# Properties

 Label 1110.2.e.a.739.2 Level $1110$ Weight $2$ Character 1110.739 Analytic conductor $8.863$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.86339462436$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 739.2 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1110.739 Dual form 1110.2.e.a.739.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000i q^{6} -3.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000i q^{6} -3.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(-2.00000 - 1.00000i) q^{10} -3.00000 q^{11} +1.00000i q^{12} -4.00000 q^{13} +3.00000i q^{14} +(-1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +7.00000 q^{17} +1.00000 q^{18} +4.00000i q^{19} +(2.00000 + 1.00000i) q^{20} +3.00000 q^{21} +3.00000 q^{22} +6.00000 q^{23} -1.00000i q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} -1.00000i q^{27} -3.00000i q^{28} +9.00000i q^{29} +(1.00000 - 2.00000i) q^{30} +5.00000i q^{31} -1.00000 q^{32} -3.00000i q^{33} -7.00000 q^{34} +(3.00000 - 6.00000i) q^{35} -1.00000 q^{36} +(6.00000 + 1.00000i) q^{37} -4.00000i q^{38} -4.00000i q^{39} +(-2.00000 - 1.00000i) q^{40} +7.00000 q^{41} -3.00000 q^{42} +1.00000 q^{43} -3.00000 q^{44} +(-2.00000 - 1.00000i) q^{45} -6.00000 q^{46} -8.00000i q^{47} +1.00000i q^{48} -2.00000 q^{49} +(-3.00000 - 4.00000i) q^{50} +7.00000i q^{51} -4.00000 q^{52} -1.00000i q^{53} +1.00000i q^{54} +(-6.00000 - 3.00000i) q^{55} +3.00000i q^{56} -4.00000 q^{57} -9.00000i q^{58} -6.00000i q^{59} +(-1.00000 + 2.00000i) q^{60} +5.00000i q^{61} -5.00000i q^{62} +3.00000i q^{63} +1.00000 q^{64} +(-8.00000 - 4.00000i) q^{65} +3.00000i q^{66} +2.00000i q^{67} +7.00000 q^{68} +6.00000i q^{69} +(-3.00000 + 6.00000i) q^{70} +12.0000 q^{71} +1.00000 q^{72} +4.00000i q^{73} +(-6.00000 - 1.00000i) q^{74} +(-4.00000 + 3.00000i) q^{75} +4.00000i q^{76} +9.00000i q^{77} +4.00000i q^{78} +4.00000i q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -7.00000 q^{82} +14.0000i q^{83} +3.00000 q^{84} +(14.0000 + 7.00000i) q^{85} -1.00000 q^{86} -9.00000 q^{87} +3.00000 q^{88} -6.00000i q^{89} +(2.00000 + 1.00000i) q^{90} +12.0000i q^{91} +6.00000 q^{92} -5.00000 q^{93} +8.00000i q^{94} +(-4.00000 + 8.00000i) q^{95} -1.00000i q^{96} +7.00000 q^{97} +2.00000 q^{98} +3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{2} + 2q^{4} + 4q^{5} - 2q^{8} - 2q^{9} + O(q^{10})$$ $$2q - 2q^{2} + 2q^{4} + 4q^{5} - 2q^{8} - 2q^{9} - 4q^{10} - 6q^{11} - 8q^{13} - 2q^{15} + 2q^{16} + 14q^{17} + 2q^{18} + 4q^{20} + 6q^{21} + 6q^{22} + 12q^{23} + 6q^{25} + 8q^{26} + 2q^{30} - 2q^{32} - 14q^{34} + 6q^{35} - 2q^{36} + 12q^{37} - 4q^{40} + 14q^{41} - 6q^{42} + 2q^{43} - 6q^{44} - 4q^{45} - 12q^{46} - 4q^{49} - 6q^{50} - 8q^{52} - 12q^{55} - 8q^{57} - 2q^{60} + 2q^{64} - 16q^{65} + 14q^{68} - 6q^{70} + 24q^{71} + 2q^{72} - 12q^{74} - 8q^{75} + 4q^{80} + 2q^{81} - 14q^{82} + 6q^{84} + 28q^{85} - 2q^{86} - 18q^{87} + 6q^{88} + 4q^{90} + 12q^{92} - 10q^{93} - 8q^{95} + 14q^{97} + 4q^{98} + 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$$.

 $$n$$ $$371$$ $$631$$ $$667$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 1.00000i 0.577350i
$$4$$ 1.00000 0.500000
$$5$$ 2.00000 + 1.00000i 0.894427 + 0.447214i
$$6$$ 1.00000i 0.408248i
$$7$$ 3.00000i 1.13389i −0.823754 0.566947i $$-0.808125\pi$$
0.823754 0.566947i $$-0.191875\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −1.00000 −0.333333
$$10$$ −2.00000 1.00000i −0.632456 0.316228i
$$11$$ −3.00000 −0.904534 −0.452267 0.891883i $$-0.649385\pi$$
−0.452267 + 0.891883i $$0.649385\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 3.00000i 0.801784i
$$15$$ −1.00000 + 2.00000i −0.258199 + 0.516398i
$$16$$ 1.00000 0.250000
$$17$$ 7.00000 1.69775 0.848875 0.528594i $$-0.177281\pi$$
0.848875 + 0.528594i $$0.177281\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 4.00000i 0.917663i 0.888523 + 0.458831i $$0.151732\pi$$
−0.888523 + 0.458831i $$0.848268\pi$$
$$20$$ 2.00000 + 1.00000i 0.447214 + 0.223607i
$$21$$ 3.00000 0.654654
$$22$$ 3.00000 0.639602
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ 1.00000i 0.204124i
$$25$$ 3.00000 + 4.00000i 0.600000 + 0.800000i
$$26$$ 4.00000 0.784465
$$27$$ 1.00000i 0.192450i
$$28$$ 3.00000i 0.566947i
$$29$$ 9.00000i 1.67126i 0.549294 + 0.835629i $$0.314897\pi$$
−0.549294 + 0.835629i $$0.685103\pi$$
$$30$$ 1.00000 2.00000i 0.182574 0.365148i
$$31$$ 5.00000i 0.898027i 0.893525 + 0.449013i $$0.148224\pi$$
−0.893525 + 0.449013i $$0.851776\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 3.00000i 0.522233i
