$ 9.89949i 0.380468i 0.981739 + 0.190234i $$0.0609248\pi$$
−0.981739 + 0.190234i $$0.939075\pi$$
$$678$$ 0 0
$$679$$ 10.0000i 0.383765i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −7.07107 −0.270567 −0.135283 0.990807i $$-0.543195\pi$$
−0.135283 + 0.990807i $$0.543195\pi$$
$$684$$ 0 0
$$685$$ −36.0000 −1.37549
$$686$$ 0 0
$$687$$ −42.4264 + 30.0000i −1.61867 + 1.14457i
$$688$$ 0 0
$$689$$ 11.3137i 0.431018i
$$690$$ 0 0
$$691$$ 14.0000i 0.532585i 0.963892 + 0.266293i $$0.0857987\pi$$
−0.963892 + 0.266293i $$0.914201\pi$$
$$692$$ 0 0
$$693$$ 12.0000 + 4.24264i 0.455842 + 0.161165i
$$694$$ 0 0
$$695$$ −42.4264 −1.60933
$$696$$ 0 0
$$697$$ 10.0000 0.378777
$$698$$ 0 0
$$699$$ −19.7990 28.0000i −0.748867 1.05906i
$$700$$ 0 0
$$701$$ 25.4558i 0.961454i −0.876870 0.480727i $$-0.840373\pi$$
0.876870 0.480727i $$-0.159627\pi$$
$$702$$ 0 0
$$703$$ 16.0000i 0.603451i
$$704$$ 0 0
$$705$$ 12.0000 + 16.9706i 0.451946 + 0.639148i
$$706$$ 0 0
$$707$$ 4.24264 0.159561
$$708$$ 0 0
$$709$$ 38.0000 1.42712 0.713560 0.700594i $$-0.247082\pi$$
0.713560 + 0.700594i $$0.247082\pi$$
$$710$$ 0 0
$$711$$ 11.3137 + 4.00000i 0.424297 + 0.150012i
$$712$$ 0 0
$$713$$ 2.82843i 0.105925i
$$714$$ 0 0
$$715$$ 36.0000i 1.34632i
$$716$$ 0 0
$$717$$ 26.0000 18.3848i 0.970988 0.686592i
$$718$$ 0 0
$$719$$ 22.6274 0.843860 0.421930 0.906628i $$-0.361353\pi$$
0.421930 + 0.906628i $$0.361353\pi$$
$$720$$ 0 0
$$721$$ 6.00000 0.223452
$$722$$ 0 0
$$723$$ −25.4558 + 18.0000i −0.946713 + 0.669427i
$$724$$ 0 0
$$725$$ 36.7696i 1.36559i
$$726$$ 0 0
$$727$$ 34.0000i 1.26099i −0.776193 0.630495i $$-0.782852\pi$$
0.776193 0.630495i $$-0.217148\pi$$
$$728$$ 0 0
$$729$$ −23.0000 + 14.1421i −0.851852 + 0.523783i
$$730$$ 0 0
$$731$$ −56.5685 −2.09226
$$732$$ 0 0
$$733$$ −14.0000 −0.517102 −0.258551 0.965998i $$-0.583245\pi$$
−0.258551 + 0.965998i $$0.583245\pi$$
$$734$$ 0 0
$$735$$ 4.24264 + 6.00000i 0.156492 + 0.221313i
$$736$$ 0 0
$$737$$ 33.9411i 1.25024i
$$738$$ 0 0
$$739$$ 4.00000i 0.147142i −0.997290 0.0735712i $$-0.976560\pi$$
0.997290 0.0735712i $$-0.0234396\pi$$
$$740$$ 0 0
$$741$$ 8.00000 + 11.3137i 0.293887 + 0.415619i
$$742$$ 0 0
$$743$$ −1.41421 −0.0518825 −0.0259412 0.999663i $$-0.508258\pi$$
−0.0259412 + 0.999663i $$0.508258\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 2.82843 8.00000i 0.103487 0.292705i
$$748$$ 0 0
$$749$$ 1.41421i 0.0516742i
$$750$$ 0 0
$$751$$ 36.0000i 1.31366i 0.754039 + 0.656829i $$0.228103\pi$$
−0.754039 + 0.656829i $$0.771897\pi$$
$$752$$ 0 0
$$753$$ −8.00000 + 5.65685i −0.291536 + 0.206147i
$$754$$ 0 0
$$755$$ 101.823 3.70573
$$756$$ 0 0
$$757$$ −42.0000 −1.52652 −0.763258 0.646094i $$-0.776401\pi$$
−0.763258 + 0.646094i $$0.776401\pi$$
$$758$$ 0 0
$$759$$ 8.48528 6.00000i 0.307996 0.217786i
$$760$$ 0 0
$$761$$ 21.2132i 0.768978i 0.923130 + 0.384489i $$0.125622\pi$$
−0.923130 + 0.384489i $$0.874378\pi$$
$$762$$ 0 0
$$763$$ 2.00000i 0.0724049i
$$764$$ 0 0
$$765$$ 30.0000 84.8528i 1.08465 3.06786i
$$766$$ 0 0
$$767$$ −22.6274 −0.817029
$$768$$ 0 0
$$769$$ −26.0000 −0.937584 −0.468792 0.883309i $$-0.655311\pi$$
−0.468792 + 0.883309i $$0.655311\pi$$
$$770$$ 0 0
$$771$$ −1.41421 2.00000i −0.0509317 0.0720282i
$$772$$ 0 0
$$773$$ 32.5269i 1.16991i 0.811065 + 0.584956i $$0.198888\pi$$
−0.811065 + 0.584956i $$0.801112\pi$$
$$774$$ 0 0
$$775$$ 26.0000i 0.933948i
$$776$$ 0 0
$$777$$ −4.00000 5.65685i −0.143499 0.202939i
$$778$$ 0 0
$$779$$ −5.65685 −0.202678
$$780$$ 0 0
$$781$$ 54.0000 1.93227
$$782$$ 0 0
$$783$$ −14.1421 + 4.00000i −0.505399 + 0.142948i
$$784$$ 0 0
$$785$$ 59.3970i 2.11997i
$$786$$ 0 0
$$787$$ 22.0000i 0.784215i −0.919919 0.392108i $$-0.871746\pi$$
0.919919 0.392108i $$-0.128254\pi$$
$$788$$ 0 0
$$789$$ −42.0000 + 29.6985i −1.49524 + 1.05729i
$$790$$ 0 0
$$791$$ −11.3137 −0.402269
$$792$$ 0 0
$$793$$ 4.00000 0.142044
$$794$$ 0 0
$$795$$ 33.9411 24.0000i 1.20377 0.851192i
$$796$$ 0 0
$$797$$ 32.5269i 1.15216i 0.817392 + 0.576081i $$0.195419\pi$$
−0.817392 + 0.576081i $$0.804581\pi$$
$$798$$ 0 0
$$799$$ 20.0000i 0.707549i
$$800$$ 0 0
$$801$$ −28.0000 9.89949i −0.989331 0.349781i