# Properties

 Label 1024.2.e.m.769.2 Level $1024$ Weight $2$ Character 1024.769 Analytic conductor $8.177$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1024 = 2^{10}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1024.e (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.17668116698$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 128) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 769.2 Root $$0.707107 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 1024.769 Dual form 1024.2.e.m.257.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.41421 - 1.41421i) q^{3} +(1.41421 + 1.41421i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +O(q^{10})$$ $$q+(1.41421 - 1.41421i) q^{3} +(1.41421 + 1.41421i) q^{5} +4.00000i q^{7} -1.00000i q^{9} +(-1.41421 - 1.41421i) q^{11} +(1.41421 - 1.41421i) q^{13} +4.00000 q^{15} +2.00000 q^{17} +(-1.41421 + 1.41421i) q^{19} +(5.65685 + 5.65685i) q^{21} +4.00000i q^{23} -1.00000i q^{25} +(2.82843 + 2.82843i) q^{27} +(4.24264 - 4.24264i) q^{29} -4.00000 q^{33} +(-5.65685 + 5.65685i) q^{35} +(7.07107 + 7.07107i) q^{37} -4.00000i q^{39} +6.00000i q^{41} +(4.24264 + 4.24264i) q^{43} +(1.41421 - 1.41421i) q^{45} -8.00000 q^{47} -9.00000 q^{49} +(2.82843 - 2.82843i) q^{51} +(4.24264 + 4.24264i) q^{53} -4.00000i q^{55} +4.00000i q^{57} +(-9.89949 - 9.89949i) q^{59} +(-1.41421 + 1.41421i) q^{61} +4.00000 q^{63} +4.00000 q^{65} +(7.07107 - 7.07107i) q^{67} +(5.65685 + 5.65685i) q^{69} -12.0000i q^{71} -14.0000i q^{73} +(-1.41421 - 1.41421i) q^{75} +(5.65685 - 5.65685i) q^{77} -8.00000 q^{79} +11.0000 q^{81} +(4.24264 - 4.24264i) q^{83} +(2.82843 + 2.82843i) q^{85} -12.0000i q^{87} -2.00000i q^{89} +(5.65685 + 5.65685i) q^{91} -4.00000 q^{95} -2.00000 q^{97} +(-1.41421 + 1.41421i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + O(q^{10})$$ $$4q + 16q^{15} + 8q^{17} - 16q^{33} - 32q^{47} - 36q^{49} + 16q^{63} + 16q^{65} - 32q^{79} + 44q^{81} - 16q^{95} - 8q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$1023$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$1$$

## 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 1.41421i 0.816497 0.816497i −0.169102 0.985599i $$-0.554087\pi$$
0.985599 + 0.169102i $$0.0540867\pi$$
$$4$$ 0 0
$$5$$ 1.41421 + 1.41421i 0.632456 + 0.632456i 0.948683 0.316228i $$-0.102416\pi$$
−0.316228 + 0.948683i $$0.602416\pi$$
$$6$$ 0 0
$$7$$ 4.00000i 1.51186i 0.654654 + 0.755929i $$0.272814\pi$$
−0.654654 + 0.755929i $$0.727186\pi$$
$$8$$ 0 0
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ −1.41421 1.41421i −0.426401 0.426401i 0.460999 0.887401i $$-0.347491\pi$$
−0.887401 + 0.460999i $$0.847491\pi$$
$$12$$ 0 0
$$13$$ 1.41421 1.41421i 0.392232 0.392232i −0.483250 0.875482i $$-0.660544\pi$$
0.875482 + 0.483250i $$0.160544\pi$$
$$14$$ 0 0
$$15$$ 4.00000 1.03280
$$16$$ 0 0
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ −1.41421 + 1.41421i −0.324443 + 0.324443i −0.850469 0.526026i $$-0.823682\pi$$
0.526026 + 0.850469i $$0.323682\pi$$
$$20$$ 0 0
$$21$$ 5.65685 + 5.65685i 1.23443 + 1.23443i
$$22$$ 0 0
$$23$$ 4.00000i 0.834058i 0.908893 + 0.417029i $$0.136929\pi$$
−0.908893 + 0.417029i $$0.863071\pi$$
$$24$$ 0 0
$$25$$ 1.00000i 0.200000i
$$26$$ 0 0
$$27$$ 2.82843 + 2.82843i 0.544331 + 0.544331i
$$28$$ 0 0
$$29$$ 4.24264 4.24264i 0.787839 0.787839i −0.193301 0.981140i $$-0.561919\pi$$
0.981140 + 0.193301i $$0.0619194\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ −4.00000 −0.696311
$$34$$ 0 0
$$35$$ −5.65685 + 5.65685i −0.956183 + 0.956183i
$$36$$ 0 0
$$37$$ 7.07107 + 7.07107i 1.16248 + 1.16248i 0.983932 + 0.178545i $$0.0571389\pi$$
0.178545 + 0.983932i $$0.442861\pi$$
$$38$$ 0 0
$$39$$ 4.00000i 0.640513i
$$40$$ 0 0
$$41$$ 6.00000i 0.937043i 0.883452 + 0.468521i $$0.155213\pi$$
−0.883452 + 0.468521i $$0.844787\pi$$
$$42$$ 0 0
