# Properties

 Label 1960.2.q.p.361.2 Level $1960$ Weight $2$ Character 1960.361 Analytic conductor $15.651$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1960 = 2^{3} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1960.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.6506787962$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.2 Root $$0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1960.361 Dual form 1960.2.q.p.961.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$$ $$q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +(0.500000 - 0.866025i) q^{11} +2.41421 q^{13} +0.414214 q^{15} +(0.207107 - 0.358719i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(1.12132 + 1.94218i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.41421 q^{27} +1.00000 q^{29} +(-0.878680 + 1.52192i) q^{31} +(-0.207107 - 0.358719i) q^{33} +(3.94975 + 6.84116i) q^{37} +(0.500000 - 0.866025i) q^{39} +7.41421 q^{41} -0.343146 q^{43} +(-1.41421 + 2.44949i) q^{45} +(-5.20711 - 9.01897i) q^{47} +(-0.0857864 - 0.148586i) q^{51} +(-4.70711 + 8.15295i) q^{53} +1.00000 q^{55} -0.828427 q^{57} +(-5.12132 + 8.87039i) q^{59} +(0.585786 + 1.01461i) q^{61} +(1.20711 + 2.09077i) q^{65} +(-0.707107 + 1.22474i) q^{67} +0.928932 q^{69} +14.4853 q^{71} +(2.58579 - 4.47871i) q^{73} +(0.207107 + 0.358719i) q^{75} +(7.32843 + 12.6932i) q^{79} +(-3.74264 + 6.48244i) q^{81} +11.3137 q^{83} +0.414214 q^{85} +(0.207107 - 0.358719i) q^{87} +(0.828427 + 1.43488i) q^{89} +(0.363961 + 0.630399i) q^{93} +(1.00000 - 1.73205i) q^{95} -0.0710678 q^{97} +2.82843 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{3} + 2q^{5} + O(q^{10})$$ $$4q - 2q^{3} + 2q^{5} + 2q^{11} + 4q^{13} - 4q^{15} - 2q^{17} - 4q^{19} - 4q^{23} - 2q^{25} + 4q^{27} + 4q^{29} - 12q^{31} + 2q^{33} - 4q^{37} + 2q^{39} + 24q^{41} - 24q^{43} - 18q^{47} - 6q^{51} - 16q^{53} + 4q^{55} + 8q^{57} - 12q^{59} + 8q^{61} + 2q^{65} + 32q^{69} + 24q^{71} + 16q^{73} - 2q^{75} + 18q^{79} + 2q^{81} - 4q^{85} - 2q^{87} - 8q^{89} - 24q^{93} + 4q^{95} + 28q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$$.

 $$n$$ $$981$$ $$1081$$ $$1177$$ $$1471$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.207107 0.358719i 0.119573 0.207107i −0.800025 0.599966i $$-0.795181\pi$$
0.919599 + 0.392859i $$0.128514\pi$$
$$4$$ 0 0
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.41421 + 2.44949i 0.471405 + 0.816497i
$$10$$ 0 0
$$11$$ 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i $$-0.785163\pi$$
0.931505 + 0.363727i $$0.118496\pi$$
$$12$$ 0 0
$$13$$ 2.41421 0.669582 0.334791 0.942292i $$-0.391334\pi$$
