# Properties

 Label 325.2.c.e.51.2 Level $325$ Weight $2$ Character 325.51 Analytic conductor $2.595$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$325 = 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 325.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.59513806569$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 65) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 51.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 325.51 Dual form 325.2.c.e.51.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000i q^{6} +3.00000i q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000i q^{6} +3.00000i q^{8} +1.00000 q^{9} -2.00000i q^{11} +2.00000 q^{12} +(-2.00000 + 3.00000i) q^{13} -1.00000 q^{16} +1.00000i q^{18} -6.00000i q^{19} +2.00000 q^{22} +6.00000 q^{23} +6.00000i q^{24} +(-3.00000 - 2.00000i) q^{26} -4.00000 q^{27} -6.00000 q^{29} -6.00000i q^{31} +5.00000i q^{32} -4.00000i q^{33} +1.00000 q^{36} -6.00000i q^{37} +6.00000 q^{38} +(-4.00000 + 6.00000i) q^{39} +8.00000i q^{41} -6.00000 q^{43} -2.00000i q^{44} +6.00000i q^{46} +8.00000i q^{47} -2.00000 q^{48} +7.00000 q^{49} +(-2.00000 + 3.00000i) q^{52} -12.0000 q^{53} -4.00000i q^{54} -12.0000i q^{57} -6.00000i q^{58} +2.00000i q^{59} +6.00000 q^{61} +6.00000 q^{62} -7.00000 q^{64} +4.00000 q^{66} -12.0000i q^{67} +12.0000 q^{69} +2.00000i q^{71} +3.00000i q^{72} -6.00000i q^{73} +6.00000 q^{74} -6.00000i q^{76} +(-6.00000 - 4.00000i) q^{78} -11.0000 q^{81} -8.00000 q^{82} -4.00000i q^{83} -6.00000i q^{86} -12.0000 q^{87} +6.00000 q^{88} -8.00000i q^{89} +6.00000 q^{92} -12.0000i q^{93} -8.00000 q^{94} +10.0000i q^{96} +6.00000i q^{97} +7.00000i q^{98} -2.00000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 4 q^{3} + 2 q^{4} + 2 q^{9} + O(q^{10})$$ $$2 q + 4 q^{3} + 2 q^{4} + 2 q^{9} + 4 q^{12} - 4 q^{13} - 2 q^{16} + 4 q^{22} + 12 q^{23} - 6 q^{26} - 8 q^{27} - 12 q^{29} + 2 q^{36} + 12 q^{38} - 8 q^{39} - 12 q^{43} - 4 q^{48} + 14 q^{49} - 4 q^{52} - 24 q^{53} + 12 q^{61} + 12 q^{62} - 14 q^{64} + 8 q^{66} + 24 q^{69} + 12 q^{74} - 12 q^{78} - 22 q^{81} - 16 q^{82} - 24 q^{87} + 12 q^{88} + 12 q^{92} - 16 q^{94} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$$.

 $$n$$ $$27$$ $$301$$ $$\chi(n)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i 0.935414 + 0.353553i $$0.115027\pi$$
−0.935414 + 0.353553i $$0.884973\pi$$
$$3$$ 2.00000 1.15470 0.577350 0.816497i $$-0.304087\pi$$
0.577350 + 0.816497i $$0.304087\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 2.00000i 0.816497i
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 3.00000i 1.06066i
$$9$$ 1.00000 0.333333
$$10$$ 0 0
$$11$$ 2.00000i 0.603023i −0.953463 0.301511i $$-0.902509\pi$$
0.953463 0.301511i $$-0.0974911\pi$$
$$12$$ 2.00000 0.577350
$$13$$ −2.00000 + 3.00000i −0.554700 + 0.832050i
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 6.00000i 1.37649i −0.725476 0.688247i $$-0.758380\pi$$
0.725476 0.688247i $$-0.241620\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 2.00000 0.426401
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ 6.00000i 1.22474i
$$25$$ 0 0
$$26$$ −3.00000 2.00000i −0.588348 0.392232i
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 6.00000i 1.07763i −0.842424 0.538816i $$-0.818872\pi$$
0.842424 0.538816i $$-0.181128\pi$$
$$32$$ 5.00000i 0.883883i
$$33$$ 4.00000i 0.696311i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 6.00000i 0.986394i −0.869918 0.493197i $$-0.835828\pi$$
0.869918 0.493197i $$-0.164172\pi$$
$$38$$ 6.00000 0.973329
$$39$$ −4.00000 + 6.00000i −0.640513 + 0.960769i
$$40$$ 0 0