$$43$$ 4.24264 + 4.24264i 0.646997 + 0.646997i 0.952266 0.305269i $$-0.0987465\pi$$
−0.305269 + 0.952266i $$0.598747\pi$$
$$44$$ 0 0
$$45$$ 1.41421 1.41421i 0.210819 0.210819i
$$46$$ 0 0
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ 0 0
$$49$$ −9.00000 −1.28571
$$50$$ 0 0
$$51$$ 2.82843 2.82843i 0.396059 0.396059i
$$52$$ 0 0
$$53$$ 4.24264 + 4.24264i 0.582772 + 0.582772i 0.935664 0.352892i $$-0.114802\pi$$
−0.352892 + 0.935664i $$0.614802\pi$$
$$54$$ 0 0
$$55$$ 4.00000i 0.539360i
$$56$$ 0 0
$$57$$ 4.00000i 0.529813i
$$58$$ 0 0
$$59$$ −9.89949 9.89949i −1.28880 1.28880i −0.935513 0.353291i $$-0.885063\pi$$
−0.353291 0.935513i $$-0.614937\pi$$
$$60$$ 0 0
$$61$$ −1.41421 + 1.41421i −0.181071 + 0.181071i −0.791823 0.610751i $$-0.790868\pi$$
0.610751 + 0.791823i $$0.290868\pi$$
$$62$$ 0 0
$$63$$ 4.00000 0.503953
$$64$$ 0 0
$$65$$ 4.00000 0.496139
$$66$$ 0 0
$$67$$ 7.07107 7.07107i 0.863868 0.863868i −0.127917 0.991785i $$-0.540829\pi$$
0.991785 + 0.127917i $$0.0408290\pi$$
$$68$$ 0 0
$$69$$ 5.65685 + 5.65685i 0.681005 + 0.681005i
$$70$$ 0 0
$$71$$ 12.0000i 1.42414i −0.702109 0.712069i $$-0.747758\pi$$
0.702109 0.712069i $$-0.252242\pi$$
$$72$$ 0 0
$$73$$ 14.0000i 1.63858i −0.573382 0.819288i $$-0.694369\pi$$
0.573382 0.819288i $$-0.305631\pi$$
$$74$$ 0 0
$$75$$ −1.41421 1.41421i −0.163299 0.163299i
$$76$$ 0 0
$$77$$ 5.65685 5.65685i 0.644658 0.644658i
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 11.0000 1.22222
$$82$$ 0 0
$$83$$ 4.24264 4.24264i 0.465690 0.465690i −0.434825 0.900515i $$-0.643190\pi$$
0.900515 + 0.434825i $$0.143190\pi$$
$$84$$ 0 0
$$85$$ 2.82843 + 2.82843i 0.306786 + 0.306786i
$$86$$ 0 0
$$87$$ 12.0000i 1.28654i
$$88$$ 0 0
$$89$$ 2.00000i 0.212000i −0.994366 0.106000i $$-0.966196\pi$$
0.994366 0.106000i $$-0.0338043\pi$$
$$90$$ 0 0
$$91$$ 5.65685 + 5.65685i 0.592999 + 0.592999i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −4.00000 −0.410391
$$96$$ 0 0
$$97$$ −2.00000 −0.203069 −0.101535 0.994832i $$-0.532375\pi$$
−0.101535 + 0.994832i $$0.532375\pi$$
$$98$$ 0 0
$$99$$ −1.41421 + 1.41421i −0.142134 + 0.142134i
$$100$$ 0 0
$$101$$ −4.24264 4.24264i −0.422159 0.422159i 0.463788 0.885946i $$-0.346490\pi$$
−0.885946 + 0.463788i $$0.846490\pi$$
$$102$$ 0 0
$$103$$ 4.00000i 0.394132i 0.980390 + 0.197066i $$0.0631413\pi$$
−0.980390 + 0.197066i $$0.936859\pi$$
$$104$$ 0 0
$$105$$ 16.0000i 1.56144i
$$106$$ 0 0
$$107$$ −1.41421 1.41421i −0.136717 0.136717i 0.635436 0.772153i $$-0.280820\pi$$
−0.772153 + 0.635436i $$0.780820\pi$$
$$108$$ 0 0
$$109$$ −4.24264 + 4.24264i −0.406371 + 0.406371i −0.880471 0.474100i $$-0.842774\pi$$
0.474100 + 0.880471i $$0.342774\pi$$
$$110$$ 0 0
$$111$$ 20.0000 1.89832
$$112$$ 0 0
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ −5.65685 + 5.65685i −0.527504 + 0.527504i
$$116$$ 0 0
$$117$$ −1.41421 1.41421i −0.130744 0.130744i
$$118$$ 0 0
$$119$$ 8.00000i 0.733359i
$$120$$ 0 0
$$121$$ 7.00000i 0.636364i
$$122$$ 0 0
$$123$$ 8.48528 + 8.48528i 0.765092 + 0.765092i
$$124$$ 0 0
$$125$$ 8.48528 8.48528i 0.758947 0.758947i
$$126$$ 0 0
$$127$$ −16.0000 −1.41977 −0.709885 0.704317i $$-0.751253\pi$$
−0.709885 + 0.704317i $$0.751253\pi$$
$$128$$ 0 0
$$129$$ 12.0000 1.05654
$$130$$ 0 0
$$131$$ −4.24264 + 4.24264i −0.370681 + 0.370681i −0.867725 0.497044i $$-0.834419\pi$$
0.497044 + 0.867725i $$0.334419\pi$$
$$132$$ 0 0
$$133$$ −5.65685 5.65685i −0.490511 0.490511i
$$134$$ 0 0
$$135$$ 8.00000i 0.688530i
$$136$$ 0 0
$$137$$ 10.0000i 0.854358i −0.904167 0.427179i $$-0.859507\pi$$
0.904167 0.427179i $$-0.140493\pi$$
$$138$$ 0 0
$$139$$ −7.07107 7.07107i −0.599760 0.599760i 0.340489 0.940249i $$-0.389408\pi$$
−0.940249 + 0.340489i $$0.889408\pi$$
$$140$$ 0 0
$$141$$ −11.3137 + 11.3137i −0.952786 + 0.952786i
$$142$$ 0 0
$$143$$ −4.00000 −0.334497
$$144$$ 0 0
$$145$$ 12.0000 0.996546
$$146$$ 0 0
