# Properties

 Label 387.2.h.d.307.1 Level 387 Weight 2 Character 387.307 Analytic conductor 3.090 Analytic rank 0 Dimension 4 CM no Inner twists 2

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$387 = 3^{2} \cdot 43$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 387.h (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.09021055822$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{5})$$ Defining polynomial: $$x^{4} - x^{3} + 2 x^{2} + x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 43) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 307.1 Root $$-0.309017 + 0.535233i$$ of defining polynomial Character $$\chi$$ $$=$$ 387.307 Dual form 387.2.h.d.208.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+0.381966 q^{2} -1.85410 q^{4} +(0.618034 - 1.07047i) q^{5} +(2.11803 + 3.66854i) q^{7} -1.47214 q^{8} +O(q^{10})$$ $$q+0.381966 q^{2} -1.85410 q^{4} +(0.618034 - 1.07047i) q^{5} +(2.11803 + 3.66854i) q^{7} -1.47214 q^{8} +(0.236068 - 0.408882i) q^{10} +3.61803 q^{11} +(-0.690983 - 1.19682i) q^{13} +(0.809017 + 1.40126i) q^{14} +3.14590 q^{16} +(3.04508 + 5.27424i) q^{17} +(0.618034 - 1.07047i) q^{19} +(-1.14590 + 1.98475i) q^{20} +1.38197 q^{22} +(2.19098 - 3.79489i) q^{23} +(1.73607 + 3.00696i) q^{25} +(-0.263932 - 0.457144i) q^{26} +(-3.92705 - 6.80185i) q^{28} +(1.50000 + 2.59808i) q^{29} +4.14590 q^{32} +(1.16312 + 2.01458i) q^{34} +5.23607 q^{35} +(2.42705 - 4.20378i) q^{37} +(0.236068 - 0.408882i) q^{38} +(-0.909830 + 1.57587i) q^{40} -9.47214 q^{41} +(-6.50000 + 0.866025i) q^{43} -6.70820 q^{44} +(0.836881 - 1.44952i) q^{46} -1.14590 q^{47} +(-5.47214 + 9.47802i) q^{49} +(0.663119 + 1.14856i) q^{50} +(1.28115 + 2.21902i) q^{52} +(-0.690983 + 1.19682i) q^{53} +(2.23607 - 3.87298i) q^{55} +(-3.11803 - 5.40059i) q^{56} +(0.572949 + 0.992377i) q^{58} -5.09017 q^{59} +(-1.42705 - 2.47172i) q^{61} -4.70820 q^{64} -1.70820 q^{65} +(1.92705 - 3.33775i) q^{67} +(-5.64590 - 9.77898i) q^{68} +2.00000 q^{70} +(-5.39919 - 9.35167i) q^{71} +(-0.927051 - 1.60570i) q^{73} +(0.927051 - 1.60570i) q^{74} +(-1.14590 + 1.98475i) q^{76} +(7.66312 + 13.2729i) q^{77} +(0.690983 + 1.19682i) q^{79} +(1.94427 - 3.36758i) q^{80} -3.61803 q^{82} +(8.01722 - 13.8862i) q^{83} +7.52786 q^{85} +(-2.48278 + 0.330792i) q^{86} -5.32624 q^{88} +(-0.927051 + 1.60570i) q^{89} +(2.92705 - 5.06980i) q^{91} +(-4.06231 + 7.03612i) q^{92} -0.437694 q^{94} +(-0.763932 - 1.32317i) q^{95} -9.23607 q^{97} +(-2.09017 + 3.62028i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 6q^{2} + 6q^{4} - 2q^{5} + 4q^{7} + 12q^{8} + O(q^{10})$$ $$4q + 6q^{2} + 6q^{4} - 2q^{5} + 4q^{7} + 12q^{8} - 8q^{10} + 10q^{11} - 5q^{13} + q^{14} + 26q^{16} + q^{17} - 2q^{19} - 18q^{20} + 10q^{22} + 11q^{23} - 2q^{25} - 10q^{26} - 9q^{28} + 6q^{29} + 30q^{32} - 11q^{34} + 12q^{35} + 3q^{37} - 8q^{38} - 26q^{40} - 20q^{41} - 26q^{43} + 19q^{46} - 18q^{47} - 4q^{49} - 13q^{50} - 15q^{52} - 5q^{53} - 8q^{56} + 9q^{58} + 2q^{59} + q^{61} + 8q^{64} + 20q^{65} + q^{67} - 36q^{68} + 8q^{70} + 3q^{71} + 3q^{73} - 3q^{74} - 18q^{76} + 15q^{77} + 5q^{79} - 28q^{80} - 10q^{82} + 3q^{83} + 48q^{85} - 39q^{86} + 10q^{88} + 3q^{89} + 5q^{91} + 24q^{92} - 42q^{94} - 12q^{95} - 28q^{97} + 14q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$$.

 $$n$$ $$46$$ $$173$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.381966 0.270091 0.135045 0.990839i $$-0.456882\pi$$
0.135045 + 0.990839i $$0.456882\pi$$
$$3$$ 0 0
$$4$$ −1.85410 −0.927051
$$5$$ 0.618034 1.07047i 0.276393 0.478727i −0.694092 0.719886i $$-0.744194\pi$$
0.970486 + 0.241159i $$0.0775275\pi$$
$$6$$ 0 0
$$7$$ 2.11803 + 3.66854i 0.800542 + 1.38658i 0.919260 + 0.393651i $$0.128788\pi$$
−0.118718 + 0.992928i $$0.537879\pi$$
$$8$$ −1.47214 −0.520479
$$9$$ 0 0
$$10$$ 0.236068 0.408882i 0.0746512 0.129300i
$$11$$ 3.61803 1.09088 0.545439 0.838150i $$-0.316363\pi$$
0.545439 + 0.838150i $$0.316363\pi$$
$$12$$ 0 0
$$13$$ −0.690983 1.19682i −0.191644 0.331937i 0.754151 0.656701i $$-0.228049\pi$$
−0.945795 + 0.324763i $$0.894715\pi$$
$$14$$ 0.809017 + 1.40126i 0.216219 + 0.374502i
$$15$$ 0 0
$$16$$ 3.14590 0.786475
$$17$$ 3.04508 + 5.27424i 0.738542 + 1.27919i 0.953152 + 0.302492i $$0.0978185\pi$$
−0.214610 + 0.976700i $$0.568848\pi$$
$$18$$ 0 0
$$19$$ 0.618034 1.07047i 0.141787 0.245582i −0.786383 0.617740i $$-0.788049\pi$$
0.928170 + 0.372158i $$0.121382\pi$$
$$20$$ −1.14590 + 1.98475i −0.256231 + 0.443804i
$$21$$ 0 0
$$22$$ 1.38197 0.294636
$$23$$ 2.19098 3.79489i 0.456852 0.791290i −0.541941 0.840417i $$-0.682310\pi$$
0.998793 + 0.0491264i $$0.0156437\pi$$
$$24$$ 0 0
$$25$$ 1.73607 + 3.00696i 0.347214 + 0.601392i
$$26$$ −0.263932 0.457144i −0.0517613 0.0896533i
$$27$$ 0 0
$$28$$ −3.92705 6.80185i −0.742143 1.28543i
