# Properties

 Label 3330.2.e.b.739.2 Level $3330$ Weight $2$ Character 3330.739 Analytic conductor $26.590$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3330.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$26.5901838731$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1110) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 739.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 3330.739 Dual form 3330.2.e.b.739.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +3.00000i q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +3.00000i q^{7} +1.00000 q^{8} +(-2.00000 + 1.00000i) q^{10} +3.00000 q^{11} -4.00000 q^{13} +3.00000i q^{14} +1.00000 q^{16} -7.00000 q^{17} -4.00000i q^{19} +(-2.00000 + 1.00000i) q^{20} +3.00000 q^{22} -6.00000 q^{23} +(3.00000 - 4.00000i) q^{25} -4.00000 q^{26} +3.00000i q^{28} +9.00000i q^{29} -5.00000i q^{31} +1.00000 q^{32} -7.00000 q^{34} +(-3.00000 - 6.00000i) q^{35} +(6.00000 - 1.00000i) q^{37} -4.00000i q^{38} +(-2.00000 + 1.00000i) q^{40} -7.00000 q^{41} +1.00000 q^{43} +3.00000 q^{44} -6.00000 q^{46} -8.00000i q^{47} -2.00000 q^{49} +(3.00000 - 4.00000i) q^{50} -4.00000 q^{52} -1.00000i q^{53} +(-6.00000 + 3.00000i) q^{55} +3.00000i q^{56} +9.00000i q^{58} -6.00000i q^{59} -5.00000i q^{61} -5.00000i q^{62} +1.00000 q^{64} +(8.00000 - 4.00000i) q^{65} -2.00000i q^{67} -7.00000 q^{68} +(-3.00000 - 6.00000i) q^{70} -12.0000 q^{71} -4.00000i q^{73} +(6.00000 - 1.00000i) q^{74} -4.00000i q^{76} +9.00000i q^{77} -4.00000i q^{79} +(-2.00000 + 1.00000i) q^{80} -7.00000 q^{82} +14.0000i q^{83} +(14.0000 - 7.00000i) q^{85} +1.00000 q^{86} +3.00000 q^{88} -6.00000i q^{89} -12.0000i q^{91} -6.00000 q^{92} -8.00000i q^{94} +(4.00000 + 8.00000i) q^{95} +7.00000 q^{97} -2.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{2} + 2q^{4} - 4q^{5} + 2q^{8} + O(q^{10})$$ $$2q + 2q^{2} + 2q^{4} - 4q^{5} + 2q^{8} - 4q^{10} + 6q^{11} - 8q^{13} + 2q^{16} - 14q^{17} - 4q^{20} + 6q^{22} - 12q^{23} + 6q^{25} - 8q^{26} + 2q^{32} - 14q^{34} - 6q^{35} + 12q^{37} - 4q^{40} - 14q^{41} + 2q^{43} + 6q^{44} - 12q^{46} - 4q^{49} + 6q^{50} - 8q^{52} - 12q^{55} + 2q^{64} + 16q^{65} - 14q^{68} - 6q^{70} - 24q^{71} + 12q^{74} - 4q^{80} - 14q^{82} + 28q^{85} + 2q^{86} + 6q^{88} - 12q^{92} + 8q^{95} + 14q^{97} - 4q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times$$.

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

## 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
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −2.00000 + 1.00000i −0.894427 + 0.447214i
$$6$$ 0 0
$$7$$ 3.00000i 1.13389i 0.823754 + 0.566947i $$0.191875\pi$$
−0.823754 + 0.566947i $$0.808125\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ −2.00000 + 1.00000i −0.632456 + 0.316228i
$$11$$ 3.00000 0.904534 0.452267 0.891883i $$-0.350615\pi$$
0.452267 + 0.891883i $$0.350615\pi$$
$$12$$ 0 0
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 3.00000i 0.801784i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −7.00000 −1.69775 −0.848875 0.528594i $$-0.822719\pi$$
−0.848875 + 0.528594i $$0.822719\pi$$
$$18$$ 0 0
$$19$$ 4.00000i 0.917663i −0.888523 0.458831i $$-0.848268\pi$$
0.888523 0.458831i $$-0.151732\pi$$
$$20$$ −2.00000 + 1.00000i −0.447214 + 0.223607i
$$21$$ 0 0
$$22$$ 3.00000 0.639602
$$23$$ −6.00000 −1.25109 −0.625543 0.780189i $$-0.715123\pi$$
−0.625543 + 0.780189i $$0.715123\pi$$
$$24$$ 0 0
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ −4.00000 −0.784465
$$27$$ 0 0
$$28$$ 3.00000i 0.566947i
$$29$$ 9.00000i 1.67126i 0.549294 + 0.835629i $$0.314897\pi$$
−0.549294 + 0.835629i $$0.685103\pi$$
$$30$$ 0 0
$$31$$ 5.00000i 0.898027i −0.893525 0.449013i $$-0.851776\pi$$
0.893525 0.449013i $$-0.148224\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ −7.00000 −1.20049