$$34$$ −7.00000 −1.20049
$$35$$ 3.00000 6.00000i 0.507093 1.01419i
$$36$$ −1.00000 −0.166667
$$37$$ 6.00000 + 1.00000i 0.986394 + 0.164399i
$$38$$ 4.00000i 0.648886i
$$39$$ 4.00000i 0.640513i
$$40$$ −2.00000 1.00000i −0.316228 0.158114i
$$41$$ 7.00000 1.09322 0.546608 0.837389i $$-0.315919\pi$$
0.546608 + 0.837389i $$0.315919\pi$$
$$42$$ −3.00000 −0.462910
$$43$$ 1.00000 0.152499 0.0762493 0.997089i $$-0.475706\pi$$
0.0762493 + 0.997089i $$0.475706\pi$$
$$44$$ −3.00000 −0.452267
$$45$$ −2.00000 1.00000i −0.298142 0.149071i
$$46$$ −6.00000 −0.884652
$$47$$ 8.00000i 1.16692i −0.812142 0.583460i $$-0.801699\pi$$
0.812142 0.583460i $$-0.198301\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ −2.00000 −0.285714
$$50$$ −3.00000 4.00000i −0.424264 0.565685i
$$51$$ 7.00000i 0.980196i
$$52$$ −4.00000 −0.554700
$$53$$ 1.00000i 0.137361i −0.997639 0.0686803i $$-0.978121\pi$$
0.997639 0.0686803i $$-0.0218788\pi$$
$$54$$ 1.00000i 0.136083i
$$55$$ −6.00000 3.00000i −0.809040 0.404520i
$$56$$ 3.00000i 0.400892i
$$57$$ −4.00000 −0.529813
$$58$$ 9.00000i 1.18176i
$$59$$ 6.00000i 0.781133i −0.920575 0.390567i $$-0.872279\pi$$
0.920575 0.390567i $$-0.127721\pi$$
$$60$$ −1.00000 + 2.00000i −0.129099 + 0.258199i
$$61$$ 5.00000i 0.640184i 0.947386 + 0.320092i $$0.103714\pi$$
−0.947386 + 0.320092i $$0.896286\pi$$
$$62$$ 5.00000i 0.635001i
$$63$$ 3.00000i 0.377964i
$$64$$ 1.00000 0.125000
$$65$$ −8.00000 4.00000i −0.992278 0.496139i
$$66$$ 3.00000i 0.369274i
$$67$$ 2.00000i 0.244339i 0.992509 + 0.122169i $$0.0389851\pi$$
−0.992509 + 0.122169i $$0.961015\pi$$
$$68$$ 7.00000 0.848875
$$69$$ 6.00000i 0.722315i
$$70$$ −3.00000 + 6.00000i −0.358569 + 0.717137i
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 1.00000 0.117851
$$73$$ 4.00000i 0.468165i 0.972217 + 0.234082i $$0.0752085\pi$$
−0.972217 + 0.234082i $$0.924791\pi$$
$$74$$ −6.00000 1.00000i −0.697486 0.116248i
$$75$$ −4.00000 + 3.00000i −0.461880 + 0.346410i
$$76$$ 4.00000i 0.458831i
$$77$$ 9.00000i 1.02565i
$$78$$ 4.00000i 0.452911i
$$79$$ 4.00000i 0.450035i 0.974355 + 0.225018i $$0.0722440\pi$$
−0.974355 + 0.225018i $$0.927756\pi$$
$$80$$ 2.00000 + 1.00000i 0.223607 + 0.111803i
$$81$$ 1.00000 0.111111
$$82$$ −7.00000 −0.773021
$$83$$ 14.0000i 1.53670i 0.640030 + 0.768350i $$0.278922\pi$$
−0.640030 + 0.768350i $$0.721078\pi$$
$$84$$ 3.00000 0.327327
$$85$$ 14.0000 + 7.00000i 1.51851 + 0.759257i
$$86$$ −1.00000 −0.107833
$$87$$ −9.00000 −0.964901
$$88$$ 3.00000 0.319801
$$89$$ 6.00000i 0.635999i −0.948091 0.317999i $$-0.896989\pi$$
0.948091 0.317999i $$-0.103011\pi$$
$$90$$ 2.00000 + 1.00000i 0.210819 + 0.105409i
$$91$$ 12.0000i 1.25794i
$$92$$ 6.00000 0.625543
$$93$$ −5.00000 −0.518476
$$94$$ 8.00000i 0.825137i
$$95$$ −4.00000 + 8.00000i −0.410391 + 0.820783i
$$96$$ 1.00000i 0.102062i
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ 2.00000 0.202031
$$99$$ 3.00000 0.301511
$$100$$ 3.00000 + 4.00000i 0.300000 + 0.400000i
$$101$$ 2.00000 0.199007 0.0995037 0.995037i $$-0.468274\pi$$
0.0995037 + 0.995037i $$0.468274\pi$$
$$102$$ 7.00000i 0.693103i
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ 4.00000 0.392232
$$105$$ 6.00000 + 3.00000i 0.585540 + 0.292770i
$$106$$ 1.00000i 0.0971286i
$$107$$ 18.0000i 1.74013i −0.492941 0.870063i $$-0.664078\pi$$
0.492941 0.870063i $$-0.335922\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ 11.0000i 1.05361i −0.849987 0.526804i $$-0.823390\pi$$
0.849987 0.526804i $$-0.176610\pi$$
$$110$$ 6.00000 + 3.00000i 0.572078 + 0.286039i
$$111$$ −1.00000 + 6.00000i −0.0949158 + 0.569495i
$$112$$ 3.00000i 0.283473i
$$113$$ 1.00000 0.0940721 0.0470360 0.998893i $$-0.485022\pi$$
0.0470360 + 0.998893i $$0.485022\pi$$
$$114$$ 4.00000 0.374634
$$115$$ 12.0000 + 6.00000i 1.11901 + 0.559503i
$$116$$ 9.00000i 0.835629i
$$117$$ 4.00000 0.369800
$$118$$ 6.00000i 0.552345i
$$119$$ 21.0000i 1.92507i
$$120$$ 1.00000 2.00000i 0.0912871 0.182574i
$$121$$ −2.00000 −0.181818
$$122$$ 5.00000i 0.452679i
$$123$$ 7.00000i 0.631169i
$$124$$ 5.00000i 0.449013i
$$125$$ 2.00000 + 11.0000i 0.178885 + 0.983870i
$$126$$ 3.00000i 0.267261i
$$127$$ 8.00000i 0.709885i −0.934888 0.354943i $$-0.884500\pi$$
0.934888 0.354943i $$-0.115500\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 1.00000i 0.0880451i
$$130$$ 8.00000 + 4.00000i 0.701646 + 0.350823i
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 3.00000i 0.261116i
$$133$$ 12.0000 1.04053
$$134$$ 2.00000i 0.172774i
$$135$$ 1.00000 2.00000i 0.0860663 0.172133i
$$136$$ −7.00000 −0.600245
$$137$$ 12.0000i 1.02523i 0.858619 + 0.512615i $$0.171323\pi$$