$$41$$ 8.00000i 1.24939i 0.780869 + 0.624695i $$0.214777\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ −6.00000 −0.914991 −0.457496 0.889212i $$-0.651253\pi$$
−0.457496 + 0.889212i $$0.651253\pi$$
$$44$$ 2.00000i 0.301511i
$$45$$ 0 0
$$46$$ 6.00000i 0.884652i
$$47$$ 8.00000i 1.16692i 0.812142 + 0.583460i $$0.198301\pi$$
−0.812142 + 0.583460i $$0.801699\pi$$
$$48$$ −2.00000 −0.288675
$$49$$ 7.00000 1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −2.00000 + 3.00000i −0.277350 + 0.416025i
$$53$$ −12.0000 −1.64833 −0.824163 0.566352i $$-0.808354\pi$$
−0.824163 + 0.566352i $$0.808354\pi$$
$$54$$ 4.00000i 0.544331i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 12.0000i 1.58944i
$$58$$ 6.00000i 0.787839i
$$59$$ 2.00000i 0.260378i 0.991489 + 0.130189i $$0.0415584\pi$$
−0.991489 + 0.130189i $$0.958442\pi$$
$$60$$ 0 0
$$61$$ 6.00000 0.768221 0.384111 0.923287i $$-0.374508\pi$$
0.384111 + 0.923287i $$0.374508\pi$$
$$62$$ 6.00000 0.762001
$$63$$ 0 0
$$64$$ −7.00000 −0.875000
$$65$$ 0 0
$$66$$ 4.00000 0.492366
$$67$$ 12.0000i 1.46603i −0.680211 0.733017i $$-0.738112\pi$$
0.680211 0.733017i $$-0.261888\pi$$
$$68$$ 0 0
$$69$$ 12.0000 1.44463
$$70$$ 0 0
$$71$$ 2.00000i 0.237356i 0.992933 + 0.118678i $$0.0378657\pi$$
−0.992933 + 0.118678i $$0.962134\pi$$
$$72$$ 3.00000i 0.353553i
$$73$$ 6.00000i 0.702247i −0.936329 0.351123i $$-0.885800\pi$$
0.936329 0.351123i $$-0.114200\pi$$
$$74$$ 6.00000 0.697486
$$75$$ 0 0
$$76$$ 6.00000i 0.688247i
$$77$$ 0 0
$$78$$ −6.00000 4.00000i −0.679366 0.452911i
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ −11.0000 −1.22222
$$82$$ −8.00000 −0.883452
$$83$$ 4.00000i 0.439057i −0.975606 0.219529i $$-0.929548\pi$$
0.975606 0.219529i $$-0.0704519\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 6.00000i 0.646997i
$$87$$ −12.0000 −1.28654
$$88$$ 6.00000 0.639602
$$89$$ 8.00000i 0.847998i −0.905663 0.423999i $$-0.860626\pi$$
0.905663 0.423999i $$-0.139374\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 6.00000 0.625543
$$93$$ 12.0000i 1.24434i
$$94$$ −8.00000 −0.825137
$$95$$ 0 0
$$96$$ 10.0000i 1.02062i
$$97$$ 6.00000i 0.609208i 0.952479 + 0.304604i $$0.0985241\pi$$
−0.952479 + 0.304604i $$0.901476\pi$$
$$98$$ 7.00000i 0.707107i
$$99$$ 2.00000i 0.201008i
$$100$$ 0 0
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ 0 0
$$103$$ 6.00000 0.591198 0.295599 0.955312i $$-0.404481\pi$$
0.295599 + 0.955312i $$0.404481\pi$$
$$104$$ −9.00000 6.00000i −0.882523 0.588348i
$$105$$ 0 0
$$106$$ 12.0000i 1.16554i
$$107$$ 6.00000 0.580042 0.290021 0.957020i $$-0.406338\pi$$
0.290021 + 0.957020i $$0.406338\pi$$
$$108$$ −4.00000 −0.384900
$$109$$ 12.0000i 1.14939i 0.818367 + 0.574696i $$0.194880\pi$$
−0.818367 + 0.574696i $$0.805120\pi$$
$$110$$ 0 0
$$111$$ 12.0000i 1.13899i
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 12.0000 1.12390
$$115$$ 0 0
$$116$$ −6.00000 −0.557086
$$117$$ −2.00000 + 3.00000i −0.184900 + 0.277350i
$$118$$ −2.00000 −0.184115
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 7.00000 0.636364
$$122$$ 6.00000i 0.543214i
$$123$$ 16.0000i 1.44267i
$$124$$ 6.00000i 0.538816i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ 3.00000i 0.265165i
$$129$$ −12.0000 −1.05654
$$130$$ 0 0
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 4.00000i 0.348155i
$$133$$ 0 0
$$134$$ 12.0000 1.03664
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2.00000i 0.170872i −0.996344 0.0854358i $$-0.972772\pi$$
0.996344 0.0854358i $$-0.0272282\pi$$
$$138$$ 12.0000i 1.02151i
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ 16.0000i 1.34744i
$$142$$ −2.00000 −0.167836
$$143$$ 6.00000 + 4.00000i 0.501745 + 0.334497i
$$144$$ −1.00000 −0.0833333
$$145$$ 0 0