$$29$$ 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i $$-0.0768152\pi$$
−0.692480 + 0.721437i $$0.743482\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ 4.14590 0.732898
$$33$$ 0 0
$$34$$ 1.16312 + 2.01458i 0.199473 + 0.345498i
$$35$$ 5.23607 0.885057
$$36$$ 0 0
$$37$$ 2.42705 4.20378i 0.399005 0.691096i −0.594599 0.804023i $$-0.702689\pi$$
0.993603 + 0.112926i $$0.0360224\pi$$
$$38$$ 0.236068 0.408882i 0.0382953 0.0663294i
$$39$$ 0 0
$$40$$ −0.909830 + 1.57587i −0.143857 + 0.249167i
$$41$$ −9.47214 −1.47930 −0.739650 0.672992i $$-0.765009\pi$$
−0.739650 + 0.672992i $$0.765009\pi$$
$$42$$ 0 0
$$43$$ −6.50000 + 0.866025i −0.991241 + 0.132068i
$$44$$ −6.70820 −1.01130
$$45$$ 0 0
$$46$$ 0.836881 1.44952i 0.123391 0.213720i
$$47$$ −1.14590 −0.167146 −0.0835732 0.996502i $$-0.526633\pi$$
−0.0835732 + 0.996502i $$0.526633\pi$$
$$48$$ 0 0
$$49$$ −5.47214 + 9.47802i −0.781734 + 1.35400i
$$50$$ 0.663119 + 1.14856i 0.0937792 + 0.162430i
$$51$$ 0 0
$$52$$ 1.28115 + 2.21902i 0.177664 + 0.307723i
$$53$$ −0.690983 + 1.19682i −0.0949138 + 0.164396i −0.909573 0.415545i $$-0.863591\pi$$
0.814659 + 0.579941i $$0.196924\pi$$
$$54$$ 0 0
$$55$$ 2.23607 3.87298i 0.301511 0.522233i
$$56$$ −3.11803 5.40059i −0.416665 0.721685i
$$57$$ 0 0
$$58$$ 0.572949 + 0.992377i 0.0752319 + 0.130305i
$$59$$ −5.09017 −0.662684 −0.331342 0.943511i $$-0.607501\pi$$
−0.331342 + 0.943511i $$0.607501\pi$$
$$60$$ 0 0
$$61$$ −1.42705 2.47172i −0.182715 0.316472i 0.760089 0.649819i $$-0.225155\pi$$
−0.942804 + 0.333347i $$0.891822\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −4.70820 −0.588525
$$65$$ −1.70820 −0.211877
$$66$$ 0 0
$$67$$ 1.92705 3.33775i 0.235427 0.407771i −0.723970 0.689832i $$-0.757685\pi$$
0.959397 + 0.282061i $$0.0910179\pi$$
$$68$$ −5.64590 9.77898i −0.684666 1.18588i
$$69$$ 0 0
$$70$$ 2.00000 0.239046
$$71$$ −5.39919 9.35167i −0.640766 1.10984i −0.985262 0.171051i $$-0.945284\pi$$
0.344497 0.938788i $$-0.388050\pi$$
$$72$$ 0 0
$$73$$ −0.927051 1.60570i −0.108503 0.187933i 0.806661 0.591015i $$-0.201272\pi$$
−0.915164 + 0.403082i $$0.867939\pi$$
$$74$$ 0.927051 1.60570i 0.107767 0.186659i
$$75$$ 0 0
$$76$$ −1.14590 + 1.98475i −0.131444 + 0.227667i
$$77$$ 7.66312 + 13.2729i 0.873293 + 1.51259i
$$78$$ 0 0
$$79$$ 0.690983 + 1.19682i 0.0777417 + 0.134653i 0.902275 0.431161i $$-0.141896\pi$$
−0.824534 + 0.565813i $$0.808562\pi$$
$$80$$ 1.94427 3.36758i 0.217376 0.376507i
$$81$$ 0 0
$$82$$ −3.61803 −0.399545
$$83$$ 8.01722 13.8862i 0.880004 1.52421i 0.0286698 0.999589i $$-0.490873\pi$$
0.851335 0.524623i $$-0.175794\pi$$
$$84$$ 0 0
$$85$$ 7.52786 0.816511
$$86$$ −2.48278 + 0.330792i −0.267725 + 0.0356702i
$$87$$ 0 0
$$88$$ −5.32624 −0.567779
$$89$$ −0.927051 + 1.60570i −0.0982672 + 0.170204i −0.910968 0.412478i $$-0.864663\pi$$
0.812700 + 0.582682i $$0.197997\pi$$
$$90$$ 0 0
$$91$$ 2.92705 5.06980i 0.306838 0.531460i
$$92$$ −4.06231 + 7.03612i −0.423525 + 0.733566i
$$93$$ 0 0
$$94$$ −0.437694 −0.0451447
$$95$$ −0.763932 1.32317i −0.0783778 0.135754i
$$96$$ 0 0
$$97$$ −9.23607 −0.937781 −0.468890 0.883256i $$-0.655346\pi$$
−0.468890 + 0.883256i $$0.655346\pi$$
$$98$$ −2.09017 + 3.62028i −0.211139 + 0.365704i
$$99$$ 0 0
$$100$$ −3.21885 5.57521i −0.321885 0.557521i
$$101$$ 1.88197 + 3.25966i 0.187263 + 0.324348i 0.944337 0.328981i $$-0.106705\pi$$
−0.757074 + 0.653329i $$0.773372\pi$$
$$102$$ 0 0
$$103$$ 8.20820 + 14.2170i 0.808778 + 1.40085i 0.913710 + 0.406366i $$0.133204\pi$$
−0.104932 + 0.994479i $$0.533463\pi$$
$$104$$ 1.01722 + 1.76188i 0.0997467 + 0.172766i
$$105$$ 0 0
$$106$$ −0.263932 + 0.457144i −0.0256353 + 0.0444017i
$$107$$ −7.52786 −0.727746 −0.363873 0.931449i $$-0.618546\pi$$
−0.363873 + 0.931449i $$0.618546\pi$$
$$108$$ 0 0
$$109$$ 6.92705 11.9980i 0.663491 1.14920i −0.316201 0.948692i $$-0.602407\pi$$
0.979692 0.200508i $$-0.0642593\pi$$
$$110$$ 0.854102 1.47935i 0.0814354 0.141050i
$$111$$ 0 0
$$112$$ 6.66312 + 11.5409i 0.629606 + 1.09051i
$$113$$ 15.6180 1.46922 0.734611 0.678489i $$-0.237365\pi$$
0.734611 + 0.678489i $$0.237365\pi$$
$$114$$ 0 0
$$115$$ −2.70820 4.69075i −0.252541 0.437414i
$$116$$ −2.78115 4.81710i −0.258224 0.447256i
$$117$$ 0 0
$$118$$ −1.94427 −0.178985
$$119$$ −12.8992 + 22.3420i −1.18247 + 2.04809i
$$120$$ 0 0
$$121$$ 2.09017 0.190015
$$122$$ −0.545085 0.944115i −0.0493497 0.0854761i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 10.4721 0.936656
$$126$$ 0 0
$$127$$ −14.6525 −1.30020 −0.650098 0.759850i $$-0.725272\pi$$
−0.650098 + 0.759850i $$0.725272\pi$$
$$128$$ −10.0902 −0.891853
$$129$$ 0 0
$$130$$ −0.652476 −0.0572259
$$131$$ −9.94427 −0.868835 −0.434418 0.900712i $$-0.643046\pi$$
−0.434418 + 0.900712i $$0.643046\pi$$
$$132$$ 0 0
$$133$$ 5.23607 0.454025
$$134$$ 0.736068 1.27491i 0.0635866 0.110135i
$$135$$ 0 0