0.334791 + 0.942292i $$0.391334\pi$$
$$14$$ 0 0
$$15$$ 0.414214 0.106949
$$16$$ 0 0
$$17$$ 0.207107 0.358719i 0.0502308 0.0870023i −0.839817 0.542870i $$-0.817338\pi$$
0.890048 + 0.455868i $$0.150671\pi$$
$$18$$ 0 0
$$19$$ −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i $$-0.240348\pi$$
−0.957635 + 0.287984i $$0.907015\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 1.12132 + 1.94218i 0.233811 + 0.404973i 0.958927 0.283654i $$-0.0915468\pi$$
−0.725115 + 0.688628i $$0.758213\pi$$
$$24$$ 0 0
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 0 0
$$27$$ 2.41421 0.464616
$$28$$ 0 0
$$29$$ 1.00000 0.185695 0.0928477 0.995680i $$-0.470403\pi$$
0.0928477 + 0.995680i $$0.470403\pi$$
$$30$$ 0 0
$$31$$ −0.878680 + 1.52192i −0.157816 + 0.273345i −0.934081 0.357062i $$-0.883778\pi$$
0.776265 + 0.630407i $$0.217112\pi$$
$$32$$ 0 0
$$33$$ −0.207107 0.358719i −0.0360527 0.0624450i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 3.94975 + 6.84116i 0.649334 + 1.12468i 0.983282 + 0.182089i $$0.0582858\pi$$
−0.333948 + 0.942592i $$0.608381\pi$$
$$38$$ 0 0
$$39$$ 0.500000 0.866025i 0.0800641 0.138675i
$$40$$ 0 0
$$41$$ 7.41421 1.15791 0.578953 0.815361i $$-0.303462\pi$$
0.578953 + 0.815361i $$0.303462\pi$$
$$42$$ 0 0
$$43$$ −0.343146 −0.0523292 −0.0261646 0.999658i $$-0.508329\pi$$
−0.0261646 + 0.999658i $$0.508329\pi$$
$$44$$ 0 0
$$45$$ −1.41421 + 2.44949i −0.210819 + 0.365148i
$$46$$ 0 0
$$47$$ −5.20711 9.01897i −0.759535 1.31555i −0.943088 0.332543i $$-0.892093\pi$$
0.183554 0.983010i $$-0.441240\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −0.0857864 0.148586i −0.0120125 0.0208063i
$$52$$ 0 0
$$53$$ −4.70711 + 8.15295i −0.646571 + 1.11989i 0.337365 + 0.941374i $$0.390464\pi$$
−0.983936 + 0.178520i $$0.942869\pi$$
$$54$$ 0 0
$$55$$ 1.00000 0.134840
$$56$$ 0 0
$$57$$ −0.828427 −0.109728
$$58$$ 0 0
$$59$$ −5.12132 + 8.87039i −0.666739 + 1.15483i 0.312072 + 0.950059i $$0.398977\pi$$
−0.978811 + 0.204767i $$0.934356\pi$$
$$60$$ 0 0
$$61$$ 0.585786 + 1.01461i 0.0750023 + 0.129908i 0.901087 0.433638i $$-0.142770\pi$$
−0.826085 + 0.563546i $$0.809437\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 1.20711 + 2.09077i 0.149723 + 0.259328i
$$66$$ 0 0
$$67$$ −0.707107 + 1.22474i −0.0863868 + 0.149626i −0.905981 0.423318i $$-0.860865\pi$$
0.819594 + 0.572944i $$0.194199\pi$$
$$68$$ 0 0
$$69$$ 0.928932 0.111830
$$70$$ 0 0
$$71$$ 14.4853 1.71909 0.859543 0.511063i $$-0.170748\pi$$
0.859543 + 0.511063i $$0.170748\pi$$
$$72$$ 0 0
$$73$$ 2.58579 4.47871i 0.302643 0.524194i −0.674090 0.738649i $$-0.735464\pi$$
0.976734 + 0.214455i $$0.0687975\pi$$
$$74$$ 0 0