$$146$$ 6.00000 0.496564
$$147$$ 14.0000 1.15470
$$148$$ 6.00000i 0.493197i
$$149$$ 20.0000i 1.63846i 0.573462 + 0.819232i $$0.305600\pi$$
−0.573462 + 0.819232i $$0.694400\pi$$
$$150$$ 0 0
$$151$$ 18.0000i 1.46482i 0.680864 + 0.732410i $$0.261604\pi$$
−0.680864 + 0.732410i $$0.738396\pi$$
$$152$$ 18.0000 1.45999
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −4.00000 + 6.00000i −0.320256 + 0.480384i
$$157$$ −12.0000 −0.957704 −0.478852 0.877896i $$-0.658947\pi$$
−0.478852 + 0.877896i $$0.658947\pi$$
$$158$$ 0 0
$$159$$ −24.0000 −1.90332
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 11.0000i 0.864242i
$$163$$ 12.0000i 0.939913i 0.882690 + 0.469956i $$0.155730\pi$$
−0.882690 + 0.469956i $$0.844270\pi$$
$$164$$ 8.00000i 0.624695i
$$165$$ 0 0
$$166$$ 4.00000 0.310460
$$167$$ 16.0000i 1.23812i 0.785345 + 0.619059i $$0.212486\pi$$
−0.785345 + 0.619059i $$0.787514\pi$$
$$168$$ 0 0
$$169$$ −5.00000 12.0000i −0.384615 0.923077i
$$170$$ 0 0
$$171$$ 6.00000i 0.458831i
$$172$$ −6.00000 −0.457496
$$173$$ 12.0000 0.912343 0.456172 0.889892i $$-0.349220\pi$$
0.456172 + 0.889892i $$0.349220\pi$$
$$174$$ 12.0000i 0.909718i
$$175$$ 0 0
$$176$$ 2.00000i 0.150756i
$$177$$ 4.00000i 0.300658i
$$178$$ 8.00000 0.599625
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 12.0000 0.887066
$$184$$ 18.0000i 1.32698i
$$185$$ 0 0
$$186$$ 12.0000 0.879883
$$187$$ 0 0
$$188$$ 8.00000i 0.583460i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ −14.0000 −1.01036
$$193$$ 6.00000i 0.431889i −0.976406 0.215945i $$-0.930717\pi$$
0.976406 0.215945i $$-0.0692831\pi$$
$$194$$ −6.00000 −0.430775
$$195$$ 0 0
$$196$$ 7.00000 0.500000
$$197$$ 2.00000i 0.142494i 0.997459 + 0.0712470i $$0.0226979\pi$$
−0.997459 + 0.0712470i $$0.977302\pi$$
$$198$$ 2.00000 0.142134
$$199$$ 24.0000 1.70131 0.850657 0.525720i $$-0.176204\pi$$
0.850657 + 0.525720i $$0.176204\pi$$
$$200$$ 0 0
$$201$$ 24.0000i 1.69283i
$$202$$ 6.00000i 0.422159i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 6.00000i 0.418040i
$$207$$ 6.00000 0.417029
$$208$$ 2.00000 3.00000i 0.138675 0.208013i
$$209$$ −12.0000 −0.830057
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ −12.0000 −0.824163
$$213$$ 4.00000i 0.274075i
$$214$$ 6.00000i 0.410152i
$$215$$ 0 0
$$216$$ 12.0000i 0.816497i
$$217$$ 0 0
$$218$$ −12.0000 −0.812743
$$219$$ 12.0000i 0.810885i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 12.0000 0.805387
$$223$$ 24.0000i 1.60716i 0.595198 + 0.803579i $$0.297074\pi$$
−0.595198 + 0.803579i $$0.702926\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 4.00000i 0.265489i 0.991150 + 0.132745i $$0.0423790\pi$$
−0.991150 + 0.132745i $$0.957621\pi$$
$$228$$ 12.0000i 0.794719i
$$229$$ 12.0000i 0.792982i −0.918039 0.396491i $$-0.870228\pi$$
0.918039 0.396491i $$-0.129772\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 18.0000i 1.18176i
$$233$$ −24.0000 −1.57229 −0.786146 0.618041i $$-0.787927\pi$$
−0.786146 + 0.618041i $$0.787927\pi$$
$$234$$ −3.00000 2.00000i −0.196116 0.130744i
$$235$$ 0 0
$$236$$ 2.00000i 0.130189i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 10.0000i 0.646846i −0.946254 0.323423i $$-0.895166\pi$$
0.946254 0.323423i $$-0.104834\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 7.00000i 0.449977i
$$243$$ −10.0000 −0.641500
$$244$$ 6.00000 0.384111
$$245$$ 0 0
$$246$$ −16.0000 −1.02012
$$247$$ 18.0000 + 12.0000i 1.14531 + 0.763542i
$$248$$ 18.0000 1.14300
$$249$$ 8.00000i 0.506979i
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 12.0000i 0.754434i
$$254$$ 2.00000i 0.125491i
$$255$$ 0 0
$$256$$ −17.0000 −1.06250
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 12.0000i 0.747087i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 12.0000i 0.741362i
