# Properties

 Label 1008.2.r.m.337.1 Level 1008 Weight 2 Character 1008.337 Analytic conductor 8.049 Analytic rank 0 Dimension 8 CM no Inner twists 2

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1008.r (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.04892052375$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: 8.0.508277025.1 Defining polynomial: $$x^{8} - 3 x^{7} + 5 x^{6} - 15 x^{5} + 21 x^{4} + 3 x^{3} - 22 x^{2} + 3 x + 19$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 504) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 337.1 Root $$-0.577806 - 2.22188i$$ of defining polynomial Character $$\chi$$ $$=$$ 1008.337 Dual form 1008.2.r.m.673.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.71311 + 0.255482i) q^{3} +(1.81197 - 3.13842i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.86946 - 0.875335i) q^{9} +O(q^{10})$$ $$q+(-1.71311 + 0.255482i) q^{3} +(1.81197 - 3.13842i) q^{5} +(0.500000 + 0.866025i) q^{7} +(2.86946 - 0.875335i) q^{9} +(1.95863 + 3.39245i) q^{11} +(-2.53644 + 4.39324i) q^{13} +(-2.30228 + 5.83936i) q^{15} +1.03225 q^{17} +2.50895 q^{19} +(-1.07781 - 1.35585i) q^{21} +(2.47895 - 4.29366i) q^{23} +(-4.06644 - 7.04328i) q^{25} +(-4.69205 + 2.23263i) q^{27} +(4.60288 + 7.97242i) q^{29} +(-0.422194 + 0.731261i) q^{31} +(-4.22205 - 5.31123i) q^{33} +3.62393 q^{35} +4.84439 q^{37} +(3.22279 - 8.17410i) q^{39} +(2.07362 - 3.59161i) q^{41} +(-2.20174 - 3.81352i) q^{43} +(2.45219 - 10.5916i) q^{45} +(-3.93758 - 6.82008i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-1.76835 + 0.263721i) q^{51} +12.2786 q^{53} +14.1959 q^{55} +(-4.29809 + 0.640990i) q^{57} +(-5.60288 + 9.70447i) q^{59} +(-0.208348 - 0.360870i) q^{61} +(2.19279 + 2.04736i) q^{63} +(9.19188 + 15.9208i) q^{65} +(5.02507 - 8.70368i) q^{67} +(-3.14974 + 7.98882i) q^{69} +5.05162 q^{71} +7.20723 q^{73} +(8.76567 + 11.0270i) q^{75} +(-1.95863 + 3.39245i) q^{77} +(7.56570 + 13.1042i) q^{79} +(7.46758 - 5.02347i) q^{81} +(0.932821 + 1.61569i) q^{83} +(1.87040 - 3.23963i) q^{85} +(-9.92202 - 12.4816i) q^{87} -0.669401 q^{89} -5.07288 q^{91} +(0.536438 - 1.36059i) q^{93} +(4.54612 - 7.87412i) q^{95} +(-7.63513 - 13.2244i) q^{97} +(8.58974 + 8.02003i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + O(q^{10})$$ $$8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + 6q^{11} - 3q^{13} - 4q^{15} - 16q^{17} + 4q^{19} - q^{21} + 5q^{23} - 14q^{25} - 5q^{27} + q^{29} - 11q^{31} + 8q^{35} + 54q^{37} + 12q^{39} + 2q^{41} + 11q^{43} + 26q^{45} - 7q^{47} - 4q^{49} - 17q^{51} - 8q^{53} - 12q^{55} - 13q^{57} - 9q^{59} - 7q^{61} + 5q^{63} - 9q^{65} + 12q^{67} + 4q^{69} + 24q^{71} + 26q^{73} + 23q^{75} - 6q^{77} + 22q^{79} + 34q^{81} + 6q^{83} - 11q^{85} - 37q^{87} - 28q^{89} - 6q^{91} - 13q^{93} + 23q^{95} - q^{97} + 42q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$577$$ $$757$$ $$785$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.71311 + 0.255482i −0.989062 + 0.147503i
$$4$$ 0 0
$$5$$ 1.81197 3.13842i 0.810336 1.40354i −0.102294 0.994754i $$-0.532618\pi$$
0.912629 0.408788i $$-0.134049\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 0.866025i 0.188982 + 0.327327i
$$8$$ 0 0
$$9$$ 2.86946 0.875335i 0.956486 0.291778i
$$10$$ 0 0
$$11$$ 1.95863 + 3.39245i 0.590550 + 1.02286i 0.994158 + 0.107930i $$0.0344224\pi$$
−0.403609 + 0.914932i $$0.632244\pi$$
$$12$$ 0 0
$$13$$ −2.53644 + 4.39324i −0.703481 + 1.21847i 0.263755 + 0.964590i $$0.415039\pi$$
−0.967237 + 0.253876i $$0.918295\pi$$
$$14$$ 0 0
$$15$$ −2.30228 + 5.83936i −0.594446 + 1.50772i
$$16$$ 0 0
$$17$$ 1.03225 0.250357 0.125178 0.992134i $$-0.460050\pi$$
0.125178 + 0.992134i $$0.460050\pi$$
$$18$$ 0 0
$$19$$ 2.50895 0.575592 0.287796 0.957692i $$-0.407078\pi$$
0.287796 + 0.957692i $$0.407078\pi$$
$$20$$ 0 0
$$21$$ −1.07781 1.35585i −0.235197 0.295871i
$$22$$ 0 0
$$23$$ 2.47895 4.29366i 0.516896 0.895290i −0.482912 0.875669i $$-0.660421\pi$$
0.999807 0.0196209i $$-0.00624592\pi$$
$$24$$ 0 0
$$25$$ −4.06644 7.04328i −0.813288 1.40866i
$$26$$ 0 0
$$27$$ −4.69205 + 2.23263i −0.902986 + 0.429671i
$$28$$ 0 0
$$29$$ 4.60288 + 7.97242i 0.854733 + 1.48044i 0.876893 + 0.480686i $$0.159612\pi$$
−0.0221599 + 0.999754i $$0.507054\pi$$
$$30$$ 0 0
$$31$$ −0.422194 + 0.731261i −0.0758282 + 0.131338i −0.901446 0.432891i $$-0.857493\pi$$
0.825618 + 0.564230i $$0.190827\pi$$