$$35$$ −3.00000 6.00000i −0.507093 1.01419i
$$36$$ 0 0
$$37$$ 6.00000 1.00000i 0.986394 0.164399i
$$38$$ 4.00000i 0.648886i
$$39$$ 0 0
$$40$$ −2.00000 + 1.00000i −0.316228 + 0.158114i
$$41$$ −7.00000 −1.09322 −0.546608 0.837389i $$-0.684081\pi$$
−0.546608 + 0.837389i $$0.684081\pi$$
$$42$$ 0 0
$$43$$ 1.00000 0.152499 0.0762493 0.997089i $$-0.475706\pi$$
0.0762493 + 0.997089i $$0.475706\pi$$
$$44$$ 3.00000 0.452267
$$45$$ 0 0
$$46$$ −6.00000 −0.884652
$$47$$ 8.00000i 1.16692i −0.812142 0.583460i $$-0.801699\pi$$
0.812142 0.583460i $$-0.198301\pi$$
$$48$$ 0 0
$$49$$ −2.00000 −0.285714
$$50$$ 3.00000 4.00000i 0.424264 0.565685i
$$51$$ 0 0
$$52$$ −4.00000 −0.554700
$$53$$ 1.00000i 0.137361i −0.997639 0.0686803i $$-0.978121\pi$$
0.997639 0.0686803i $$-0.0218788\pi$$
$$54$$ 0 0
$$55$$ −6.00000 + 3.00000i −0.809040 + 0.404520i
$$56$$ 3.00000i 0.400892i
$$57$$ 0 0
$$58$$ 9.00000i 1.18176i
$$59$$ 6.00000i 0.781133i −0.920575 0.390567i $$-0.872279\pi$$
0.920575 0.390567i $$-0.127721\pi$$
$$60$$ 0 0
$$61$$ 5.00000i 0.640184i −0.947386 0.320092i $$-0.896286\pi$$
0.947386 0.320092i $$-0.103714\pi$$
$$62$$ 5.00000i 0.635001i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 8.00000 4.00000i 0.992278 0.496139i
$$66$$ 0 0
$$67$$ 2.00000i 0.244339i −0.992509 0.122169i $$-0.961015\pi$$
0.992509 0.122169i $$-0.0389851\pi$$
$$68$$ −7.00000 −0.848875
$$69$$ 0 0
$$70$$ −3.00000 6.00000i −0.358569 0.717137i
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 0 0
$$73$$ 4.00000i 0.468165i −0.972217 0.234082i $$-0.924791\pi$$
0.972217 0.234082i $$-0.0752085\pi$$
$$74$$ 6.00000 1.00000i 0.697486 0.116248i
$$75$$ 0 0
$$76$$ 4.00000i 0.458831i
$$77$$ 9.00000i 1.02565i
$$78$$ 0 0
$$79$$ 4.00000i 0.450035i −0.974355 0.225018i $$-0.927756\pi$$
0.974355 0.225018i $$-0.0722440\pi$$
$$80$$ −2.00000 + 1.00000i −0.223607 + 0.111803i
$$81$$ 0 0
$$82$$ −7.00000 −0.773021
$$83$$ 14.0000i 1.53670i 0.640030 + 0.768350i $$0.278922\pi$$
−0.640030 + 0.768350i $$0.721078\pi$$
$$84$$ 0 0
$$85$$ 14.0000 7.00000i 1.51851 0.759257i
$$86$$ 1.00000 0.107833
$$87$$ 0 0
$$88$$ 3.00000 0.319801
$$89$$ 6.00000i 0.635999i −0.948091 0.317999i $$-0.896989\pi$$
0.948091 0.317999i $$-0.103011\pi$$
$$90$$ 0 0
$$91$$ 12.0000i 1.25794i
$$92$$ −6.00000 −0.625543
$$93$$ 0 0
$$94$$ 8.00000i 0.825137i
$$95$$ 4.00000 + 8.00000i 0.410391 + 0.820783i
$$96$$ 0 0
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ −2.00000 −0.202031
$$99$$ 0 0
$$100$$ 3.00000 4.00000i 0.300000 0.400000i
$$101$$ −2.00000 −0.199007 −0.0995037 0.995037i $$-0.531726\pi$$
−0.0995037 + 0.995037i $$0.531726\pi$$
$$102$$ 0 0
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ −4.00000 −0.392232
$$105$$ 0 0
$$106$$ 1.00000i 0.0971286i
$$107$$ 18.0000i 1.74013i −0.492941 0.870063i $$-0.664078\pi$$
0.492941 0.870063i $$-0.335922\pi$$
$$108$$ 0 0
$$109$$ 11.0000i 1.05361i 0.849987 + 0.526804i $$0.176610\pi$$
−0.849987 + 0.526804i $$0.823390\pi$$
$$110$$ −6.00000 + 3.00000i −0.572078 + 0.286039i
$$111$$ 0 0
$$112$$ 3.00000i 0.283473i
$$113$$ −1.00000 −0.0940721 −0.0470360 0.998893i $$-0.514978\pi$$
−0.0470360 + 0.998893i $$0.514978\pi$$
$$114$$ 0 0
$$115$$ 12.0000 6.00000i 1.11901 0.559503i
$$116$$ 9.00000i 0.835629i
$$117$$ 0 0
$$118$$ 6.00000i 0.552345i
$$119$$ 21.0000i 1.92507i
$$120$$ 0 0
$$121$$ −2.00000 −0.181818
$$122$$ 5.00000i 0.452679i
$$123$$ 0 0
$$124$$ 5.00000i 0.449013i
$$125$$ −2.00000 + 11.0000i −0.178885 + 0.983870i
$$126$$ 0 0
$$127$$ 8.00000i 0.709885i 0.934888 + 0.354943i $$0.115500\pi$$
−0.934888 + 0.354943i $$0.884500\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 8.00000 4.00000i 0.701646 0.350823i
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 12.0000 1.04053
$$134$$ 2.00000i 0.172774i
$$135$$ 0 0
$$136$$ −7.00000 −0.600245