$$147$$ −12.7279 + 12.7279i −1.04978 + 1.04978i
$$148$$ 0 0
$$149$$ −12.7279 12.7279i −1.04271 1.04271i −0.999046 0.0436658i $$-0.986096\pi$$
−0.0436658 0.999046i $$-0.513904\pi$$
$$150$$ 0 0
$$151$$ 4.00000i 0.325515i 0.986666 + 0.162758i $$0.0520389\pi$$
−0.986666 + 0.162758i $$0.947961\pi$$
$$152$$ 0 0
$$153$$ 2.00000i 0.161690i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −12.7279 + 12.7279i −1.01580 + 1.01580i −0.0159256 + 0.999873i $$0.505069\pi$$
−0.999873 + 0.0159256i $$0.994931\pi$$
$$158$$ 0 0
$$159$$ 12.0000 0.951662
$$160$$ 0 0
$$161$$ −16.0000 −1.26098
$$162$$ 0 0
$$163$$ 1.41421 1.41421i 0.110770 0.110770i −0.649550 0.760319i $$-0.725042\pi$$
0.760319 + 0.649550i $$0.225042\pi$$
$$164$$ 0 0
$$165$$ −5.65685 5.65685i −0.440386 0.440386i
$$166$$ 0 0
$$167$$ 20.0000i 1.54765i 0.633402 + 0.773823i $$0.281658\pi$$
−0.633402 + 0.773823i $$0.718342\pi$$
$$168$$ 0 0
$$169$$ 9.00000i 0.692308i
$$170$$ 0 0
$$171$$ 1.41421 + 1.41421i 0.108148 + 0.108148i
$$172$$ 0 0
$$173$$ 12.7279 12.7279i 0.967686 0.967686i −0.0318080 0.999494i $$-0.510127\pi$$
0.999494 + 0.0318080i $$0.0101265\pi$$
$$174$$ 0 0
$$175$$ 4.00000 0.302372
$$176$$ 0 0
$$177$$ −28.0000 −2.10461
$$178$$ 0 0
$$179$$ 4.24264 4.24264i 0.317110 0.317110i −0.530546 0.847656i $$-0.678013\pi$$
0.847656 + 0.530546i $$0.178013\pi$$
$$180$$ 0 0
$$181$$ −1.41421 1.41421i −0.105118 0.105118i 0.652592 0.757710i $$-0.273682\pi$$
−0.757710 + 0.652592i $$0.773682\pi$$
$$182$$ 0 0
$$183$$ 4.00000i 0.295689i
$$184$$ 0 0
$$185$$ 20.0000i 1.47043i
$$186$$ 0 0
$$187$$ −2.82843 2.82843i −0.206835 0.206835i
$$188$$ 0 0
$$189$$ −11.3137 + 11.3137i −0.822951 + 0.822951i
$$190$$ 0 0
$$191$$ 16.0000 1.15772 0.578860 0.815427i $$-0.303498\pi$$
0.578860 + 0.815427i $$0.303498\pi$$
$$192$$ 0 0
$$193$$ −2.00000 −0.143963 −0.0719816 0.997406i $$-0.522932\pi$$
−0.0719816 + 0.997406i $$0.522932\pi$$
$$194$$ 0 0
$$195$$ 5.65685 5.65685i 0.405096 0.405096i
$$196$$ 0 0
$$197$$ −9.89949 9.89949i −0.705310 0.705310i 0.260235 0.965545i $$-0.416200\pi$$
−0.965545 + 0.260235i $$0.916200\pi$$
$$198$$ 0 0
$$199$$ 4.00000i 0.283552i 0.989899 + 0.141776i $$0.0452813\pi$$
−0.989899 + 0.141776i $$0.954719\pi$$
$$200$$ 0 0
$$201$$ 20.0000i 1.41069i
$$202$$ 0 0
$$203$$ 16.9706 + 16.9706i 1.19110 + 1.19110i
$$204$$ 0 0
$$205$$ −8.48528 + 8.48528i −0.592638 + 0.592638i
$$206$$ 0 0
$$207$$ 4.00000 0.278019
$$208$$ 0 0
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ 15.5563 15.5563i 1.07094 1.07094i 0.0736598 0.997283i $$-0.476532\pi$$
0.997283 0.0736598i $$-0.0234679\pi$$
$$212$$ 0 0
$$213$$ −16.9706 16.9706i −1.16280 1.16280i
$$214$$ 0 0
$$215$$ 12.0000i 0.818393i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −19.7990 19.7990i −1.33789 1.33789i
$$220$$ 0 0
$$221$$ 2.82843 2.82843i 0.190261 0.190261i
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ 0 0
$$227$$ 12.7279 12.7279i 0.844782 0.844782i −0.144695 0.989476i $$-0.546220\pi$$
0.989476 + 0.144695i $$0.0462199\pi$$
$$228$$ 0 0
$$229$$ −9.89949 9.89949i −0.654177 0.654177i 0.299819 0.953996i $$-0.403074\pi$$
−0.953996 + 0.299819i $$0.903074\pi$$
$$230$$ 0 0
$$231$$ 16.0000i 1.05272i
$$232$$ 0 0
$$233$$ 18.0000i 1.17922i 0.807688 + 0.589610i $$0.200718\pi$$
−0.807688 + 0.589610i $$0.799282\pi$$
$$234$$ 0 0
$$235$$ −11.3137 11.3137i −0.738025 0.738025i
$$236$$ 0 0
$$237$$ −11.3137 + 11.3137i −0.734904 + 0.734904i
$$238$$ 0 0
$$239$$ −24.0000 −1.55243 −0.776215 0.630468i $$-0.782863\pi$$
−0.776215 + 0.630468i $$0.782863\pi$$
$$240$$ 0 0
$$241$$ 2.00000 0.128831 0.0644157 0.997923i $$-0.479482\pi$$
0.0644157 + 0.997923i $$0.479482\pi$$
$$242$$ 0 0
$$243$$ 7.07107 7.07107i 0.453609 0.453609i
$$244$$ 0 0
$$245$$ −12.7279 12.7279i −0.813157 0.813157i
$$246$$ 0 0
$$247$$ 4.00000i 0.254514i
$$248$$ 0 0
$$249$$ 12.0000i 0.760469i
$$250$$ 0 0
