# Properties

 Label 688.2.i.e.49.1 Level 688 Weight 2 Character 688.49 Analytic conductor 5.494 Analytic rank 0 Dimension 4 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$688 = 2^{4} \cdot 43$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 688.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.49370765906$$ 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 49.1 Root $$0.809017 - 1.40126i$$ of defining polynomial Character $$\chi$$ $$=$$ 688.49 Dual form 688.2.i.e.337.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.30902 + 2.26728i) q^{3} +(-0.618034 + 1.07047i) q^{5} +(-2.11803 - 3.66854i) q^{7} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})$$ $$q+(-1.30902 + 2.26728i) q^{3} +(-0.618034 + 1.07047i) q^{5} +(-2.11803 - 3.66854i) q^{7} +(-1.92705 - 3.33775i) q^{9} +3.61803 q^{11} +(-0.690983 - 1.19682i) q^{13} +(-1.61803 - 2.80252i) q^{15} +(-3.04508 - 5.27424i) q^{17} +(-0.618034 + 1.07047i) q^{19} +11.0902 q^{21} +(2.19098 - 3.79489i) q^{23} +(1.73607 + 3.00696i) q^{25} +2.23607 q^{27} +(-1.50000 - 2.59808i) q^{29} +(-4.73607 + 8.20311i) q^{33} +5.23607 q^{35} +(2.42705 - 4.20378i) q^{37} +3.61803 q^{39} +9.47214 q^{41} +(6.50000 - 0.866025i) q^{43} +4.76393 q^{45} -1.14590 q^{47} +(-5.47214 + 9.47802i) q^{49} +15.9443 q^{51} +(0.690983 - 1.19682i) q^{53} +(-2.23607 + 3.87298i) q^{55} +(-1.61803 - 2.80252i) q^{57} -5.09017 q^{59} +(-1.42705 - 2.47172i) q^{61} +(-8.16312 + 14.1389i) q^{63} +1.70820 q^{65} +(-1.92705 + 3.33775i) q^{67} +(5.73607 + 9.93516i) q^{69} +(-5.39919 - 9.35167i) q^{71} +(-0.927051 - 1.60570i) q^{73} -9.09017 q^{75} +(-7.66312 - 13.2729i) q^{77} +(-0.690983 - 1.19682i) q^{79} +(2.85410 - 4.94345i) q^{81} +(8.01722 - 13.8862i) q^{83} +7.52786 q^{85} +7.85410 q^{87} +(0.927051 - 1.60570i) q^{89} +(-2.92705 + 5.06980i) q^{91} +(-0.763932 - 1.32317i) q^{95} -9.23607 q^{97} +(-6.97214 - 12.0761i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 3q^{3} + 2q^{5} - 4q^{7} - q^{9} + O(q^{10})$$ $$4q - 3q^{3} + 2q^{5} - 4q^{7} - q^{9} + 10q^{11} - 5q^{13} - 2q^{15} - q^{17} + 2q^{19} + 22q^{21} + 11q^{23} - 2q^{25} - 6q^{29} - 10q^{33} + 12q^{35} + 3q^{37} + 10q^{39} + 20q^{41} + 26q^{43} + 28q^{45} - 18q^{47} - 4q^{49} + 28q^{51} + 5q^{53} - 2q^{57} + 2q^{59} + q^{61} - 17q^{63} - 20q^{65} - q^{67} + 14q^{69} + 3q^{71} + 3q^{73} - 14q^{75} - 15q^{77} - 5q^{79} - 2q^{81} + 3q^{83} + 48q^{85} + 18q^{87} - 3q^{89} - 5q^{91} - 12q^{95} - 28q^{97} - 10q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/688\mathbb{Z}\right)^\times$$.