$$137$$ 12.0000i 1.02523i 0.858619 + 0.512615i $$0.171323\pi$$
−0.858619 + 0.512615i $$0.828677\pi$$
$$138$$ 0 0
$$139$$ −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
$$141$$ 0 0
$$142$$ −12.0000 −1.00702
$$143$$ −12.0000 −1.00349
$$144$$ 0 0
$$145$$ −9.00000 18.0000i −0.747409 1.49482i
$$146$$ 4.00000i 0.331042i
$$147$$ 0 0
$$148$$ 6.00000 1.00000i 0.493197 0.0821995i
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ 2.00000 0.162758 0.0813788 0.996683i $$-0.474068\pi$$
0.0813788 + 0.996683i $$0.474068\pi$$
$$152$$ 4.00000i 0.324443i
$$153$$ 0 0
$$154$$ 9.00000i 0.725241i
$$155$$ 5.00000 + 10.0000i 0.401610 + 0.803219i
$$156$$ 0 0
$$157$$ 7.00000i 0.558661i −0.960195 0.279330i $$-0.909888\pi$$
0.960195 0.279330i $$-0.0901125\pi$$
$$158$$ 4.00000i 0.318223i
$$159$$ 0 0
$$160$$ −2.00000 + 1.00000i −0.158114 + 0.0790569i
$$161$$ 18.0000i 1.41860i
$$162$$ 0 0
$$163$$ −9.00000 −0.704934 −0.352467 0.935824i $$-0.614657\pi$$
−0.352467 + 0.935824i $$0.614657\pi$$
$$164$$ −7.00000 −0.546608
$$165$$ 0 0
$$166$$ 14.0000i 1.08661i
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 14.0000 7.00000i 1.07375 0.536875i
$$171$$ 0 0
$$172$$ 1.00000 0.0762493
$$173$$ 9.00000i 0.684257i 0.939653 + 0.342129i $$0.111148\pi$$
−0.939653 + 0.342129i $$0.888852\pi$$
$$174$$ 0 0
$$175$$ 12.0000 + 9.00000i 0.907115 + 0.680336i
$$176$$ 3.00000 0.226134
$$177$$ 0 0
$$178$$ 6.00000i 0.449719i
$$179$$ 4.00000i 0.298974i 0.988764 + 0.149487i $$0.0477622\pi$$
−0.988764 + 0.149487i $$0.952238\pi$$
$$180$$ 0 0
$$181$$ −18.0000 −1.33793 −0.668965 0.743294i $$-0.733262\pi$$
−0.668965 + 0.743294i $$0.733262\pi$$
$$182$$ 12.0000i 0.889499i
$$183$$ 0 0
$$184$$ −6.00000 −0.442326
$$185$$ −11.0000 + 8.00000i −0.808736 + 0.588172i
$$186$$ 0 0
$$187$$ −21.0000 −1.53567
$$188$$ 8.00000i 0.583460i
$$189$$ 0 0
$$190$$ 4.00000 + 8.00000i 0.290191 + 0.580381i
$$191$$ 15.0000i 1.08536i 0.839939 + 0.542681i $$0.182591\pi$$
−0.839939 + 0.542681i $$0.817409\pi$$
$$192$$ 0 0
$$193$$ −14.0000 −1.00774 −0.503871 0.863779i $$-0.668091\pi$$
−0.503871 + 0.863779i $$0.668091\pi$$
$$194$$ 7.00000 0.502571
$$195$$ 0 0
$$196$$ −2.00000 −0.142857
$$197$$ 18.0000i 1.28245i −0.767354 0.641223i $$-0.778427\pi$$
0.767354 0.641223i $$-0.221573\pi$$
$$198$$ 0 0
$$199$$ 16.0000i 1.13421i 0.823646 + 0.567105i $$0.191937\pi$$
−0.823646 + 0.567105i $$0.808063\pi$$
$$200$$ 3.00000 4.00000i 0.212132 0.282843i
$$201$$ 0 0
$$202$$ −2.00000 −0.140720
$$203$$ −27.0000 −1.89503
$$204$$ 0 0
$$205$$ 14.0000 7.00000i 0.977802 0.488901i
$$206$$ −14.0000 −0.975426
$$207$$ 0 0
$$208$$ −4.00000 −0.277350
$$209$$ 12.0000i 0.830057i
$$210$$ 0 0
$$211$$ −13.0000 −0.894957 −0.447478 0.894295i $$-0.647678\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 1.00000i 0.0686803i
$$213$$ 0 0
$$214$$ 18.0000i 1.23045i
$$215$$ −2.00000 + 1.00000i −0.136399 + 0.0681994i
$$216$$ 0 0
$$217$$ 15.0000 1.01827
$$218$$ 11.0000i 0.745014i
$$219$$ 0 0
$$220$$ −6.00000 + 3.00000i −0.404520 + 0.202260i
$$221$$ 28.0000 1.88348
$$222$$ 0 0
$$223$$ 11.0000i 0.736614i 0.929704 + 0.368307i $$0.120063\pi$$
−0.929704 + 0.368307i $$0.879937\pi$$
$$224$$ 3.00000i 0.200446i
$$225$$ 0 0
$$226$$ −1.00000 −0.0665190
$$227$$ 13.0000 0.862840 0.431420 0.902151i $$-0.358013\pi$$
0.431420 + 0.902151i $$0.358013\pi$$
$$228$$ 0 0
$$229$$ 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
$$231$$ 0 0
$$232$$ 9.00000i 0.590879i
$$233$$ 6.00000i 0.393073i −0.980497 0.196537i $$-0.937031\pi$$
0.980497 0.196537i $$-0.0629694\pi$$
$$234$$ 0 0
$$235$$ 8.00000 + 16.0000i 0.521862 + 1.04372i
$$236$$ 6.00000i 0.390567i
$$237$$ 0 0
$$238$$ 21.0000i 1.36123i
$$239$$ 9.00000i 0.582162i 0.956698 + 0.291081i $$0.0940149\pi$$
−0.956698 + 0.291081i $$0.905985\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ −2.00000 −0.128565
$$243$$ 0 0