$$263$$ 6.00000 0.369976 0.184988 0.982741i $$-0.440775\pi$$
0.184988 + 0.982741i $$0.440775\pi$$
$$264$$ 12.0000 0.738549
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 16.0000i 0.979184i
$$268$$ 12.0000i 0.733017i
$$269$$ 18.0000 1.09748 0.548740 0.835993i $$-0.315108\pi$$
0.548740 + 0.835993i $$0.315108\pi$$
$$270$$ 0 0
$$271$$ 6.00000i 0.364474i −0.983255 0.182237i $$-0.941666\pi$$
0.983255 0.182237i $$-0.0583338\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 2.00000 0.120824
$$275$$ 0 0
$$276$$ 12.0000 0.722315
$$277$$ 12.0000 0.721010 0.360505 0.932757i $$-0.382604\pi$$
0.360505 + 0.932757i $$0.382604\pi$$
$$278$$ 4.00000i 0.239904i
$$279$$ 6.00000i 0.359211i
$$280$$ 0 0
$$281$$ 8.00000i 0.477240i −0.971113 0.238620i $$-0.923305\pi$$
0.971113 0.238620i $$-0.0766950\pi$$
$$282$$ −16.0000 −0.952786
$$283$$ −22.0000 −1.30776 −0.653882 0.756596i $$-0.726861\pi$$
−0.653882 + 0.756596i $$0.726861\pi$$
$$284$$ 2.00000i 0.118678i
$$285$$ 0 0
$$286$$ −4.00000 + 6.00000i −0.236525 + 0.354787i
$$287$$ 0 0
$$288$$ 5.00000i 0.294628i
$$289$$ −17.0000 −1.00000
$$290$$ 0 0
$$291$$ 12.0000i 0.703452i
$$292$$ 6.00000i 0.351123i
$$293$$ 26.0000i 1.51894i −0.650545 0.759468i $$-0.725459\pi$$
0.650545 0.759468i $$-0.274541\pi$$
$$294$$ 14.0000i 0.816497i
$$295$$ 0 0
$$296$$ 18.0000 1.04623
$$297$$ 8.00000i 0.464207i
$$298$$ −20.0000 −1.15857
$$299$$ −12.0000 + 18.0000i −0.693978 + 1.04097i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −18.0000 −1.03578
$$303$$ 12.0000 0.689382
$$304$$ 6.00000i 0.344124i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 12.0000i 0.684876i −0.939540 0.342438i $$-0.888747\pi$$
0.939540 0.342438i $$-0.111253\pi$$
$$308$$ 0 0
$$309$$ 12.0000 0.682656
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ −18.0000 12.0000i −1.01905 0.679366i
$$313$$ 8.00000 0.452187 0.226093 0.974106i $$-0.427405\pi$$
0.226093 + 0.974106i $$0.427405\pi$$
$$314$$ 12.0000i 0.677199i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2.00000i 0.112331i 0.998421 + 0.0561656i $$0.0178875\pi$$
−0.998421 + 0.0561656i $$0.982113\pi$$
$$318$$ 24.0000i 1.34585i
$$319$$ 12.0000i 0.671871i
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −11.0000 −0.611111
$$325$$ 0 0
$$326$$ −12.0000 −0.664619
$$327$$ 24.0000i 1.32720i
$$328$$ −24.0000 −1.32518
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 30.0000i 1.64895i 0.565899 + 0.824475i $$0.308529\pi$$
−0.565899 + 0.824475i $$0.691471\pi$$
$$332$$ 4.00000i 0.219529i
$$333$$ 6.00000i 0.328798i
$$334$$ −16.0000 −0.875481
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −32.0000 −1.74315 −0.871576 0.490261i $$-0.836901\pi$$
−0.871576 + 0.490261i $$0.836901\pi$$
$$338$$ 12.0000 5.00000i 0.652714 0.271964i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −12.0000 −0.649836
$$342$$ 6.00000 0.324443
$$343$$ 0 0
$$344$$ 18.0000i 0.970495i
$$345$$ 0 0
$$346$$ 12.0000i 0.645124i
$$347$$ 6.00000 0.322097 0.161048 0.986947i $$-0.448512\pi$$
0.161048 + 0.986947i $$0.448512\pi$$
$$348$$ −12.0000 −0.643268
$$349$$ 12.0000i 0.642345i 0.947021 + 0.321173i $$0.104077\pi$$
−0.947021 + 0.321173i $$0.895923\pi$$
$$350$$ 0 0
$$351$$ 8.00000 12.0000i 0.427008 0.640513i
$$352$$ 10.0000 0.533002
$$353$$ 14.0000i 0.745145i −0.928003 0.372572i $$-0.878476\pi$$
0.928003 0.372572i $$-0.121524\pi$$
$$354$$ −4.00000 −0.212598
$$355$$ 0 0
$$356$$ 8.00000i 0.423999i
$$357$$ 0 0
$$358$$ 12.0000i 0.634220i
$$359$$ 2.00000i 0.105556i −0.998606 0.0527780i $$-0.983192\pi$$
0.998606 0.0527780i $$-0.0168076\pi$$
$$360$$ 0 0
$$361$$ −17.0000 −0.894737