$$251$$ 12.7279 + 12.7279i 0.803379 + 0.803379i 0.983622 0.180243i $$-0.0576884\pi$$
−0.180243 + 0.983622i $$0.557688\pi$$
$$252$$ 0 0
$$253$$ 5.65685 5.65685i 0.355643 0.355643i
$$254$$ 0 0
$$255$$ 8.00000 0.500979
$$256$$ 0 0
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ −28.2843 + 28.2843i −1.75750 + 1.75750i
$$260$$ 0 0
$$261$$ −4.24264 4.24264i −0.262613 0.262613i
$$262$$ 0 0
$$263$$ 12.0000i 0.739952i −0.929041 0.369976i $$-0.879366\pi$$
0.929041 0.369976i $$-0.120634\pi$$
$$264$$ 0 0
$$265$$ 12.0000i 0.737154i
$$266$$ 0 0
$$267$$ −2.82843 2.82843i −0.173097 0.173097i
$$268$$ 0 0
$$269$$ 7.07107 7.07107i 0.431131 0.431131i −0.457882 0.889013i $$-0.651392\pi$$
0.889013 + 0.457882i $$0.151392\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ 0 0
$$273$$ 16.0000 0.968364
$$274$$ 0 0
$$275$$ −1.41421 + 1.41421i −0.0852803 + 0.0852803i
$$276$$ 0 0
$$277$$ 4.24264 + 4.24264i 0.254916 + 0.254916i 0.822982 0.568067i $$-0.192309\pi$$
−0.568067 + 0.822982i $$0.692309\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 18.0000i 1.07379i −0.843649 0.536895i $$-0.819597\pi$$
0.843649 0.536895i $$-0.180403\pi$$
$$282$$ 0 0
$$283$$ −4.24264 4.24264i −0.252199 0.252199i 0.569673 0.821872i $$-0.307070\pi$$
−0.821872 + 0.569673i $$0.807070\pi$$
$$284$$ 0 0
$$285$$ −5.65685 + 5.65685i −0.335083 + 0.335083i
$$286$$ 0 0
$$287$$ −24.0000 −1.41668
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ −2.82843 + 2.82843i −0.165805 + 0.165805i
$$292$$ 0 0
$$293$$ −9.89949 9.89949i −0.578335 0.578335i 0.356110 0.934444i $$-0.384103\pi$$
−0.934444 + 0.356110i $$0.884103\pi$$
$$294$$ 0 0
$$295$$ 28.0000i 1.63022i
$$296$$ 0 0
$$297$$ 8.00000i 0.464207i
$$298$$ 0 0
$$299$$ 5.65685 + 5.65685i 0.327144 + 0.327144i
$$300$$ 0 0
$$301$$ −16.9706 + 16.9706i −0.978167 + 0.978167i
$$302$$ 0 0
$$303$$ −12.0000 −0.689382
$$304$$ 0 0
$$305$$ −4.00000 −0.229039
$$306$$ 0 0
$$307$$ −12.7279 + 12.7279i −0.726421 + 0.726421i −0.969905 0.243484i $$-0.921710\pi$$
0.243484 + 0.969905i $$0.421710\pi$$
$$308$$ 0 0
$$309$$ 5.65685 + 5.65685i 0.321807 + 0.321807i
$$310$$ 0 0
$$311$$ 28.0000i 1.58773i −0.608091 0.793867i $$-0.708065\pi$$
0.608091 0.793867i $$-0.291935\pi$$
$$312$$ 0 0
$$313$$ 10.0000i 0.565233i 0.959233 + 0.282617i $$0.0912024\pi$$
−0.959233 + 0.282617i $$0.908798\pi$$
$$314$$ 0 0
$$315$$ 5.65685 + 5.65685i 0.318728 + 0.318728i
$$316$$ 0 0
$$317$$ 4.24264 4.24264i 0.238290 0.238290i −0.577851 0.816142i $$-0.696109\pi$$
0.816142 + 0.577851i $$0.196109\pi$$
$$318$$ 0 0
$$319$$ −12.0000 −0.671871
$$320$$ 0 0
$$321$$ −4.00000 −0.223258
$$322$$ 0 0
$$323$$ −2.82843 + 2.82843i −0.157378 + 0.157378i
$$324$$ 0 0
$$325$$ −1.41421 1.41421i −0.0784465 0.0784465i
$$326$$ 0 0
$$327$$ 12.0000i 0.663602i
$$328$$ 0 0
$$329$$ 32.0000i 1.76422i
$$330$$ 0 0
$$331$$ 9.89949 + 9.89949i 0.544125 + 0.544125i 0.924736 0.380610i $$-0.124286\pi$$
−0.380610 + 0.924736i $$0.624286\pi$$
$$332$$ 0 0
$$333$$ 7.07107 7.07107i 0.387492 0.387492i
$$334$$ 0 0
$$335$$ 20.0000 1.09272
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ 0 0
$$339$$ −2.82843 + 2.82843i −0.153619 + 0.153619i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 8.00000i 0.431959i
$$344$$ 0 0
$$345$$ 16.0000i 0.861411i
$$346$$ 0 0
$$347$$ 12.7279 + 12.7279i 0.683271 + 0.683271i 0.960736 0.277465i $$-0.0894943\pi$$
−0.277465 + 0.960736i $$0.589494\pi$$
$$348$$ 0 0
$$349$$ −7.07107 + 7.07107i −0.378506 + 0.378506i −0.870563 0.492057i $$-0.836245\pi$$
0.492057 + 0.870563i $$0.336245\pi$$
$$350$$ 0 0
$$351$$ 8.00000 0.427008
$$352$$ 0 0
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ 0 0
$$355$$ 16.9706 16.9706i 0.900704 0.900704i
$$356$$ 0 0
$$357$$ 11.3137 + 11.3137i 0.598785 + 0.598785i
$$358$$ 0 0
$$359$$ 4.00000i 0.211112i 0.994413 + 0.105556i $$0.0336622\pi$$
−0.994413 + 0.105556i $$0.966338\pi$$
$$360$$ 0 0
$$361$$ 15.0000i 0.789474i
$$362$$ 0 0