−0.858619 + 0.512615i $$0.828677\pi$$
$$138$$ 6.00000i 0.510754i
$$139$$ −15.0000 −1.27228 −0.636142 0.771572i $$-0.719471\pi$$
−0.636142 + 0.771572i $$0.719471\pi$$
$$140$$ 3.00000 6.00000i 0.253546 0.507093i
$$141$$ 8.00000 0.673722
$$142$$ −12.0000 −1.00702
$$143$$ 12.0000 1.00349
$$144$$ −1.00000 −0.0833333
$$145$$ −9.00000 + 18.0000i −0.747409 + 1.49482i
$$146$$ 4.00000i 0.331042i
$$147$$ 2.00000i 0.164957i
$$148$$ 6.00000 + 1.00000i 0.493197 + 0.0821995i
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 4.00000 3.00000i 0.326599 0.244949i
$$151$$ 2.00000 0.162758 0.0813788 0.996683i $$-0.474068\pi$$
0.0813788 + 0.996683i $$0.474068\pi$$
$$152$$ 4.00000i 0.324443i
$$153$$ −7.00000 −0.565916
$$154$$ 9.00000i 0.725241i
$$155$$ −5.00000 + 10.0000i −0.401610 + 0.803219i
$$156$$ 4.00000i 0.320256i
$$157$$ 7.00000i 0.558661i 0.960195 + 0.279330i $$0.0901125\pi$$
−0.960195 + 0.279330i $$0.909888\pi$$
$$158$$ 4.00000i 0.318223i
$$159$$ 1.00000 0.0793052
$$160$$ −2.00000 1.00000i −0.158114 0.0790569i
$$161$$ 18.0000i 1.41860i
$$162$$ −1.00000 −0.0785674
$$163$$ −9.00000 −0.704934 −0.352467 0.935824i $$-0.614657\pi$$
−0.352467 + 0.935824i $$0.614657\pi$$
$$164$$ 7.00000 0.546608
$$165$$ 3.00000 6.00000i 0.233550 0.467099i
$$166$$ 14.0000i 1.08661i
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ −3.00000 −0.231455
$$169$$ 3.00000 0.230769
$$170$$ −14.0000 7.00000i −1.07375 0.536875i
$$171$$ 4.00000i 0.305888i
$$172$$ 1.00000 0.0762493
$$173$$ 9.00000i 0.684257i 0.939653 + 0.342129i $$0.111148\pi$$
−0.939653 + 0.342129i $$0.888852\pi$$
$$174$$ 9.00000 0.682288
$$175$$ 12.0000 9.00000i 0.907115 0.680336i
$$176$$ −3.00000 −0.226134
$$177$$ 6.00000 0.450988
$$178$$ 6.00000i 0.449719i
$$179$$ 4.00000i 0.298974i 0.988764 + 0.149487i $$0.0477622\pi$$
−0.988764 + 0.149487i $$0.952238\pi$$
$$180$$ −2.00000 1.00000i −0.149071 0.0745356i
$$181$$ −18.0000 −1.33793 −0.668965 0.743294i $$-0.733262\pi$$
−0.668965 + 0.743294i $$0.733262\pi$$
$$182$$ 12.0000i 0.889499i
$$183$$ −5.00000 −0.369611
$$184$$ −6.00000 −0.442326
$$185$$ 11.0000 + 8.00000i 0.808736 + 0.588172i
$$186$$ 5.00000 0.366618
$$187$$ −21.0000 −1.53567
$$188$$ 8.00000i 0.583460i
$$189$$ −3.00000 −0.218218
$$190$$ 4.00000 8.00000i 0.290191 0.580381i
$$191$$ 15.0000i 1.08536i 0.839939 + 0.542681i $$0.182591\pi$$
−0.839939 + 0.542681i $$0.817409\pi$$
$$192$$ 1.00000i 0.0721688i
$$193$$ −14.0000 −1.00774 −0.503871 0.863779i $$-0.668091\pi$$
−0.503871 + 0.863779i $$0.668091\pi$$
$$194$$ −7.00000 −0.502571
$$195$$ 4.00000 8.00000i 0.286446 0.572892i
$$196$$ −2.00000 −0.142857
$$197$$ 18.0000i 1.28245i −0.767354 0.641223i $$-0.778427\pi$$
0.767354 0.641223i $$-0.221573\pi$$
$$198$$ −3.00000 −0.213201
$$199$$ 16.0000i 1.13421i −0.823646 0.567105i $$-0.808063\pi$$
0.823646 0.567105i $$-0.191937\pi$$
$$200$$ −3.00000 4.00000i −0.212132 0.282843i
$$201$$ −2.00000 −0.141069
$$202$$ −2.00000 −0.140720
$$203$$ 27.0000 1.89503
$$204$$ 7.00000i 0.490098i
$$205$$ 14.0000 + 7.00000i 0.977802 + 0.488901i
$$206$$ 14.0000 0.975426
$$207$$ −6.00000 −0.417029
$$208$$ −4.00000 −0.277350
$$209$$ 12.0000i 0.830057i
$$210$$ −6.00000 3.00000i −0.414039 0.207020i
$$211$$ −13.0000 −0.894957 −0.447478 0.894295i $$-0.647678\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 1.00000i 0.0686803i
$$213$$ 12.0000i 0.822226i
$$214$$ 18.0000i 1.23045i
$$215$$ 2.00000 + 1.00000i 0.136399 + 0.0681994i
$$216$$ 1.00000i 0.0680414i
$$217$$ 15.0000 1.01827
$$218$$ 11.0000i 0.745014i
$$219$$ −4.00000 −0.270295
$$220$$ −6.00000 3.00000i −0.404520 0.202260i
$$221$$ −28.0000 −1.88348
$$222$$ 1.00000 6.00000i 0.0671156 0.402694i
$$223$$ 11.0000i 0.736614i −0.929704 0.368307i $$-0.879937\pi$$
0.929704 0.368307i $$-0.120063\pi$$
$$224$$ 3.00000i 0.200446i
$$225$$ −3.00000 4.00000i −0.200000 0.266667i
$$226$$ −1.00000 −0.0665190
$$227$$ −13.0000 −0.862840 −0.431420 0.902151i $$-0.641987\pi$$
−0.431420 + 0.902151i $$0.641987\pi$$
$$228$$ −4.00000 −0.264906
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ −12.0000 6.00000i −0.791257 0.395628i
$$231$$ −9.00000 −0.592157
$$232$$ 9.00000i 0.590879i
$$233$$ 6.00000i 0.393073i −0.980497 0.196537i $$-0.937031\pi$$
0.980497 0.196537i $$-0.0629694\pi$$
$$234$$ −4.00000 −0.261488
$$235$$ 8.00000 16.0000i 0.521862 1.04372i
$$236$$ 6.00000i 0.390567i
$$237$$ −4.00000 −0.259828
$$238$$ 21.0000i 1.36123i
$$239$$ 9.00000i 0.582162i 0.956698 + 0.291081i $$0.0940149\pi$$
−0.956698 + 0.291081i $$0.905985\pi$$
$$240$$ −1.00000 + 2.00000i −0.0645497 + 0.129099i