$$362$$ 2.00000i 0.105118i
$$363$$ 14.0000 0.734809
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 12.0000i 0.627250i
$$367$$ 18.0000 0.939592 0.469796 0.882775i $$-0.344327\pi$$
0.469796 + 0.882775i $$0.344327\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ 8.00000i 0.416463i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 12.0000i 0.622171i
$$373$$ 4.00000 0.207112 0.103556 0.994624i $$-0.466978\pi$$
0.103556 + 0.994624i $$0.466978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −24.0000 −1.23771
$$377$$ 12.0000 18.0000i 0.618031 0.927047i
$$378$$ 0 0
$$379$$ 18.0000i 0.924598i 0.886724 + 0.462299i $$0.152975\pi$$
−0.886724 + 0.462299i $$0.847025\pi$$
$$380$$ 0 0
$$381$$ 4.00000 0.204926
$$382$$ 0 0
$$383$$ 8.00000i 0.408781i 0.978889 + 0.204390i $$0.0655212\pi$$
−0.978889 + 0.204390i $$0.934479\pi$$
$$384$$ 6.00000i 0.306186i
$$385$$ 0 0
$$386$$ 6.00000 0.305392
$$387$$ −6.00000 −0.304997
$$388$$ 6.00000i 0.304604i
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 21.0000i 1.06066i
$$393$$ −24.0000 −1.21064
$$394$$ −2.00000 −0.100759
$$395$$ 0 0
$$396$$ 2.00000i 0.100504i
$$397$$ 18.0000i 0.903394i 0.892171 + 0.451697i $$0.149181\pi$$
−0.892171 + 0.451697i $$0.850819\pi$$
$$398$$ 24.0000i 1.20301i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 16.0000i 0.799002i −0.916733 0.399501i $$-0.869183\pi$$
0.916733 0.399501i $$-0.130817\pi$$
$$402$$ 24.0000 1.19701
$$403$$ 18.0000 + 12.0000i 0.896644 + 0.597763i
$$404$$ 6.00000 0.298511
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −12.0000 −0.594818
$$408$$ 0 0
$$409$$ 24.0000i 1.18672i −0.804936 0.593362i $$-0.797800\pi$$
0.804936 0.593362i $$-0.202200\pi$$
$$410$$ 0 0
$$411$$ 4.00000i 0.197305i
$$412$$ 6.00000 0.295599
$$413$$ 0 0
$$414$$ 6.00000i 0.294884i
$$415$$ 0 0
$$416$$ −15.0000 10.0000i −0.735436 0.490290i
$$417$$ 8.00000 0.391762
$$418$$ 12.0000i 0.586939i
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ 36.0000i 1.75453i −0.480004 0.877266i $$-0.659365\pi$$
0.480004 0.877266i $$-0.340635\pi$$
$$422$$ 12.0000i 0.584151i
$$423$$ 8.00000i 0.388973i
$$424$$ 36.0000i 1.74831i
$$425$$ 0 0
$$426$$ −4.00000 −0.193801
$$427$$ 0 0
$$428$$ 6.00000 0.290021
$$429$$ 12.0000 + 8.00000i 0.579365 + 0.386244i
$$430$$ 0 0
$$431$$ 10.0000i 0.481683i 0.970564 + 0.240842i $$0.0774234\pi$$
−0.970564 + 0.240842i $$0.922577\pi$$
$$432$$ 4.00000 0.192450
$$433$$ 16.0000 0.768911 0.384455 0.923144i $$-0.374389\pi$$
0.384455 + 0.923144i $$0.374389\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 12.0000i 0.574696i
$$437$$ 36.0000i 1.72211i
$$438$$ 12.0000 0.573382
$$439$$ −8.00000 −0.381819 −0.190910 0.981608i $$-0.561144\pi$$
−0.190910 + 0.981608i $$0.561144\pi$$
$$440$$ 0 0
$$441$$ 7.00000 0.333333
$$442$$ 0 0
$$443$$ −6.00000 −0.285069 −0.142534 0.989790i $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ 12.0000i 0.569495i
$$445$$ 0 0
$$446$$ −24.0000 −1.13643
$$447$$ 40.0000i 1.89194i
$$448$$ 0 0
$$449$$ 16.0000i 0.755087i −0.925992 0.377543i $$-0.876769\pi$$
0.925992 0.377543i $$-0.123231\pi$$
$$450$$ 0 0
$$451$$ 16.0000 0.753411
$$452$$ 0 0
$$453$$ 36.0000i 1.69143i
$$454$$ −4.00000 −0.187729
$$455$$ 0 0
$$456$$ 36.0000 1.68585
$$457$$ 30.0000i 1.40334i 0.712502 + 0.701670i $$0.247562\pi$$
−0.712502 + 0.701670i $$0.752438\pi$$
$$458$$ 12.0000 0.560723
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 4.00000i 0.186299i 0.995652 + 0.0931493i $$0.0296934\pi$$
−0.995652 + 0.0931493i $$0.970307\pi$$
$$462$$ 0 0
$$463$$ 24.0000i 1.11537i −0.830051 0.557687i $$-0.811689\pi$$
0.830051 0.557687i $$-0.188311\pi$$
$$464$$ 6.00000 0.278543
$$465$$ 0 0
$$466$$ 24.0000i 1.11178i