$$244$$ 5.00000i 0.320092i
$$245$$ 4.00000 2.00000i 0.255551 0.127775i
$$246$$ 0 0
$$247$$ 16.0000i 1.01806i
$$248$$ 5.00000i 0.317500i
$$249$$ 0 0
$$250$$ −2.00000 + 11.0000i −0.126491 + 0.695701i
$$251$$ 20.0000i 1.26239i −0.775625 0.631194i $$-0.782565\pi$$
0.775625 0.631194i $$-0.217435\pi$$
$$252$$ 0 0
$$253$$ −18.0000 −1.13165
$$254$$ 8.00000i 0.501965i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 0 0
$$259$$ 3.00000 + 18.0000i 0.186411 + 1.11847i
$$260$$ 8.00000 4.00000i 0.496139 0.248069i
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 31.0000i 1.91154i −0.294112 0.955771i $$-0.595024\pi$$
0.294112 0.955771i $$-0.404976\pi$$
$$264$$ 0 0
$$265$$ 1.00000 + 2.00000i 0.0614295 + 0.122859i
$$266$$ 12.0000 0.735767
$$267$$ 0 0
$$268$$ 2.00000i 0.122169i
$$269$$ −20.0000 −1.21942 −0.609711 0.792624i $$-0.708714\pi$$
−0.609711 + 0.792624i $$0.708714\pi$$
$$270$$ 0 0
$$271$$ 22.0000 1.33640 0.668202 0.743980i $$-0.267064\pi$$
0.668202 + 0.743980i $$0.267064\pi$$
$$272$$ −7.00000 −0.424437
$$273$$ 0 0
$$274$$ 12.0000i 0.724947i
$$275$$ 9.00000 12.0000i 0.542720 0.723627i
$$276$$ 0 0
$$277$$ −28.0000 −1.68236 −0.841178 0.540758i $$-0.818138\pi$$
−0.841178 + 0.540758i $$0.818138\pi$$
$$278$$ −15.0000 −0.899640
$$279$$ 0 0
$$280$$ −3.00000 6.00000i −0.179284 0.358569i
$$281$$ 30.0000i 1.78965i 0.446417 + 0.894825i $$0.352700\pi$$
−0.446417 + 0.894825i $$0.647300\pi$$
$$282$$ 0 0
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ 0 0
$$286$$ −12.0000 −0.709575
$$287$$ 21.0000i 1.23959i
$$288$$ 0 0
$$289$$ 32.0000 1.88235
$$290$$ −9.00000 18.0000i −0.528498 1.05700i
$$291$$ 0 0
$$292$$ 4.00000i 0.234082i
$$293$$ 29.0000i 1.69420i 0.531435 + 0.847099i $$0.321653\pi$$
−0.531435 + 0.847099i $$0.678347\pi$$
$$294$$ 0 0
$$295$$ 6.00000 + 12.0000i 0.349334 + 0.698667i
$$296$$ 6.00000 1.00000i 0.348743 0.0581238i
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 24.0000 1.38796
$$300$$ 0 0
$$301$$ 3.00000i 0.172917i
$$302$$ 2.00000 0.115087
$$303$$ 0 0
$$304$$ 4.00000i 0.229416i
$$305$$ 5.00000 + 10.0000i 0.286299 + 0.572598i
$$306$$ 0 0
$$307$$ 18.0000i 1.02731i 0.857996 + 0.513657i $$0.171710\pi$$
−0.857996 + 0.513657i $$0.828290\pi$$
$$308$$ 9.00000i 0.512823i
$$309$$ 0 0
$$310$$ 5.00000 + 10.0000i 0.283981 + 0.567962i
$$311$$ 15.0000i 0.850572i −0.905059 0.425286i $$-0.860174\pi$$
0.905059 0.425286i $$-0.139826\pi$$
$$312$$ 0 0
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ 7.00000i 0.395033i
$$315$$ 0 0
$$316$$ 4.00000i 0.225018i
$$317$$ 27.0000i 1.51647i 0.651981 + 0.758236i $$0.273938\pi$$
−0.651981 + 0.758236i $$0.726062\pi$$
$$318$$ 0 0
$$319$$ 27.0000i 1.51171i
$$320$$ −2.00000 + 1.00000i −0.111803 + 0.0559017i
$$321$$ 0 0
$$322$$ 18.0000i 1.00310i
$$323$$ 28.0000i 1.55796i
$$324$$ 0 0
$$325$$ −12.0000 + 16.0000i −0.665640 + 0.887520i
$$326$$ −9.00000 −0.498464
$$327$$ 0 0
$$328$$ −7.00000 −0.386510
$$329$$ 24.0000 1.32316
$$330$$ 0 0
$$331$$ 20.0000i 1.09930i −0.835395 0.549650i $$-0.814761\pi$$
0.835395 0.549650i $$-0.185239\pi$$
$$332$$ 14.0000i 0.768350i
$$333$$ 0 0
$$334$$ −12.0000 −0.656611
$$335$$ 2.00000 + 4.00000i 0.109272 + 0.218543i
$$336$$ 0 0
$$337$$ 18.0000i 0.980522i 0.871576 + 0.490261i $$0.163099\pi$$
−0.871576 + 0.490261i $$0.836901\pi$$
$$338$$ 3.00000 0.163178
$$339$$ 0 0
$$340$$ 14.0000 7.00000i 0.759257 0.379628i
$$341$$ 15.0000i 0.812296i
$$342$$ 0 0
$$343$$ 15.0000i 0.809924i
$$344$$ 1.00000 0.0539164
$$345$$ 0 0
$$346$$ 9.00000i 0.483843i
$$347$$ 28.0000 1.50312 0.751559 0.659665i $$-0.229302\pi$$
0.751559 + 0.659665i $$0.229302\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 12.0000 + 9.00000i 0.641427 + 0.481070i
$$351$$ 0 0
$$352$$ 3.00000 0.159901
$$353$$ −31.0000 −1.64996 −0.824982 0.565159i $$-0.808815\pi$$
−0.824982 + 0.565159i $$0.808815\pi$$