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 2.00000 0.128565
$$243$$ 1.00000i 0.0641500i
$$244$$ 5.00000i 0.320092i
$$245$$ −4.00000 2.00000i −0.255551 0.127775i
$$246$$ 7.00000i 0.446304i
$$247$$ 16.0000i 1.01806i
$$248$$ 5.00000i 0.317500i
$$249$$ −14.0000 −0.887214
$$250$$ −2.00000 11.0000i −0.126491 0.695701i
$$251$$ 20.0000i 1.26239i −0.775625 0.631194i $$-0.782565\pi$$
0.775625 0.631194i $$-0.217435\pi$$
$$252$$ 3.00000i 0.188982i
$$253$$ −18.0000 −1.13165
$$254$$ 8.00000i 0.501965i
$$255$$ −7.00000 + 14.0000i −0.438357 + 0.876714i
$$256$$ 1.00000 0.0625000
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 1.00000i 0.0622573i
$$259$$ 3.00000 18.0000i 0.186411 1.11847i
$$260$$ −8.00000 4.00000i −0.496139 0.248069i
$$261$$ 9.00000i 0.557086i
$$262$$ 0 0
$$263$$ 31.0000i 1.91154i −0.294112 0.955771i $$-0.595024\pi$$
0.294112 0.955771i $$-0.404976\pi$$
$$264$$ 3.00000i 0.184637i
$$265$$ 1.00000 2.00000i 0.0614295 0.122859i
$$266$$ −12.0000 −0.735767
$$267$$ 6.00000 0.367194
$$268$$ 2.00000i 0.122169i
$$269$$ 20.0000 1.21942 0.609711 0.792624i $$-0.291286\pi$$
0.609711 + 0.792624i $$0.291286\pi$$
$$270$$ −1.00000 + 2.00000i −0.0608581 + 0.121716i
$$271$$ 22.0000 1.33640 0.668202 0.743980i $$-0.267064\pi$$
0.668202 + 0.743980i $$0.267064\pi$$
$$272$$ 7.00000 0.424437
$$273$$ −12.0000 −0.726273
$$274$$ 12.0000i 0.724947i
$$275$$ −9.00000 12.0000i −0.542720 0.723627i
$$276$$ 6.00000i 0.361158i
$$277$$ −28.0000 −1.68236 −0.841178 0.540758i $$-0.818138\pi$$
−0.841178 + 0.540758i $$0.818138\pi$$
$$278$$ 15.0000 0.899640
$$279$$ 5.00000i 0.299342i
$$280$$ −3.00000 + 6.00000i −0.179284 + 0.358569i
$$281$$ 30.0000i 1.78965i 0.446417 + 0.894825i $$0.352700\pi$$
−0.446417 + 0.894825i $$0.647300\pi$$
$$282$$ −8.00000 −0.476393
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ 12.0000 0.712069
$$285$$ −8.00000 4.00000i −0.473879 0.236940i
$$286$$ −12.0000 −0.709575
$$287$$ 21.0000i 1.23959i
$$288$$ 1.00000 0.0589256
$$289$$ 32.0000 1.88235
$$290$$ 9.00000 18.0000i 0.528498 1.05700i
$$291$$ 7.00000i 0.410347i
$$292$$ 4.00000i 0.234082i
$$293$$ 29.0000i 1.69420i 0.531435 + 0.847099i $$0.321653\pi$$
−0.531435 + 0.847099i $$0.678347\pi$$
$$294$$ 2.00000i 0.116642i
$$295$$ 6.00000 12.0000i 0.349334 0.698667i
$$296$$ −6.00000 1.00000i −0.348743 0.0581238i
$$297$$ 3.00000i 0.174078i
$$298$$ 0 0
$$299$$ −24.0000 −1.38796
$$300$$ −4.00000 + 3.00000i −0.230940 + 0.173205i
$$301$$ 3.00000i 0.172917i
$$302$$ −2.00000 −0.115087
$$303$$ 2.00000i 0.114897i
$$304$$ 4.00000i 0.229416i
$$305$$ −5.00000 + 10.0000i −0.286299 + 0.572598i
$$306$$ 7.00000 0.400163
$$307$$ 18.0000i 1.02731i −0.857996 0.513657i $$-0.828290\pi$$
0.857996 0.513657i $$-0.171710\pi$$
$$308$$ 9.00000i 0.512823i
$$309$$ 14.0000i 0.796432i
$$310$$ 5.00000 10.0000i 0.283981 0.567962i
$$311$$ 15.0000i 0.850572i −0.905059 0.425286i $$-0.860174\pi$$
0.905059 0.425286i $$-0.139826\pi$$
$$312$$ 4.00000i 0.226455i
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ 7.00000i 0.395033i
$$315$$ −3.00000 + 6.00000i −0.169031 + 0.338062i
$$316$$ 4.00000i 0.225018i
$$317$$ 27.0000i 1.51647i 0.651981 + 0.758236i $$0.273938\pi$$
−0.651981 + 0.758236i $$0.726062\pi$$
$$318$$ −1.00000 −0.0560772
$$319$$ 27.0000i 1.51171i
$$320$$ 2.00000 + 1.00000i 0.111803 + 0.0559017i
$$321$$ 18.0000 1.00466
$$322$$ 18.0000i 1.00310i
$$323$$ 28.0000i 1.55796i
$$324$$ 1.00000 0.0555556
$$325$$ −12.0000 16.0000i −0.665640 0.887520i
$$326$$ 9.00000 0.498464
$$327$$ 11.0000 0.608301
$$328$$ −7.00000 −0.386510
$$329$$ −24.0000 −1.32316
$$330$$ −3.00000 + 6.00000i −0.165145 + 0.330289i
$$331$$ 20.0000i 1.09930i 0.835395 + 0.549650i $$0.185239\pi$$
−0.835395 + 0.549650i $$0.814761\pi$$
$$332$$ 14.0000i 0.768350i
$$333$$ −6.00000 1.00000i −0.328798 0.0547997i
$$334$$ −12.0000 −0.656611
$$335$$ −2.00000 + 4.00000i −0.109272 + 0.218543i
$$336$$ 3.00000 0.163663
$$337$$ 18.0000i 0.980522i −0.871576 0.490261i $$-0.836901\pi$$
0.871576 0.490261i $$-0.163099\pi$$
$$338$$ −3.00000 −0.163178
$$339$$ 1.00000i 0.0543125i
$$340$$ 14.0000 + 7.00000i 0.759257 + 0.379628i
$$341$$ 15.0000i 0.812296i
$$342$$ 4.00000i 0.216295i
$$343$$ 15.0000i 0.809924i
$$344$$ −1.00000 −0.0539164
$$345$$ −6.00000 + 12.0000i −0.323029 + 0.646058i
$$346$$ 9.00000i 0.483843i
$$347$$ −28.0000 −1.50312 −0.751559 0.659665i $$-0.770698\pi$$
−0.751559 + 0.659665i $$0.770698\pi$$
$$348$$ −9.00000 −0.482451
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ −12.0000 + 9.00000i −0.641427 + 0.481070i
$$351$$ 4.00000i 0.213504i
$$352$$ 3.00000 0.159901
$$353$$ 31.0000 1.64996 0.824982 0.565159i $$-0.191185\pi$$