$$136$$ −4.48278 7.76440i −0.384395 0.665792i
$$137$$ −3.70820 −0.316813 −0.158407 0.987374i $$-0.550636\pi$$
−0.158407 + 0.987374i $$0.550636\pi$$
$$138$$ 0 0
$$139$$ 2.64590 4.58283i 0.224422 0.388711i −0.731724 0.681601i $$-0.761284\pi$$
0.956146 + 0.292891i $$0.0946172\pi$$
$$140$$ −9.70820 −0.820493
$$141$$ 0 0
$$142$$ −2.06231 3.57202i −0.173065 0.299757i
$$143$$ −2.50000 4.33013i −0.209061 0.362103i
$$144$$ 0 0
$$145$$ 3.70820 0.307950
$$146$$ −0.354102 0.613323i −0.0293057 0.0507589i
$$147$$ 0 0
$$148$$ −4.50000 + 7.79423i −0.369898 + 0.640682i
$$149$$ 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i $$-0.713152\pi$$
0.989355 + 0.145519i $$0.0464853\pi$$
$$150$$ 0 0
$$151$$ −8.85410 −0.720537 −0.360268 0.932849i $$-0.617315\pi$$
−0.360268 + 0.932849i $$0.617315\pi$$
$$152$$ −0.909830 + 1.57587i −0.0737970 + 0.127820i
$$153$$ 0 0
$$154$$ 2.92705 + 5.06980i 0.235868 + 0.408536i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 2.57295 + 4.45648i 0.205344 + 0.355666i 0.950242 0.311512i $$-0.100835\pi$$
−0.744898 + 0.667178i $$0.767502\pi$$
$$158$$ 0.263932 + 0.457144i 0.0209973 + 0.0363684i
$$159$$ 0 0
$$160$$ 2.56231 4.43804i 0.202568 0.350858i
$$161$$ 18.5623 1.46291
$$162$$ 0 0
$$163$$ −7.00000 12.1244i −0.548282 0.949653i −0.998392 0.0566798i $$-0.981949\pi$$
0.450110 0.892973i $$-0.351385\pi$$
$$164$$ 17.5623 1.37139
$$165$$ 0 0
$$166$$ 3.06231 5.30407i 0.237681 0.411676i
$$167$$ 7.11803 12.3288i 0.550810 0.954031i −0.447406 0.894331i $$-0.647652\pi$$
0.998216 0.0597001i $$-0.0190144\pi$$
$$168$$ 0 0
$$169$$ 5.54508 9.60437i 0.426545 0.738798i
$$170$$ 2.87539 0.220532
$$171$$ 0 0
$$172$$ 12.0517 1.60570i 0.918931 0.122433i
$$173$$ 3.76393 0.286166 0.143083 0.989711i $$-0.454298\pi$$
0.143083 + 0.989711i $$0.454298\pi$$
$$174$$ 0 0
$$175$$ −7.35410 + 12.7377i −0.555918 + 0.962878i
$$176$$ 11.3820 0.857948
$$177$$ 0 0
$$178$$ −0.354102 + 0.613323i −0.0265411 + 0.0459705i
$$179$$ 4.82624 + 8.35929i 0.360730 + 0.624803i 0.988081 0.153934i $$-0.0491943\pi$$
−0.627351 + 0.778736i $$0.715861\pi$$
$$180$$ 0 0
$$181$$ 9.69098 + 16.7853i 0.720325 + 1.24764i 0.960869 + 0.277002i $$0.0893407\pi$$
−0.240544 + 0.970638i $$0.577326\pi$$
$$182$$ 1.11803 1.93649i 0.0828742 0.143542i
$$183$$ 0 0
$$184$$ −3.22542 + 5.58660i −0.237781 + 0.411850i
$$185$$ −3.00000 5.19615i −0.220564 0.382029i
$$186$$ 0 0
$$187$$ 11.0172 + 19.0824i 0.805659 + 1.39544i
$$188$$ 2.12461 0.154953
$$189$$ 0 0
$$190$$ −0.291796 0.505406i −0.0211691 0.0366660i
$$191$$ −7.26393 + 12.5815i −0.525600 + 0.910365i 0.473956 + 0.880549i $$0.342826\pi$$
−0.999555 + 0.0298167i $$0.990508\pi$$
$$192$$ 0 0
$$193$$ 2.70820 0.194941 0.0974704 0.995238i $$-0.468925\pi$$
0.0974704 + 0.995238i $$0.468925\pi$$
$$194$$ −3.52786 −0.253286
$$195$$ 0 0
$$196$$ 10.1459 17.5732i 0.724707 1.25523i
$$197$$ −1.47214 2.54981i −0.104885 0.181667i 0.808806 0.588076i $$-0.200114\pi$$
−0.913691 + 0.406409i $$0.866781\pi$$
$$198$$ 0 0
$$199$$ 1.94427 0.137826 0.0689129 0.997623i $$-0.478047\pi$$
0.0689129 + 0.997623i $$0.478047\pi$$
$$200$$ −2.55573 4.42665i −0.180717 0.313011i
$$201$$ 0 0
$$202$$ 0.718847 + 1.24508i 0.0505779 + 0.0876035i
$$203$$ −6.35410 + 11.0056i −0.445971 + 0.772444i
$$204$$ 0 0
$$205$$ −5.85410 + 10.1396i −0.408868 + 0.708181i
$$206$$ 3.13525 + 5.43042i 0.218444 + 0.378355i
$$207$$ 0 0
$$208$$ −2.17376 3.76507i −0.150723 0.261060i
$$209$$ 2.23607 3.87298i 0.154672 0.267900i
$$210$$ 0 0
$$211$$ −9.23607 −0.635837 −0.317919 0.948118i $$-0.602984\pi$$
−0.317919 + 0.948118i $$0.602984\pi$$
$$212$$ 1.28115 2.21902i 0.0879899 0.152403i
$$213$$ 0 0
$$214$$ −2.87539 −0.196557
$$215$$ −3.09017 + 7.49326i −0.210748 + 0.511036i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 2.64590 4.58283i 0.179203 0.310388i
$$219$$ 0 0
$$220$$ −4.14590 + 7.18091i −0.279516 + 0.484137i
$$221$$ 4.20820 7.28882i 0.283074 0.490299i
$$222$$ 0 0
$$223$$ 2.76393 0.185087 0.0925433 0.995709i $$-0.470500\pi$$
0.0925433 + 0.995709i $$0.470500\pi$$
$$224$$ 8.78115 + 15.2094i 0.586715 + 1.01622i
$$225$$ 0 0
$$226$$ 5.96556 0.396823
$$227$$ −0.736068 + 1.27491i −0.0488545 + 0.0846186i −0.889419 0.457094i $$-0.848890\pi$$
0.840564 + 0.541712i $$0.182224\pi$$
$$228$$ 0 0
$$229$$ 1.14590 + 1.98475i 0.0757231 + 0.131156i 0.901400 0.432986i $$-0.142540\pi$$
−0.825677 + 0.564143i $$0.809207\pi$$
$$230$$ −1.03444 1.79171i −0.0682091 0.118142i
$$231$$ 0 0
$$232$$ −2.20820 3.82472i −0.144976 0.251105i
$$233$$ 9.01722 + 15.6183i 0.590738 + 1.02319i 0.994133 + 0.108162i $$0.0344966\pi$$
−0.403395 + 0.915026i $$0.632170\pi$$
$$234$$ 0 0
$$235$$ −0.708204 + 1.22665i −0.0461981 + 0.0800175i
$$236$$ 9.43769 0.614342
$$237$$ 0 0
$$238$$ −4.92705 + 8.53390i −0.319373 + 0.553171i
$$239$$ −4.14590 + 7.18091i −0.268176 + 0.464494i −0.968391 0.249438i $$-0.919754\pi$$