$$354$$ 0 0
$$355$$ 24.0000 12.0000i 1.27379 0.636894i
$$356$$ 6.00000i 0.317999i
$$357$$ 0 0
$$358$$ 4.00000i 0.211407i
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ 3.00000 0.157895
$$362$$ −18.0000 −0.946059
$$363$$ 0 0
$$364$$ 12.0000i 0.628971i
$$365$$ 4.00000 + 8.00000i 0.209370 + 0.418739i
$$366$$ 0 0
$$367$$ 23.0000i 1.20059i 0.799779 + 0.600295i $$0.204950\pi$$
−0.799779 + 0.600295i $$0.795050\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ 0 0
$$370$$ −11.0000 + 8.00000i −0.571863 + 0.415900i
$$371$$ 3.00000 0.155752
$$372$$ 0 0
$$373$$ 14.0000i 0.724893i −0.932005 0.362446i $$-0.881942\pi$$
0.932005 0.362446i $$-0.118058\pi$$
$$374$$ −21.0000 −1.08588
$$375$$ 0 0
$$376$$ 8.00000i 0.412568i
$$377$$ 36.0000i 1.85409i
$$378$$ 0 0
$$379$$ 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
$$381$$ 0 0
$$382$$ 15.0000i 0.767467i
$$383$$ −6.00000 −0.306586 −0.153293 0.988181i $$-0.548988\pi$$
−0.153293 + 0.988181i $$0.548988\pi$$
$$384$$ 0 0
$$385$$ −9.00000 18.0000i −0.458682 0.917365i
$$386$$ −14.0000 −0.712581
$$387$$ 0 0
$$388$$ 7.00000 0.355371
$$389$$ 31.0000i 1.57176i −0.618378 0.785881i $$-0.712210\pi$$
0.618378 0.785881i $$-0.287790\pi$$
$$390$$ 0 0
$$391$$ 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
$$396$$ 0 0
$$397$$ 38.0000i 1.90717i 0.301131 + 0.953583i $$0.402636\pi$$
−0.301131 + 0.953583i $$0.597364\pi$$
$$398$$ 16.0000i 0.802008i
$$399$$ 0 0
$$400$$ 3.00000 4.00000i 0.150000 0.200000i
$$401$$ 10.0000i 0.499376i 0.968326 + 0.249688i $$0.0803281\pi$$
−0.968326 + 0.249688i $$0.919672\pi$$
$$402$$ 0 0
$$403$$ 20.0000i 0.996271i
$$404$$ −2.00000 −0.0995037
$$405$$ 0 0
$$406$$ −27.0000 −1.33999
$$407$$ 18.0000 3.00000i 0.892227 0.148704i
$$408$$ 0 0
$$409$$ 14.0000i 0.692255i −0.938187 0.346128i $$-0.887496\pi$$
0.938187 0.346128i $$-0.112504\pi$$
$$410$$ 14.0000 7.00000i 0.691411 0.345705i
$$411$$ 0 0
$$412$$ −14.0000 −0.689730
$$413$$ 18.0000 0.885722
$$414$$ 0 0
$$415$$ −14.0000 28.0000i −0.687233 1.37447i
$$416$$ −4.00000 −0.196116
$$417$$ 0 0
$$418$$ 12.0000i 0.586939i
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 30.0000i 1.46211i 0.682318 + 0.731055i $$0.260972\pi$$
−0.682318 + 0.731055i $$0.739028\pi$$
$$422$$ −13.0000 −0.632830
$$423$$ 0 0
$$424$$ 1.00000i 0.0485643i
$$425$$ −21.0000 + 28.0000i −1.01865 + 1.35820i
$$426$$ 0 0
$$427$$ 15.0000 0.725901
$$428$$ 18.0000i 0.870063i
$$429$$ 0 0
$$430$$ −2.00000 + 1.00000i −0.0964486 + 0.0482243i
$$431$$ 25.0000i 1.20421i 0.798418 + 0.602104i $$0.205671\pi$$
−0.798418 + 0.602104i $$0.794329\pi$$
$$432$$ 0 0
$$433$$ 34.0000i 1.63394i −0.576683 0.816968i $$-0.695653\pi$$
0.576683 0.816968i $$-0.304347\pi$$
$$434$$ 15.0000 0.720023
$$435$$ 0 0
$$436$$ 11.0000i 0.526804i
$$437$$ 24.0000i 1.14808i
$$438$$ 0 0
$$439$$ 9.00000i 0.429547i −0.976664 0.214773i $$-0.931099\pi$$
0.976664 0.214773i $$-0.0689013\pi$$
$$440$$ −6.00000 + 3.00000i −0.286039 + 0.143019i
$$441$$ 0 0
$$442$$ 28.0000 1.33182
$$443$$ 36.0000i 1.71041i −0.518289 0.855206i $$-0.673431\pi$$
0.518289 0.855206i $$-0.326569\pi$$
$$444$$ 0 0
$$445$$ 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 $$-0.0452178\pi$$
$$450$$ 0 0
$$451$$ −21.0000 −0.988851
$$452$$ −1.00000 −0.0470360
$$453$$ 0 0
$$454$$ 13.0000 0.610120
$$455$$ 12.0000 + 24.0000i 0.562569 + 1.12514i
$$456$$ 0 0
$$457$$ −13.0000 −0.608114 −0.304057 0.952654i $$-0.598341\pi$$
−0.304057 + 0.952654i $$0.598341\pi$$
$$458$$ 10.0000 0.467269
$$459$$ 0 0
$$460$$ 12.0000 6.00000i 0.559503 0.279751i
$$461$$ 25.0000i 1.16437i −0.813058 0.582183i $$-0.802199\pi$$
0.813058 0.582183i $$-0.197801\pi$$
$$462$$ 0 0
$$463$$ 26.0000 1.20832 0.604161 0.796862i $$-0.293508\pi$$
0.604161 + 0.796862i $$0.293508\pi$$
$$464$$ 9.00000i 0.417815i
$$465$$ 0 0
$$466$$ 6.00000i 0.277945i