$$32$$ 0 0
$$33$$ −4.22205 5.31123i −0.734965 0.924566i
$$34$$ 0 0
$$35$$ 3.62393 0.612556
$$36$$ 0 0
$$37$$ 4.84439 0.796412 0.398206 0.917296i $$-0.369633\pi$$
0.398206 + 0.917296i $$0.369633\pi$$
$$38$$ 0 0
$$39$$ 3.22279 8.17410i 0.516060 1.30890i
$$40$$ 0 0
$$41$$ 2.07362 3.59161i 0.323844 0.560915i −0.657433 0.753513i $$-0.728358\pi$$
0.981278 + 0.192598i $$0.0616912\pi$$
$$42$$ 0 0
$$43$$ −2.20174 3.81352i −0.335762 0.581557i 0.647869 0.761752i $$-0.275660\pi$$
−0.983631 + 0.180195i $$0.942327\pi$$
$$44$$ 0 0
$$45$$ 2.45219 10.5916i 0.365552 1.57891i
$$46$$ 0 0
$$47$$ −3.93758 6.82008i −0.574355 0.994812i −0.996111 0.0881025i $$-0.971920\pi$$
0.421757 0.906709i $$-0.361414\pi$$
$$48$$ 0 0
$$49$$ −0.500000 + 0.866025i −0.0714286 + 0.123718i
$$50$$ 0 0
$$51$$ −1.76835 + 0.263721i −0.247619 + 0.0369283i
$$52$$ 0 0
$$53$$ 12.2786 1.68660 0.843300 0.537443i $$-0.180610\pi$$
0.843300 + 0.537443i $$0.180610\pi$$
$$54$$ 0 0
$$55$$ 14.1959 1.91417
$$56$$ 0 0
$$57$$ −4.29809 + 0.640990i −0.569296 + 0.0849013i
$$58$$ 0 0
$$59$$ −5.60288 + 9.70447i −0.729432 + 1.26341i 0.227691 + 0.973733i $$0.426882\pi$$
−0.957123 + 0.289681i $$0.906451\pi$$
$$60$$ 0 0
$$61$$ −0.208348 0.360870i −0.0266763 0.0462047i 0.852379 0.522924i $$-0.175159\pi$$
−0.879055 + 0.476720i $$0.841826\pi$$
$$62$$ 0 0
$$63$$ 2.19279 + 2.04736i 0.276266 + 0.257943i
$$64$$ 0 0
$$65$$ 9.19188 + 15.9208i 1.14011 + 1.97473i
$$66$$ 0 0
$$67$$ 5.02507 8.70368i 0.613910 1.06332i −0.376665 0.926350i $$-0.622929\pi$$
0.990575 0.136974i $$-0.0437376\pi$$
$$68$$ 0 0
$$69$$ −3.14974 + 7.98882i −0.379184 + 0.961741i
$$70$$ 0 0
$$71$$ 5.05162 0.599517 0.299759 0.954015i $$-0.403094\pi$$
0.299759 + 0.954015i $$0.403094\pi$$
$$72$$ 0 0
$$73$$ 7.20723 0.843543 0.421771 0.906702i $$-0.361408\pi$$
0.421771 + 0.906702i $$0.361408\pi$$
$$74$$ 0 0
$$75$$ 8.76567 + 11.0270i 1.01217 + 1.27329i
$$76$$ 0 0
$$77$$ −1.95863 + 3.39245i −0.223207 + 0.386606i
$$78$$ 0 0
$$79$$ 7.56570 + 13.1042i 0.851208 + 1.47433i 0.880119 + 0.474753i $$0.157463\pi$$
−0.0289116 + 0.999582i $$0.509204\pi$$
$$80$$ 0 0
$$81$$ 7.46758 5.02347i 0.829731 0.558164i
$$82$$ 0 0
$$83$$ 0.932821 + 1.61569i 0.102390 + 0.177345i 0.912669 0.408699i $$-0.134018\pi$$
−0.810279 + 0.586045i $$0.800684\pi$$
$$84$$ 0 0
$$85$$ 1.87040 3.23963i 0.202873 0.351387i
$$86$$ 0 0
$$87$$ −9.92202 12.4816i −1.06375 1.33817i
$$88$$ 0 0
$$89$$ −0.669401 −0.0709564 −0.0354782 0.999370i $$-0.511295\pi$$
−0.0354782 + 0.999370i $$0.511295\pi$$
$$90$$ 0 0
$$91$$ −5.07288 −0.531782
$$92$$ 0 0
$$93$$ 0.536438 1.36059i 0.0556260 0.141087i
$$94$$ 0 0
$$95$$ 4.54612 7.87412i 0.466423 0.807868i
$$96$$ 0 0
$$97$$ −7.63513 13.2244i −0.775230 1.34274i −0.934665 0.355529i $$-0.884301\pi$$
0.159436 0.987208i $$-0.449032\pi$$
$$98$$ 0 0
$$99$$ 8.58974 + 8.02003i 0.863301 + 0.806044i
$$100$$ 0 0
$$101$$ 5.87840 + 10.1817i 0.584923 + 1.01312i 0.994885 + 0.101014i $$0.0322087\pi$$
−0.409962 + 0.912103i $$0.634458\pi$$
$$102$$ 0 0
$$103$$ 5.51538 9.55293i 0.543447 0.941278i −0.455256 0.890361i $$-0.650452\pi$$
0.998703 0.0509171i $$-0.0162144\pi$$
$$104$$ 0 0
$$105$$ −6.20818 + 0.925849i −0.605856 + 0.0903536i
$$106$$ 0 0
$$107$$ 0.842907 0.0814869 0.0407434 0.999170i $$-0.487027\pi$$
0.0407434 + 0.999170i $$0.487027\pi$$
$$108$$ 0 0
$$109$$ −17.1875 −1.64627 −0.823133 0.567849i $$-0.807776\pi$$
−0.823133 + 0.567849i $$0.807776\pi$$
$$110$$ 0 0
$$111$$ −8.29894 + 1.23765i −0.787701 + 0.117473i
$$112$$ 0 0
$$113$$ −4.54538 + 7.87284i −0.427594 + 0.740614i −0.996659 0.0816784i $$-0.973972\pi$$
0.569065 + 0.822293i $$0.307305\pi$$
$$114$$ 0 0
$$115$$ −8.98353 15.5599i −0.837718 1.45097i
$$116$$ 0 0
$$117$$ −3.43265 + 14.8264i −0.317348 + 1.37071i
$$118$$ 0 0
$$119$$ 0.516124 + 0.893953i 0.0473130 + 0.0819486i
$$120$$ 0 0
$$121$$ −2.17248 + 3.76284i −0.197498 + 0.342076i
$$122$$ 0 0
$$123$$ −2.63473 + 6.68258i −0.237566 + 0.602548i
$$124$$ 0 0
$$125$$ −11.3533 −1.01547
$$126$$ 0 0
$$127$$ 14.4859 1.28541 0.642706 0.766113i $$-0.277812\pi$$
0.642706 + 0.766113i $$0.277812\pi$$
$$128$$ 0 0
$$129$$ 4.74609 + 5.97046i 0.417870 + 0.525670i
$$130$$ 0 0
$$131$$ 4.03476 6.98840i 0.352518 0.610580i −0.634172 0.773192i $$-0.718659\pi$$
0.986690 + 0.162613i $$0.0519921\pi$$
$$132$$ 0 0
$$133$$ 1.25447 + 2.17281i 0.108777 + 0.188407i
$$134$$ 0 0
$$135$$ −1.49490 + 18.7711i −0.128660 + 1.61556i