0.700215 + 0.713932i $$0.253087\pi$$
$$240$$ 0 0
$$241$$ −2.13525 3.69837i −0.137544 0.238233i 0.789022 0.614364i $$-0.210587\pi$$
−0.926566 + 0.376131i $$0.877254\pi$$
$$242$$ 0.798374 0.0513214
$$243$$ 0 0
$$244$$ 2.64590 + 4.58283i 0.169386 + 0.293386i
$$245$$ 6.76393 + 11.7155i 0.432132 + 0.748474i
$$246$$ 0 0
$$247$$ −1.70820 −0.108690
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 4.00000 0.252982
$$251$$ −14.5902 25.2709i −0.920923 1.59509i −0.797990 0.602671i $$-0.794103\pi$$
−0.122934 0.992415i $$-0.539230\pi$$
$$252$$ 0 0
$$253$$ 7.92705 13.7301i 0.498369 0.863201i
$$254$$ −5.59675 −0.351171
$$255$$ 0 0
$$256$$ 5.56231 0.347644
$$257$$ −3.43769 −0.214437 −0.107219 0.994235i $$-0.534195\pi$$
−0.107219 + 0.994235i $$0.534195\pi$$
$$258$$ 0 0
$$259$$ 20.5623 1.27768
$$260$$ 3.16718 0.196420
$$261$$ 0 0
$$262$$ −3.79837 −0.234664
$$263$$ 13.7533 23.8214i 0.848064 1.46889i −0.0348693 0.999392i $$-0.511101\pi$$
0.882933 0.469498i $$-0.155565\pi$$
$$264$$ 0 0
$$265$$ 0.854102 + 1.47935i 0.0524671 + 0.0908756i
$$266$$ 2.00000 0.122628
$$267$$ 0 0
$$268$$ −3.57295 + 6.18853i −0.218253 + 0.378025i
$$269$$ −11.5623 −0.704966 −0.352483 0.935818i $$-0.614663\pi$$
−0.352483 + 0.935818i $$0.614663\pi$$
$$270$$ 0 0
$$271$$ −6.92705 11.9980i −0.420788 0.728827i 0.575228 0.817993i $$-0.304913\pi$$
−0.996017 + 0.0891660i $$0.971580\pi$$
$$272$$ 9.57953 + 16.5922i 0.580844 + 1.00605i
$$273$$ 0 0
$$274$$ −1.41641 −0.0855683
$$275$$ 6.28115 + 10.8793i 0.378768 + 0.656045i
$$276$$ 0 0
$$277$$ 6.23607 10.8012i 0.374689 0.648980i −0.615591 0.788065i $$-0.711083\pi$$
0.990280 + 0.139085i $$0.0444161\pi$$
$$278$$ 1.01064 1.75049i 0.0606143 0.104987i
$$279$$ 0 0
$$280$$ −7.70820 −0.460653
$$281$$ 3.73607 6.47106i 0.222875 0.386031i −0.732805 0.680439i $$-0.761789\pi$$
0.955680 + 0.294408i $$0.0951224\pi$$
$$282$$ 0 0
$$283$$ −5.38197 9.32184i −0.319925 0.554126i 0.660547 0.750784i $$-0.270324\pi$$
−0.980472 + 0.196659i $$0.936991\pi$$
$$284$$ 10.0106 + 17.3389i 0.594022 + 1.02888i
$$285$$ 0 0
$$286$$ −0.954915 1.65396i −0.0564653 0.0978008i
$$287$$ −20.0623 34.7489i −1.18424 2.05116i
$$288$$ 0 0
$$289$$ −10.0451 + 17.3986i −0.590887 + 1.02345i
$$290$$ 1.41641 0.0831743
$$291$$ 0 0
$$292$$ 1.71885 + 2.97713i 0.100588 + 0.174223i
$$293$$ 12.0902 0.706315 0.353158 0.935564i $$-0.385108\pi$$
0.353158 + 0.935564i $$0.385108\pi$$
$$294$$ 0 0
$$295$$ −3.14590 + 5.44886i −0.183161 + 0.317245i
$$296$$ −3.57295 + 6.18853i −0.207673 + 0.359701i
$$297$$ 0 0
$$298$$ 1.71885 2.97713i 0.0995701 0.172461i
$$299$$ −6.05573 −0.350212
$$300$$ 0 0
$$301$$ −16.9443 22.0113i −0.976652 1.26871i
$$302$$ −3.38197 −0.194610
$$303$$ 0 0
$$304$$ 1.94427 3.36758i 0.111512 0.193144i
$$305$$ −3.52786 −0.202005
$$306$$ 0 0
$$307$$ 11.6074 20.1046i 0.662469 1.14743i −0.317496 0.948260i $$-0.602842\pi$$
0.979965 0.199170i $$-0.0638246\pi$$
$$308$$ −14.2082 24.6093i −0.809588 1.40225i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −14.9164 + 25.8360i −0.845832 + 1.46502i 0.0390649 + 0.999237i $$0.487562\pi$$
−0.884897 + 0.465787i $$0.845771\pi$$
$$312$$ 0 0
$$313$$ −6.56231 + 11.3662i −0.370923 + 0.642458i −0.989708 0.143103i $$-0.954292\pi$$
0.618784 + 0.785561i $$0.287625\pi$$
$$314$$ 0.982779 + 1.70222i 0.0554614 + 0.0960620i
$$315$$ 0 0
$$316$$ −1.28115 2.21902i −0.0720705 0.124830i
$$317$$ −33.3050 −1.87059 −0.935296 0.353866i $$-0.884867\pi$$
−0.935296 + 0.353866i $$0.884867\pi$$
$$318$$ 0 0
$$319$$ 5.42705 + 9.39993i 0.303857 + 0.526295i
$$320$$ −2.90983 + 5.03997i −0.162664 + 0.281743i
$$321$$ 0 0
$$322$$ 7.09017 0.395120
$$323$$ 7.52786 0.418862
$$324$$ 0 0
$$325$$ 2.39919 4.15551i 0.133083 0.230506i
$$326$$ −2.67376 4.63109i −0.148086 0.256492i
$$327$$ 0 0
$$328$$ 13.9443 0.769944
$$329$$ −2.42705 4.20378i −0.133808 0.231762i
$$330$$ 0 0
$$331$$ 2.73607 + 4.73901i 0.150388 + 0.260479i 0.931370 0.364074i $$-0.118614\pi$$
−0.780982 + 0.624553i $$0.785281\pi$$
$$332$$ −14.8647 + 25.7465i −0.815809 + 1.41302i
$$333$$ 0 0
$$334$$ 2.71885 4.70918i 0.148769 0.257675i
$$335$$ −2.38197 4.12569i −0.130141 0.225410i
$$336$$ 0 0
$$337$$ −14.0000 24.2487i −0.762629 1.32091i −0.941491 0.337037i $$-0.890575\pi$$
0.178863 0.983874i $$-0.442758\pi$$
$$338$$ 2.11803 3.66854i 0.115206 0.199542i
$$339$$ 0 0
$$340$$ −13.9574 −0.756948
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −16.7082 −0.902158
$$344$$ 9.56888 1.27491i 0.515920 0.0687384i
$$345$$ 0 0
$$346$$ 1.43769 0.0772909
$$347$$ 5.04508 8.73834i 0.270834 0.469099i −0.698241 0.715862i $$-0.746034\pi$$
0.969076 + 0.246764i $$0.0793671\pi$$
$$348$$ 0 0
$$349$$ −10.3541 + 17.9338i −0.554242 + 0.959976i 0.443720 + 0.896166i $$0.353659\pi$$
−0.997962 + 0.0638103i $$0.979675\pi$$
$$350$$ −2.80902 + 4.86536i −0.150148 + 0.260064i