$$467$$ −18.0000 −0.832941 −0.416470 0.909149i $$-0.636733\pi$$
−0.416470 + 0.909149i $$0.636733\pi$$
$$468$$ −2.00000 + 3.00000i −0.0924500 + 0.138675i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −24.0000 −1.10586
$$472$$ −6.00000 −0.276172
$$473$$ 12.0000i 0.551761i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −12.0000 −0.549442
$$478$$ 10.0000 0.457389
$$479$$ 22.0000i 1.00521i 0.864517 + 0.502603i $$0.167624\pi$$
−0.864517 + 0.502603i $$0.832376\pi$$
$$480$$ 0 0
$$481$$ 18.0000 + 12.0000i 0.820729 + 0.547153i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 7.00000 0.318182
$$485$$ 0 0
$$486$$ 10.0000i 0.453609i
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 18.0000i 0.814822i
$$489$$ 24.0000i 1.08532i
$$490$$ 0 0
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ 16.0000i 0.721336i
$$493$$ 0 0
$$494$$ −12.0000 + 18.0000i −0.539906 + 0.809858i
$$495$$ 0 0
$$496$$ 6.00000i 0.269408i
$$497$$ 0 0
$$498$$ 8.00000 0.358489
$$499$$ 6.00000i 0.268597i −0.990941 0.134298i $$-0.957122\pi$$
0.990941 0.134298i $$-0.0428781\pi$$
$$500$$ 0 0
$$501$$ 32.0000i 1.42965i
$$502$$ 12.0000i 0.535586i
$$503$$ 6.00000 0.267527 0.133763 0.991013i $$-0.457294\pi$$
0.133763 + 0.991013i $$0.457294\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 12.0000 0.533465
$$507$$ −10.0000 24.0000i −0.444116 1.06588i
$$508$$ 2.00000 0.0887357
$$509$$ 20.0000i 0.886484i −0.896402 0.443242i $$-0.853828\pi$$
0.896402 0.443242i $$-0.146172\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 11.0000i 0.486136i
$$513$$ 24.0000i 1.05963i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ −12.0000 −0.528271
$$517$$ 16.0000 0.703679
$$518$$ 0 0
$$519$$ 24.0000 1.05348
$$520$$ 0 0
$$521$$ −30.0000 −1.31432 −0.657162 0.753749i $$-0.728243\pi$$
−0.657162 + 0.753749i $$0.728243\pi$$
$$522$$ 6.00000i 0.262613i
$$523$$ 42.0000 1.83653 0.918266 0.395964i $$-0.129590\pi$$
0.918266 + 0.395964i $$0.129590\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 0 0
$$526$$ 6.00000i 0.261612i
$$527$$ 0 0
$$528$$ 4.00000i 0.174078i
$$529$$ 13.0000 0.565217
$$530$$ 0 0
$$531$$ 2.00000i 0.0867926i
$$532$$ 0 0
$$533$$ −24.0000 16.0000i −1.03956 0.693037i
$$534$$ 16.0000 0.692388
$$535$$ 0 0
$$536$$ 36.0000 1.55496
$$537$$ 24.0000 1.03568
$$538$$ 18.0000i 0.776035i
$$539$$ 14.0000i 0.603023i
$$540$$ 0 0
$$541$$ 12.0000i 0.515920i −0.966156 0.257960i $$-0.916950\pi$$
0.966156 0.257960i $$-0.0830503\pi$$
$$542$$ 6.00000 0.257722
$$543$$ −4.00000 −0.171656
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −18.0000 −0.769624 −0.384812 0.922995i $$-0.625734\pi$$
−0.384812 + 0.922995i $$0.625734\pi$$
$$548$$ 2.00000i 0.0854358i
$$549$$ 6.00000 0.256074
$$550$$ 0 0
$$551$$ 36.0000i 1.53365i
$$552$$ 36.0000i 1.53226i
$$553$$ 0 0
$$554$$ 12.0000i 0.509831i
$$555$$ 0 0
$$556$$ 4.00000 0.169638
$$557$$ 14.0000i 0.593199i −0.955002 0.296600i $$-0.904147\pi$$
0.955002 0.296600i $$-0.0958526\pi$$
$$558$$ 6.00000 0.254000
$$559$$ 12.0000 18.0000i 0.507546 0.761319i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 8.00000 0.337460
$$563$$ −30.0000 −1.26435 −0.632175 0.774826i $$-0.717837\pi$$
−0.632175 + 0.774826i $$0.717837\pi$$
$$564$$ 16.0000i 0.673722i
$$565$$ 0 0
$$566$$ 22.0000i 0.924729i
$$567$$ 0 0
$$568$$ −6.00000 −0.251754
$$569$$ −18.0000 −0.754599 −0.377300 0.926091i $$-0.623147\pi$$
−0.377300 + 0.926091i $$0.623147\pi$$
$$570$$ 0 0
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ 6.00000 + 4.00000i 0.250873 + 0.167248i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −7.00000 −0.291667
$$577$$ 18.0000i 0.749350i −0.927156 0.374675i $$-0.877754\pi$$
0.927156 0.374675i $$-0.122246\pi$$