$$363$$ −9.89949 9.89949i −0.519589 0.519589i
$$364$$ 0 0
$$365$$ 19.7990 19.7990i 1.03633 1.03633i
$$366$$ 0 0
$$367$$ −8.00000 −0.417597 −0.208798 0.977959i $$-0.566955\pi$$
−0.208798 + 0.977959i $$0.566955\pi$$
$$368$$ 0 0
$$369$$ 6.00000 0.312348
$$370$$ 0 0
$$371$$ −16.9706 + 16.9706i −0.881068 + 0.881068i
$$372$$ 0 0
$$373$$ −7.07107 7.07107i −0.366126 0.366126i 0.499936 0.866062i $$-0.333357\pi$$
−0.866062 + 0.499936i $$0.833357\pi$$
$$374$$ 0 0
$$375$$ 24.0000i 1.23935i
$$376$$ 0 0
$$377$$ 12.0000i 0.618031i
$$378$$ 0 0
$$379$$ 1.41421 + 1.41421i 0.0726433 + 0.0726433i 0.742495 0.669852i $$-0.233642\pi$$
−0.669852 + 0.742495i $$0.733642\pi$$
$$380$$ 0 0
$$381$$ −22.6274 + 22.6274i −1.15924 + 1.15924i
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 16.0000 0.815436
$$386$$ 0 0
$$387$$ 4.24264 4.24264i 0.215666 0.215666i
$$388$$ 0 0
$$389$$ 7.07107 + 7.07107i 0.358517 + 0.358517i 0.863266 0.504749i $$-0.168415\pi$$
−0.504749 + 0.863266i $$0.668415\pi$$
$$390$$ 0 0
$$391$$ 8.00000i 0.404577i
$$392$$ 0 0
$$393$$ 12.0000i 0.605320i
$$394$$ 0 0
$$395$$ −11.3137 11.3137i −0.569254 0.569254i
$$396$$ 0 0
$$397$$ −4.24264 + 4.24264i −0.212932 + 0.212932i −0.805512 0.592580i $$-0.798110\pi$$
0.592580 + 0.805512i $$0.298110\pi$$
$$398$$ 0 0
$$399$$ −16.0000 −0.801002
$$400$$ 0 0
$$401$$ −30.0000 −1.49813 −0.749064 0.662497i $$-0.769497\pi$$
−0.749064 + 0.662497i $$0.769497\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 15.5563 + 15.5563i 0.773001 + 0.773001i
$$406$$ 0 0
$$407$$ 20.0000i 0.991363i
$$408$$ 0 0
$$409$$ 10.0000i 0.494468i 0.968956 + 0.247234i $$0.0795217\pi$$
−0.968956 + 0.247234i $$0.920478\pi$$
$$410$$ 0 0
$$411$$ −14.1421 14.1421i −0.697580 0.697580i
$$412$$ 0 0
$$413$$ 39.5980 39.5980i 1.94849 1.94849i
$$414$$ 0 0
$$415$$ 12.0000 0.589057
$$416$$ 0 0
$$417$$ −20.0000 −0.979404
$$418$$ 0 0
$$419$$ 18.3848 18.3848i 0.898155 0.898155i −0.0971178 0.995273i $$-0.530962\pi$$
0.995273 + 0.0971178i $$0.0309624\pi$$
$$420$$ 0 0
$$421$$ 24.0416 + 24.0416i 1.17172 + 1.17172i 0.981800 + 0.189917i $$0.0608220\pi$$
0.189917 + 0.981800i $$0.439178\pi$$
$$422$$ 0 0
$$423$$ 8.00000i 0.388973i
$$424$$ 0 0
$$425$$ 2.00000i 0.0970143i
$$426$$ 0 0
$$427$$ −5.65685 5.65685i −0.273754 0.273754i
$$428$$ 0 0
$$429$$ −5.65685 + 5.65685i −0.273115 + 0.273115i
$$430$$ 0 0
$$431$$ 40.0000 1.92673 0.963366 0.268190i $$-0.0864254\pi$$
0.963366 + 0.268190i $$0.0864254\pi$$
$$432$$ 0 0
$$433$$ −30.0000 −1.44171 −0.720854 0.693087i $$-0.756250\pi$$
−0.720854 + 0.693087i $$0.756250\pi$$
$$434$$ 0 0
$$435$$ 16.9706 16.9706i 0.813676 0.813676i
$$436$$ 0 0
$$437$$ −5.65685 5.65685i −0.270604 0.270604i
$$438$$ 0 0
$$439$$ 36.0000i 1.71819i 0.511819 + 0.859093i $$0.328972\pi$$
−0.511819 + 0.859093i $$0.671028\pi$$
$$440$$ 0 0
$$441$$ 9.00000i 0.428571i
$$442$$ 0 0
$$443$$ −4.24264 4.24264i −0.201574 0.201574i 0.599100 0.800674i $$-0.295525\pi$$
−0.800674 + 0.599100i $$0.795525\pi$$
$$444$$ 0 0
$$445$$ 2.82843 2.82843i 0.134080 0.134080i
$$446$$ 0 0
$$447$$ −36.0000 −1.70274
$$448$$ 0 0
$$449$$ −34.0000 −1.60456 −0.802280 0.596948i $$-0.796380\pi$$
−0.802280 + 0.596948i $$0.796380\pi$$
$$450$$ 0 0
$$451$$ 8.48528 8.48528i 0.399556 0.399556i
$$452$$ 0 0
$$453$$ 5.65685 + 5.65685i 0.265782 + 0.265782i
$$454$$ 0 0
$$455$$ 16.0000i 0.750092i
$$456$$ 0 0
$$457$$ 6.00000i 0.280668i 0.990104 + 0.140334i $$0.0448177\pi$$
−0.990104 + 0.140334i $$0.955182\pi$$
$$458$$ 0 0
$$459$$ 5.65685 + 5.65685i 0.264039 + 0.264039i
$$460$$ 0 0
$$461$$ 7.07107 7.07107i 0.329332 0.329332i −0.523000 0.852333i $$-0.675187\pi$$
0.852333 + 0.523000i $$0.175187\pi$$
$$462$$ 0 0
$$463$$ −8.00000 −0.371792 −0.185896 0.982569i $$-0.559519\pi$$
−0.185896 + 0.982569i $$0.559519\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 9.89949 9.89949i 0.458094 0.458094i −0.439935 0.898029i $$-0.644999\pi$$