 $$n$$ $$431$$ $$433$$ $$517$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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 0
$$3$$ −1.30902 + 2.26728i −0.755761 + 1.30902i 0.189234 + 0.981932i $$0.439400\pi$$
−0.944995 + 0.327085i $$0.893934\pi$$
$$4$$ 0 0
$$5$$ −0.618034 + 1.07047i −0.276393 + 0.478727i −0.970486 0.241159i $$-0.922473\pi$$
0.694092 + 0.719886i $$0.255806\pi$$
$$6$$ 0 0
$$7$$ −2.11803 3.66854i −0.800542 1.38658i −0.919260 0.393651i $$-0.871212\pi$$
0.118718 0.992928i $$-0.462121\pi$$
$$8$$ 0 0
$$9$$ −1.92705 3.33775i −0.642350 1.11258i
$$10$$ 0 0
$$11$$ 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 0
$$15$$ −1.61803 2.80252i −0.417775 0.723607i
$$16$$ 0 0
$$17$$ −3.04508 5.27424i −0.738542 1.27919i −0.953152 0.302492i $$-0.902182\pi$$
0.214610 0.976700i $$-0.431152\pi$$
$$18$$ 0 0
$$19$$ −0.618034 + 1.07047i −0.141787 + 0.245582i −0.928170 0.372158i $$-0.878618\pi$$
0.786383 + 0.617740i $$0.211951\pi$$
$$20$$ 0 0
$$21$$ 11.0902 2.42007
$$22$$ 0 0
$$23$$ 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 0
$$27$$ 2.23607 0.430331
$$28$$ 0 0
$$29$$ −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i $$-0.256518\pi$$
−0.971023 + 0.238987i $$0.923185\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ 0 0
$$33$$ −4.73607 + 8.20311i −0.824444 + 1.42798i
$$34$$ 0 0
$$35$$ 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 0
$$39$$ 3.61803 0.579349
$$40$$ 0 0
$$41$$ 9.47214 1.47930 0.739650 0.672992i $$-0.234991\pi$$
0.739650 + 0.672992i $$0.234991\pi$$
$$42$$ 0 0
$$43$$ 6.50000 0.866025i 0.991241 0.132068i
$$44$$ 0 0
$$45$$ 4.76393 0.710165
$$46$$ 0 0
$$47$$ −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 0
$$51$$ 15.9443 2.23264
$$52$$ 0 0
$$53$$ 0.690983 1.19682i 0.0949138 0.164396i −0.814659 0.579941i $$-0.803076\pi$$
0.909573 + 0.415545i $$0.136409\pi$$
$$54$$ 0 0
$$55$$ −2.23607 + 3.87298i −0.301511 + 0.522233i
$$56$$ 0 0
$$57$$ −1.61803 2.80252i −0.214314 0.371202i
$$58$$ 0 0
$$59$$ −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
$$63$$ −8.16312 + 14.1389i −1.02846 + 1.78134i
$$64$$ 0 0
$$65$$ 1.70820 0.211877
$$66$$ 0 0
$$67$$ −1.92705 + 3.33775i −0.235427 + 0.407771i −0.959397 0.282061i $$-0.908982\pi$$
0.723970 + 0.689832i $$0.242315\pi$$
$$68$$ 0 0
$$69$$ 5.73607 + 9.93516i 0.690541 + 1.19605i
$$70$$ 0 0
$$71$$ −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 0
$$75$$ −9.09017 −1.04964
$$76$$ 0 0
$$77$$ −7.66312 13.2729i −0.873293 1.51259i
$$78$$ 0 0
$$79$$ −0.690983 1.19682i −0.0777417 0.134653i 0.824534 0.565813i $$-0.191438\pi$$
−0.902275 + 0.431161i $$0.858104\pi$$
$$80$$ 0 0
$$81$$ 2.85410 4.94345i 0.317122 0.549272i
$$82$$ 0 0
$$83$$ 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
$$86$$ 0 0
$$87$$ 7.85410 0.842048
$$88$$ 0 0
$$89$$ 0.927051 1.60570i 0.0982672 0.170204i −0.812700 0.582682i $$-0.802003\pi$$
0.910968 + 0.412478i $$0.135337\pi$$
$$90$$ 0 0
$$91$$ −2.92705 + 5.06980i −0.306838 + 0.531460i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −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 $$0.655346\pi$$
$$98$$ 0 0
$$99$$ −6.97214 12.0761i −0.700726 1.21369i
$$100$$ 0 0
$$101$$ −1.88197 3.25966i −0.187263 0.324348i 0.757074 0.653329i $$-0.226628\pi$$
−0.944337 + 0.328981i $$0.893295\pi$$
$$102$$ 0 0
$$103$$ −8.20820 14.2170i −0.808778 1.40085i −0.913710 0.406366i $$-0.866796\pi$$
0.104932 0.994479i $$-0.466537\pi$$
$$104$$ 0 0
$$105$$ −6.85410 + 11.8717i −0.668892 + 1.15855i
$$106$$ 0 0
$$107$$ −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 0