$$75$$ 0.207107 + 0.358719i 0.0239146 + 0.0414214i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 7.32843 + 12.6932i 0.824512 + 1.42810i 0.902291 + 0.431127i $$0.141884\pi$$
−0.0777789 + 0.996971i $$0.524783\pi$$
$$80$$ 0 0
$$81$$ −3.74264 + 6.48244i −0.415849 + 0.720272i
$$82$$ 0 0
$$83$$ 11.3137 1.24184 0.620920 0.783874i $$-0.286759\pi$$
0.620920 + 0.783874i $$0.286759\pi$$
$$84$$ 0 0
$$85$$ 0.414214 0.0449278
$$86$$ 0 0
$$87$$ 0.207107 0.358719i 0.0222042 0.0384588i
$$88$$ 0 0
$$89$$ 0.828427 + 1.43488i 0.0878131 + 0.152097i 0.906586 0.422020i $$-0.138679\pi$$
−0.818773 + 0.574117i $$0.805346\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0.363961 + 0.630399i 0.0377410 + 0.0653693i
$$94$$ 0 0
$$95$$ 1.00000 1.73205i 0.102598 0.177705i
$$96$$ 0 0
$$97$$ −0.0710678 −0.00721584 −0.00360792 0.999993i $$-0.501148\pi$$
−0.00360792 + 0.999993i $$0.501148\pi$$
$$98$$ 0 0
$$99$$ 2.82843 0.284268
$$100$$ 0 0
$$101$$ 3.24264 5.61642i 0.322655 0.558855i −0.658380 0.752686i $$-0.728758\pi$$
0.981035 + 0.193831i $$0.0620914\pi$$
$$102$$ 0 0
$$103$$ −7.62132 13.2005i −0.750951 1.30069i −0.947362 0.320164i $$-0.896262\pi$$
0.196411 0.980522i $$-0.437071\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.24264 2.15232i −0.120131 0.208072i 0.799688 0.600415i $$-0.204998\pi$$
−0.919819 + 0.392343i $$0.871665\pi$$
$$108$$ 0 0
$$109$$ −2.15685 + 3.73578i −0.206589 + 0.357823i −0.950638 0.310302i $$-0.899570\pi$$
0.744049 + 0.668125i $$0.232903\pi$$
$$110$$ 0 0
$$111$$ 3.27208 0.310572
$$112$$ 0 0
$$113$$ 5.07107 0.477046 0.238523 0.971137i $$-0.423337\pi$$
0.238523 + 0.971137i $$0.423337\pi$$
$$114$$ 0 0
$$115$$ −1.12132 + 1.94218i −0.104564 + 0.181110i
$$116$$ 0 0
$$117$$ 3.41421 + 5.91359i 0.315644 + 0.546712i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 + 8.66025i 0.454545 + 0.787296i
$$122$$ 0 0
$$123$$ 1.53553 2.65962i 0.138454 0.239810i
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 12.2426 1.08636 0.543179 0.839617i $$-0.317220\pi$$
0.543179 + 0.839617i $$0.317220\pi$$
$$128$$ 0 0
$$129$$ −0.0710678 + 0.123093i −0.00625717 + 0.0108377i
$$130$$ 0 0
$$131$$ −5.87868 10.1822i −0.513623 0.889620i −0.999875 0.0158021i $$-0.994970\pi$$
0.486253 0.873818i $$-0.338364\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 1.20711 + 2.09077i 0.103891 + 0.179945i
$$136$$ 0 0
$$137$$ −1.65685 + 2.86976i −0.141555 + 0.245180i −0.928082 0.372375i $$-0.878543\pi$$
0.786528 + 0.617555i $$0.211877\pi$$
$$138$$ 0 0
$$139$$ −1.41421 −0.119952 −0.0599760 0.998200i $$-0.519102\pi$$
−0.0599760 + 0.998200i $$0.519102\pi$$
$$140$$ 0 0
$$141$$ −4.31371 −0.363280