$$351$$ 0 0
$$352$$ 15.0000 0.799503
$$353$$ −8.61803 14.9269i −0.458692 0.794477i 0.540200 0.841536i $$-0.318348\pi$$
−0.998892 + 0.0470591i $$0.985015\pi$$
$$354$$ 0 0
$$355$$ −13.3475 −0.708413
$$356$$ 1.71885 2.97713i 0.0910987 0.157788i
$$357$$ 0 0
$$358$$ 1.84346 + 3.19296i 0.0974298 + 0.168753i
$$359$$ −2.67376 4.63109i −0.141116 0.244420i 0.786801 0.617206i $$-0.211736\pi$$
−0.927917 + 0.372787i $$0.878402\pi$$
$$360$$ 0 0
$$361$$ 8.73607 + 15.1313i 0.459793 + 0.796385i
$$362$$ 3.70163 + 6.41140i 0.194553 + 0.336976i
$$363$$ 0 0
$$364$$ −5.42705 + 9.39993i −0.284455 + 0.492690i
$$365$$ −2.29180 −0.119958
$$366$$ 0 0
$$367$$ −9.59017 + 16.6107i −0.500603 + 0.867069i 0.499397 + 0.866373i $$0.333555\pi$$
−1.00000 0.000696189i $$0.999778\pi$$
$$368$$ 6.89261 11.9383i 0.359302 0.622329i
$$369$$ 0 0
$$370$$ −1.14590 1.98475i −0.0595724 0.103182i
$$371$$ −5.85410 −0.303930
$$372$$ 0 0
$$373$$ −3.00000 5.19615i −0.155334 0.269047i 0.777847 0.628454i $$-0.216312\pi$$
−0.933181 + 0.359408i $$0.882979\pi$$
$$374$$ 4.20820 + 7.28882i 0.217601 + 0.376896i
$$375$$ 0 0
$$376$$ 1.68692 0.0869961
$$377$$ 2.07295 3.59045i 0.106762 0.184918i
$$378$$ 0 0
$$379$$ −27.3607 −1.40542 −0.702712 0.711475i $$-0.748028\pi$$
−0.702712 + 0.711475i $$0.748028\pi$$
$$380$$ 1.41641 + 2.45329i 0.0726602 + 0.125851i
$$381$$ 0 0
$$382$$ −2.77458 + 4.80571i −0.141960 + 0.245881i
$$383$$ −38.1246 −1.94808 −0.974038 0.226383i $$-0.927310\pi$$
−0.974038 + 0.226383i $$0.927310\pi$$
$$384$$ 0 0
$$385$$ 18.9443 0.965489
$$386$$ 1.03444 0.0526517
$$387$$ 0 0
$$388$$ 17.1246 0.869370
$$389$$ 35.0689 1.77806 0.889031 0.457846i $$-0.151379\pi$$
0.889031 + 0.457846i $$0.151379\pi$$
$$390$$ 0 0
$$391$$ 26.6869 1.34962
$$392$$ 8.05573 13.9529i 0.406876 0.704729i
$$393$$ 0 0
$$394$$ −0.562306 0.973942i −0.0283286 0.0490665i
$$395$$ 1.70820 0.0859491
$$396$$ 0 0
$$397$$ −16.2082 + 28.0734i −0.813466 + 1.40897i 0.0969574 + 0.995289i $$0.469089\pi$$
−0.910424 + 0.413677i $$0.864244\pi$$
$$398$$ 0.742646 0.0372255
$$399$$ 0 0
$$400$$ 5.46149 + 9.45958i 0.273075 + 0.472979i
$$401$$ −12.7082 22.0113i −0.634617 1.09919i −0.986596 0.163182i $$-0.947824\pi$$
0.351979 0.936008i $$-0.385509\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −3.48936 6.04374i −0.173602 0.300687i
$$405$$ 0 0
$$406$$ −2.42705 + 4.20378i −0.120453 + 0.208630i
$$407$$ 8.78115 15.2094i 0.435266 0.753902i
$$408$$ 0 0
$$409$$ 8.90983 0.440563 0.220281 0.975436i $$-0.429302\pi$$
0.220281 + 0.975436i $$0.429302\pi$$
$$410$$ −2.23607 + 3.87298i −0.110432 + 0.191273i
$$411$$ 0 0
$$412$$ −15.2188 26.3598i −0.749779 1.29865i
$$413$$ −10.7812 18.6735i −0.530506 0.918863i
$$414$$ 0 0
$$415$$ −9.90983 17.1643i −0.486454 0.842564i
$$416$$ −2.86475 4.96188i −0.140456 0.243276i
$$417$$ 0 0
$$418$$ 0.854102 1.47935i 0.0417755 0.0723573i
$$419$$ 10.2361 0.500065 0.250032 0.968237i $$-0.419559\pi$$
0.250032 + 0.968237i $$0.419559\pi$$
$$420$$ 0 0
$$421$$ 3.82624 + 6.62724i 0.186479 + 0.322992i 0.944074 0.329734i $$-0.106959\pi$$
−0.757595 + 0.652725i $$0.773626\pi$$
$$422$$ −3.52786 −0.171734
$$423$$ 0 0
$$424$$ 1.01722 1.76188i 0.0494006 0.0855644i
$$425$$ −10.5729 + 18.3129i −0.512863 + 0.888305i
$$426$$ 0 0
$$427$$ 6.04508 10.4704i 0.292542 0.506698i
$$428$$ 13.9574 0.674658
$$429$$ 0 0
$$430$$ −1.18034 + 2.86217i −0.0569210 + 0.138026i
$$431$$ 24.7984 1.19450 0.597248 0.802057i $$-0.296261\pi$$
0.597248 + 0.802057i $$0.296261\pi$$
$$432$$ 0 0
$$433$$ 17.3541 30.0582i 0.833985 1.44450i −0.0608693 0.998146i $$-0.519387\pi$$
0.894854 0.446359i $$-0.147279\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −12.8435 + 22.2455i −0.615090 + 1.06537i
$$437$$ −2.70820 4.69075i −0.129551 0.224389i
$$438$$ 0 0
$$439$$ −0.572949 0.992377i −0.0273454 0.0473636i 0.852029 0.523495i $$-0.175372\pi$$
−0.879374 + 0.476131i $$0.842039\pi$$
$$440$$ −3.29180 + 5.70156i −0.156930 + 0.271811i
$$441$$ 0 0
$$442$$ 1.60739 2.78408i 0.0764558 0.132425i
$$443$$ 1.23607 + 2.14093i 0.0587274 + 0.101719i 0.893894 0.448278i $$-0.147962\pi$$
−0.835167 + 0.549996i $$0.814629\pi$$
$$444$$ 0 0
$$445$$ 1.14590 + 1.98475i 0.0543208 + 0.0940863i
$$446$$ 1.05573 0.0499902
$$447$$ 0 0
$$448$$ −9.97214 17.2722i −0.471139 0.816037i
$$449$$ −16.4164 + 28.4341i −0.774738 + 1.34189i 0.160203 + 0.987084i $$0.448785\pi$$
−0.934942 + 0.354802i $$0.884548\pi$$
$$450$$ 0 0
$$451$$ −34.2705 −1.61374
$$452$$ −28.9574 −1.36204
$$453$$ 0 0
$$454$$ −0.281153 + 0.486971i −0.0131952 + 0.0228547i
$$455$$ −3.61803 6.26662i −0.169616 0.293784i
$$456$$ 0 0
$$457$$ −15.7082 −0.734799 −0.367399 0.930063i $$-0.619752\pi$$
−0.367399 + 0.930063i $$0.619752\pi$$
$$458$$ 0.437694 + 0.758108i 0.0204521 + 0.0354241i
$$459$$ 0 0
$$460$$ 5.02129 + 8.69712i 0.234119 + 0.405505i