$$111$$ 6.35410 + 11.0056i 0.603105 + 1.04461i
$$112$$ 0 0
$$113$$ −15.6180 −1.46922 −0.734611 0.678489i $$-0.762635\pi$$
−0.734611 + 0.678489i $$0.762635\pi$$
$$114$$ 0 0
$$115$$ 2.70820 + 4.69075i 0.252541 + 0.437414i
$$116$$ 0 0
$$117$$ −2.66312 + 4.61266i −0.246205 + 0.426440i
$$118$$ 0 0
$$119$$ −12.8992 + 22.3420i −1.18247 + 2.04809i
$$120$$ 0 0
$$121$$ 2.09017 0.190015
$$122$$ 0 0
$$123$$ −12.3992 + 21.4760i −1.11800 + 1.93643i
$$124$$ 0 0
$$125$$ −10.4721 −0.936656
$$126$$ 0 0
$$127$$ 14.6525 1.30020 0.650098 0.759850i $$-0.274728\pi$$
0.650098 + 0.759850i $$0.274728\pi$$
$$128$$ 0 0
$$129$$ −6.54508 + 15.8710i −0.576263 + 1.39736i
$$130$$ 0 0
$$131$$ −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 0
$$135$$ −1.38197 + 2.39364i −0.118941 + 0.206011i
$$136$$ 0 0
$$137$$ 3.70820 0.316813 0.158407 0.987374i $$-0.449364\pi$$
0.158407 + 0.987374i $$0.449364\pi$$
$$138$$ 0 0
$$139$$ −2.64590 + 4.58283i −0.224422 + 0.388711i −0.956146 0.292891i $$-0.905383\pi$$
0.731724 + 0.681601i $$0.238716\pi$$
$$140$$ 0 0
$$141$$ 1.50000 2.59808i 0.126323 0.218797i
$$142$$ 0 0
$$143$$ −2.50000 4.33013i −0.209061 0.362103i
$$144$$ 0 0
$$145$$ 3.70820 0.307950
$$146$$ 0 0
$$147$$ −14.3262 24.8138i −1.18161 2.04661i
$$148$$ 0 0
$$149$$ −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i $$-0.953515\pi$$
0.620701 + 0.784047i $$0.286848\pi$$
$$150$$ 0 0
$$151$$ 8.85410 0.720537 0.360268 0.932849i $$-0.382685\pi$$
0.360268 + 0.932849i $$0.382685\pi$$
$$152$$ 0 0
$$153$$ −11.7361 + 20.3275i −0.948805 + 1.64338i
$$154$$ 0 0
$$155$$ 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 0
$$159$$ 1.80902 + 3.13331i 0.143464 + 0.248488i
$$160$$ 0 0
$$161$$ −18.5623 −1.46291
$$162$$ 0 0
$$163$$ 7.00000 + 12.1244i 0.548282 + 0.949653i 0.998392 + 0.0566798i $$0.0180514\pi$$
−0.450110 + 0.892973i $$0.648615\pi$$
$$164$$ 0 0
$$165$$ −5.85410 10.1396i −0.455741 0.789367i
$$166$$ 0 0
$$167$$ 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
$$170$$ 0 0
$$171$$ 4.76393 0.364307
$$172$$ 0 0
$$173$$ −3.76393 −0.286166 −0.143083 0.989711i $$-0.545702\pi$$
−0.143083 + 0.989711i $$0.545702\pi$$
$$174$$ 0 0
$$175$$ 7.35410 12.7377i 0.555918 0.962878i
$$176$$ 0 0
$$177$$ 6.66312 11.5409i 0.500831 0.867464i
$$178$$ 0 0
$$179$$ 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 $$0.577326\pi$$
$$182$$ 0 0
$$183$$ 7.47214 0.552356
$$184$$ 0 0
$$185$$ 3.00000 + 5.19615i 0.220564 + 0.382029i
$$186$$ 0 0
$$187$$ −11.0172 19.0824i −0.805659 1.39544i
$$188$$ 0 0
$$189$$ −4.73607 8.20311i −0.344498 0.596688i
$$190$$ 0 0
$$191$$ −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 $$0.468925\pi$$
$$194$$ 0 0
$$195$$ −2.23607 + 3.87298i −0.160128 + 0.277350i
$$196$$ 0 0
$$197$$ 1.47214 + 2.54981i 0.104885 + 0.181667i 0.913691 0.406409i $$-0.133219\pi$$
−0.808806 + 0.588076i $$0.799886\pi$$
$$198$$ 0 0
$$199$$ −1.94427 −0.137826 −0.0689129 0.997623i $$-0.521953\pi$$
−0.0689129 + 0.997623i $$0.521953\pi$$
$$200$$ 0 0
$$201$$ −5.04508 8.73834i −0.355853 0.616355i
$$202$$ 0 0
$$203$$ −6.35410 + 11.0056i −0.445971 + 0.772444i
$$204$$ 0 0
$$205$$ −5.85410 + 10.1396i −0.408868 + 0.708181i
$$206$$ 0 0
$$207$$ −16.8885 −1.17383
$$208$$ 0 0
$$209$$ −2.23607 + 3.87298i −0.154672 + 0.267900i
$$210$$ 0 0
$$211$$ 9.23607 0.635837 0.317919 0.948118i $$-0.397016\pi$$
0.317919 + 0.948118i $$0.397016\pi$$
$$212$$ 0 0
$$213$$ 28.2705 1.93706
$$214$$ 0 0
$$215$$ −3.09017 + 7.49326i −0.210748 + 0.511036i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 4.85410 0.328010
$$220$$ 0 0
$$221$$ −4.20820 + 7.28882i −0.283074 + 0.490299i