$$136$$ 0 0
$$137$$ −9.85792 17.0744i −0.842219 1.45877i −0.888015 0.459815i $$-0.847916\pi$$
0.0457961 0.998951i $$-0.485418\pi$$
$$138$$ 0 0
$$139$$ 8.35960 14.4792i 0.709052 1.22811i −0.256157 0.966635i $$-0.582457\pi$$
0.965209 0.261479i $$-0.0842101\pi$$
$$140$$ 0 0
$$141$$ 8.48789 + 10.6775i 0.714809 + 0.899211i
$$142$$ 0 0
$$143$$ −19.8718 −1.66176
$$144$$ 0 0
$$145$$ 33.3610 2.77048
$$146$$ 0 0
$$147$$ 0.635299 1.61133i 0.0523986 0.132901i
$$148$$ 0 0
$$149$$ −9.16439 + 15.8732i −0.750776 + 1.30038i 0.196671 + 0.980469i $$0.436987\pi$$
−0.947447 + 0.319912i $$0.896347\pi$$
$$150$$ 0 0
$$151$$ −7.23100 12.5245i −0.588450 1.01923i −0.994436 0.105346i $$-0.966405\pi$$
0.405985 0.913880i $$-0.366928\pi$$
$$152$$ 0 0
$$153$$ 2.96199 0.903563i 0.239463 0.0730487i
$$154$$ 0 0
$$155$$ 1.53000 + 2.65004i 0.122893 + 0.212856i
$$156$$ 0 0
$$157$$ −1.92387 + 3.33225i −0.153542 + 0.265942i −0.932527 0.361100i $$-0.882401\pi$$
0.778985 + 0.627042i $$0.215735\pi$$
$$158$$ 0 0
$$159$$ −21.0346 + 3.13697i −1.66815 + 0.248778i
$$160$$ 0 0
$$161$$ 4.95789 0.390737
$$162$$ 0 0
$$163$$ −13.0322 −1.02076 −0.510382 0.859948i $$-0.670496\pi$$
−0.510382 + 0.859948i $$0.670496\pi$$
$$164$$ 0 0
$$165$$ −24.3191 + 3.62679i −1.89324 + 0.282346i
$$166$$ 0 0
$$167$$ −3.04538 + 5.27476i −0.235659 + 0.408173i −0.959464 0.281831i $$-0.909058\pi$$
0.723805 + 0.690005i $$0.242391\pi$$
$$168$$ 0 0
$$169$$ −6.36704 11.0280i −0.489772 0.848310i
$$170$$ 0 0
$$171$$ 7.19932 2.19617i 0.550546 0.167945i
$$172$$ 0 0
$$173$$ −5.89855 10.2166i −0.448458 0.776752i 0.549828 0.835278i $$-0.314693\pi$$
−0.998286 + 0.0585258i $$0.981360\pi$$
$$174$$ 0 0
$$175$$ 4.06644 7.04328i 0.307394 0.532422i
$$176$$ 0 0
$$177$$ 7.11900 18.0562i 0.535097 1.35719i
$$178$$ 0 0
$$179$$ −1.06148 −0.0793389 −0.0396694 0.999213i $$-0.512630\pi$$
−0.0396694 + 0.999213i $$0.512630\pi$$
$$180$$ 0 0
$$181$$ −16.0384 −1.19212 −0.596062 0.802938i $$-0.703269\pi$$
−0.596062 + 0.802938i $$0.703269\pi$$
$$182$$ 0 0
$$183$$ 0.449118 + 0.564979i 0.0331998 + 0.0417644i
$$184$$ 0 0
$$185$$ 8.77786 15.2037i 0.645361 1.11780i
$$186$$ 0 0
$$187$$ 2.02179 + 3.50185i 0.147848 + 0.256081i
$$188$$ 0 0
$$189$$ −4.27954 2.94712i −0.311291 0.214371i
$$190$$ 0 0
$$191$$ 11.9676 + 20.7285i 0.865944 + 1.49986i 0.866107 + 0.499858i $$0.166615\pi$$
−0.000163629 1.00000i $$0.500052\pi$$
$$192$$ 0 0
$$193$$ −6.60707 + 11.4438i −0.475587 + 0.823741i −0.999609 0.0279638i $$-0.991098\pi$$
0.524022 + 0.851705i $$0.324431\pi$$
$$194$$ 0 0
$$195$$ −19.8141 24.9256i −1.41892 1.78496i
$$196$$ 0 0
$$197$$ −25.0403 −1.78405 −0.892023 0.451990i $$-0.850714\pi$$
−0.892023 + 0.451990i $$0.850714\pi$$
$$198$$ 0 0
$$199$$ −8.28159 −0.587066 −0.293533 0.955949i $$-0.594831\pi$$
−0.293533 + 0.955949i $$0.594831\pi$$
$$200$$ 0 0
$$201$$ −6.38484 + 16.1941i −0.450352 + 1.14225i
$$202$$ 0 0
$$203$$ −4.60288 + 7.97242i −0.323059 + 0.559554i
$$204$$ 0 0
$$205$$ −7.51464 13.0157i −0.524845 0.909059i
$$206$$ 0 0
$$207$$ 3.35484 14.4904i 0.233178 1.00715i
$$208$$ 0 0
$$209$$ 4.91410 + 8.51148i 0.339916 + 0.588751i
$$210$$ 0 0
$$211$$ 1.79752 3.11340i 0.123747 0.214335i −0.797496 0.603325i $$-0.793842\pi$$
0.921242 + 0.388989i $$0.127176\pi$$
$$212$$ 0 0
$$213$$ −8.65396 + 1.29060i −0.592959 + 0.0884303i
$$214$$ 0 0
$$215$$ −15.9579 −1.08832
$$216$$ 0 0
$$217$$ −0.844387 −0.0573207
$$218$$ 0 0
$$219$$ −12.3468 + 1.84132i −0.834316 + 0.124425i
$$220$$ 0 0
$$221$$ −2.61823 + 4.53491i −0.176121 + 0.305051i
$$222$$ 0 0
$$223$$ 5.08601 + 8.80923i 0.340585 + 0.589910i 0.984541 0.175152i $$-0.0560417\pi$$
−0.643957 + 0.765062i $$0.722708\pi$$
$$224$$ 0 0
$$225$$ −17.8337 16.6509i −1.18891 1.11006i
$$226$$ 0 0
$$227$$ 6.95054 + 12.0387i 0.461324 + 0.799036i 0.999027 0.0440980i $$-0.0140414\pi$$
−0.537704 + 0.843134i $$0.680708\pi$$
$$228$$ 0 0
$$229$$ 2.84347 4.92504i 0.187902 0.325456i −0.756649 0.653822i $$-0.773165\pi$$
0.944551 + 0.328366i $$0.106498\pi$$
$$230$$ 0 0
$$231$$ 2.48863 6.31202i 0.163740 0.415300i
$$232$$ 0 0
$$233$$ 19.4775 1.27601 0.638006 0.770031i $$-0.279759\pi$$
0.638006 + 0.770031i $$0.279759\pi$$
$$234$$ 0 0
$$235$$ −28.5390 −1.86168
$$236$$ 0 0
$$237$$ −16.3087 20.5159i −1.05936 1.33265i
$$238$$ 0 0
$$239$$ 2.50000 4.33013i 0.161712 0.280093i −0.773771 0.633465i $$-0.781632\pi$$
0.935483 + 0.353373i $$0.114965\pi$$
$$240$$ 0 0