$$467$$ 23.0000 1.06431 0.532157 0.846646i $$-0.321382\pi$$
0.532157 + 0.846646i $$0.321382\pi$$
$$468$$ 0 0
$$469$$ 6.00000 0.277054
$$470$$ 8.00000 + 16.0000i 0.369012 + 0.738025i
$$471$$ 0 0
$$472$$ 6.00000i 0.276172i
$$473$$ 3.00000 0.137940
$$474$$ 0 0
$$475$$ −16.0000 12.0000i −0.734130 0.550598i
$$476$$ 21.0000i 0.962533i
$$477$$ 0 0
$$478$$ 9.00000i 0.411650i
$$479$$ 24.0000i 1.09659i 0.836286 + 0.548294i $$0.184723\pi$$
−0.836286 + 0.548294i $$0.815277\pi$$
$$480$$ 0 0
$$481$$ −24.0000 + 4.00000i −1.09431 + 0.182384i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −2.00000 −0.0909091
$$485$$ −14.0000 + 7.00000i −0.635707 + 0.317854i
$$486$$ 0 0
$$487$$ 22.0000 0.996915 0.498458 0.866914i $$-0.333900\pi$$
0.498458 + 0.866914i $$0.333900\pi$$
$$488$$ 5.00000i 0.226339i
$$489$$ 0 0
$$490$$ 4.00000 2.00000i 0.180702 0.0903508i
$$491$$ 8.00000 0.361035 0.180517 0.983572i $$-0.442223\pi$$
0.180517 + 0.983572i $$0.442223\pi$$
$$492$$ 0 0
$$493$$ 63.0000i 2.83738i
$$494$$ 16.0000i 0.719874i
$$495$$ 0 0
$$496$$ 5.00000i 0.224507i
$$497$$ 36.0000i 1.61482i
$$498$$ 0 0
$$499$$ 24.0000i 1.07439i −0.843459 0.537194i $$-0.819484\pi$$
0.843459 0.537194i $$-0.180516\pi$$
$$500$$ −2.00000 + 11.0000i −0.0894427 + 0.491935i
$$501$$ 0 0
$$502$$ 20.0000i 0.892644i
$$503$$ 14.0000 0.624229 0.312115 0.950044i $$-0.398963\pi$$
0.312115 + 0.950044i $$0.398963\pi$$
$$504$$ 0 0
$$505$$ 4.00000 2.00000i 0.177998 0.0889988i
$$506$$ −18.0000 −0.800198
$$507$$ 0 0
$$508$$ 8.00000i 0.354943i
$$509$$ 10.0000 0.443242 0.221621 0.975133i $$-0.428865\pi$$
0.221621 + 0.975133i $$0.428865\pi$$
$$510$$ 0 0
$$511$$ 12.0000 0.530849
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 18.0000 0.793946
$$515$$ 28.0000 14.0000i 1.23383 0.616914i
$$516$$ 0 0
$$517$$ 24.0000i 1.05552i
$$518$$ 3.00000 + 18.0000i 0.131812 + 0.790875i
$$519$$ 0 0
$$520$$ 8.00000 4.00000i 0.350823 0.175412i
$$521$$ −37.0000 −1.62100 −0.810500 0.585739i $$-0.800804\pi$$
−0.810500 + 0.585739i $$0.800804\pi$$
$$522$$ 0 0
$$523$$ −4.00000 −0.174908 −0.0874539 0.996169i $$-0.527873\pi$$
−0.0874539 + 0.996169i $$0.527873\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 31.0000i 1.35166i
$$527$$ 35.0000i 1.52462i
$$528$$ 0 0
$$529$$ 13.0000 0.565217
$$530$$ 1.00000 + 2.00000i 0.0434372 + 0.0868744i
$$531$$ 0 0
$$532$$ 12.0000 0.520266
$$533$$ 28.0000 1.21281
$$534$$ 0 0
$$535$$ 18.0000 + 36.0000i 0.778208 + 1.55642i
$$536$$ 2.00000i 0.0863868i
$$537$$ 0 0
$$538$$ −20.0000 −0.862261
$$539$$ −6.00000 −0.258438
$$540$$ 0 0
$$541$$ 30.0000i 1.28980i 0.764267 + 0.644900i $$0.223101\pi$$
−0.764267 + 0.644900i $$0.776899\pi$$
$$542$$ 22.0000 0.944981
$$543$$ 0 0
$$544$$ −7.00000 −0.300123
$$545$$ −11.0000 22.0000i −0.471188 0.942376i
$$546$$ 0 0
$$547$$ −23.0000 −0.983409 −0.491704 0.870762i $$-0.663626\pi$$
−0.491704 + 0.870762i $$0.663626\pi$$
$$548$$ 12.0000i 0.512615i
$$549$$ 0 0
$$550$$ 9.00000 12.0000i 0.383761 0.511682i
$$551$$ 36.0000 1.53365
$$552$$ 0 0
$$553$$ 12.0000 0.510292
$$554$$ −28.0000 −1.18961
$$555$$ 0 0
$$556$$ −15.0000 −0.636142
$$557$$ −12.0000 −0.508456 −0.254228 0.967144i $$-0.581821\pi$$
−0.254228 + 0.967144i $$0.581821\pi$$
$$558$$ 0 0
$$559$$ −4.00000 −0.169182
$$560$$ −3.00000 6.00000i −0.126773 0.253546i
$$561$$ 0 0
$$562$$ 30.0000i 1.26547i
$$563$$ −21.0000 −0.885044 −0.442522 0.896758i $$-0.645916\pi$$
−0.442522 + 0.896758i $$0.645916\pi$$
$$564$$ 0 0
$$565$$ 2.00000 1.00000i 0.0841406 0.0420703i
$$566$$ −4.00000 −0.168133
$$567$$ 0 0
$$568$$ −12.0000 −0.503509
$$569$$ 24.0000i 1.00613i 0.864248 + 0.503066i $$0.167795\pi$$
−0.864248 + 0.503066i $$0.832205\pi$$
$$570$$ 0 0
$$571$$ −33.0000 −1.38101 −0.690504 0.723329i $$-0.742611\pi$$
−0.690504 + 0.723329i $$0.742611\pi$$
$$572$$ −12.0000 −0.501745
$$573$$ 0 0
$$574$$ 21.0000i 0.876523i