$$222$$ 0 0
$$223$$ −2.76393 −0.185087 −0.0925433 0.995709i $$-0.529500\pi$$
−0.0925433 + 0.995709i $$0.529500\pi$$
$$224$$ 0 0
$$225$$ 6.69098 11.5891i 0.446066 0.772608i
$$226$$ 0 0
$$227$$ −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 $$0.809207\pi$$
$$230$$ 0 0
$$231$$ 40.1246 2.64001
$$232$$ 0 0
$$233$$ −9.01722 15.6183i −0.590738 1.02319i −0.994133 0.108162i $$-0.965503\pi$$
0.403395 0.915026i $$-0.367830\pi$$
$$234$$ 0 0
$$235$$ 0.708204 1.22665i 0.0461981 0.0800175i
$$236$$ 0 0
$$237$$ 3.61803 0.235017
$$238$$ 0 0
$$239$$ −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 0
$$243$$ 10.8262 + 18.7516i 0.694503 + 1.20292i
$$244$$ 0 0
$$245$$ −6.76393 11.7155i −0.432132 0.748474i
$$246$$ 0 0
$$247$$ 1.70820 0.108690
$$248$$ 0 0
$$249$$ 20.9894 + 36.3546i 1.33015 + 2.30388i
$$250$$ 0 0
$$251$$ −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
$$254$$ 0 0
$$255$$ −9.85410 + 17.0678i −0.617088 + 1.06883i
$$256$$ 0 0
$$257$$ 3.43769 0.214437 0.107219 0.994235i $$-0.465805\pi$$
0.107219 + 0.994235i $$0.465805\pi$$
$$258$$ 0 0
$$259$$ −20.5623 −1.27768
$$260$$ 0 0
$$261$$ −5.78115 + 10.0133i −0.357844 + 0.619805i
$$262$$ 0 0
$$263$$ 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
$$266$$ 0 0
$$267$$ 2.42705 + 4.20378i 0.148533 + 0.257267i
$$268$$ 0 0
$$269$$ 11.5623 0.704966 0.352483 0.935818i $$-0.385337\pi$$
0.352483 + 0.935818i $$0.385337\pi$$
$$270$$ 0 0
$$271$$ 6.92705 + 11.9980i 0.420788 + 0.728827i 0.996017 0.0891660i $$-0.0284202\pi$$
−0.575228 + 0.817993i $$0.695087\pi$$
$$272$$ 0 0
$$273$$ −7.66312 13.2729i −0.463793 0.803313i
$$274$$ 0 0
$$275$$ 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 $$0.0444161\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −3.73607 + 6.47106i −0.222875 + 0.386031i −0.955680 0.294408i $$-0.904878\pi$$
0.732805 + 0.680439i $$0.238211\pi$$
$$282$$ 0 0
$$283$$ 5.38197 + 9.32184i 0.319925 + 0.554126i 0.980472 0.196659i $$-0.0630091\pi$$
−0.660547 + 0.750784i $$0.729676\pi$$
$$284$$ 0 0
$$285$$ 4.00000 0.236940
$$286$$ 0 0
$$287$$ −20.0623 34.7489i −1.18424 2.05116i
$$288$$ 0 0
$$289$$ −10.0451 + 17.3986i −0.590887 + 1.02345i
$$290$$ 0 0
$$291$$ 12.0902 20.9408i 0.708738 1.22757i
$$292$$ 0 0
$$293$$ −12.0902 −0.706315 −0.353158 0.935564i $$-0.614892\pi$$
−0.353158 + 0.935564i $$0.614892\pi$$
$$294$$ 0 0
$$295$$ 3.14590 5.44886i 0.183161 0.317245i
$$296$$ 0 0
$$297$$ 8.09017 0.469439
$$298$$ 0 0
$$299$$ −6.05573 −0.350212
$$300$$ 0 0
$$301$$ −16.9443 22.0113i −0.976652 1.26871i
$$302$$ 0 0
$$303$$ 9.85410 0.566103
$$304$$ 0 0
$$305$$ 3.52786 0.202005
$$306$$ 0 0
$$307$$ −11.6074 + 20.1046i −0.662469 + 1.14743i 0.317496 + 0.948260i $$0.397158\pi$$
−0.979965 + 0.199170i $$0.936175\pi$$
$$308$$ 0 0
$$309$$ 42.9787 2.44497
$$310$$ 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 0
$$315$$ −10.0902 17.4767i −0.568517 0.984700i
$$316$$ 0 0
$$317$$ 33.3050 1.87059 0.935296 0.353866i $$-0.115133\pi$$
0.935296 + 0.353866i $$0.115133\pi$$
$$318$$ 0 0
$$319$$ −5.42705 9.39993i −0.303857 0.526295i
$$320$$ 0 0
$$321$$ 9.85410 17.0678i 0.550002 0.952632i
$$322$$ 0 0
$$323$$ 7.52786 0.418862
$$324$$ 0 0
$$325$$ 2.39919 4.15551i 0.133083 0.230506i
$$326$$ 0 0
$$327$$ 18.1353 + 31.4112i 1.00288 + 1.73704i
$$328$$ 0 0
$$329$$ 2.42705 + 4.20378i 0.133808 + 0.231762i
$$330$$ 0 0
$$331$$ −2.73607 4.73901i −0.150388 0.260479i 0.780982 0.624553i $$-0.214719\pi$$
−0.931370 + 0.364074i $$0.881386\pi$$
$$332$$ 0 0
$$333$$ −18.7082 −1.02520
$$334$$ 0 0
$$335$$ −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 $$-0.442758\pi$$