$$142$$ 0 0
$$143$$ 1.20711 2.09077i 0.100943 0.174839i
$$144$$ 0 0
$$145$$ 0.500000 + 0.866025i 0.0415227 + 0.0719195i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 7.41421 + 12.8418i 0.607396 + 1.05204i 0.991668 + 0.128821i $$0.0411192\pi$$
−0.384272 + 0.923220i $$0.625547\pi$$
$$150$$ 0 0
$$151$$ −2.32843 + 4.03295i −0.189485 + 0.328197i −0.945079 0.326843i $$-0.894015\pi$$
0.755594 + 0.655040i $$0.227348\pi$$
$$152$$ 0 0
$$153$$ 1.17157 0.0947161
$$154$$ 0 0
$$155$$ −1.75736 −0.141154
$$156$$ 0 0
$$157$$ 3.24264 5.61642i 0.258791 0.448239i −0.707127 0.707086i $$-0.750009\pi$$
0.965918 + 0.258847i $$0.0833426\pi$$
$$158$$ 0 0
$$159$$ 1.94975 + 3.37706i 0.154625 + 0.267818i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −8.53553 14.7840i −0.668555 1.15797i −0.978308 0.207154i $$-0.933580\pi$$
0.309754 0.950817i $$-0.399753\pi$$
$$164$$ 0 0
$$165$$ 0.207107 0.358719i 0.0161232 0.0279263i
$$166$$ 0 0
$$167$$ 10.4142 0.805876 0.402938 0.915227i $$-0.367989\pi$$
0.402938 + 0.915227i $$0.367989\pi$$
$$168$$ 0 0
$$169$$ −7.17157 −0.551659
$$170$$ 0 0
$$171$$ 2.82843 4.89898i 0.216295 0.374634i
$$172$$ 0 0
$$173$$ −5.86396 10.1567i −0.445829 0.772198i 0.552281 0.833658i $$-0.313758\pi$$
−0.998110 + 0.0614602i $$0.980424\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 2.12132 + 3.67423i 0.159448 + 0.276172i
$$178$$ 0 0
$$179$$ 12.0711 20.9077i 0.902234 1.56272i 0.0776462 0.996981i $$-0.475260\pi$$
0.824588 0.565734i $$-0.191407\pi$$
$$180$$ 0 0
$$181$$ 5.55635 0.413000 0.206500 0.978447i $$-0.433793\pi$$
0.206500 + 0.978447i $$0.433793\pi$$
$$182$$ 0 0
$$183$$ 0.485281 0.0358730
$$184$$ 0 0
$$185$$ −3.94975 + 6.84116i −0.290391 + 0.502972i
$$186$$ 0 0
$$187$$ −0.207107 0.358719i −0.0151451 0.0262322i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −4.08579 7.07679i −0.295637 0.512059i 0.679496 0.733679i $$-0.262199\pi$$
−0.975133 + 0.221621i $$0.928865\pi$$
$$192$$ 0 0
$$193$$ −11.6569 + 20.1903i −0.839079 + 1.45333i 0.0515871 + 0.998668i $$0.483572\pi$$
−0.890666 + 0.454658i $$0.849761\pi$$
$$194$$ 0 0
$$195$$ 1.00000 0.0716115
$$196$$ 0 0
$$197$$ −3.75736 −0.267701 −0.133850 0.991002i $$-0.542734\pi$$
−0.133850 + 0.991002i $$0.542734\pi$$
$$198$$ 0 0
$$199$$ −12.1924 + 21.1178i −0.864295 + 1.49700i 0.00344954 + 0.999994i $$0.498902\pi$$
−0.867745 + 0.497010i $$0.834431\pi$$
$$200$$ 0 0
$$201$$ 0.292893 + 0.507306i 0.0206591 + 0.0357826i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 3.70711 + 6.42090i 0.258916 + 0.448455i
$$206$$ 0 0
$$207$$ −3.17157 + 5.49333i −0.220440 + 0.381813i
$$208$$ 0 0
$$209$$ −2.00000 −0.138343
$$210$$ 0 0