$$461$$ −15.7984 + 27.3636i −0.735804 + 1.27445i 0.218566 + 0.975822i $$0.429862\pi$$
−0.954370 + 0.298627i $$0.903471\pi$$
$$462$$ 0 0
$$463$$ 14.9164 25.8360i 0.693224 1.20070i −0.277551 0.960711i $$-0.589523\pi$$
0.970776 0.239989i $$-0.0771438\pi$$
$$464$$ 4.71885 + 8.17328i 0.219067 + 0.379435i
$$465$$ 0 0
$$466$$ 3.44427 + 5.96565i 0.159553 + 0.276354i
$$467$$ −7.52786 + 13.0386i −0.348348 + 0.603356i −0.985956 0.167004i $$-0.946591\pi$$
0.637608 + 0.770361i $$0.279924\pi$$
$$468$$ 0 0
$$469$$ 16.3262 0.753876
$$470$$ −0.270510 + 0.468537i −0.0124777 + 0.0216120i
$$471$$ 0 0
$$472$$ 7.49342 0.344913
$$473$$ −23.5172 + 3.13331i −1.08132 + 0.144070i
$$474$$ 0 0
$$475$$ 4.29180 0.196921
$$476$$ 23.9164 41.4244i 1.09621 1.89869i
$$477$$ 0 0
$$478$$ −1.58359 + 2.74286i −0.0724318 + 0.125456i
$$479$$ −6.90983 + 11.9682i −0.315718 + 0.546840i −0.979590 0.201007i $$-0.935579\pi$$
0.663872 + 0.747846i $$0.268912\pi$$
$$480$$ 0 0
$$481$$ −6.70820 −0.305868
$$482$$ −0.815595 1.41265i −0.0371493 0.0643445i
$$483$$ 0 0
$$484$$ −3.87539 −0.176154
$$485$$ −5.70820 + 9.88690i −0.259196 + 0.448941i
$$486$$ 0 0
$$487$$ −0.663119 1.14856i −0.0300488 0.0520460i 0.850610 0.525797i $$-0.176233\pi$$
−0.880659 + 0.473751i $$0.842900\pi$$
$$488$$ 2.10081 + 3.63871i 0.0950993 + 0.164717i
$$489$$ 0 0
$$490$$ 2.58359 + 4.47491i 0.116715 + 0.202156i
$$491$$ 10.8262 + 18.7516i 0.488581 + 0.846248i 0.999914 0.0131354i $$-0.00418125\pi$$
−0.511332 + 0.859383i $$0.670848\pi$$
$$492$$ 0 0
$$493$$ −9.13525 + 15.8227i −0.411431 + 0.712620i
$$494$$ −0.652476 −0.0293563
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 22.8713 39.6143i 1.02592 1.77694i
$$498$$ 0 0
$$499$$ −6.92705 11.9980i −0.310097 0.537104i 0.668286 0.743905i $$-0.267028\pi$$
−0.978383 + 0.206800i $$0.933695\pi$$
$$500$$ −19.4164 −0.868328
$$501$$ 0 0
$$502$$ −5.57295 9.65263i −0.248733 0.430818i
$$503$$ −6.73607 11.6672i −0.300346 0.520215i 0.675868 0.737023i $$-0.263769\pi$$
−0.976214 + 0.216807i $$0.930436\pi$$
$$504$$ 0 0
$$505$$ 4.65248 0.207032
$$506$$ 3.02786 5.24441i 0.134605 0.233143i
$$507$$ 0 0
$$508$$ 27.1672 1.20535
$$509$$ 9.35410 + 16.2018i 0.414613 + 0.718131i 0.995388 0.0959332i $$-0.0305835\pi$$
−0.580774 + 0.814064i $$0.697250\pi$$
$$510$$ 0 0
$$511$$ 3.92705 6.80185i 0.173723 0.300896i
$$512$$ 22.3050 0.985749
$$513$$ 0 0
$$514$$ −1.31308 −0.0579176
$$515$$ 20.2918 0.894163
$$516$$ 0 0
$$517$$ −4.14590 −0.182336
$$518$$ 7.85410 0.345089
$$519$$ 0 0
$$520$$ 2.51471 0.110277
$$521$$ −11.0172 + 19.0824i −0.482673 + 0.836015i −0.999802 0.0198930i $$-0.993667\pi$$
0.517129 + 0.855908i $$0.327001\pi$$
$$522$$ 0 0
$$523$$ −17.9164 31.0321i −0.783430 1.35694i −0.929933 0.367730i $$-0.880135\pi$$
0.146503 0.989210i $$-0.453198\pi$$
$$524$$ 18.4377 0.805454
$$525$$ 0 0
$$526$$ 5.25329 9.09896i 0.229054 0.396734i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.89919 + 3.28949i 0.0825733 + 0.143021i
$$530$$ 0.326238 + 0.565061i 0.0141709 + 0.0245447i
$$531$$ 0 0
$$532$$ −9.70820 −0.420904
$$533$$ 6.54508 + 11.3364i 0.283499 + 0.491035i
$$534$$ 0 0
$$535$$ −4.65248 + 8.05832i −0.201144 + 0.348392i
$$536$$ −2.83688 + 4.91362i −0.122535 + 0.212236i
$$537$$ 0 0
$$538$$ −4.41641 −0.190405
$$539$$ −19.7984 + 34.2918i −0.852776 + 1.47705i
$$540$$ 0 0
$$541$$ 18.9721 + 32.8607i 0.815676 + 1.41279i 0.908842 + 0.417141i $$0.136968\pi$$
−0.0931658 + 0.995651i $$0.529699\pi$$
$$542$$ −2.64590 4.58283i −0.113651 0.196849i
$$543$$ 0 0
$$544$$ 12.6246 + 21.8665i 0.541276 + 0.937517i
$$545$$ −8.56231 14.8303i −0.366769 0.635262i
$$546$$ 0 0
$$547$$ −10.5000 + 18.1865i −0.448948 + 0.777600i −0.998318 0.0579790i $$-0.981534\pi$$
0.549370 + 0.835579i $$0.314868\pi$$
$$548$$ 6.87539 0.293702
$$549$$ 0 0
$$550$$ 2.39919 + 4.15551i 0.102302 + 0.177192i
$$551$$ 3.70820 0.157975
$$552$$ 0 0
$$553$$ −2.92705 + 5.06980i −0.124471 + 0.215590i
$$554$$ 2.38197 4.12569i 0.101200 0.175284i
$$555$$ 0 0
$$556$$ −4.90576 + 8.49703i −0.208051 + 0.360354i
$$557$$ 38.5623 1.63394 0.816969 0.576682i $$-0.195653\pi$$
0.816969 + 0.576682i $$0.195653\pi$$
$$558$$ 0 0
$$559$$ 5.52786 + 7.18091i 0.233804 + 0.303720i
$$560$$ 16.4721 0.696075
$$561$$ 0 0
$$562$$ 1.42705 2.47172i 0.0601965 0.104263i
$$563$$ 1.32624 0.0558943 0.0279471 0.999609i $$-0.491103\pi$$
0.0279471 + 0.999609i $$0.491103\pi$$
$$564$$ 0 0
$$565$$ 9.65248 16.7186i 0.406083 0.703356i
$$566$$ −2.05573 3.56063i −0.0864087 0.149664i
$$567$$ 0 0
$$568$$ 7.94834 + 13.7669i 0.333505 + 0.577647i
$$569$$ −12.9721 + 22.4684i −0.543820 + 0.941924i 0.454860 + 0.890563i $$0.349689\pi$$
−0.998680 + 0.0513613i $$0.983644\pi$$
$$570$$ 0 0
$$571$$ 21.5902 37.3953i 0.903520 1.56494i 0.0806295 0.996744i $$-0.474307\pi$$
0.822891 0.568199i $$-0.192360\pi$$
$$572$$ 4.63525 + 8.02850i 0.193810 + 0.335688i