$$338$$ 0 0
$$339$$ 20.4443 35.4105i 1.11038 1.92324i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 16.7082 0.902158
$$344$$ 0 0
$$345$$ −14.1803 −0.763444
$$346$$ 0 0
$$347$$ 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 $$0.979675\pi$$
$$350$$ 0 0
$$351$$ −1.54508 2.67617i −0.0824705 0.142843i
$$352$$ 0 0
$$353$$ 8.61803 + 14.9269i 0.458692 + 0.794477i 0.998892 0.0470591i $$-0.0149849\pi$$
−0.540200 + 0.841536i $$0.681652\pi$$
$$354$$ 0 0
$$355$$ 13.3475 0.708413
$$356$$ 0 0
$$357$$ −33.7705 58.4922i −1.78732 3.09574i
$$358$$ 0 0
$$359$$ −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
$$362$$ 0 0
$$363$$ −2.73607 + 4.73901i −0.143606 + 0.248733i
$$364$$ 0 0
$$365$$ 2.29180 0.119958
$$366$$ 0 0
$$367$$ 9.59017 16.6107i 0.500603 0.867069i −0.499397 0.866373i $$-0.666445\pi$$
1.00000 0.000696189i $$-0.000221604\pi$$
$$368$$ 0 0
$$369$$ −18.2533 31.6156i −0.950228 1.64584i
$$370$$ 0 0
$$371$$ −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 $$0.882979\pi$$
$$374$$ 0 0
$$375$$ 13.7082 23.7433i 0.707889 1.22610i
$$376$$ 0 0
$$377$$ −2.07295 + 3.59045i −0.106762 + 0.184918i
$$378$$ 0 0
$$379$$ 27.3607 1.40542 0.702712 0.711475i $$-0.251972\pi$$
0.702712 + 0.711475i $$0.251972\pi$$
$$380$$ 0 0
$$381$$ −19.1803 + 33.2213i −0.982639 + 1.70198i
$$382$$ 0 0
$$383$$ −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
$$386$$ 0 0
$$387$$ −15.4164 20.0265i −0.783660 1.01800i
$$388$$ 0 0
$$389$$ −35.0689 −1.77806 −0.889031 0.457846i $$-0.848621\pi$$
−0.889031 + 0.457846i $$0.848621\pi$$
$$390$$ 0 0
$$391$$ −26.6869 −1.34962
$$392$$ 0 0
$$393$$ 13.0172 22.5465i 0.656632 1.13732i
$$394$$ 0 0
$$395$$ 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 0
$$399$$ −6.85410 + 11.8717i −0.343134 + 0.594326i
$$400$$ 0 0
$$401$$ 12.7082 + 22.0113i 0.634617 + 1.09919i 0.986596 + 0.163182i $$0.0521756\pi$$
−0.351979 + 0.936008i $$0.614491\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 3.52786 + 6.11044i 0.175301 + 0.303630i
$$406$$ 0 0
$$407$$ 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 $$0.429302\pi$$
$$410$$ 0 0
$$411$$ −4.85410 + 8.40755i −0.239435 + 0.414714i
$$412$$ 0 0
$$413$$ 10.7812 + 18.6735i 0.530506 + 0.918863i
$$414$$ 0 0
$$415$$ 9.90983 + 17.1643i 0.486454 + 0.842564i
$$416$$ 0 0
$$417$$ −6.92705 11.9980i −0.339219 0.587545i
$$418$$ 0 0
$$419$$ 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 $$0.773626\pi$$
$$422$$ 0 0
$$423$$ 2.20820 + 3.82472i 0.107367 + 0.185964i
$$424$$ 0 0
$$425$$ 10.5729 18.3129i 0.512863 0.888305i
$$426$$ 0 0
$$427$$ −6.04508 + 10.4704i −0.292542 + 0.506698i
$$428$$ 0 0
$$429$$ 13.0902 0.631999
$$430$$ 0 0
$$431$$ 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
$$435$$ −4.85410 + 8.40755i −0.232736 + 0.403111i
$$436$$ 0 0
$$437$$ 2.70820 + 4.69075i 0.129551 + 0.224389i
$$438$$ 0 0
$$439$$ 0.572949 + 0.992377i 0.0273454 + 0.0473636i 0.879374 0.476131i $$-0.157961\pi$$
−0.852029 + 0.523495i $$0.824628\pi$$
$$440$$ 0 0
$$441$$ 42.1803 2.00859
$$442$$ 0 0
$$443$$ 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
$$446$$ 0 0
$$447$$ −11.7812 20.4056i −0.557229 0.965150i
$$448$$ 0 0
$$449$$ 16.4164 28.4341i 0.774738 1.34189i −0.160203 0.987084i $$-0.551215\pi$$
0.934942 0.354802i $$-0.115452\pi$$
$$450$$ 0 0
$$451$$ 34.2705 1.61374
$$452$$ 0 0
$$453$$ −11.5902 + 20.0748i −0.544554 + 0.943195i
$$454$$ 0 0
$$455$$ −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 0
$$459$$ −6.80902 11.7936i −0.317818 0.550476i
$$460$$ 0 0