$$241$$ −5.14080 8.90412i −0.331148 0.573565i 0.651589 0.758572i $$-0.274103\pi$$
−0.982737 + 0.185007i $$0.940769\pi$$
$$242$$ 0 0
$$243$$ −11.5093 + 10.5136i −0.738325 + 0.674446i
$$244$$ 0 0
$$245$$ 1.81197 + 3.13842i 0.115762 + 0.200506i
$$246$$ 0 0
$$247$$ −6.36379 + 11.0224i −0.404918 + 0.701339i
$$248$$ 0 0
$$249$$ −2.01080 2.52953i −0.127429 0.160303i
$$250$$ 0 0
$$251$$ 0.829685 0.0523693 0.0261846 0.999657i $$-0.491664\pi$$
0.0261846 + 0.999657i $$0.491664\pi$$
$$252$$ 0 0
$$253$$ 19.4214 1.22101
$$254$$ 0 0
$$255$$ −2.37652 + 6.02767i −0.148824 + 0.377467i
$$256$$ 0 0
$$257$$ 6.87516 11.9081i 0.428860 0.742808i −0.567912 0.823089i $$-0.692249\pi$$
0.996772 + 0.0802814i $$0.0255819\pi$$
$$258$$ 0 0
$$259$$ 2.42219 + 4.19536i 0.150508 + 0.260687i
$$260$$ 0 0
$$261$$ 20.1863 + 18.8475i 1.24950 + 1.16663i
$$262$$ 0 0
$$263$$ 12.9285 + 22.3929i 0.797208 + 1.38081i 0.921427 + 0.388550i $$0.127024\pi$$
−0.124219 + 0.992255i $$0.539643\pi$$
$$264$$ 0 0
$$265$$ 22.2485 38.5355i 1.36671 2.36721i
$$266$$ 0 0
$$267$$ 1.14675 0.171020i 0.0701802 0.0104662i
$$268$$ 0 0
$$269$$ 9.32410 0.568500 0.284250 0.958750i $$-0.408255\pi$$
0.284250 + 0.958750i $$0.408255\pi$$
$$270$$ 0 0
$$271$$ −25.7421 −1.56372 −0.781861 0.623453i $$-0.785729\pi$$
−0.781861 + 0.623453i $$0.785729\pi$$
$$272$$ 0 0
$$273$$ 8.69037 1.29603i 0.525965 0.0784392i
$$274$$ 0 0
$$275$$ 15.9293 27.5904i 0.960574 1.66376i
$$276$$ 0 0
$$277$$ 5.06570 + 8.77405i 0.304368 + 0.527181i 0.977120 0.212686i $$-0.0682213\pi$$
−0.672752 + 0.739868i $$0.734888\pi$$
$$278$$ 0 0
$$279$$ −0.571369 + 2.46788i −0.0342070 + 0.147748i
$$280$$ 0 0
$$281$$ 3.47969 + 6.02699i 0.207581 + 0.359540i 0.950952 0.309339i $$-0.100108\pi$$
−0.743371 + 0.668879i $$0.766774\pi$$
$$282$$ 0 0
$$283$$ −3.95920 + 6.85753i −0.235350 + 0.407638i −0.959374 0.282136i $$-0.908957\pi$$
0.724024 + 0.689774i $$0.242290\pi$$
$$284$$ 0 0
$$285$$ −5.77629 + 14.6506i −0.342158 + 0.867829i
$$286$$ 0 0
$$287$$ 4.14723 0.244803
$$288$$ 0 0
$$289$$ −15.9345 −0.937321
$$290$$ 0 0
$$291$$ 16.4584 + 20.7042i 0.964807 + 1.21370i
$$292$$ 0 0
$$293$$ 5.63128 9.75367i 0.328983 0.569815i −0.653327 0.757076i $$-0.726627\pi$$
0.982310 + 0.187260i $$0.0599608\pi$$
$$294$$ 0 0
$$295$$ 20.3044 + 35.1683i 1.18217 + 2.04758i
$$296$$ 0 0
$$297$$ −16.7641 11.5446i −0.972752 0.669888i
$$298$$ 0 0
$$299$$ 12.5754 + 21.7812i 0.727253 + 1.25964i
$$300$$ 0 0
$$301$$ 2.20174 3.81352i 0.126906 0.219808i
$$302$$ 0 0
$$303$$ −12.6716 15.9405i −0.727962 0.915757i
$$304$$ 0 0
$$305$$ −1.51008 −0.0864669
$$306$$ 0 0
$$307$$ −23.0142 −1.31349 −0.656744 0.754113i $$-0.728067\pi$$
−0.656744 + 0.754113i $$0.728067\pi$$
$$308$$ 0 0
$$309$$ −7.00783 + 17.7742i −0.398662 + 1.01114i
$$310$$ 0 0
$$311$$ −6.78832 + 11.7577i −0.384930 + 0.666719i −0.991760 0.128114i $$-0.959108\pi$$
0.606829 + 0.794832i $$0.292441\pi$$
$$312$$ 0 0
$$313$$ 8.92362 + 15.4562i 0.504393 + 0.873634i 0.999987 + 0.00507958i $$0.00161689\pi$$
−0.495595 + 0.868554i $$0.665050\pi$$
$$314$$ 0 0
$$315$$ 10.3987 3.17215i 0.585901 0.178731i
$$316$$ 0 0
$$317$$ 9.69755 + 16.7966i 0.544669 + 0.943394i 0.998628 + 0.0523711i $$0.0166779\pi$$
−0.453959 + 0.891022i $$0.649989\pi$$
$$318$$ 0 0
$$319$$ −18.0307 + 31.2301i −1.00952 + 1.74855i
$$320$$ 0 0
$$321$$ −1.44399 + 0.215347i −0.0805956 + 0.0120195i
$$322$$ 0 0
$$323$$ 2.58986 0.144103
$$324$$ 0 0
$$325$$ 41.2571 2.28853
$$326$$ 0 0
$$327$$ 29.4440 4.39110i 1.62826 0.242828i
$$328$$ 0 0
$$329$$ 3.93758 6.82008i 0.217086 0.376003i
$$330$$ 0 0
$$331$$ 7.28729 + 12.6220i 0.400546 + 0.693765i 0.993792 0.111256i $$-0.0354873\pi$$
−0.593246 + 0.805021i $$0.702154\pi$$
$$332$$ 0 0
$$333$$ 13.9008 4.24046i 0.761757 0.232376i
$$334$$ 0 0
$$335$$ −18.2105 31.5415i −0.994946 1.72330i
$$336$$ 0 0
$$337$$ −13.8962 + 24.0689i −0.756975 + 1.31112i 0.187412 + 0.982281i $$0.439990\pi$$
−0.944387 + 0.328837i $$0.893343\pi$$
$$338$$ 0 0
$$339$$ 5.77535 14.6483i 0.313674 0.795584i
$$340$$ 0 0
$$341$$ −3.30769 −0.179121
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ 0 0
$$345$$ 19.3650 + 24.3607i 1.04258 + 1.31153i
$$346$$ 0 0
$$347$$ 7.45604 12.9142i 0.400261 0.693273i −0.593496 0.804837i $$-0.702253\pi$$
0.993757 + 0.111564i $$0.0355861\pi$$
$$348$$ 0 0
$$349$$ 10.9579 + 18.9796i 0.586562 + 1.01596i 0.994679 + 0.103026i $$0.0328525\pi$$
−0.408116 + 0.912930i $$0.633814\pi$$