$$573$$ 0 0
$$574$$ −7.66312 13.2729i −0.319852 0.554001i
$$575$$ 15.2148 0.634500
$$576$$ 0 0
$$577$$ 14.1074 + 24.4347i 0.587298 + 1.01723i 0.994585 + 0.103930i $$0.0331418\pi$$
−0.407286 + 0.913301i $$0.633525\pi$$
$$578$$ −3.83688 + 6.64567i −0.159593 + 0.276424i
$$579$$ 0 0
$$580$$ −6.87539 −0.285485
$$581$$ 67.9230 2.81792
$$582$$ 0 0
$$583$$ −2.50000 + 4.33013i −0.103539 + 0.179336i
$$584$$ 1.36475 + 2.36381i 0.0564736 + 0.0978151i
$$585$$ 0 0
$$586$$ 4.61803 0.190769
$$587$$ 7.87132 + 13.6335i 0.324884 + 0.562716i 0.981489 0.191519i $$-0.0613413\pi$$
−0.656605 + 0.754235i $$0.728008\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −1.20163 + 2.08128i −0.0494702 + 0.0856848i
$$591$$ 0 0
$$592$$ 7.63525 13.2246i 0.313807 0.543530i
$$593$$ −15.2361 26.3896i −0.625670 1.08369i −0.988411 0.151803i $$-0.951492\pi$$
0.362741 0.931890i $$-0.381841\pi$$
$$594$$ 0 0
$$595$$ 15.9443 + 27.6163i 0.653651 + 1.13216i
$$596$$ −8.34346 + 14.4513i −0.341761 + 0.591948i
$$597$$ 0 0
$$598$$ −2.31308 −0.0945890
$$599$$ 18.1180 31.3814i 0.740283 1.28221i −0.212084 0.977252i $$-0.568025\pi$$
0.952366 0.304956i $$-0.0986417\pi$$
$$600$$ 0 0
$$601$$ 29.4164 1.19992 0.599960 0.800030i $$-0.295183\pi$$
0.599960 + 0.800030i $$0.295183\pi$$
$$602$$ −6.47214 8.40755i −0.263785 0.342666i
$$603$$ 0 0
$$604$$ 16.4164 0.667974
$$605$$ 1.29180 2.23746i 0.0525190 0.0909655i
$$606$$ 0 0
$$607$$ 11.9271 20.6583i 0.484104 0.838493i −0.515729 0.856752i $$-0.672479\pi$$
0.999833 + 0.0182588i $$0.00581228\pi$$
$$608$$ 2.56231 4.43804i 0.103915 0.179986i
$$609$$ 0 0
$$610$$ −1.34752 −0.0545597
$$611$$ 0.791796 + 1.37143i 0.0320326 + 0.0554822i
$$612$$ 0 0
$$613$$ 5.20163 0.210092 0.105046 0.994467i $$-0.466501\pi$$
0.105046 + 0.994467i $$0.466501\pi$$
$$614$$ 4.43363 7.67927i 0.178927 0.309910i
$$615$$ 0 0
$$616$$ −11.2812 19.5395i −0.454531 0.787270i
$$617$$ 4.85410 + 8.40755i 0.195419 + 0.338475i 0.947038 0.321122i $$-0.104060\pi$$
−0.751619 + 0.659598i $$0.770727\pi$$
$$618$$ 0 0
$$619$$ 15.1353 + 26.2150i 0.608337 + 1.05367i 0.991514 + 0.129996i $$0.0414965\pi$$
−0.383177 + 0.923675i $$0.625170\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −5.69756 + 9.86846i −0.228451 + 0.395689i
$$623$$ −7.85410 −0.314668
$$624$$ 0 0
$$625$$ −2.20820 + 3.82472i −0.0883282 + 0.152989i
$$626$$ −2.50658 + 4.34152i −0.100183 + 0.173522i
$$627$$ 0 0
$$628$$ −4.77051 8.26277i −0.190364 0.329720i
$$629$$ 29.5623 1.17873
$$630$$ 0 0
$$631$$ 13.5451 + 23.4608i 0.539221 + 0.933959i 0.998946 + 0.0458973i $$0.0146147\pi$$
−0.459725 + 0.888061i $$0.652052\pi$$
$$632$$ −1.01722 1.76188i −0.0404629 0.0700838i
$$633$$ 0 0
$$634$$ −12.7214 −0.505230
$$635$$ −9.05573 + 15.6850i −0.359366 + 0.622439i
$$636$$ 0 0
$$637$$ 15.1246 0.599259
$$638$$ 2.07295 + 3.59045i 0.0820688 + 0.142147i
$$639$$ 0 0
$$640$$ −6.23607 + 10.8012i −0.246502 + 0.426954i
$$641$$ −10.8197 −0.427351 −0.213675 0.976905i $$-0.568543\pi$$
−0.213675 + 0.976905i $$0.568543\pi$$
$$642$$ 0 0
$$643$$ 9.43769 0.372186 0.186093 0.982532i $$-0.440417\pi$$
0.186093 + 0.982532i $$0.440417\pi$$
$$644$$ −34.4164 −1.35620
$$645$$ 0 0
$$646$$ 2.87539 0.113131
$$647$$ 21.6738 0.852084 0.426042 0.904703i $$-0.359908\pi$$
0.426042 + 0.904703i $$0.359908\pi$$
$$648$$ 0 0
$$649$$ −18.4164 −0.722907
$$650$$ 0.916408 1.58726i 0.0359445 0.0622577i
$$651$$ 0 0
$$652$$ 12.9787 + 22.4798i 0.508286 + 0.880377i
$$653$$ 32.8885 1.28703 0.643514 0.765434i $$-0.277476\pi$$
0.643514 + 0.765434i $$0.277476\pi$$
$$654$$ 0 0
$$655$$ −6.14590 + 10.6450i −0.240140 + 0.415935i
$$656$$ −29.7984 −1.16343
$$657$$ 0 0
$$658$$ −0.927051 1.60570i −0.0361402 0.0625967i
$$659$$ −14.6803 25.4271i −0.571865 0.990499i −0.996375 0.0850756i $$-0.972887\pi$$
0.424510 0.905423i $$-0.360447\pi$$
$$660$$ 0 0
$$661$$ −43.3951 −1.68787 −0.843937 0.536442i $$-0.819768\pi$$
−0.843937 + 0.536442i $$0.819768\pi$$
$$662$$ 1.04508 + 1.81014i 0.0406184 + 0.0703531i
$$663$$ 0 0
$$664$$ −11.8024 + 20.4424i −0.458023 + 0.793320i
$$665$$ 3.23607 5.60503i 0.125489 0.217354i
$$666$$ 0 0
$$667$$ 13.1459 0.509011
$$668$$ −13.1976 + 22.8588i −0.510629 + 0.884435i
$$669$$ 0 0
$$670$$ −0.909830 1.57587i −0.0351498 0.0608812i
$$671$$ −5.16312 8.94278i −0.199320 0.345232i
$$672$$ 0 0
$$673$$ −6.91641 11.9796i −0.266608 0.461778i 0.701376 0.712792i $$-0.252570\pi$$
−0.967984 + 0.251013i $$0.919236\pi$$
$$674$$ −5.34752 9.26218i −0.205979 0.356766i
$$675$$ 0 0
$$676$$ −10.2812 + 17.8075i −0.395429 + 0.684903i
$$677$$ 31.7639 1.22079 0.610394 0.792098i $$-0.291011\pi$$
0.610394 + 0.792098i $$0.291011\pi$$
$$678$$ 0 0
$$679$$ −19.5623 33.8829i −0.750732 1.30031i
$$680$$ −11.0820 −0.424977
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −5.56231 + 9.63420i −0.212836 + 0.368642i −0.952601 0.304223i $$-0.901603\pi$$