$$461$$ 15.7984 27.3636i 0.735804 1.27445i −0.218566 0.975822i $$-0.570138\pi$$
0.954370 0.298627i $$-0.0965287\pi$$
$$462$$ 0 0
$$463$$ −14.9164 + 25.8360i −0.693224 + 1.20070i 0.277551 + 0.960711i $$0.410477\pi$$
−0.970776 + 0.239989i $$0.922856\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −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 0
$$471$$ −13.4721 −0.620763
$$472$$ 0 0
$$473$$ 23.5172 3.13331i 1.08132 0.144070i
$$474$$ 0 0
$$475$$ −4.29180 −0.196921
$$476$$ 0 0
$$477$$ −5.32624 −0.243872
$$478$$ 0 0
$$479$$ −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 0
$$483$$ 24.2984 42.0860i 1.10561 1.91498i
$$484$$ 0 0
$$485$$ 5.70820 9.88690i 0.259196 0.448941i
$$486$$ 0 0
$$487$$ 0.663119 + 1.14856i 0.0300488 + 0.0520460i 0.880659 0.473751i $$-0.157100\pi$$
−0.850610 + 0.525797i $$0.823767\pi$$
$$488$$ 0 0
$$489$$ −36.6525 −1.65748
$$490$$ 0 0
$$491$$ 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 0
$$495$$ 17.2361 0.774704
$$496$$ 0 0
$$497$$ −22.8713 + 39.6143i −1.02592 + 1.77694i
$$498$$ 0 0
$$499$$ 6.92705 + 11.9980i 0.310097 + 0.537104i 0.978383 0.206800i $$-0.0663050\pi$$
−0.668286 + 0.743905i $$0.732972\pi$$
$$500$$ 0 0
$$501$$ 18.6353 + 32.2772i 0.832562 + 1.44204i
$$502$$ 0 0
$$503$$ −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
$$506$$ 0 0
$$507$$ 14.5172 + 25.1446i 0.644732 + 1.11671i
$$508$$ 0 0
$$509$$ −9.35410 16.2018i −0.414613 0.718131i 0.580774 0.814064i $$-0.302750\pi$$
−0.995388 + 0.0959332i $$0.969416\pi$$
$$510$$ 0 0
$$511$$ −3.92705 + 6.80185i −0.173723 + 0.300896i
$$512$$ 0 0
$$513$$ −1.38197 + 2.39364i −0.0610153 + 0.105682i
$$514$$ 0 0
$$515$$ 20.2918 0.894163
$$516$$ 0 0
$$517$$ −4.14590 −0.182336
$$518$$ 0 0
$$519$$ 4.92705 8.53390i 0.216274 0.374597i
$$520$$ 0 0
$$521$$ 11.0172 19.0824i 0.482673 0.836015i −0.517129 0.855908i $$-0.672999\pi$$
0.999802 + 0.0198930i $$0.00633256\pi$$
$$522$$ 0 0
$$523$$ 17.9164 + 31.0321i 0.783430 + 1.35694i 0.929933 + 0.367730i $$0.119865\pi$$
−0.146503 + 0.989210i $$0.546802\pi$$
$$524$$ 0 0
$$525$$ 19.2533 + 33.3477i 0.840282 + 1.45541i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.89919 + 3.28949i 0.0825733 + 0.143021i
$$530$$ 0 0
$$531$$ 9.80902 + 16.9897i 0.425675 + 0.737291i
$$532$$ 0 0
$$533$$ −6.54508 11.3364i −0.283499 0.491035i
$$534$$ 0 0
$$535$$ 4.65248 8.05832i 0.201144 0.348392i
$$536$$ 0 0
$$537$$ −25.2705 −1.09050
$$538$$ 0 0
$$539$$ −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 $$0.529699\pi$$
$$542$$ 0 0
$$543$$ −50.7426 −2.17758
$$544$$ 0 0
$$545$$ 8.56231 + 14.8303i 0.366769 + 0.635262i
$$546$$ 0 0
$$547$$ 10.5000 18.1865i 0.448948 0.777600i −0.549370 0.835579i $$-0.685132\pi$$
0.998318 + 0.0579790i $$0.0184657\pi$$
$$548$$ 0 0
$$549$$ −5.50000 + 9.52628i −0.234734 + 0.406572i
$$550$$ 0 0
$$551$$ 3.70820 0.157975
$$552$$ 0 0
$$553$$ −2.92705 + 5.06980i −0.124471 + 0.215590i
$$554$$ 0 0
$$555$$ −15.7082 −0.666776
$$556$$ 0 0
$$557$$ −38.5623 −1.63394 −0.816969 0.576682i $$-0.804347\pi$$
−0.816969 + 0.576682i $$0.804347\pi$$
$$558$$ 0 0
$$559$$ −5.52786 7.18091i −0.233804 0.303720i
$$560$$ 0 0
$$561$$ 57.6869 2.43554
$$562$$ 0 0
$$563$$ 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
$$566$$ 0 0
$$567$$ −24.1803 −1.01548
$$568$$ 0 0
$$569$$ 12.9721 22.4684i 0.543820 0.941924i −0.454860 0.890563i $$-0.650311\pi$$
0.998680 0.0513613i $$-0.0163560\pi$$
$$570$$ 0 0
$$571$$ −21.5902 + 37.3953i −0.903520 + 1.56494i −0.0806295 + 0.996744i $$0.525693\pi$$
−0.822891 + 0.568199i $$0.807640\pi$$
$$572$$ 0 0
$$573$$ −19.0172 32.9388i −0.794456 1.37604i
$$574$$ 0 0