$$211$$ −11.1421 −0.767056 −0.383528 0.923529i $$-0.625291\pi$$
−0.383528 + 0.923529i $$0.625291\pi$$
$$212$$ 0 0
$$213$$ 3.00000 5.19615i 0.205557 0.356034i
$$214$$ 0 0
$$215$$ −0.171573 0.297173i −0.0117012 0.0202670i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −1.07107 1.85514i −0.0723761 0.125359i
$$220$$ 0 0
$$221$$ 0.500000 0.866025i 0.0336336 0.0582552i
$$222$$ 0 0
$$223$$ 19.3848 1.29810 0.649050 0.760745i $$-0.275166\pi$$
0.649050 + 0.760745i $$0.275166\pi$$
$$224$$ 0 0
$$225$$ −2.82843 −0.188562
$$226$$ 0 0
$$227$$ −2.20711 + 3.82282i −0.146491 + 0.253730i −0.929928 0.367741i $$-0.880131\pi$$
0.783437 + 0.621471i $$0.213465\pi$$
$$228$$ 0 0
$$229$$ 11.9497 + 20.6976i 0.789662 + 1.36773i 0.926174 + 0.377096i $$0.123077\pi$$
−0.136513 + 0.990638i $$0.543589\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −10.2426 17.7408i −0.671018 1.16224i −0.977616 0.210398i $$-0.932524\pi$$
0.306598 0.951839i $$-0.400809\pi$$
$$234$$ 0 0
$$235$$ 5.20711 9.01897i 0.339674 0.588333i
$$236$$ 0 0
$$237$$ 6.07107 0.394358
$$238$$ 0 0
$$239$$ 6.65685 0.430596 0.215298 0.976548i $$-0.430928\pi$$
0.215298 + 0.976548i $$0.430928\pi$$
$$240$$ 0 0
$$241$$ 13.1924 22.8499i 0.849796 1.47189i −0.0315933 0.999501i $$-0.510058\pi$$
0.881390 0.472390i $$-0.156609\pi$$
$$242$$ 0 0
$$243$$ 5.17157 + 8.95743i 0.331757 + 0.574619i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −2.41421 4.18154i −0.153613 0.266065i
$$248$$ 0 0
$$249$$ 2.34315 4.05845i 0.148491 0.257194i
$$250$$ 0 0
$$251$$ −23.5563 −1.48686 −0.743432 0.668812i $$-0.766803\pi$$
−0.743432 + 0.668812i $$0.766803\pi$$
$$252$$ 0 0
$$253$$ 2.24264 0.140994
$$254$$ 0 0
$$255$$ 0.0857864 0.148586i 0.00537216 0.00930485i
$$256$$ 0 0
$$257$$ 3.24264 + 5.61642i 0.202270 + 0.350343i 0.949260 0.314494i $$-0.101835\pi$$
−0.746989 + 0.664836i $$0.768501\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 1.41421 + 2.44949i 0.0875376 + 0.151620i
$$262$$ 0 0
$$263$$ 7.48528 12.9649i 0.461562 0.799449i −0.537477 0.843279i $$-0.680622\pi$$
0.999039 + 0.0438293i $$0.0139558\pi$$
$$264$$ 0 0
$$265$$ −9.41421 −0.578311
$$266$$ 0 0
$$267$$ 0.686292 0.0420004
$$268$$ 0 0
$$269$$ −10.7071 + 18.5453i −0.652824 + 1.13072i 0.329611 + 0.944117i $$0.393082\pi$$
−0.982435 + 0.186607i $$0.940251\pi$$
$$270$$ 0 0
$$271$$ −6.82843 11.8272i −0.414797 0.718450i 0.580610 0.814182i $$-0.302814\pi$$
−0.995407 + 0.0957318i $$0.969481\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0.500000 + 0.866025i 0.0301511 + 0.0522233i
$$276$$ 0 0
$$277$$ −0.535534 + 0.927572i −0.0321771 + 0.0557324i −0.881666 0.471875i $$-0.843577\pi$$