0.824982 + 0.565159i $$0.191185\pi$$
$$354$$ −6.00000 −0.318896
$$355$$ 24.0000 + 12.0000i 1.27379 + 0.636894i
$$356$$ 6.00000i 0.317999i
$$357$$ 21.0000 1.11144
$$358$$ 4.00000i 0.211407i
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 2.00000 + 1.00000i 0.105409 + 0.0527046i
$$361$$ 3.00000 0.157895
$$362$$ 18.0000 0.946059
$$363$$ 2.00000i 0.104973i
$$364$$ 12.0000i 0.628971i
$$365$$ −4.00000 + 8.00000i −0.209370 + 0.418739i
$$366$$ 5.00000 0.261354
$$367$$ 23.0000i 1.20059i −0.799779 0.600295i $$-0.795050\pi$$
0.799779 0.600295i $$-0.204950\pi$$
$$368$$ 6.00000 0.312772
$$369$$ −7.00000 −0.364405
$$370$$ −11.0000 8.00000i −0.571863 0.415900i
$$371$$ −3.00000 −0.155752
$$372$$ −5.00000 −0.259238
$$373$$ 14.0000i 0.724893i 0.932005 + 0.362446i $$0.118058\pi$$
−0.932005 + 0.362446i $$0.881942\pi$$
$$374$$ 21.0000 1.08588
$$375$$ −11.0000 + 2.00000i −0.568038 + 0.103280i
$$376$$ 8.00000i 0.412568i
$$377$$ 36.0000i 1.85409i
$$378$$ 3.00000 0.154303
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ −4.00000 + 8.00000i −0.205196 + 0.410391i
$$381$$ 8.00000 0.409852
$$382$$ 15.0000i 0.767467i
$$383$$ 6.00000 0.306586 0.153293 0.988181i $$-0.451012\pi$$
0.153293 + 0.988181i $$0.451012\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ −9.00000 + 18.0000i −0.458682 + 0.917365i
$$386$$ 14.0000 0.712581
$$387$$ −1.00000 −0.0508329
$$388$$ 7.00000 0.355371
$$389$$ 31.0000i 1.57176i −0.618378 0.785881i $$-0.712210\pi$$
0.618378 0.785881i $$-0.287790\pi$$
$$390$$ −4.00000 + 8.00000i −0.202548 + 0.405096i
$$391$$ 42.0000 2.12403
$$392$$ 2.00000 0.101015
$$393$$ 0 0
$$394$$ 18.0000i 0.906827i
$$395$$ −4.00000 + 8.00000i −0.201262 + 0.402524i
$$396$$ 3.00000 0.150756
$$397$$ 38.0000i 1.90717i −0.301131 0.953583i $$-0.597364\pi$$
0.301131 0.953583i $$-0.402636\pi$$
$$398$$ 16.0000i 0.802008i
$$399$$ 12.0000i 0.600751i
$$400$$ 3.00000 + 4.00000i 0.150000 + 0.200000i
$$401$$ 10.0000i 0.499376i 0.968326 + 0.249688i $$0.0803281\pi$$
−0.968326 + 0.249688i $$0.919672\pi$$
$$402$$ 2.00000 0.0997509
$$403$$ 20.0000i 0.996271i
$$404$$ 2.00000 0.0995037
$$405$$ 2.00000 + 1.00000i 0.0993808 + 0.0496904i
$$406$$ −27.0000 −1.33999
$$407$$ −18.0000 3.00000i −0.892227 0.148704i
$$408$$ 7.00000i 0.346552i
$$409$$ 14.0000i 0.692255i 0.938187 + 0.346128i $$0.112504\pi$$
−0.938187 + 0.346128i $$0.887496\pi$$
$$410$$ −14.0000 7.00000i −0.691411 0.345705i
$$411$$ −12.0000 −0.591916
$$412$$ −14.0000 −0.689730
$$413$$ −18.0000 −0.885722
$$414$$ 6.00000 0.294884
$$415$$ −14.0000 + 28.0000i −0.687233 + 1.37447i
$$416$$ 4.00000 0.196116
$$417$$ 15.0000i 0.734553i
$$418$$ 12.0000i 0.586939i
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 6.00000 + 3.00000i 0.292770 + 0.146385i
$$421$$ 30.0000i 1.46211i −0.682318 0.731055i $$-0.739028\pi$$
0.682318 0.731055i $$-0.260972\pi$$
$$422$$ 13.0000 0.632830
$$423$$ 8.00000i 0.388973i
$$424$$ 1.00000i 0.0485643i
$$425$$ 21.0000 + 28.0000i 1.01865 + 1.35820i
$$426$$ 12.0000i 0.581402i
$$427$$ 15.0000 0.725901
$$428$$ 18.0000i 0.870063i
$$429$$ 12.0000i 0.579365i
$$430$$ −2.00000 1.00000i −0.0964486 0.0482243i
$$431$$ 25.0000i 1.20421i 0.798418 + 0.602104i $$0.205671\pi$$
−0.798418 + 0.602104i $$0.794329\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ 34.0000i 1.63394i 0.576683 + 0.816968i $$0.304347\pi$$
−0.576683 + 0.816968i $$0.695653\pi$$
$$434$$ −15.0000 −0.720023
$$435$$ −18.0000 9.00000i −0.863034 0.431517i
$$436$$ 11.0000i 0.526804i
$$437$$ 24.0000i 1.14808i
$$438$$ 4.00000 0.191127
$$439$$ 9.00000i 0.429547i 0.976664 + 0.214773i $$0.0689013\pi$$
−0.976664 + 0.214773i $$0.931099\pi$$
$$440$$ 6.00000 + 3.00000i 0.286039 + 0.143019i
$$441$$ 2.00000 0.0952381
$$442$$ 28.0000 1.33182
$$443$$ 36.0000i 1.71041i −0.518289 0.855206i $$-0.673431\pi$$
0.518289 0.855206i $$-0.326569\pi$$
$$444$$ −1.00000 + 6.00000i −0.0474579 + 0.284747i
$$445$$ 6.00000 12.0000i 0.284427 0.568855i
$$446$$ 11.0000i 0.520865i
$$447$$ 0 0
$$448$$ 3.00000i 0.141737i
$$449$$ 6.00000i 0.283158i −0.989927 0.141579i $$-0.954782\pi$$
0.989927 0.141579i $$-0.0452178\pi$$
$$450$$ 3.00000 + 4.00000i 0.141421 + 0.188562i
$$451$$ −21.0000 −0.988851
$$452$$ 1.00000 0.0470360
$$453$$ 2.00000i 0.0939682i
$$454$$ 13.0000 0.610120
$$455$$ −12.0000 + 24.0000i −0.562569 + 1.12514i
$$456$$ 4.00000 0.187317
$$457$$ −13.0000 −0.608114 −0.304057 0.952654i $$-0.598341\pi$$
−0.304057 + 0.952654i $$0.598341\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ 7.00000i 0.326732i
$$460$$ 12.0000 + 6.00000i 0.559503 + 0.279751i