$$578$$ 17.0000i 0.707107i
$$579$$ 12.0000i 0.498703i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −12.0000 −0.497416
$$583$$ 24.0000i 0.993978i
$$584$$ 18.0000 0.744845
$$585$$ 0 0
$$586$$ 26.0000 1.07405
$$587$$ 20.0000i 0.825488i −0.910847 0.412744i $$-0.864570\pi$$
0.910847 0.412744i $$-0.135430\pi$$
$$588$$ 14.0000 0.577350
$$589$$ −36.0000 −1.48335
$$590$$ 0 0
$$591$$ 4.00000i 0.164538i
$$592$$ 6.00000i 0.246598i
$$593$$ 22.0000i 0.903432i −0.892162 0.451716i $$-0.850812\pi$$
0.892162 0.451716i $$-0.149188\pi$$
$$594$$ −8.00000 −0.328244
$$595$$ 0 0
$$596$$ 20.0000i 0.819232i
$$597$$ 48.0000 1.96451
$$598$$ −18.0000 12.0000i −0.736075 0.490716i
$$599$$ −24.0000 −0.980613 −0.490307 0.871550i $$-0.663115\pi$$
−0.490307 + 0.871550i $$0.663115\pi$$
$$600$$ 0 0
$$601$$ −6.00000 −0.244745 −0.122373 0.992484i $$-0.539050\pi$$
−0.122373 + 0.992484i $$0.539050\pi$$
$$602$$ 0 0
$$603$$ 12.0000i 0.488678i
$$604$$ 18.0000i 0.732410i
$$605$$ 0 0
$$606$$ 12.0000i 0.487467i
$$607$$ 18.0000 0.730597 0.365299 0.930890i $$-0.380967\pi$$
0.365299 + 0.930890i $$0.380967\pi$$
$$608$$ 30.0000 1.21666
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −24.0000 16.0000i −0.970936 0.647291i
$$612$$ 0 0
$$613$$ 30.0000i 1.21169i 0.795583 + 0.605844i $$0.207165\pi$$
−0.795583 + 0.605844i $$0.792835\pi$$
$$614$$ 12.0000 0.484281
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 34.0000i 1.36879i −0.729112 0.684394i $$-0.760067\pi$$
0.729112 0.684394i $$-0.239933\pi$$
$$618$$ 12.0000i 0.482711i
$$619$$ 18.0000i 0.723481i 0.932279 + 0.361741i $$0.117817\pi$$
−0.932279 + 0.361741i $$0.882183\pi$$
$$620$$ 0 0
$$621$$ −24.0000 −0.963087
$$622$$ 24.0000i 0.962312i
$$623$$ 0 0
$$624$$ 4.00000 6.00000i 0.160128 0.240192i
$$625$$ 0 0
$$626$$ 8.00000i 0.319744i
$$627$$ −24.0000 −0.958468
$$628$$ −12.0000 −0.478852
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 30.0000i 1.19428i −0.802137 0.597141i $$-0.796303\pi$$
0.802137 0.597141i $$-0.203697\pi$$
$$632$$ 0 0
$$633$$ −24.0000 −0.953914
$$634$$ −2.00000 −0.0794301
$$635$$ 0 0
$$636$$ −24.0000 −0.951662
$$637$$ −14.0000 + 21.0000i −0.554700 + 0.832050i
$$638$$ −12.0000 −0.475085
$$639$$ 2.00000i 0.0791188i
$$640$$ 0 0
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ 12.0000i 0.473602i
$$643$$ 36.0000i 1.41970i −0.704352 0.709851i $$-0.748762\pi$$
0.704352 0.709851i $$-0.251238\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −6.00000 −0.235884 −0.117942 0.993020i $$-0.537630\pi$$
−0.117942 + 0.993020i $$0.537630\pi$$
$$648$$ 33.0000i 1.29636i
$$649$$ 4.00000 0.157014
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 12.0000i 0.469956i
$$653$$ −36.0000 −1.40879 −0.704394 0.709809i $$-0.748781\pi$$
−0.704394 + 0.709809i $$0.748781\pi$$
$$654$$ −24.0000 −0.938474
$$655$$ 0 0
$$656$$ 8.00000i 0.312348i
$$657$$ 6.00000i 0.234082i
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ 12.0000i 0.466746i 0.972387 + 0.233373i $$0.0749763\pi$$
−0.972387 + 0.233373i $$0.925024\pi$$
$$662$$ −30.0000 −1.16598
$$663$$ 0 0
$$664$$ 12.0000 0.465690
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ −36.0000 −1.39393
$$668$$ 16.0000i 0.619059i
$$669$$ 48.0000i 1.85579i
$$670$$ 0 0
$$671$$ 12.0000i 0.463255i
$$672$$ 0 0
$$673$$ 48.0000 1.85026 0.925132 0.379646i $$-0.123954\pi$$
0.925132 + 0.379646i $$0.123954\pi$$
$$674$$ 32.0000i 1.23259i
$$675$$ 0 0
$$676$$ −5.00000 12.0000i −0.192308 0.461538i
$$677$$ −36.0000 −1.38359 −0.691796 0.722093i $$-0.743180\pi$$
−0.691796 + 0.722093i $$0.743180\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 8.00000i 0.306561i
$$682$$ 12.0000i 0.459504i