$$575$$ 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 $$0.633525\pi$$
$$578$$ 0 0
$$579$$ −3.54508 + 6.14027i −0.147329 + 0.255181i
$$580$$ 0 0
$$581$$ −67.9230 −2.81792
$$582$$ 0 0
$$583$$ 2.50000 4.33013i 0.103539 0.179336i
$$584$$ 0 0
$$585$$ −3.29180 5.70156i −0.136099 0.235730i
$$586$$ 0 0
$$587$$ 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
$$590$$ 0 0
$$591$$ −7.70820 −0.317073
$$592$$ 0 0
$$593$$ 15.2361 + 26.3896i 0.625670 + 1.08369i 0.988411 + 0.151803i $$0.0485078\pi$$
−0.362741 + 0.931890i $$0.618159\pi$$
$$594$$ 0 0
$$595$$ −15.9443 27.6163i −0.653651 1.13216i
$$596$$ 0 0
$$597$$ 2.54508 4.40822i 0.104163 0.180416i
$$598$$ 0 0
$$599$$ 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 $$0.295183\pi$$
$$602$$ 0 0
$$603$$ 14.8541 0.604906
$$604$$ 0 0
$$605$$ −1.29180 + 2.23746i −0.0525190 + 0.0909655i
$$606$$ 0 0
$$607$$ −11.9271 + 20.6583i −0.484104 + 0.838493i −0.999833 0.0182588i $$-0.994188\pi$$
0.515729 + 0.856752i $$0.327521\pi$$
$$608$$ 0 0
$$609$$ −16.6353 28.8131i −0.674095 1.16757i
$$610$$ 0 0
$$611$$ 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 $$0.466501\pi$$
$$614$$ 0 0
$$615$$ −15.3262 26.5458i −0.618014 1.07043i
$$616$$ 0 0
$$617$$ −4.85410 8.40755i −0.195419 0.338475i 0.751619 0.659598i $$-0.229273\pi$$
−0.947038 + 0.321122i $$0.895940\pi$$
$$618$$ 0 0
$$619$$ −15.1353 26.2150i −0.608337 1.05367i −0.991514 0.129996i $$-0.958503\pi$$
0.383177 0.923675i $$-0.374830\pi$$
$$620$$ 0 0
$$621$$ 4.89919 8.48564i 0.196598 0.340517i
$$622$$ 0 0
$$623$$ −7.85410 −0.314668
$$624$$ 0 0
$$625$$ −2.20820 + 3.82472i −0.0883282 + 0.152989i
$$626$$ 0 0
$$627$$ −5.85410 10.1396i −0.233790 0.404937i
$$628$$ 0 0
$$629$$ −29.5623 −1.17873
$$630$$ 0 0
$$631$$ −13.5451 23.4608i −0.539221 0.933959i −0.998946 0.0458973i $$-0.985385\pi$$
0.459725 0.888061i $$-0.347948\pi$$
$$632$$ 0 0
$$633$$ −12.0902 + 20.9408i −0.480541 + 0.832322i
$$634$$ 0 0
$$635$$ −9.05573 + 15.6850i −0.359366 + 0.622439i
$$636$$ 0 0
$$637$$ 15.1246 0.599259
$$638$$ 0 0
$$639$$ −20.8090 + 36.0423i −0.823192 + 1.42581i
$$640$$ 0 0
$$641$$ 10.8197 0.427351 0.213675 0.976905i $$-0.431457\pi$$
0.213675 + 0.976905i $$0.431457\pi$$
$$642$$ 0 0
$$643$$ −9.43769 −0.372186 −0.186093 0.982532i $$-0.559583\pi$$
−0.186093 + 0.982532i $$0.559583\pi$$
$$644$$ 0 0
$$645$$ −12.9443 16.8151i −0.509680 0.662094i
$$646$$ 0 0
$$647$$ 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 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −32.8885 −1.28703 −0.643514 0.765434i $$-0.722524\pi$$
−0.643514 + 0.765434i $$0.722524\pi$$
$$654$$ 0 0
$$655$$ 6.14590 10.6450i 0.240140 0.415935i
$$656$$ 0 0
$$657$$ −3.57295 + 6.18853i −0.139394 + 0.241438i
$$658$$ 0 0
$$659$$ −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 $$0.819768\pi$$
$$662$$ 0 0
$$663$$ −11.0172 19.0824i −0.427873 0.741098i
$$664$$ 0 0
$$665$$ −3.23607 + 5.60503i −0.125489 + 0.217354i
$$666$$ 0 0
$$667$$ −13.1459 −0.509011
$$668$$ 0 0
$$669$$ 3.61803 6.26662i 0.139881 0.242281i
$$670$$ 0 0
$$671$$ −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 $$0.919236\pi$$
$$674$$ 0 0
$$675$$ 3.88197 + 6.72376i 0.149417 + 0.258798i
$$676$$ 0 0
$$677$$ −31.7639 −1.22079 −0.610394 0.792098i $$-0.708989\pi$$
−0.610394 + 0.792098i $$0.708989\pi$$
$$678$$ 0 0
$$679$$ 19.5623 + 33.8829i 0.750732 + 1.30031i
$$680$$ 0 0
$$681$$ −1.92705 3.33775i −0.0738448 0.127903i
$$682$$ 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
$$686$$ 0 0
$$687$$ −6.00000 −0.228914
$$688$$ 0 0
$$689$$ −1.90983 −0.0727587
$$690$$ 0 0