$$575$$ −18.0000 + 24.0000i −0.750652 + 1.00087i
$$576$$ 0 0
$$577$$ 22.0000 0.915872 0.457936 0.888985i $$-0.348589\pi$$
0.457936 + 0.888985i $$0.348589\pi$$
$$578$$ 32.0000 1.33102
$$579$$ 0 0
$$580$$ −9.00000 18.0000i −0.373705 0.747409i
$$581$$ −42.0000 −1.74245
$$582$$ 0 0
$$583$$ 3.00000i 0.124247i
$$584$$ 4.00000i 0.165521i
$$585$$ 0 0
$$586$$ 29.0000i 1.19798i
$$587$$ −47.0000 −1.93990 −0.969949 0.243309i $$-0.921767\pi$$
−0.969949 + 0.243309i $$0.921767\pi$$
$$588$$ 0 0
$$589$$ −20.0000 −0.824086
$$590$$ 6.00000 + 12.0000i 0.247016 + 0.494032i
$$591$$ 0 0
$$592$$ 6.00000 1.00000i 0.246598 0.0410997i
$$593$$ 46.0000i 1.88899i −0.328521 0.944497i $$-0.606550\pi$$
0.328521 0.944497i $$-0.393450\pi$$
$$594$$ 0 0
$$595$$ 21.0000 + 42.0000i 0.860916 + 1.72183i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 24.0000 0.981433
$$599$$ 30.0000 1.22577 0.612883 0.790173i $$-0.290010\pi$$
0.612883 + 0.790173i $$0.290010\pi$$
$$600$$ 0 0
$$601$$ −23.0000 −0.938190 −0.469095 0.883148i $$-0.655420\pi$$
−0.469095 + 0.883148i $$0.655420\pi$$
$$602$$ 3.00000i 0.122271i
$$603$$ 0 0
$$604$$ 2.00000 0.0813788
$$605$$ 4.00000 2.00000i 0.162623 0.0813116i
$$606$$ 0 0
$$607$$ 32.0000 1.29884 0.649420 0.760430i $$-0.275012\pi$$
0.649420 + 0.760430i $$0.275012\pi$$
$$608$$ 4.00000i 0.162221i
$$609$$ 0 0
$$610$$ 5.00000 + 10.0000i 0.202444 + 0.404888i
$$611$$ 32.0000i 1.29458i
$$612$$ 0 0
$$613$$ 31.0000i 1.25208i 0.779792 + 0.626039i $$0.215325\pi$$
−0.779792 + 0.626039i $$0.784675\pi$$
$$614$$ 18.0000i 0.726421i
$$615$$ 0 0
$$616$$ 9.00000i 0.362620i
$$617$$ 8.00000i 0.322068i −0.986949 0.161034i $$-0.948517\pi$$
0.986949 0.161034i $$-0.0514829\pi$$
$$618$$ 0 0
$$619$$ 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
$$621$$ 0 0
$$622$$ 15.0000i 0.601445i
$$623$$ 18.0000 0.721155
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 6.00000 0.239808
$$627$$ 0 0
$$628$$ 7.00000i 0.279330i
$$629$$ −42.0000 + 7.00000i −1.67465 + 0.279108i
$$630$$ 0 0
$$631$$ 25.0000i 0.995234i −0.867397 0.497617i $$-0.834208\pi$$
0.867397 0.497617i $$-0.165792\pi$$
$$632$$ 4.00000i 0.159111i
$$633$$ 0 0
$$634$$ 27.0000i 1.07231i
$$635$$ −8.00000 16.0000i −0.317470 0.634941i
$$636$$ 0 0
$$637$$ 8.00000 0.316972
$$638$$ 27.0000i 1.06894i
$$639$$ 0 0
$$640$$ −2.00000 + 1.00000i −0.0790569 + 0.0395285i
$$641$$ −17.0000 −0.671460 −0.335730 0.941958i $$-0.608983\pi$$
−0.335730 + 0.941958i $$0.608983\pi$$
$$642$$ 0 0
$$643$$ 31.0000 1.22252 0.611260 0.791430i $$-0.290663\pi$$
0.611260 + 0.791430i $$0.290663\pi$$
$$644$$ 18.0000i 0.709299i
$$645$$ 0 0
$$646$$ 28.0000i 1.10165i
$$647$$ 48.0000 1.88707 0.943537 0.331266i $$-0.107476\pi$$
0.943537 + 0.331266i $$0.107476\pi$$
$$648$$ 0 0
$$649$$ 18.0000i 0.706562i
$$650$$ −12.0000 + 16.0000i −0.470679 + 0.627572i
$$651$$ 0 0
$$652$$ −9.00000 −0.352467
$$653$$ −36.0000 −1.40879 −0.704394 0.709809i $$-0.748781\pi$$
−0.704394 + 0.709809i $$0.748781\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −7.00000 −0.273304
$$657$$ 0 0
$$658$$ 24.0000 0.935617
$$659$$ 20.0000 0.779089 0.389545 0.921008i $$-0.372632\pi$$
0.389545 + 0.921008i $$0.372632\pi$$
$$660$$ 0 0
$$661$$ 35.0000i 1.36134i −0.732589 0.680671i $$-0.761688\pi$$
0.732589 0.680671i $$-0.238312\pi$$
$$662$$ 20.0000i 0.777322i
$$663$$ 0 0
$$664$$ 14.0000i 0.543305i
$$665$$ −24.0000 + 12.0000i −0.930680 + 0.465340i
$$666$$ 0 0
$$667$$ 54.0000i 2.09089i
$$668$$ −12.0000 −0.464294
$$669$$ 0 0
$$670$$ 2.00000 + 4.00000i 0.0772667 + 0.154533i
$$671$$ 15.0000i 0.579069i
$$672$$ 0 0
$$673$$ 26.0000i 1.00223i 0.865382 + 0.501113i $$0.167076\pi$$
−0.865382 + 0.501113i $$0.832924\pi$$
$$674$$ 18.0000i 0.693334i
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ 42.0000i 1.61419i 0.590421 + 0.807096i $$0.298962\pi$$