$$461$$ 25.0000i 1.16437i −0.813058 0.582183i $$-0.802199\pi$$
0.813058 0.582183i $$-0.197801\pi$$
$$462$$ 9.00000 0.418718
$$463$$ 26.0000 1.20832 0.604161 0.796862i $$-0.293508\pi$$
0.604161 + 0.796862i $$0.293508\pi$$
$$464$$ 9.00000i 0.417815i
$$465$$ −10.0000 5.00000i −0.463739 0.231869i
$$466$$ 6.00000i 0.277945i
$$467$$ −23.0000 −1.06431 −0.532157 0.846646i $$-0.678618\pi$$
−0.532157 + 0.846646i $$0.678618\pi$$
$$468$$ 4.00000 0.184900
$$469$$ 6.00000 0.277054
$$470$$ −8.00000 + 16.0000i −0.369012 + 0.738025i
$$471$$ −7.00000 −0.322543
$$472$$ 6.00000i 0.276172i
$$473$$ −3.00000 −0.137940
$$474$$ 4.00000 0.183726
$$475$$ −16.0000 + 12.0000i −0.734130 + 0.550598i
$$476$$ 21.0000i 0.962533i
$$477$$ 1.00000i 0.0457869i
$$478$$ 9.00000i 0.411650i
$$479$$ 24.0000i 1.09659i 0.836286 + 0.548294i $$0.184723\pi$$
−0.836286 + 0.548294i $$0.815277\pi$$
$$480$$ 1.00000 2.00000i 0.0456435 0.0912871i
$$481$$ −24.0000 4.00000i −1.09431 0.182384i
$$482$$ 0 0
$$483$$ 18.0000 0.819028
$$484$$ −2.00000 −0.0909091
$$485$$ 14.0000 + 7.00000i 0.635707 + 0.317854i
$$486$$ 1.00000i 0.0453609i
$$487$$ 22.0000 0.996915 0.498458 0.866914i $$-0.333900\pi$$
0.498458 + 0.866914i $$0.333900\pi$$
$$488$$ 5.00000i 0.226339i
$$489$$ 9.00000i 0.406994i
$$490$$ 4.00000 + 2.00000i 0.180702 + 0.0903508i
$$491$$ −8.00000 −0.361035 −0.180517 0.983572i $$-0.557777\pi$$
−0.180517 + 0.983572i $$0.557777\pi$$
$$492$$ 7.00000i 0.315584i
$$493$$ 63.0000i 2.83738i
$$494$$ 16.0000i 0.719874i
$$495$$ 6.00000 + 3.00000i 0.269680 + 0.134840i
$$496$$ 5.00000i 0.224507i
$$497$$ 36.0000i 1.61482i
$$498$$ 14.0000 0.627355
$$499$$ 24.0000i 1.07439i 0.843459 + 0.537194i $$0.180516\pi$$
−0.843459 + 0.537194i $$0.819484\pi$$
$$500$$ 2.00000 + 11.0000i 0.0894427 + 0.491935i
$$501$$ 12.0000i 0.536120i
$$502$$ 20.0000i 0.892644i
$$503$$ −14.0000 −0.624229 −0.312115 0.950044i $$-0.601037\pi$$
−0.312115 + 0.950044i $$0.601037\pi$$
$$504$$ 3.00000i 0.133631i
$$505$$ 4.00000 + 2.00000i 0.177998 + 0.0889988i
$$506$$ 18.0000 0.800198
$$507$$ 3.00000i 0.133235i
$$508$$ 8.00000i 0.354943i
$$509$$ −10.0000 −0.443242 −0.221621 0.975133i $$-0.571135\pi$$
−0.221621 + 0.975133i $$0.571135\pi$$
$$510$$ 7.00000 14.0000i 0.309965 0.619930i
$$511$$ 12.0000 0.530849
$$512$$ −1.00000 −0.0441942
$$513$$ 4.00000 0.176604
$$514$$ 18.0000 0.793946
$$515$$ −28.0000 14.0000i −1.23383 0.616914i
$$516$$ 1.00000i 0.0440225i
$$517$$ 24.0000i 1.05552i
$$518$$ −3.00000 + 18.0000i −0.131812 + 0.790875i
$$519$$ −9.00000 −0.395056
$$520$$ 8.00000 + 4.00000i 0.350823 + 0.175412i
$$521$$ 37.0000 1.62100 0.810500 0.585739i $$-0.199196\pi$$
0.810500 + 0.585739i $$0.199196\pi$$
$$522$$ 9.00000i 0.393919i
$$523$$ −4.00000 −0.174908 −0.0874539 0.996169i $$-0.527873\pi$$
−0.0874539 + 0.996169i $$0.527873\pi$$
$$524$$ 0 0
$$525$$ 9.00000 + 12.0000i 0.392792 + 0.523723i
$$526$$ 31.0000i 1.35166i
$$527$$ 35.0000i 1.52462i
$$528$$ 3.00000i 0.130558i
$$529$$ 13.0000 0.565217
$$530$$ −1.00000 + 2.00000i −0.0434372 + 0.0868744i
$$531$$ 6.00000i 0.260378i
$$532$$ 12.0000 0.520266
$$533$$ −28.0000 −1.21281
$$534$$ −6.00000 −0.259645
$$535$$ 18.0000 36.0000i 0.778208 1.55642i
$$536$$ 2.00000i 0.0863868i
$$537$$ −4.00000 −0.172613
$$538$$ −20.0000 −0.862261
$$539$$ 6.00000 0.258438
$$540$$ 1.00000 2.00000i 0.0430331 0.0860663i
$$541$$ 30.0000i 1.28980i −0.764267 0.644900i $$-0.776899\pi$$
0.764267 0.644900i $$-0.223101\pi$$
$$542$$ −22.0000 −0.944981
$$543$$ 18.0000i 0.772454i
$$544$$ −7.00000 −0.300123
$$545$$ 11.0000 22.0000i 0.471188 0.942376i
$$546$$ 12.0000 0.513553
$$547$$ −23.0000 −0.983409 −0.491704 0.870762i $$-0.663626\pi$$
−0.491704 + 0.870762i $$0.663626\pi$$
$$548$$ 12.0000i 0.512615i
$$549$$ 5.00000i 0.213395i
$$550$$ 9.00000 + 12.0000i 0.383761 + 0.511682i
$$551$$ −36.0000 −1.53365
$$552$$ 6.00000i 0.255377i
$$553$$ 12.0000 0.510292
$$554$$ 28.0000 1.18961
$$555$$ −8.00000 + 11.0000i −0.339581 + 0.466924i
$$556$$ −15.0000 −0.636142
$$557$$ 12.0000 0.508456 0.254228 0.967144i $$-0.418179\pi$$
0.254228 + 0.967144i $$0.418179\pi$$
$$558$$ 5.00000i 0.211667i
$$559$$ −4.00000 −0.169182
$$560$$ 3.00000 6.00000i 0.126773 0.253546i
$$561$$ 21.0000i 0.886621i
$$562$$ 30.0000i 1.26547i
$$563$$ 21.0000 0.885044 0.442522 0.896758i $$-0.354084\pi$$
0.442522 + 0.896758i $$0.354084\pi$$
$$564$$ 8.00000 0.336861
$$565$$ 2.00000 + 1.00000i 0.0841406 + 0.0420703i
$$566$$ 4.00000 0.168133
$$567$$ 3.00000i 0.125988i
$$568$$ −12.0000 −0.503509
$$569$$ 24.0000i 1.00613i 0.864248 + 0.503066i $$0.167795\pi$$
−0.864248 + 0.503066i $$0.832205\pi$$
$$570$$ 8.00000 + 4.00000i 0.335083 + 0.167542i