$$691$$ 7.86475 13.6221i 0.299189 0.518211i −0.676762 0.736202i $$-0.736617\pi$$
0.975951 + 0.217992i $$0.0699506\pi$$
$$692$$ 0 0
$$693$$ −29.5344 + 51.1552i −1.12192 + 1.94322i
$$694$$ 0 0
$$695$$ −3.27051 5.66469i −0.124058 0.214874i
$$696$$ 0 0
$$697$$ −28.8435 49.9583i −1.09252 1.89231i
$$698$$ 0 0
$$699$$ 47.2148 1.78583
$$700$$ 0 0
$$701$$ 7.25329 + 12.5631i 0.273953 + 0.474500i 0.969870 0.243621i $$-0.0783354\pi$$
−0.695917 + 0.718122i $$0.745002\pi$$
$$702$$ 0 0
$$703$$ 3.00000 + 5.19615i 0.113147 + 0.195977i
$$704$$ 0 0
$$705$$ 1.85410 + 3.21140i 0.0698295 + 0.120948i
$$706$$ 0 0
$$707$$ −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 $$0.317491\pi$$
$$710$$ 0 0
$$711$$ −2.66312 + 4.61266i −0.0998748 + 0.172988i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 6.18034 0.231132
$$716$$ 0 0
$$717$$ −10.8541 18.7999i −0.405354 0.702093i
$$718$$ 0 0
$$719$$ −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
$$722$$ 0 0
$$723$$ 11.1803 0.415801
$$724$$ 0 0
$$725$$ 5.20820 9.02087i 0.193428 0.335027i
$$726$$ 0 0
$$727$$ 17.9787 0.666794 0.333397 0.942787i $$-0.391805\pi$$
0.333397 + 0.942787i $$0.391805\pi$$
$$728$$ 0 0
$$729$$ −39.5623 −1.46527
$$730$$ 0 0
$$731$$ −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 $$0.350275\pi$$
$$734$$ 0 0
$$735$$ 35.4164 1.30635
$$736$$ 0 0
$$737$$ −6.97214 + 12.0761i −0.256822 + 0.444829i
$$738$$ 0 0
$$739$$ −49.5410 −1.82240 −0.911198 0.411969i $$-0.864841\pi$$
−0.911198 + 0.411969i $$0.864841\pi$$
$$740$$ 0 0
$$741$$ −2.23607 + 3.87298i −0.0821440 + 0.142278i
$$742$$ 0 0
$$743$$ 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
$$746$$ 0 0
$$747$$ −61.7984 −2.26108
$$748$$ 0 0
$$749$$ 15.9443 + 27.6163i 0.582591 + 1.00908i
$$750$$ 0 0
$$751$$ −18.9894 + 32.8905i −0.692931 + 1.20019i 0.277942 + 0.960598i $$0.410348\pi$$
−0.970873 + 0.239595i $$0.922985\pi$$
$$752$$ 0 0
$$753$$ 76.3951 2.78399
$$754$$ 0 0
$$755$$ −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 $$0.642992\pi$$
$$758$$ 0 0
$$759$$ 20.7533 + 35.9458i 0.753297 + 1.30475i
$$760$$ 0 0
$$761$$ −0.545085 0.944115i −0.0197593 0.0342241i 0.855977 0.517014i $$-0.172957\pi$$
−0.875736 + 0.482790i $$0.839623\pi$$
$$762$$ 0 0
$$763$$ −58.6869 −2.12461
$$764$$ 0 0
$$765$$ −14.5066 25.1261i −0.524486 0.908437i
$$766$$ 0 0
$$767$$ 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 $$0.283412\pi$$
$$770$$ 0 0
$$771$$ −4.50000 + 7.79423i −0.162064 + 0.280702i
$$772$$ 0 0
$$773$$ 15.5967 0.560976 0.280488 0.959858i $$-0.409504\pi$$
0.280488 + 0.959858i $$0.409504\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 26.9164 46.6206i 0.965621 1.67250i
$$778$$ 0 0
$$779$$ −5.85410 + 10.1396i −0.209745 + 0.363289i
$$780$$ 0 0
$$781$$ −19.5344 33.8346i −0.698997 1.21070i
$$782$$ 0 0
$$783$$ −3.35410 5.80948i −0.119866 0.207614i
$$784$$ 0 0
$$785$$ −6.36068 −0.227022
$$786$$ 0 0
$$787$$ 5.22542 + 9.05070i 0.186266 + 0.322623i 0.944002 0.329938i $$-0.107028\pi$$
−0.757736 + 0.652561i $$0.773695\pi$$
$$788$$ 0 0
$$789$$ 36.0066 + 62.3652i 1.28187 + 2.22026i
$$790$$ 0 0
$$791$$ 33.0795 + 57.2954i 1.17617 + 2.03719i
$$792$$ 0 0
$$793$$ −1.97214 + 3.41584i −0.0700326 + 0.121300i
$$794$$ 0 0
$$795$$ −4.47214 −0.158610
$$796$$ 0 0
$$797$$ 4.11803 7.13264i 0.145868 0.252651i −0.783828 0.620978i $$-0.786736\pi$$
0.929697 + 0.368326i $$0.120069\pi$$
$$798$$ 0 0
$$799$$ 3.48936 + 6.04374i 0.123445 + 0.213812i
$$800$$ 0 0
$$801$$ −7.14590 −0.252488
$$802$$ 0 0
$$803$$ −3.35410 5.80948i −0.118364 0.205012i
$$804$$ 0 0
$$805$$ 11.4721 19.8703i 0.404340 0.700337i
$$806$$ 0 0