0.898029 + 0.439935i $$0.144999\pi$$
$$468$$ 0 0
$$469$$ 28.2843 + 28.2843i 1.30605 + 1.30605i
$$470$$ 0 0
$$471$$ 36.0000i 1.65879i
$$472$$ 0 0
$$473$$ 12.0000i 0.551761i
$$474$$ 0 0
$$475$$ 1.41421 + 1.41421i 0.0648886 + 0.0648886i
$$476$$ 0 0
$$477$$ 4.24264 4.24264i 0.194257 0.194257i
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 20.0000 0.911922
$$482$$ 0 0
$$483$$ −22.6274 + 22.6274i −1.02958 + 1.02958i
$$484$$ 0 0
$$485$$ −2.82843 2.82843i −0.128432 0.128432i
$$486$$ 0 0
$$487$$ 20.0000i 0.906287i 0.891438 + 0.453143i $$0.149697\pi$$
−0.891438 + 0.453143i $$0.850303\pi$$
$$488$$ 0 0
$$489$$ 4.00000i 0.180886i
$$490$$ 0 0
$$491$$ −7.07107 7.07107i −0.319113 0.319113i 0.529313 0.848426i $$-0.322450\pi$$
−0.848426 + 0.529313i $$0.822450\pi$$
$$492$$ 0 0
$$493$$ 8.48528 8.48528i 0.382158 0.382158i
$$494$$ 0 0
$$495$$ −4.00000 −0.179787
$$496$$ 0 0
$$497$$ 48.0000 2.15309
$$498$$ 0 0
$$499$$ 15.5563 15.5563i 0.696398 0.696398i −0.267234 0.963632i $$-0.586110\pi$$
0.963632 + 0.267234i $$0.0861096\pi$$
$$500$$ 0 0
$$501$$ 28.2843 + 28.2843i 1.26365 + 1.26365i
$$502$$ 0 0
$$503$$ 20.0000i 0.891756i 0.895094 + 0.445878i $$0.147108\pi$$
−0.895094 + 0.445878i $$0.852892\pi$$
$$504$$ 0 0
$$505$$ 12.0000i 0.533993i
$$506$$ 0 0
$$507$$ 12.7279 + 12.7279i 0.565267 + 0.565267i
$$508$$ 0 0
$$509$$ 9.89949 9.89949i 0.438787 0.438787i −0.452816 0.891604i $$-0.649581\pi$$
0.891604 + 0.452816i $$0.149581\pi$$
$$510$$ 0 0
$$511$$ 56.0000 2.47729
$$512$$ 0 0
$$513$$ −8.00000 −0.353209
$$514$$ 0 0
$$515$$ −5.65685 + 5.65685i −0.249271 + 0.249271i
$$516$$ 0 0
$$517$$ 11.3137 + 11.3137i 0.497576 + 0.497576i
$$518$$ 0 0
$$519$$ 36.0000i 1.58022i
$$520$$ 0 0
$$521$$ 22.0000i 0.963837i 0.876216 + 0.481919i $$0.160060\pi$$
−0.876216 + 0.481919i $$0.839940\pi$$
$$522$$ 0 0
$$523$$ 9.89949 + 9.89949i 0.432875 + 0.432875i 0.889605 0.456730i $$-0.150980\pi$$
−0.456730 + 0.889605i $$0.650980\pi$$
$$524$$ 0 0
$$525$$ 5.65685 5.65685i 0.246885 0.246885i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 7.00000 0.304348
$$530$$ 0 0
$$531$$ −9.89949 + 9.89949i −0.429601 + 0.429601i
$$532$$ 0 0
$$533$$ 8.48528 + 8.48528i 0.367538 + 0.367538i
$$534$$ 0 0
$$535$$ 4.00000i 0.172935i
$$536$$ 0 0
$$537$$ 12.0000i 0.517838i
$$538$$ 0 0
$$539$$ 12.7279 + 12.7279i 0.548230 + 0.548230i
$$540$$ 0 0
$$541$$ −24.0416 + 24.0416i −1.03363 + 1.03363i −0.0342160 + 0.999414i $$0.510893\pi$$
−0.999414 + 0.0342160i $$0.989107\pi$$
$$542$$ 0 0
$$543$$ −4.00000 −0.171656
$$544$$ 0 0
$$545$$ −12.0000 −0.514024
$$546$$ 0 0
$$547$$ −26.8701 + 26.8701i −1.14888 + 1.14888i −0.162108 + 0.986773i $$0.551829\pi$$
−0.986773 + 0.162108i $$0.948171\pi$$
$$548$$ 0 0
$$549$$ 1.41421 + 1.41421i 0.0603572 + 0.0603572i
$$550$$ 0 0
$$551$$ 12.0000i 0.511217i
$$552$$ 0 0
$$553$$ 32.0000i 1.36078i
$$554$$ 0 0
$$555$$ 28.2843 + 28.2843i 1.20060 + 1.20060i
$$556$$ 0 0
$$557$$ 1.41421 1.41421i 0.0599222 0.0599222i −0.676511 0.736433i $$-0.736509\pi$$
0.736433 + 0.676511i $$0.236509\pi$$
$$558$$ 0 0
$$559$$ 12.0000 0.507546
$$560$$ 0 0
$$561$$ −8.00000 −0.337760
$$562$$ 0 0
$$563$$ −12.7279 + 12.7279i −0.536418 + 0.536418i −0.922475 0.386057i $$-0.873837\pi$$
0.386057 + 0.922475i $$0.373837\pi$$
$$564$$ 0 0
$$565$$ −2.82843 2.82843i −0.118993 0.118993i
$$566$$ 0 0
$$567$$ 44.0000i 1.84783i
$$568$$ 0 0
$$569$$ 26.0000i 1.08998i 0.838444 + 0.544988i $$0.183466\pi$$
−0.838444 + 0.544988i $$0.816534\pi$$
$$570$$ 0 0
$$571$$ −26.8701 26.8701i −1.12448 1.12448i −0.991060 0.133417i $$-0.957405\pi$$
−0.133417 0.991060i $$-0.542595\pi$$
$$572$$ 0 0
$$573$$ 22.6274 22.6274i 0.945274 0.945274i
$$574$$ 0 0
$$575$$ 4.00000 0.166812
$$576$$ 0 0
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ 0 0
$$579$$ −2.82843 + 2.82843i −0.117545 + 0.117545i
$$580$$ 0 0
$$581$$ 16.9706 + 16.9706i 0.704058 + 0.704058i