$$571$$ −33.0000 −1.38101 −0.690504 0.723329i $$-0.742611\pi$$
−0.690504 + 0.723329i $$0.742611\pi$$
$$572$$ 12.0000 0.501745
$$573$$ −15.0000 −0.626634
$$574$$ 21.0000i 0.876523i
$$575$$ 18.0000 + 24.0000i 0.750652 + 1.00087i
$$576$$ −1.00000 −0.0416667
$$577$$ 22.0000 0.915872 0.457936 0.888985i $$-0.348589\pi$$
0.457936 + 0.888985i $$0.348589\pi$$
$$578$$ −32.0000 −1.33102
$$579$$ 14.0000i 0.581820i
$$580$$ −9.00000 + 18.0000i −0.373705 + 0.747409i
$$581$$ 42.0000 1.74245
$$582$$ 7.00000i 0.290159i
$$583$$ 3.00000i 0.124247i
$$584$$ 4.00000i 0.165521i
$$585$$ 8.00000 + 4.00000i 0.330759 + 0.165380i
$$586$$ 29.0000i 1.19798i
$$587$$ 47.0000 1.93990 0.969949 0.243309i $$-0.0782329\pi$$
0.969949 + 0.243309i $$0.0782329\pi$$
$$588$$ 2.00000i 0.0824786i
$$589$$ −20.0000 −0.824086
$$590$$ −6.00000 + 12.0000i −0.247016 + 0.494032i
$$591$$ 18.0000 0.740421
$$592$$ 6.00000 + 1.00000i 0.246598 + 0.0410997i
$$593$$ 46.0000i 1.88899i −0.328521 0.944497i $$-0.606550\pi$$
0.328521 0.944497i $$-0.393450\pi$$
$$594$$ 3.00000i 0.123091i
$$595$$ 21.0000 42.0000i 0.860916 1.72183i
$$596$$ 0 0
$$597$$ 16.0000 0.654836
$$598$$ 24.0000 0.981433
$$599$$ −30.0000 −1.22577 −0.612883 0.790173i $$-0.709990\pi$$
−0.612883 + 0.790173i $$0.709990\pi$$
$$600$$ 4.00000 3.00000i 0.163299 0.122474i
$$601$$ −23.0000 −0.938190 −0.469095 0.883148i $$-0.655420\pi$$
−0.469095 + 0.883148i $$0.655420\pi$$
$$602$$ 3.00000i 0.122271i
$$603$$ 2.00000i 0.0814463i
$$604$$ 2.00000 0.0813788
$$605$$ −4.00000 2.00000i −0.162623 0.0813116i
$$606$$ 2.00000i 0.0812444i
$$607$$ 32.0000 1.29884 0.649420 0.760430i $$-0.275012\pi$$
0.649420 + 0.760430i $$0.275012\pi$$
$$608$$ 4.00000i 0.162221i
$$609$$ 27.0000i 1.09410i
$$610$$ 5.00000 10.0000i 0.202444 0.404888i
$$611$$ 32.0000i 1.29458i
$$612$$ −7.00000 −0.282958
$$613$$ 31.0000i 1.25208i −0.779792 0.626039i $$-0.784675\pi$$
0.779792 0.626039i $$-0.215325\pi$$
$$614$$ 18.0000i 0.726421i
$$615$$ −7.00000 + 14.0000i −0.282267 + 0.564534i
$$616$$ 9.00000i 0.362620i
$$617$$ 8.00000i 0.322068i −0.986949 0.161034i $$-0.948517\pi$$
0.986949 0.161034i $$-0.0514829\pi$$
$$618$$ 14.0000i 0.563163i
$$619$$ 25.0000 1.00483 0.502417 0.864625i $$-0.332444\pi$$
0.502417 + 0.864625i $$0.332444\pi$$
$$620$$ −5.00000 + 10.0000i −0.200805 + 0.401610i
$$621$$ 6.00000i 0.240772i
$$622$$ 15.0000i 0.601445i
$$623$$ −18.0000 −0.721155
$$624$$ 4.00000i 0.160128i
$$625$$ −7.00000 + 24.0000i −0.280000 + 0.960000i
$$626$$ −6.00000 −0.239808
$$627$$ 12.0000 0.479234
$$628$$ 7.00000i 0.279330i
$$629$$ 42.0000 + 7.00000i 1.67465 + 0.279108i
$$630$$ 3.00000 6.00000i 0.119523 0.239046i
$$631$$ 25.0000i 0.995234i 0.867397 + 0.497617i $$0.165792\pi$$
−0.867397 + 0.497617i $$0.834208\pi$$
$$632$$ 4.00000i 0.159111i
$$633$$ 13.0000i 0.516704i
$$634$$ 27.0000i 1.07231i
$$635$$ 8.00000 16.0000i 0.317470 0.634941i
$$636$$ 1.00000 0.0396526
$$637$$ 8.00000 0.316972
$$638$$ 27.0000i 1.06894i
$$639$$ −12.0000 −0.474713
$$640$$ −2.00000 1.00000i −0.0790569 0.0395285i
$$641$$ 17.0000 0.671460 0.335730 0.941958i $$-0.391017\pi$$
0.335730 + 0.941958i $$0.391017\pi$$
$$642$$ −18.0000 −0.710403
$$643$$ 31.0000 1.22252 0.611260 0.791430i $$-0.290663\pi$$
0.611260 + 0.791430i $$0.290663\pi$$
$$644$$ 18.0000i 0.709299i
$$645$$ −1.00000 + 2.00000i −0.0393750 + 0.0787499i
$$646$$ 28.0000i 1.10165i
$$647$$ −48.0000 −1.88707 −0.943537 0.331266i $$-0.892524\pi$$
−0.943537 + 0.331266i $$0.892524\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 18.0000i 0.706562i
$$650$$ 12.0000 + 16.0000i 0.470679 + 0.627572i
$$651$$ 15.0000i 0.587896i
$$652$$ −9.00000 −0.352467
$$653$$ 36.0000 1.40879 0.704394 0.709809i $$-0.251219\pi$$
0.704394 + 0.709809i $$0.251219\pi$$
$$654$$ −11.0000 −0.430134
$$655$$ 0 0
$$656$$ 7.00000 0.273304
$$657$$ 4.00000i 0.156055i
$$658$$ 24.0000 0.935617
$$659$$ −20.0000 −0.779089 −0.389545 0.921008i $$-0.627368\pi$$
−0.389545 + 0.921008i $$0.627368\pi$$
$$660$$ 3.00000 6.00000i 0.116775 0.233550i
$$661$$ 35.0000i 1.36134i 0.732589 + 0.680671i $$0.238312\pi$$
−0.732589 + 0.680671i $$0.761688\pi$$
$$662$$ 20.0000i 0.777322i
$$663$$ 28.0000i 1.08743i
$$664$$ 14.0000i 0.543305i
$$665$$ 24.0000 + 12.0000i 0.930680 + 0.465340i
$$666$$ 6.00000 + 1.00000i 0.232495 + 0.0387492i
$$667$$ 54.0000i 2.09089i
$$668$$ 12.0000 0.464294
$$669$$ 11.0000 0.425285
$$670$$ 2.00000 4.00000i 0.0772667 0.154533i
$$671$$ 15.0000i 0.579069i
$$672$$ −3.00000 −0.115728
$$673$$ 26.0000i 1.00223i −0.865382 0.501113i $$-0.832924\pi$$
0.865382 0.501113i $$-0.167076\pi$$
$$674$$ 18.0000i 0.693334i