$$350$$ 0 0
$$351$$ 2.09260 26.2762i 0.111695 1.40252i
$$352$$ 0 0
$$353$$ −7.73100 13.3905i −0.411480 0.712703i 0.583572 0.812061i $$-0.301654\pi$$
−0.995052 + 0.0993578i $$0.968321\pi$$
$$354$$ 0 0
$$355$$ 9.15337 15.8541i 0.485810 0.841448i
$$356$$ 0 0
$$357$$ −1.11256 1.39958i −0.0588831 0.0740734i
$$358$$ 0 0
$$359$$ −7.56506 −0.399269 −0.199634 0.979870i $$-0.563975\pi$$
−0.199634 + 0.979870i $$0.563975\pi$$
$$360$$ 0 0
$$361$$ −12.7052 −0.668694
$$362$$ 0 0
$$363$$ 2.76034 7.00117i 0.144880 0.367466i
$$364$$ 0 0
$$365$$ 13.0593 22.6193i 0.683553 1.18395i
$$366$$ 0 0
$$367$$ −14.5046 25.1227i −0.757133 1.31139i −0.944307 0.329066i $$-0.893266\pi$$
0.187174 0.982327i $$-0.440067\pi$$
$$368$$ 0 0
$$369$$ 2.80630 12.1211i 0.146090 0.630998i
$$370$$ 0 0
$$371$$ 6.13932 + 10.6336i 0.318737 + 0.552069i
$$372$$ 0 0
$$373$$ −0.655525 + 1.13540i −0.0339418 + 0.0587889i −0.882497 0.470317i $$-0.844139\pi$$
0.848556 + 0.529106i $$0.177473\pi$$
$$374$$ 0 0
$$375$$ 19.4495 2.90057i 1.00437 0.149785i
$$376$$ 0 0
$$377$$ −46.6997 −2.40515
$$378$$ 0 0
$$379$$ 15.7015 0.806531 0.403265 0.915083i $$-0.367875\pi$$
0.403265 + 0.915083i $$0.367875\pi$$
$$380$$ 0 0
$$381$$ −24.8158 + 3.70088i −1.27135 + 0.189602i
$$382$$ 0 0
$$383$$ −10.4804 + 18.1525i −0.535522 + 0.927551i 0.463616 + 0.886036i $$0.346552\pi$$
−0.999138 + 0.0415148i $$0.986782\pi$$
$$384$$ 0 0
$$385$$ 7.09795 + 12.2940i 0.361745 + 0.626561i
$$386$$ 0 0
$$387$$ −9.65590 9.01548i −0.490837 0.458283i
$$388$$ 0 0
$$389$$ −5.80937 10.0621i −0.294547 0.510170i 0.680333 0.732904i $$-0.261835\pi$$
−0.974879 + 0.222733i $$0.928502\pi$$
$$390$$ 0 0
$$391$$ 2.55889 4.43212i 0.129409 0.224142i
$$392$$ 0 0
$$393$$ −5.12655 + 13.0027i −0.258600 + 0.655898i
$$394$$ 0 0
$$395$$ 54.8351 2.75906
$$396$$ 0 0
$$397$$ −35.5217 −1.78278 −0.891390 0.453237i $$-0.850269\pi$$
−0.891390 + 0.453237i $$0.850269\pi$$
$$398$$ 0 0
$$399$$ −2.70416 3.40176i −0.135377 0.170301i
$$400$$ 0 0
$$401$$ 2.45388 4.25024i 0.122541 0.212247i −0.798228 0.602355i $$-0.794229\pi$$
0.920769 + 0.390108i $$0.127562\pi$$
$$402$$ 0 0
$$403$$ −2.14174 3.70960i −0.106687 0.184788i
$$404$$ 0 0
$$405$$ −2.23475 32.5387i −0.111046 1.61686i
$$406$$ 0 0
$$407$$ 9.48837 + 16.4343i 0.470321 + 0.814620i
$$408$$ 0 0
$$409$$ −2.21561 + 3.83756i −0.109555 + 0.189755i −0.915590 0.402113i $$-0.868276\pi$$
0.806035 + 0.591868i $$0.201609\pi$$
$$410$$ 0 0
$$411$$ 21.2499 + 26.7317i 1.04818 + 1.31858i
$$412$$ 0 0
$$413$$ −11.2058 −0.551399
$$414$$ 0 0
$$415$$ 6.76096 0.331882
$$416$$ 0 0
$$417$$ −10.6217 + 26.9402i −0.520146 + 1.31927i
$$418$$ 0 0
$$419$$ 17.7719 30.7819i 0.868216 1.50379i 0.00439727 0.999990i $$-0.498600\pi$$
0.863818 0.503803i $$-0.168066\pi$$
$$420$$ 0 0
$$421$$ 1.81923 + 3.15100i 0.0886639 + 0.153570i 0.906947 0.421246i $$-0.138407\pi$$
−0.818283 + 0.574816i $$0.805074\pi$$
$$422$$ 0 0
$$423$$ −17.2686 16.1232i −0.839627 0.783939i
$$424$$ 0 0
$$425$$ −4.19757 7.27041i −0.203612 0.352667i
$$426$$ 0 0
$$427$$ 0.208348 0.360870i 0.0100827 0.0174637i
$$428$$ 0 0
$$429$$ 34.0425 5.07688i 1.64359 0.245114i
$$430$$ 0 0
$$431$$ −10.9303 −0.526495 −0.263247 0.964728i $$-0.584794\pi$$
−0.263247 + 0.964728i $$0.584794\pi$$
$$432$$ 0 0
$$433$$ 15.3189 0.736180 0.368090 0.929790i $$-0.380012\pi$$
0.368090 + 0.929790i $$0.380012\pi$$
$$434$$ 0 0
$$435$$ −57.1509 + 8.52314i −2.74018 + 0.408653i
$$436$$ 0 0
$$437$$ 6.21954 10.7726i 0.297521 0.515322i
$$438$$ 0 0
$$439$$ 5.30117 + 9.18189i 0.253011 + 0.438228i 0.964353 0.264618i $$-0.0852458\pi$$
−0.711343 + 0.702846i $$0.751913\pi$$
$$440$$ 0 0
$$441$$ −0.676667 + 2.92269i −0.0322222 + 0.139176i
$$442$$ 0 0
$$443$$ −10.0680 17.4383i −0.478347 0.828521i 0.521345 0.853346i $$-0.325430\pi$$
−0.999692 + 0.0248251i $$0.992097\pi$$
$$444$$ 0 0
$$445$$ −1.21293 + 2.10086i −0.0574985 + 0.0995903i
$$446$$ 0 0
$$447$$ 11.6442 29.5338i 0.550754 1.39690i
$$448$$ 0 0
$$449$$ −2.74616 −0.129599 −0.0647997 0.997898i $$-0.520641\pi$$
−0.0647997 + 0.997898i $$0.520641\pi$$
$$450$$ 0 0
$$451$$ 16.2458 0.764985
$$452$$ 0 0
$$453$$ 15.5872 + 19.6083i 0.732352 + 0.921279i
$$454$$ 0 0
$$455$$ −9.19188 + 15.9208i −0.430922 + 0.746379i
$$456$$ 0 0
$$457$$ −12.7715 22.1208i −0.597423 1.03477i −0.993200 0.116421i $$-0.962858\pi$$
0.395777 0.918347i $$-0.370475\pi$$
$$458$$ 0 0
$$459$$ −4.84336 + 2.30463i −0.226069 + 0.107571i