$$582$$ 0 0
$$583$$ 12.0000i 0.496989i
$$584$$ 0 0
$$585$$ 4.00000i 0.165380i
$$586$$ 0 0
$$587$$ −24.0416 24.0416i −0.992304 0.992304i 0.00766632 0.999971i $$-0.497560\pi$$
−0.999971 + 0.00766632i $$0.997560\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −28.0000 −1.15177
$$592$$ 0 0
$$593$$ −18.0000 −0.739171 −0.369586 0.929197i $$-0.620500\pi$$
−0.369586 + 0.929197i $$0.620500\pi$$
$$594$$ 0 0
$$595$$ −11.3137 + 11.3137i −0.463817 + 0.463817i
$$596$$ 0 0
$$597$$ 5.65685 + 5.65685i 0.231520 + 0.231520i
$$598$$ 0 0
$$599$$ 12.0000i 0.490307i −0.969484 0.245153i $$-0.921162\pi$$
0.969484 0.245153i $$-0.0788383\pi$$
$$600$$ 0 0
$$601$$ 30.0000i 1.22373i 0.790964 + 0.611863i $$0.209580\pi$$
−0.790964 + 0.611863i $$0.790420\pi$$
$$602$$ 0 0
$$603$$ −7.07107 7.07107i −0.287956 0.287956i
$$604$$ 0 0
$$605$$ 9.89949 9.89949i 0.402472 0.402472i
$$606$$ 0 0
$$607$$ 16.0000 0.649420 0.324710 0.945814i $$-0.394733\pi$$
0.324710 + 0.945814i $$0.394733\pi$$
$$608$$ 0 0
$$609$$ 48.0000 1.94506
$$610$$ 0 0
$$611$$ −11.3137 + 11.3137i −0.457704 + 0.457704i
$$612$$ 0 0
$$613$$ 24.0416 + 24.0416i 0.971032 + 0.971032i 0.999592 0.0285598i $$-0.00909209\pi$$
−0.0285598 + 0.999592i $$0.509092\pi$$
$$614$$ 0 0
$$615$$ 24.0000i 0.967773i
$$616$$ 0 0
$$617$$ 2.00000i 0.0805170i 0.999189 + 0.0402585i $$0.0128181\pi$$
−0.999189 + 0.0402585i $$0.987182\pi$$
$$618$$ 0 0
$$619$$ 32.5269 + 32.5269i 1.30737 + 1.30737i 0.923309 + 0.384058i $$0.125474\pi$$
0.384058 + 0.923309i $$0.374526\pi$$
$$620$$ 0 0
$$621$$ −11.3137 + 11.3137i −0.454003 + 0.454003i
$$622$$ 0 0
$$623$$ 8.00000 0.320513
$$624$$ 0 0
$$625$$ 19.0000 0.760000
$$626$$ 0 0
$$627$$ 5.65685 5.65685i 0.225913 0.225913i
$$628$$ 0 0
$$629$$ 14.1421 + 14.1421i 0.563884 + 0.563884i
$$630$$ 0 0
$$631$$ 44.0000i 1.75161i −0.482663 0.875806i $$-0.660330\pi$$
0.482663 0.875806i $$-0.339670\pi$$
$$632$$ 0 0
$$633$$ 44.0000i 1.74884i
$$634$$ 0 0
$$635$$ −22.6274 22.6274i −0.897942 0.897942i
$$636$$ 0 0
$$637$$ −12.7279 + 12.7279i −0.504299 + 0.504299i
$$638$$ 0 0
$$639$$ −12.0000 −0.474713
$$640$$ 0 0
$$641$$ 30.0000 1.18493 0.592464 0.805597i $$-0.298155\pi$$
0.592464 + 0.805597i $$0.298155\pi$$
$$642$$ 0 0
$$643$$ 29.6985 29.6985i 1.17119 1.17119i 0.189269 0.981925i $$-0.439388\pi$$
0.981925 0.189269i $$-0.0606117\pi$$
$$644$$ 0 0
$$645$$ 16.9706 + 16.9706i 0.668215 + 0.668215i
$$646$$ 0 0
$$647$$ 12.0000i 0.471769i −0.971781 0.235884i $$-0.924201\pi$$
0.971781 0.235884i $$-0.0757987\pi$$
$$648$$ 0 0
$$649$$ 28.0000i 1.09910i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 29.6985 29.6985i 1.16219 1.16219i 0.178197 0.983995i $$-0.442974\pi$$
0.983995 0.178197i $$-0.0570263\pi$$
$$654$$ 0 0
$$655$$ −12.0000 −0.468879
$$656$$ 0 0
$$657$$ −14.0000 −0.546192
$$658$$ 0 0
$$659$$ 4.24264 4.24264i 0.165270 0.165270i −0.619627 0.784897i $$-0.712716\pi$$
0.784897 + 0.619627i $$0.212716\pi$$
$$660$$ 0 0
$$661$$ −24.0416 24.0416i −0.935111 0.935111i 0.0629083 0.998019i $$-0.479962\pi$$
−0.998019 + 0.0629083i $$0.979962\pi$$
$$662$$ 0 0
$$663$$ 8.00000i 0.310694i
$$664$$ 0 0
$$665$$ 16.0000i 0.620453i
$$666$$ 0 0
$$667$$ 16.9706 + 16.9706i 0.657103 + 0.657103i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 4.00000 0.154418
$$672$$ 0 0
$$673$$ −2.00000 −0.0770943 −0.0385472 0.999257i $$-0.512273\pi$$
−0.0385472 + 0.999257i $$0.512273\pi$$
$$674$$ 0 0
$$675$$ 2.82843 2.82843i 0.108866 0.108866i
$$676$$ 0 0
$$677$$ −15.5563 15.5563i −0.597879 0.597879i 0.341869 0.939748i $$-0.388940\pi$$
−0.939748 + 0.341869i $$0.888940\pi$$
$$678$$ 0 0
$$679$$ 8.00000i 0.307012i
$$680$$ 0 0
$$681$$ 36.0000i 1.37952i
$$682$$ 0 0
$$683$$ −29.6985 29.6985i −1.13638 1.13638i −0.989094 0.147287i $$-0.952946\pi$$
−0.147287 0.989094i $$-0.547054\pi$$
$$684$$ 0 0
$$685$$ 14.1421 14.1421i 0.540343 0.540343i
$$686$$ 0 0
$$687$$ −28.0000 −1.06827