$$675$$ 4.00000 3.00000i 0.153960 0.115470i
$$676$$ 3.00000 0.115385
$$677$$ 42.0000i 1.61419i 0.590421 + 0.807096i $$0.298962\pi$$
−0.590421 + 0.807096i $$0.701038\pi$$
$$678$$ 1.00000i 0.0384048i
$$679$$ 21.0000i 0.805906i
$$680$$ −14.0000 7.00000i −0.536875 0.268438i
$$681$$ 13.0000i 0.498161i
$$682$$ 15.0000i 0.574380i
$$683$$ 1.00000 0.0382639 0.0191320 0.999817i $$-0.493910\pi$$
0.0191320 + 0.999817i $$0.493910\pi$$
$$684$$ 4.00000i 0.152944i
$$685$$ −12.0000 + 24.0000i −0.458496 + 0.916993i
$$686$$ 15.0000i 0.572703i
$$687$$ 10.0000i 0.381524i
$$688$$ 1.00000 0.0381246
$$689$$ 4.00000i 0.152388i
$$690$$ 6.00000 12.0000i 0.228416 0.456832i
$$691$$ −43.0000 −1.63580 −0.817899 0.575362i $$-0.804861\pi$$
−0.817899 + 0.575362i $$0.804861\pi$$
$$692$$ 9.00000i 0.342129i
$$693$$ 9.00000i 0.341882i
$$694$$ 28.0000 1.06287
$$695$$ −30.0000 15.0000i −1.13796 0.568982i
$$696$$ 9.00000 0.341144
$$697$$ 49.0000 1.85601
$$698$$ 0 0
$$699$$ 6.00000 0.226941
$$700$$ 12.0000 9.00000i 0.453557 0.340168i
$$701$$ 10.0000i 0.377695i 0.982006 + 0.188847i $$0.0604752\pi$$
−0.982006 + 0.188847i $$0.939525\pi$$
$$702$$ 4.00000i 0.150970i
$$703$$ −4.00000 + 24.0000i −0.150863 + 0.905177i
$$704$$ −3.00000 −0.113067
$$705$$ 16.0000 + 8.00000i 0.602595 + 0.301297i
$$706$$ −31.0000 −1.16670
$$707$$ 6.00000i 0.225653i
$$708$$ 6.00000 0.225494
$$709$$ 11.0000i 0.413114i −0.978435 0.206557i $$-0.933774\pi$$
0.978435 0.206557i $$-0.0662258\pi$$
$$710$$ −24.0000 12.0000i −0.900704 0.450352i
$$711$$ 4.00000i 0.150012i
$$712$$ 6.00000i 0.224860i
$$713$$ 30.0000i 1.12351i
$$714$$ −21.0000 −0.785905
$$715$$ 24.0000 + 12.0000i 0.897549 + 0.448775i
$$716$$ 4.00000i 0.149487i
$$717$$ −9.00000 −0.336111
$$718$$ 0 0
$$719$$ 50.0000 1.86469 0.932343 0.361576i $$-0.117761\pi$$
0.932343 + 0.361576i $$0.117761\pi$$
$$720$$ −2.00000 1.00000i −0.0745356 0.0372678i
$$721$$ 42.0000i 1.56416i
$$722$$ −3.00000 −0.111648
$$723$$ 0 0
$$724$$ −18.0000 −0.668965
$$725$$ −36.0000 + 27.0000i −1.33701 + 1.00275i
$$726$$ 2.00000i 0.0742270i
$$727$$ −18.0000 −0.667583 −0.333792 0.942647i $$-0.608328\pi$$
−0.333792 + 0.942647i $$0.608328\pi$$
$$728$$ 12.0000i 0.444750i
$$729$$ −1.00000 −0.0370370
$$730$$ 4.00000 8.00000i 0.148047 0.296093i
$$731$$ 7.00000 0.258904
$$732$$ −5.00000 −0.184805
$$733$$ 11.0000i 0.406294i −0.979148 0.203147i $$-0.934883\pi$$
0.979148 0.203147i $$-0.0651170\pi$$
$$734$$ 23.0000i 0.848945i
$$735$$ 2.00000 4.00000i 0.0737711 0.147542i
$$736$$ −6.00000 −0.221163
$$737$$ 6.00000i 0.221013i
$$738$$ 7.00000 0.257674
$$739$$ 5.00000 0.183928 0.0919640 0.995762i $$-0.470686\pi$$
0.0919640 + 0.995762i $$0.470686\pi$$
$$740$$ 11.0000 + 8.00000i 0.404368 + 0.294086i
$$741$$ 16.0000 0.587775
$$742$$ 3.00000 0.110133
$$743$$ 51.0000i 1.87101i −0.353315 0.935504i $$-0.614946\pi$$
0.353315 0.935504i $$-0.385054\pi$$
$$744$$ 5.00000 0.183309
$$745$$ 0 0
$$746$$ 14.0000i 0.512576i
$$747$$ 14.0000i 0.512233i
$$748$$ −21.0000 −0.767836
$$749$$ −54.0000 −1.97312
$$750$$ 11.0000 2.00000i 0.401663 0.0730297i
$$751$$ −18.0000 −0.656829 −0.328415 0.944534i $$-0.606514\pi$$
−0.328415 + 0.944534i $$0.606514\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ 20.0000 0.728841
$$754$$ 36.0000i 1.31104i
$$755$$ 4.00000 + 2.00000i 0.145575 + 0.0727875i
$$756$$ −3.00000 −0.109109
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ −20.0000 −0.726433
$$759$$ 18.0000i 0.653359i
$$760$$ 4.00000 8.00000i 0.145095 0.290191i
$$761$$ −13.0000 −0.471250 −0.235625 0.971844i $$-0.575714\pi$$
−0.235625 + 0.971844i $$0.575714\pi$$
$$762$$ −8.00000 −0.289809
$$763$$ −33.0000 −1.19468
$$764$$ 15.0000i 0.542681i
$$765$$ −14.0000 7.00000i −0.506171 0.253086i
$$766$$ −6.00000 −0.216789
$$767$$ 24.0000i 0.866590i
$$768$$ 1.00000i 0.0360844i
$$769$$ 26.0000i 0.937584i −0.883309 0.468792i $$-0.844689\pi$$
0.883309 0.468792i $$-0.155311\pi$$
$$770$$ 9.00000 18.0000i 0.324337 0.648675i
$$771$$ 18.0000i 0.648254i
$$772$$ −14.0000 −0.503871
$$773$$ 11.0000i 0.395643i −0.980238 0.197821i $$-0.936613\pi$$
0.980238 0.197821i $$-0.0633866\pi$$
$$774$$ 1.00000 0.0359443
$$775$$ −20.0000 + 15.0000i −0.718421 + 0.538816i
$$776$$ −7.00000 −0.251285
$$777$$ 18.0000 + 3.00000i 0.645746 + 0.107624i
$$778$$ 31.0000i 1.11140i
$$779$$ 28.0000i 1.00320i
$$780$$ 4.00000 8.00000i 0.143223 0.286446i
$$781$$ −36.0000 −1.28818
$$782$$ −42.0000 −1.50192
$$783$$ 9.00000 0.321634
$$784$$ −2.00000 −0.0714286
$$785$$ −7.00000 + 14.0000i −0.249841 + 0.499681i
$$786$$ 0 0
$$787$$ 28.0000i 0.998092i −0.866575 0.499046i $$-0.833684\pi$$
0.866575