0.739765 + 0.672865i $$0.234937\pi$$
$$684$$ 0 0
$$685$$ −2.29180 + 3.96951i −0.0875650 + 0.151667i
$$686$$ −6.38197 −0.243665
$$687$$ 0 0
$$688$$ −20.4483 + 2.72443i −0.779586 + 0.103868i
$$689$$ 1.90983 0.0727587
$$690$$ 0 0
$$691$$ −7.86475 + 13.6221i −0.299189 + 0.518211i −0.975951 0.217992i $$-0.930049\pi$$
0.676762 + 0.736202i $$0.263383\pi$$
$$692$$ −6.97871 −0.265291
$$693$$ 0 0
$$694$$ 1.92705 3.33775i 0.0731499 0.126699i
$$695$$ −3.27051 5.66469i −0.124058 0.214874i
$$696$$ 0 0
$$697$$ −28.8435 49.9583i −1.09252 1.89231i
$$698$$ −3.95492 + 6.85011i −0.149696 + 0.259281i
$$699$$ 0 0
$$700$$ 13.6353 23.6170i 0.515364 0.892637i
$$701$$ −7.25329 12.5631i −0.273953 0.474500i 0.695917 0.718122i $$-0.254998\pi$$
−0.969870 + 0.243621i $$0.921665\pi$$
$$702$$ 0 0
$$703$$ −3.00000 5.19615i −0.113147 0.195977i
$$704$$ −17.0344 −0.642010
$$705$$ 0 0
$$706$$ −3.29180 5.70156i −0.123888 0.214581i
$$707$$ −7.97214 + 13.8081i −0.299823 + 0.519309i
$$708$$ 0 0
$$709$$ 28.8885 1.08493 0.542466 0.840078i $$-0.317491\pi$$
0.542466 + 0.840078i $$0.317491\pi$$
$$710$$ −5.09830 −0.191336
$$711$$ 0 0
$$712$$ 1.36475 2.36381i 0.0511460 0.0885874i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −6.18034 −0.231132
$$716$$ −8.94834 15.4990i −0.334415 0.579224i
$$717$$ 0 0
$$718$$ −1.02129 1.76892i −0.0381141 0.0660155i
$$719$$ −5.39919 + 9.35167i −0.201356 + 0.348758i −0.948965 0.315380i $$-0.897868\pi$$
0.747610 + 0.664138i $$0.231201\pi$$
$$720$$ 0 0
$$721$$ −34.7705 + 60.2243i −1.29492 + 2.24287i
$$722$$ 3.33688 + 5.77965i 0.124186 + 0.215096i
$$723$$ 0 0
$$724$$ −17.9681 31.1216i −0.667778 1.15663i
$$725$$ −5.20820 + 9.02087i −0.193428 + 0.335027i
$$726$$ 0 0
$$727$$ −17.9787 −0.666794 −0.333397 0.942787i $$-0.608195\pi$$
−0.333397 + 0.942787i $$0.608195\pi$$
$$728$$ −4.30902 + 7.46344i −0.159703 + 0.276613i
$$729$$ 0 0
$$730$$ −0.875388 −0.0323996
$$731$$ −24.3607 31.6455i −0.901012 1.17045i
$$732$$ 0 0
$$733$$ 24.5410 0.906443 0.453222 0.891398i $$-0.350275\pi$$
0.453222 + 0.891398i $$0.350275\pi$$
$$734$$ −3.66312 + 6.34471i −0.135208 + 0.234187i
$$735$$ 0 0
$$736$$ 9.08359 15.7332i 0.334826 0.579935i
$$737$$ 6.97214 12.0761i 0.256822 0.444829i
$$738$$ 0 0
$$739$$ 49.5410 1.82240 0.911198 0.411969i $$-0.135159\pi$$
0.911198 + 0.411969i $$0.135159\pi$$
$$740$$ 5.56231 + 9.63420i 0.204474 + 0.354160i
$$741$$ 0 0
$$742$$ −2.23607 −0.0820886
$$743$$ 16.6803 28.8912i 0.611942 1.05992i −0.378970 0.925409i $$-0.623722\pi$$
0.990913 0.134506i $$-0.0429449\pi$$
$$744$$ 0 0
$$745$$ −5.56231 9.63420i −0.203787 0.352970i
$$746$$ −1.14590 1.98475i −0.0419543 0.0726670i
$$747$$ 0 0
$$748$$ −20.4271 35.3807i −0.746887 1.29365i
$$749$$ −15.9443 27.6163i −0.582591 1.00908i
$$750$$ 0 0
$$751$$ 18.9894 32.8905i 0.692931 1.20019i −0.277942 0.960598i $$-0.589652\pi$$
0.970873 0.239595i $$-0.0770145\pi$$
$$752$$ −3.60488 −0.131456
$$753$$ 0 0
$$754$$ 0.791796 1.37143i 0.0288355 0.0499446i
$$755$$ −5.47214 + 9.47802i −0.199151 + 0.344940i
$$756$$ 0 0
$$757$$ 15.4894 + 26.8284i 0.562970 + 0.975093i 0.997235 + 0.0743080i $$0.0236748\pi$$
−0.434265 + 0.900785i $$0.642992\pi$$
$$758$$ −10.4508 −0.379592
$$759$$ 0 0
$$760$$ 1.12461 + 1.94788i 0.0407940 + 0.0706572i
$$761$$ 0.545085 + 0.944115i 0.0197593 + 0.0342241i 0.875736 0.482790i $$-0.160377\pi$$
−0.855977 + 0.517014i $$0.827043\pi$$
$$762$$ 0 0
$$763$$ 58.6869 2.12461
$$764$$ 13.4681 23.3274i 0.487258 0.843955i
$$765$$ 0 0
$$766$$ −14.5623 −0.526157
$$767$$ 3.51722 + 6.09201i 0.126999 + 0.219970i
$$768$$ 0 0
$$769$$ −9.94427 + 17.2240i −0.358600 + 0.621113i −0.987727 0.156189i $$-0.950079\pi$$
0.629128 + 0.777302i $$0.283412\pi$$
$$770$$ 7.23607 0.260770
$$771$$ 0 0
$$772$$ −5.02129 −0.180720
$$773$$ −15.5967 −0.560976 −0.280488 0.959858i $$-0.590496\pi$$
−0.280488 + 0.959858i $$0.590496\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 13.5967 0.488095
$$777$$ 0 0
$$778$$ 13.3951 0.480238
$$779$$ −5.85410 + 10.1396i −0.209745 + 0.363289i
$$780$$ 0 0
$$781$$ −19.5344 33.8346i −0.698997 1.21070i
$$782$$ 10.1935 0.364519
$$783$$ 0 0
$$784$$ −17.2148 + 29.8169i −0.614814 + 1.06489i
$$785$$ 6.36068 0.227022
$$786$$ 0 0
$$787$$ −5.22542 9.05070i −0.186266 0.322623i 0.757736 0.652561i $$-0.226305\pi$$
−0.944002 + 0.329938i $$0.892972\pi$$
$$788$$ 2.72949 + 4.72762i 0.0972341 + 0.168414i
$$789$$ 0 0
$$790$$ 0.652476 0.0232140
$$791$$ 33.0795 + 57.2954i 1.17617 + 2.03719i
$$792$$ 0 0
$$793$$ −1.97214 + 3.41584i −0.0700326 + 0.121300i
$$794$$ −6.19098 + 10.7231i −0.219710 + 0.380548i
$$795$$ 0 0
$$796$$ −3.60488 −0.127772
$$797$$ −4.11803 + 7.13264i −0.145868 + 0.252651i −0.929697 0.368326i $$-0.879931\pi$$
0.783828 + 0.620978i $$0.213264\pi$$
$$798$$ 0 0
$$799$$ −3.48936 6.04374i −0.123445 0.213812i