$$688$$ 0 0
$$689$$ 12.0000 0.457164
$$690$$ 0 0
$$691$$ 4.24264 4.24264i 0.161398 0.161398i −0.621788 0.783186i $$-0.713593\pi$$
0.783186 + 0.621788i $$0.213593\pi$$
$$692$$ 0 0
$$693$$ −5.65685 5.65685i −0.214886 0.214886i
$$694$$ 0 0
$$695$$ 20.0000i 0.758643i
$$696$$ 0 0
$$697$$ 12.0000i 0.454532i
$$698$$ 0 0
$$699$$ 25.4558 + 25.4558i 0.962828 + 0.962828i
$$700$$ 0 0
$$701$$ −1.41421 + 1.41421i −0.0534141 + 0.0534141i −0.733309 0.679895i $$-0.762025\pi$$
0.679895 + 0.733309i $$0.262025\pi$$
$$702$$ 0 0
$$703$$ −20.0000 −0.754314
$$704$$ 0 0
$$705$$ −32.0000 −1.20519
$$706$$ 0 0
$$707$$ 16.9706 16.9706i 0.638244 0.638244i
$$708$$ 0 0
$$709$$ −15.5563 15.5563i −0.584231 0.584231i 0.351832 0.936063i $$-0.385559\pi$$
−0.936063 + 0.351832i $$0.885559\pi$$
$$710$$ 0 0
$$711$$ 8.00000i 0.300023i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −5.65685 5.65685i −0.211554 0.211554i
$$716$$ 0 0
$$717$$ −33.9411 + 33.9411i −1.26755 + 1.26755i
$$718$$ 0 0
$$719$$ 24.0000 0.895049 0.447524 0.894272i $$-0.352306\pi$$
0.447524 + 0.894272i $$0.352306\pi$$
$$720$$ 0 0
$$721$$ −16.0000 −0.595871
$$722$$ 0 0
$$723$$ 2.82843 2.82843i 0.105190 0.105190i
$$724$$ 0 0
$$725$$ −4.24264 4.24264i −0.157568 0.157568i
$$726$$ 0 0
$$727$$ 12.0000i 0.445055i −0.974926 0.222528i $$-0.928569\pi$$
0.974926 0.222528i $$-0.0714308\pi$$
$$728$$ 0 0
$$729$$ 13.0000i 0.481481i
$$730$$ 0 0
$$731$$ 8.48528 + 8.48528i 0.313839 + 0.313839i
$$732$$ 0 0
$$733$$ 4.24264 4.24264i 0.156706 0.156706i −0.624400 0.781105i $$-0.714656\pi$$
0.781105 + 0.624400i $$0.214656\pi$$
$$734$$ 0 0
$$735$$ −36.0000 −1.32788
$$736$$ 0 0
$$737$$ −20.0000 −0.736709
$$738$$ 0 0
$$739$$ 12.7279 12.7279i 0.468204 0.468204i −0.433128 0.901332i $$-0.642590\pi$$
0.901332 + 0.433128i $$0.142590\pi$$
$$740$$ 0 0
$$741$$ 5.65685 + 5.65685i 0.207810 + 0.207810i
$$742$$ 0 0
$$743$$ 44.0000i 1.61420i −0.590412 0.807102i $$-0.701035\pi$$
0.590412 0.807102i $$-0.298965\pi$$
$$744$$ 0 0
$$745$$ 36.0000i 1.31894i
$$746$$ 0 0
$$747$$ −4.24264 4.24264i −0.155230 0.155230i
$$748$$ 0 0
$$749$$ 5.65685 5.65685i 0.206697 0.206697i
$$750$$ 0 0
$$751$$ 8.00000 0.291924 0.145962 0.989290i $$-0.453372\pi$$
0.145962 + 0.989290i $$0.453372\pi$$
$$752$$ 0 0
$$753$$ 36.0000 1.31191
$$754$$ 0 0
$$755$$ −5.65685 + 5.65685i −0.205874 + 0.205874i
$$756$$ 0 0
$$757$$ 32.5269 + 32.5269i 1.18221 + 1.18221i 0.979170 + 0.203040i $$0.0650823\pi$$
0.203040 + 0.979170i $$0.434918\pi$$
$$758$$ 0 0
$$759$$ 16.0000i 0.580763i
$$760$$ 0 0
$$761$$ 10.0000i 0.362500i 0.983437 + 0.181250i $$0.0580143\pi$$
−0.983437 + 0.181250i $$0.941986\pi$$
$$762$$ 0 0
$$763$$ −16.9706 16.9706i −0.614376 0.614376i
$$764$$ 0 0
$$765$$ 2.82843 2.82843i 0.102262 0.102262i
$$766$$ 0 0
$$767$$ −28.0000 −1.01102
$$768$$ 0 0
$$769$$ −34.0000 −1.22607 −0.613036 0.790055i $$-0.710052\pi$$
−0.613036 + 0.790055i $$0.710052\pi$$
$$770$$ 0 0
$$771$$ 25.4558 25.4558i 0.916770 0.916770i
$$772$$ 0 0
$$773$$ −38.1838 38.1838i −1.37337 1.37337i −0.855390 0.517985i $$-0.826682\pi$$
−0.517985 0.855390i $$-0.673318\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 80.0000i 2.86998i
$$778$$ 0 0
$$779$$ −8.48528 8.48528i −0.304017 0.304017i
$$780$$ 0 0
$$781$$ −16.9706 + 16.9706i −0.607254 + 0.607254i
$$782$$ 0 0
$$783$$ 24.0000 0.857690
$$784$$ 0 0
$$785$$ −36.0000 −1.28490
$$786$$ 0 0
$$787$$ 15.5563 15.5563i 0.554524 0.554524i −0.373219 0.927743i $$-0.621746\pi$$
0.927743 + 0.373219i $$0.121746\pi$$
$$788$$ 0 0
$$789$$ −16.9706 16.9706i −0.604168 0.604168i
$$790$$ 0 0
$$791$$ 8.00000i 0.284447i
$$792$$ 0 0
$$793$$ 4.00000i 0.142044i
$$794$$ 0 0
$$795$$ 16.9706 + 16.9706i 0.601884 + 0.601884i
$$796$$ 0 0
$$797$$ −12.7279 + 12.7279i −0.450846 + 0.450846i −0.895635 0.444789i $$-0.853279\pi$$
0.444789 + 0.895635i $$0.353279\pi$$
$$798$$ 0 0
$$799$$ −16.0000 −0.566039