$$683$$ 44.0000i 1.68361i −0.539779 0.841807i $$-0.681492\pi$$
0.539779 0.841807i $$-0.318508\pi$$
$$684$$ 6.00000i 0.229416i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 24.0000i 0.915657i
$$688$$ 6.00000 0.228748
$$689$$ 24.0000 36.0000i 0.914327 1.37149i
$$690$$ 0 0
$$691$$ 42.0000i 1.59776i −0.601494 0.798878i $$-0.705427\pi$$
0.601494 0.798878i $$-0.294573\pi$$
$$692$$ 12.0000 0.456172
$$693$$ 0 0
$$694$$ 6.00000i 0.227757i
$$695$$ 0 0
$$696$$ 36.0000i 1.36458i
$$697$$ 0 0
$$698$$ −12.0000 −0.454207
$$699$$ −48.0000 −1.81553
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 12.0000 + 8.00000i 0.452911 + 0.301941i
$$703$$ −36.0000 −1.35777
$$704$$ 14.0000i 0.527645i
$$705$$ 0 0
$$706$$ 14.0000 0.526897
$$707$$ 0 0
$$708$$ 4.00000i 0.150329i
$$709$$ 12.0000i 0.450669i −0.974281 0.225335i $$-0.927652\pi$$
0.974281 0.225335i $$-0.0723476\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 24.0000 0.899438
$$713$$ 36.0000i 1.34821i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 12.0000 0.448461
$$717$$ 20.0000i 0.746914i
$$718$$ 2.00000 0.0746393
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 17.0000i 0.632674i
$$723$$ 0 0
$$724$$ −2.00000 −0.0743294
$$725$$ 0 0
$$726$$ 14.0000i 0.519589i
$$727$$ 26.0000 0.964287 0.482143 0.876092i $$-0.339858\pi$$
0.482143 + 0.876092i $$0.339858\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 12.0000 0.443533
$$733$$ 42.0000i 1.55131i −0.631160 0.775653i $$-0.717421\pi$$
0.631160 0.775653i $$-0.282579\pi$$
$$734$$ 18.0000i 0.664392i
$$735$$ 0 0
$$736$$ 30.0000i 1.10581i
$$737$$ −24.0000 −0.884051
$$738$$ −8.00000 −0.294484
$$739$$ 6.00000i 0.220714i −0.993892 0.110357i $$-0.964801\pi$$
0.993892 0.110357i $$-0.0351994\pi$$
$$740$$ 0 0
$$741$$ 36.0000 + 24.0000i 1.32249 + 0.881662i
$$742$$ 0 0
$$743$$ 16.0000i 0.586983i −0.955962 0.293492i $$-0.905183\pi$$
0.955962 0.293492i $$-0.0948173\pi$$
$$744$$ 36.0000 1.31982
$$745$$ 0 0
$$746$$ 4.00000i 0.146450i
$$747$$ 4.00000i 0.146352i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −32.0000 −1.16770 −0.583848 0.811863i $$-0.698454\pi$$
−0.583848 + 0.811863i $$0.698454\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ 24.0000 0.874609
$$754$$ 18.0000 + 12.0000i 0.655521 + 0.437014i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −20.0000 −0.726912 −0.363456 0.931611i $$-0.618403\pi$$
−0.363456 + 0.931611i $$0.618403\pi$$
$$758$$ −18.0000 −0.653789
$$759$$ 24.0000i 0.871145i
$$760$$ 0 0
$$761$$ 40.0000i 1.45000i 0.688749 + 0.724999i $$0.258160\pi$$
−0.688749 + 0.724999i $$0.741840\pi$$
$$762$$ 4.00000i 0.144905i
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −8.00000 −0.289052
$$767$$ −6.00000 4.00000i −0.216647 0.144432i
$$768$$ −34.0000 −1.22687
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 6.00000i 0.215945i
$$773$$ 38.0000i 1.36677i 0.730061 + 0.683383i $$0.239492\pi$$
−0.730061 + 0.683383i $$0.760508\pi$$
$$774$$ 6.00000i 0.215666i
$$775$$ 0 0
$$776$$ −18.0000 −0.646162
$$777$$ 0 0
$$778$$ 6.00000i 0.215110i
$$779$$ 48.0000 1.71978
$$780$$ 0 0
$$781$$ 4.00000 0.143131
$$782$$ 0 0
$$783$$ 24.0000 0.857690
$$784$$ −7.00000 −0.250000
$$785$$ 0 0
$$786$$ 24.0000i 0.856052i
$$787$$ 12.0000i 0.427754i −0.976861 0.213877i $$-0.931391\pi$$
0.976861 0.213877i $$-0.0686091\pi$$
$$788$$ 2.00000i 0.0712470i
$$789$$ 12.0000 0.427211
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 6.00000 0.213201
$$793$$ −12.0000 + 18.0000i −0.426132 + 0.639199i
$$794$$ −18.0000 −0.638796
$$795$$ 0 0
$$796$$ 24.0000 0.850657
$$797$$ −12.0000 −0.425062 −0.212531 0.977154i $$-0.568171\pi$$
−0.212531 + 0.977154i $$0.568171\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$