$$460$$ 0 0
$$461$$ 8.82316 + 15.2822i 0.410936 + 0.711761i 0.994992 0.0999516i $$-0.0318688\pi$$
−0.584057 + 0.811713i $$0.698535\pi$$
$$462$$ 0 0
$$463$$ 13.2501 22.9499i 0.615785 1.06657i −0.374461 0.927242i $$-0.622172\pi$$
0.990246 0.139328i $$-0.0444943\pi$$
$$464$$ 0 0
$$465$$ −3.29809 4.14891i −0.152945 0.192401i
$$466$$ 0 0
$$467$$ −20.1735 −0.933519 −0.466759 0.884384i $$-0.654579\pi$$
−0.466759 + 0.884384i $$0.654579\pi$$
$$468$$ 0 0
$$469$$ 10.0501 0.464072
$$470$$ 0 0
$$471$$ 2.44447 6.20001i 0.112635 0.285681i
$$472$$ 0 0
$$473$$ 8.62479 14.9386i 0.396568 0.686876i
$$474$$ 0 0
$$475$$ −10.2025 17.6712i −0.468122 0.810811i
$$476$$ 0 0
$$477$$ 35.2330 10.7479i 1.61321 0.492113i
$$478$$ 0 0
$$479$$ −4.92470 8.52984i −0.225015 0.389738i 0.731309 0.682047i $$-0.238910\pi$$
−0.956324 + 0.292309i $$0.905577\pi$$
$$480$$ 0 0
$$481$$ −12.2875 + 21.2826i −0.560261 + 0.970401i
$$482$$ 0 0
$$483$$ −8.49339 + 1.26665i −0.386463 + 0.0576346i
$$484$$ 0 0
$$485$$ −55.3383 −2.51278
$$486$$ 0 0
$$487$$ −10.0278 −0.454403 −0.227202 0.973848i $$-0.572958\pi$$
−0.227202 + 0.973848i $$0.572958\pi$$
$$488$$ 0 0
$$489$$ 22.3256 3.32950i 1.00960 0.150565i
$$490$$ 0 0
$$491$$ −0.610055 + 1.05665i −0.0275314 + 0.0476858i −0.879463 0.475968i $$-0.842098\pi$$
0.851931 + 0.523653i $$0.175431\pi$$
$$492$$ 0 0
$$493$$ 4.75131 + 8.22951i 0.213988 + 0.370639i
$$494$$ 0 0
$$495$$ 40.7345 12.4262i 1.83088 0.558514i
$$496$$ 0 0
$$497$$ 2.52581 + 4.37483i 0.113298 + 0.196238i
$$498$$ 0 0
$$499$$ 10.3222 17.8786i 0.462086 0.800356i −0.536979 0.843596i $$-0.680434\pi$$
0.999065 + 0.0432393i $$0.0137678\pi$$
$$500$$ 0 0
$$501$$ 3.86946 9.81426i 0.172875 0.438469i
$$502$$ 0 0
$$503$$ −8.85094 −0.394644 −0.197322 0.980339i $$-0.563224\pi$$
−0.197322 + 0.980339i $$0.563224\pi$$
$$504$$ 0 0
$$505$$ 42.6059 1.89594
$$506$$ 0 0
$$507$$ 13.7249 + 17.2655i 0.609543 + 0.766788i
$$508$$ 0 0
$$509$$ 12.8460 22.2499i 0.569388 0.986209i −0.427238 0.904139i $$-0.640513\pi$$
0.996627 0.0820702i $$-0.0261532\pi$$
$$510$$ 0 0
$$511$$ 3.60362 + 6.24165i 0.159415 + 0.276114i
$$512$$ 0 0
$$513$$ −11.7721 + 5.60156i −0.519751 + 0.247315i
$$514$$ 0 0
$$515$$ −19.9874 34.6191i −0.880749 1.52550i
$$516$$ 0 0
$$517$$ 15.4245 26.7161i 0.678370 1.17497i
$$518$$ 0 0
$$519$$ 12.7150 + 15.9951i 0.558126 + 0.702107i
$$520$$ 0 0
$$521$$ −14.6797 −0.643129 −0.321565 0.946888i $$-0.604209\pi$$
−0.321565 + 0.946888i $$0.604209\pi$$
$$522$$ 0 0
$$523$$ −20.7922 −0.909182 −0.454591 0.890700i $$-0.650214\pi$$
−0.454591 + 0.890700i $$0.650214\pi$$
$$524$$ 0 0
$$525$$ −5.16681 + 13.1048i −0.225498 + 0.571939i
$$526$$ 0 0
$$527$$ −0.435809 + 0.754843i −0.0189841 + 0.0328815i
$$528$$ 0 0
$$529$$ −0.790345 1.36892i −0.0343628 0.0595181i
$$530$$ 0 0
$$531$$ −7.58256 + 32.7510i −0.329055 + 1.42127i
$$532$$ 0 0
$$533$$ 10.5192 + 18.2198i 0.455637 + 0.789187i
$$534$$ 0 0
$$535$$ 1.52732 2.64539i 0.0660317 0.114370i
$$536$$ 0 0
$$537$$ 1.81843 0.271189i 0.0784710 0.0117027i
$$538$$ 0 0
$$539$$ −3.91726 −0.168728
$$540$$ 0 0
$$541$$ −30.9593 −1.33104 −0.665521 0.746379i $$-0.731791\pi$$
−0.665521 + 0.746379i $$0.731791\pi$$
$$542$$ 0 0
$$543$$ 27.4755 4.09752i 1.17909 0.175841i
$$544$$ 0 0
$$545$$ −31.1432 + 53.9416i −1.33403 + 2.31060i
$$546$$ 0 0
$$547$$ −5.80535 10.0552i −0.248219 0.429928i 0.714813 0.699316i $$-0.246512\pi$$
−0.963032 + 0.269388i $$0.913179\pi$$
$$548$$ 0 0
$$549$$ −0.913729 0.853127i −0.0389970 0.0364106i
$$550$$ 0 0
$$551$$ 11.5484 + 20.0024i 0.491977 + 0.852130i
$$552$$ 0 0
$$553$$ −7.56570 + 13.1042i −0.321726 + 0.557246i
$$554$$ 0 0
$$555$$ −11.1531 + 28.2881i −0.473424 + 1.20076i
$$556$$ 0 0
$$557$$ 19.0116 0.805546 0.402773 0.915300i $$-0.368046\pi$$
0.402773 + 0.915300i $$0.368046\pi$$
$$558$$ 0 0
$$559$$ 22.3383 0.944809
$$560$$ 0 0
$$561$$ −4.35821 5.48251i −0.184004 0.231472i
$$562$$ 0 0
$$563$$ −10.7959 + 18.6990i −0.454992 + 0.788069i −0.998688 0.0512136i $$-0.983691\pi$$
0.543696 + 0.839282i $$0.317024\pi$$
$$564$$ 0 0
$$565$$ 16.4722 + 28.5306i 0.692989 + 1.20029i
$$566$$ 0 0
$$567$$ 8.08424 + 3.95538i 0.339506 + 0.166110i
$$568$$ 0 0
$$569$$ −9.28858 16.0883i −0.389397 0.674456i 0.602971 0.797763i $$-0.293983\pi$$
−0.992369 + 0.123307i $$0.960650\pi$$
$$570$$ 0 0
$$571$$ −4.42902 + 7.67130i −0.185349 + 0.321034i −0.943694 0.330820i $$-0.892675\pi$$
0.758345 + 0.651853i $$0.226008\pi$$