−0.590421 + 0.807096i $$0.701038\pi$$
$$678$$ 0 0
$$679$$ 21.0000i 0.805906i
$$680$$ 14.0000 7.00000i 0.536875 0.268438i
$$681$$ 0 0
$$682$$ 15.0000i 0.574380i
$$683$$ −1.00000 −0.0382639 −0.0191320 0.999817i $$-0.506090\pi$$
−0.0191320 + 0.999817i $$0.506090\pi$$
$$684$$ 0 0
$$685$$ −12.0000 24.0000i −0.458496 0.916993i
$$686$$ 15.0000i 0.572703i
$$687$$ 0 0
$$688$$ 1.00000 0.0381246
$$689$$ 4.00000i 0.152388i
$$690$$ 0 0
$$691$$ −43.0000 −1.63580 −0.817899 0.575362i $$-0.804861\pi$$
−0.817899 + 0.575362i $$0.804861\pi$$
$$692$$ 9.00000i 0.342129i
$$693$$ 0 0
$$694$$ 28.0000 1.06287
$$695$$ 30.0000 15.0000i 1.13796 0.568982i
$$696$$ 0 0
$$697$$ 49.0000 1.85601
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 12.0000 + 9.00000i 0.453557 + 0.340168i
$$701$$ 10.0000i 0.377695i 0.982006 + 0.188847i $$0.0604752\pi$$
−0.982006 + 0.188847i $$0.939525\pi$$
$$702$$ 0 0
$$703$$ −4.00000 24.0000i −0.150863 0.905177i
$$704$$ 3.00000 0.113067
$$705$$ 0 0
$$706$$ −31.0000 −1.16670
$$707$$ 6.00000i 0.225653i
$$708$$ 0 0
$$709$$ 11.0000i 0.413114i 0.978435 + 0.206557i $$0.0662258\pi$$
−0.978435 + 0.206557i $$0.933774\pi$$
$$710$$ 24.0000 12.0000i 0.900704 0.450352i
$$711$$ 0 0
$$712$$ 6.00000i 0.224860i
$$713$$ 30.0000i 1.12351i
$$714$$ 0 0
$$715$$ 24.0000 12.0000i 0.897549 0.448775i
$$716$$ 4.00000i 0.149487i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −50.0000 −1.86469 −0.932343 0.361576i $$-0.882239\pi$$
−0.932343 + 0.361576i $$0.882239\pi$$
$$720$$ 0 0
$$721$$ 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
$$726$$ 0 0
$$727$$ −18.0000 −0.667583 −0.333792 0.942647i $$-0.608328\pi$$
−0.333792 + 0.942647i $$0.608328\pi$$
$$728$$ 12.0000i 0.444750i
$$729$$ 0 0
$$730$$ 4.00000 + 8.00000i 0.148047 + 0.296093i
$$731$$ −7.00000 −0.258904
$$732$$ 0 0
$$733$$ 11.0000i 0.406294i 0.979148 + 0.203147i $$0.0651170\pi$$
−0.979148 + 0.203147i $$0.934883\pi$$
$$734$$ 23.0000i 0.848945i
$$735$$ 0 0
$$736$$ −6.00000 −0.221163
$$737$$ 6.00000i 0.221013i
$$738$$ 0 0
$$739$$ 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
$$741$$ 0 0
$$742$$ 3.00000 0.110133
$$743$$ 51.0000i 1.87101i −0.353315 0.935504i $$-0.614946\pi$$
0.353315 0.935504i $$-0.385054\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 14.0000i 0.512576i
$$747$$ 0 0
$$748$$ −21.0000 −0.767836
$$749$$ 54.0000 1.97312
$$750$$ 0 0
$$751$$ −18.0000 −0.656829 −0.328415 0.944534i $$-0.606514\pi$$
−0.328415 + 0.944534i $$0.606514\pi$$
$$752$$ 8.00000i 0.291730i
$$753$$ 0 0
$$754$$ 36.0000i 1.31104i
$$755$$ −4.00000 + 2.00000i −0.145575 + 0.0727875i
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 20.0000 0.726433
$$759$$ 0 0
$$760$$ 4.00000 + 8.00000i 0.145095 + 0.290191i
$$761$$ 13.0000 0.471250 0.235625 0.971844i $$-0.424286\pi$$
0.235625 + 0.971844i $$0.424286\pi$$
$$762$$ 0 0
$$763$$ −33.0000 −1.19468
$$764$$ 15.0000i 0.542681i
$$765$$ 0 0
$$766$$ −6.00000 −0.216789
$$767$$ 24.0000i 0.866590i
$$768$$ 0 0
$$769$$ 26.0000i 0.937584i 0.883309 + 0.468792i $$0.155311\pi$$
−0.883309 + 0.468792i $$0.844689\pi$$
$$770$$ −9.00000 18.0000i −0.324337 0.648675i
$$771$$ 0 0
$$772$$ −14.0000 −0.503871
$$773$$ 11.0000i 0.395643i −0.980238 0.197821i $$-0.936613\pi$$
0.980238 0.197821i $$-0.0633866\pi$$
$$774$$ 0 0
$$775$$ −20.0000 15.0000i −0.718421 0.538816i
$$776$$ 7.00000 0.251285
$$777$$ 0 0
$$778$$ 31.0000i 1.11140i
$$779$$ 28.0000i 1.00320i
$$780$$ 0 0
$$781$$ −36.0000 −1.28818
$$782$$ 42.0000 1.50192
$$783$$ 0 0
$$784$$ −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 $$0.166316\pi$$
−0.866575 + 0.499046i $$0.833684\pi$$
$$788$$ 18.0000i 0.641223i
$$789$$ 0 0
$$790$$ 4.00000 + 8.00000i 0.142314 + 0.284627i
$$791$$ 3.00000i 0.106668i
$$792$$ 0 0
$$793$$ 20.0000i 0.710221i
$$794$$ 38.0000i 1.34857i
$$795$$ 0 0
$$796$$ 16.0000i 0.567105i
$$797$$ 28.0000