$$572$$ 0 0
$$573$$ −25.7975 32.4525i −1.07770 1.35572i
$$574$$ 0 0
$$575$$ −40.3219 −1.68154
$$576$$ 0 0
$$577$$ −3.76684 −0.156816 −0.0784078 0.996921i $$-0.524984\pi$$
−0.0784078 + 0.996921i $$0.524984\pi$$
$$578$$ 0 0
$$579$$ 8.39492 21.2924i 0.348881 0.884881i
$$580$$ 0 0
$$581$$ −0.932821 + 1.61569i −0.0386999 + 0.0670302i
$$582$$ 0 0
$$583$$ 24.0493 + 41.6546i 0.996021 + 1.72516i
$$584$$ 0 0
$$585$$ 40.3117 + 37.6381i 1.66669 + 1.55614i
$$586$$ 0 0
$$587$$ 8.37616 + 14.5079i 0.345721 + 0.598806i 0.985484 0.169766i $$-0.0543010\pi$$
−0.639763 + 0.768572i $$0.720968\pi$$
$$588$$ 0 0
$$589$$ −1.05926 + 1.83469i −0.0436461 + 0.0755973i
$$590$$ 0 0
$$591$$ 42.8966 6.39734i 1.76453 0.263151i
$$592$$ 0 0
$$593$$ 30.3776 1.24746 0.623729 0.781640i $$-0.285617\pi$$
0.623729 + 0.781640i $$0.285617\pi$$
$$594$$ 0 0
$$595$$ 3.74080 0.153358
$$596$$ 0 0
$$597$$ 14.1872 2.11580i 0.580645 0.0865938i
$$598$$ 0 0
$$599$$ 8.97578 15.5465i 0.366741 0.635213i −0.622313 0.782768i $$-0.713807\pi$$
0.989054 + 0.147555i $$0.0471403\pi$$
$$600$$ 0 0
$$601$$ 2.66678 + 4.61900i 0.108780 + 0.188413i 0.915276 0.402826i $$-0.131972\pi$$
−0.806496 + 0.591239i $$0.798639\pi$$
$$602$$ 0 0
$$603$$ 6.80060 29.3735i 0.276942 1.19618i
$$604$$ 0 0
$$605$$ 7.87291 + 13.6363i 0.320079 + 0.554393i
$$606$$ 0 0
$$607$$ −9.11826 + 15.7933i −0.370099 + 0.641030i −0.989580 0.143981i $$-0.954010\pi$$
0.619482 + 0.785011i $$0.287343\pi$$
$$608$$ 0 0
$$609$$ 5.84840 14.8335i 0.236989 0.601085i
$$610$$ 0 0
$$611$$ 39.9497 1.61619
$$612$$ 0 0
$$613$$ 24.2030 0.977550 0.488775 0.872410i $$-0.337444\pi$$
0.488775 + 0.872410i $$0.337444\pi$$
$$614$$ 0 0
$$615$$ 16.1987 + 20.3775i 0.653193 + 0.821699i
$$616$$ 0 0
$$617$$ 3.15635 5.46696i 0.127070 0.220092i −0.795470 0.605993i $$-0.792776\pi$$
0.922540 + 0.385901i $$0.126109\pi$$
$$618$$ 0 0
$$619$$ 7.03450 + 12.1841i 0.282740 + 0.489721i 0.972059 0.234738i $$-0.0754232\pi$$
−0.689318 + 0.724459i $$0.742090\pi$$
$$620$$ 0 0
$$621$$ −2.04516 + 25.6807i −0.0820696 + 1.03053i
$$622$$ 0 0
$$623$$ −0.334701 0.579718i −0.0134095 0.0232259i
$$624$$ 0 0
$$625$$ −0.239656 + 0.415097i −0.00958625 + 0.0166039i
$$626$$ 0 0
$$627$$ −10.5929 13.3256i −0.423040 0.532173i
$$628$$ 0 0
$$629$$ 5.00061 0.199387
$$630$$ 0 0
$$631$$ 1.75345 0.0698036 0.0349018 0.999391i $$-0.488888\pi$$
0.0349018 + 0.999391i $$0.488888\pi$$
$$632$$ 0 0
$$633$$ −2.28393 + 5.79282i −0.0907780 + 0.230244i
$$634$$ 0 0
$$635$$ 26.2479 45.4627i 1.04162 1.80413i
$$636$$ 0 0
$$637$$ −2.53644 4.39324i −0.100497 0.174066i
$$638$$ 0 0
$$639$$ 14.4954 4.42186i 0.573430 0.174926i
$$640$$ 0 0
$$641$$ −13.6942 23.7191i −0.540889 0.936847i −0.998853 0.0478765i $$-0.984755\pi$$
0.457964 0.888971i $$-0.348579\pi$$
$$642$$ 0 0
$$643$$ −21.3323 + 36.9486i −0.841263 + 1.45711i 0.0475644 + 0.998868i $$0.484854\pi$$
−0.888827 + 0.458242i $$0.848479\pi$$
$$644$$ 0 0
$$645$$ 27.3375 4.07695i 1.07641 0.160530i
$$646$$ 0 0
$$647$$ −45.7615 −1.79907 −0.899536 0.436847i $$-0.856095\pi$$
−0.899536 + 0.436847i $$0.856095\pi$$
$$648$$ 0 0
$$649$$ −43.8959 −1.72306
$$650$$ 0 0
$$651$$ 1.44652 0.215726i 0.0566938 0.00845496i
$$652$$ 0 0
$$653$$ 0.388265 0.672494i 0.0151940 0.0263167i −0.858328 0.513101i $$-0.828497\pi$$
0.873522 + 0.486784i $$0.161830\pi$$
$$654$$ 0 0
$$655$$ −14.6217 25.3255i −0.571316 0.989549i
$$656$$ 0 0
$$657$$ 20.6809 6.30874i 0.806837 0.246127i
$$658$$ 0 0
$$659$$ −5.97934 10.3565i −0.232922 0.403433i 0.725745 0.687964i $$-0.241495\pi$$
−0.958667 + 0.284531i $$0.908162\pi$$
$$660$$ 0 0
$$661$$ −6.31373 + 10.9357i −0.245576 + 0.425350i −0.962293 0.272014i $$-0.912310\pi$$
0.716718 + 0.697364i $$0.245644\pi$$
$$662$$ 0 0
$$663$$ 3.32672 8.43770i 0.129199 0.327693i
$$664$$ 0 0
$$665$$ 9.09225 0.352582
$$666$$ 0 0
$$667$$ 45.6411 1.76723
$$668$$ 0 0
$$669$$ −10.9635 13.7918i −0.423872 0.533220i
$$670$$ 0 0
$$671$$ 0.816155 1.41362i 0.0315073 0.0545723i
$$672$$ 0 0
$$673$$ −14.5735 25.2421i −0.561768 0.973011i −0.997342 0.0728584i $$-0.976788\pi$$
0.435574 0.900153i $$-0.356545\pi$$
$$674$$ 0 0
$$675$$ 34.8050 + 23.9685i 1.33965 + 0.922550i
$$676$$ 0 0
$$677$$ 3.92732 + 6.80232i 0.150939 + 0.261435i 0.931573 0.363554i $$-0.118437\pi$$
−0.780634 + 0.624989i $$0.785104\pi$$
$$678$$ 0 0
$$679$$ 7.63513 13.2244i 0.293009 0.507507i
$$680$$ 0 0
$$681$$ −14.9827 18.8478i −0.574137 0.722249i
$$682$$ 0 0
$$683$$ −8.87441 −0.339570 −0.169785 0.985481i $$-0.554307\pi$$
−0.169785 + 0.985481i $$0.554307\pi$$
$$684$$ 0 0
$$685$$ −71.4488 −2.72992
$$686$$ 0 0
$$687$$ −3.61291 + 9.16357i −0.137841 + 0.349612i
$$688$$ 0 0
$$689$$ −31.1440 + 53.9430i −1.18649 + 2.05506i
$$690$$ 0 0
$$691$$ −1.82008 3.15248i −0.0692392 0.119926i 0.829327 0.558763i $$-0.188724\pi$$
−0.898567 + 0.438837i $$0.855391\pi$$
$$692$$ 0 0
$$693$$ −2.65068 + 11.4490i −0.100691 + 0.434910i
$$694$$ 0 0
$$695$$ −30.2946 52.4718i −1.14914 1.99037i
$$696$$ 0 0
$$697$$ 2.14049 3.70743i 0.0810767 0.140429i
$$698$$ 0 0
$$699$$ −33.3670 + 4.97615i −1.26206 + 0.188215i
$$700$$ 0 0
$$701$$ 18.1003 0.683638 0.341819 0.939766i $$-0.388957\pi$$
0.341819 + 0.939766i $$0.388957\pi$$
$$702$$ 0 0
$$703$$ 12.1543 0.458408
$$704$$ 0 0
$$705$$ 48.8903 7.29120i 1.84132 0.274603i
$$706$$ 0 0
$$707$$ −5.87840 + 10.1817i −0.221080 + 0.382922i
$$708$$ 0 0
$$709$$ −17.5624 30.4191i −0.659572 1.14241i −0.980727 0.195385i $$-0.937404\pi$$
0.321155 0.947027i $$-0.395929\pi$$
$$710$$ 0 0
$$711$$ 33.1800 + 30.9794i 1.24435 + 1.16182i
$$712$$ 0 0
$$713$$ 2.09319 + 3.62551i 0.0783906 + 0.135776i
$$714$$ 0 0
$$715$$ −36.0070 + 62.3660i −1.34659 + 2.33235i
$$716$$ 0 0
$$717$$ −3.17649 + 8.05667i −0.118628 + 0.300882i
$$718$$ 0 0
$$719$$ 23.8092 0.887933 0.443966 0.896044i $$-0.353571\pi$$
0.443966 + 0.896044i $$0.353571\pi$$
$$720$$ 0 0
$$721$$ 11.0308 0.410807
$$722$$ 0 0
$$723$$ 11.0816 + 13.9403i 0.412128 + 0.518446i
$$724$$ 0 0
$$725$$ 37.4346 64.8387i 1.39029 2.40805i
$$726$$ 0 0
$$727$$ 1.29251 + 2.23869i 0.0479364 + 0.0830283i 0.888998 0.457911i $$-0.151402\pi$$
−0.841062 + 0.540939i $$0.818069\pi$$
$$728$$ 0 0
$$729$$ 17.0307 20.9513i 0.630766 0.775973i
$$730$$ 0 0
$$731$$ −2.27274 3.93650i −0.0840603 0.145597i
$$732$$ 0 0
$$733$$ 11.7493 20.3505i 0.433972 0.751661i −0.563239 0.826294i $$-0.690445\pi$$
0.997211 + 0.0746325i $$0.0237784\pi$$
$$734$$ 0 0
$$735$$ −3.90590 4.91351i −0.144071 0.181238i
$$736$$ 0 0
$$737$$ 39.3691 1.45018
$$738$$ 0 0
$$739$$ −16.9236 −0.622544 −0.311272 0.950321i $$-0.600755\pi$$
−0.311272 + 0.950321i $$0.600755\pi$$
$$740$$ 0 0
$$741$$ 8.08581 20.5084i 0.297040 0.753394i
$$742$$ 0 0
$$743$$ 4.39163 7.60652i 0.161113 0.279056i −0.774155 0.632996i $$-0.781825\pi$$
0.935268 + 0.353940i $$0.115158\pi$$
$$744$$ 0 0
$$745$$ 33.2111 + 57.5233i 1.21676 + 2.10749i
$$746$$ 0 0
$$747$$ 4.09096 + 3.81963i 0.149680 + 0.139753i
$$748$$ 0 0
$$749$$ 0.421453 + 0.729979i 0.0153996 + 0.0266728i
$$750$$ 0 0
$$751$$ 0.983876 1.70412i 0.0359021 0.0621843i −0.847516 0.530770i $$-0.821903\pi$$
0.883418 + 0.468585i $$0.155236\pi$$
$$752$$ 0 0
$$753$$ −1.42134 + 0.211970i −0.0517964 + 0.00772460i
$$754$$ 0 0
$$755$$ −52.4093 −1.90737
$$756$$ 0 0
$$757$$ −10.3423 −0.375899 −0.187949 0.982179i $$-0.560184\pi$$
−0.187949 + 0.982179i $$0.560184\pi$$
$$758$$ 0 0
$$759$$ −33.2708 + 4.96181i −1.20766 + 0.180102i
$$760$$ 0 0
$$761$$ 7.88205 13.6521i 0.285724 0.494889i −0.687060 0.726600i $$-0.741099\pi$$
0.972785 + 0.231711i $$0.0744325\pi$$
$$762$$ 0 0
$$763$$ −8.59376 14.8848i −0.311115 0.538867i
$$764$$ 0 0
$$765$$ 2.53127 10.9332i 0.0915184 0.395290i
$$766$$ 0 0
$$767$$ −28.4227 49.2296i −1.02628 1.77758i
$$768$$ 0 0
$$769$$ 22.1895 38.4333i 0.800172 1.38594i −0.119330 0.992855i $$-0.538075\pi$$
0.919502 0.393084i $$-0.128592\pi$$
$$770$$ 0 0
$$771$$ −8.73555 + 22.1563i −0.314603 + 0.797941i
$$772$$ 0 0
$$773$$ −25.5222 −0.917969 −0.458984 0.888444i $$-0.651787\pi$$
−0.458984 + 0.888444i $$0.651787\pi$$
$$774$$ 0 0
$$775$$ 6.86730 0.246681
$$776$$ 0 0
$$777$$ −5.22131 6.56827i −0.187314 0.235635i
$$778$$ 0 0
$$779$$ 5.20259 9.01116i 0.186402 0.322858i
$$780$$ 0 0
$$781$$ 9.89427 + 17.1374i 0.354045 + 0.613223i
$$782$$ 0 0
$$783$$ −39.3964 27.1304i −1.40791 0.969563i
$$784$$ 0 0
$$785$$ 6.97199 + 12.0758i 0.248841 + 0.431005i
$$786$$ 0 0
$$787$$ 12.2841 21.2767i 0.437882 0.758434i −0.559644 0.828733i $$-0.689062\pi$$
0.997526 + 0.0702995i $$0.0223955\pi$$
$$788$$ 0 0
$$789$$ −27.8689 35.0584i −0.992160 1.24811i
$$790$$ 0 0
$$791$$ −9.09077 −0.323231
$$792$$ 0 0
$$793$$ 2.11385 0.0750650
$$794$$ 0 0
$$795$$ −28.2688 + 71.6994i −1.00259 + 2.54291i
$$796$$ 0 0
$$797$$ 18.6983 32.3864i 0.662328 1.14719i −0.317674 0.948200i $$-0.602902\pi$$
0.980002 0.198986i $$-0.0637649\pi$$
$$798$$ 0