0.849488 + 0.527607i $$0.176911\pi$$
$$278$$ 0 0
$$279$$ −4.97056 −0.297580
$$280$$ 0 0
$$281$$ −4.31371 −0.257334 −0.128667 0.991688i $$-0.541070\pi$$
−0.128667 + 0.991688i $$0.541070\pi$$
$$282$$ 0 0
$$283$$ 11.5208 19.9546i 0.684841 1.18618i −0.288645 0.957436i $$-0.593205\pi$$
0.973487 0.228744i $$-0.0734619\pi$$
$$284$$ 0 0
$$285$$ −0.414214 0.717439i −0.0245359 0.0424974i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 8.41421 + 14.5738i 0.494954 + 0.857285i
$$290$$ 0 0
$$291$$ −0.0147186 + 0.0254934i −0.000862821 + 0.00149445i
$$292$$ 0 0
$$293$$ −15.5858 −0.910531 −0.455266 0.890356i $$-0.650456\pi$$
−0.455266 + 0.890356i $$0.650456\pi$$
$$294$$ 0 0
$$295$$ −10.2426 −0.596350
$$296$$ 0 0
$$297$$ 1.20711 2.09077i 0.0700434 0.121319i
$$298$$ 0 0
$$299$$ 2.70711 + 4.68885i 0.156556 + 0.271163i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −1.34315 2.32640i −0.0771617 0.133648i
$$304$$ 0 0
$$305$$ −0.585786 + 1.01461i −0.0335420 + 0.0580965i
$$306$$ 0 0
$$307$$ −26.0711 −1.48795 −0.743977 0.668205i $$-0.767063\pi$$
−0.743977 + 0.668205i $$0.767063\pi$$
$$308$$ 0 0
$$309$$ −6.31371 −0.359174
$$310$$ 0 0
$$311$$ −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i $$-0.924837\pi$$
0.688726 + 0.725022i $$0.258170\pi$$
$$312$$ 0 0
$$313$$ −0.863961 1.49642i −0.0488340 0.0845829i 0.840575 0.541695i $$-0.182217\pi$$
−0.889409 + 0.457112i $$0.848884\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −11.8284 20.4874i −0.664351 1.15069i −0.979461 0.201634i $$-0.935375\pi$$
0.315110 0.949055i $$-0.397958\pi$$
$$318$$ 0 0
$$319$$ 0.500000 0.866025i 0.0279946 0.0484881i
$$320$$ 0 0
$$321$$ −1.02944 −0.0574576
$$322$$ 0 0
$$323$$ −0.828427 −0.0460949
$$324$$ 0 0
$$325$$ −1.20711 + 2.09077i −0.0669582 + 0.115975i
$$326$$ 0 0
$$327$$ 0.893398 + 1.54741i 0.0494050 + 0.0855720i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −13.2426 22.9369i −0.727881 1.26073i −0.957777 0.287512i $$-0.907172\pi$$
0.229896 0.973215i $$-0.426162\pi$$
$$332$$ 0 0
$$333$$ −11.1716 + 19.3497i −0.612198 + 1.06036i
$$334$$ 0 0
$$335$$ −1.41421 −0.0772667
$$336$$ 0 0
$$337$$ 1.07107 0.0583448 0.0291724 0.999574i $$-0.490713\pi$$
0.0291724 + 0.999574i $$0.490713\pi$$
$$338$$ 0 0
$$339$$ 1.05025 1.81909i 0.0570419 0.0987994i
$$340$$ 0 0
$$341$$ 0.878680 + 1.52192i 0.0475832 + 0.0824165i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0.464466 + 0.804479i 0.0250060 + 0.0433117i
$$346$$ 0 0
$$347$$ 12.4350 21.5381i 0.667547 1.15623i −0.311041 0.950397i $$-0.600678\pi$$
0.978588 0.205829i $$-0.0659892\pi$$
$$348$$ 0 0
$$349$$ −29.3137 −1.56913 −0.784563 0.620049i $$-0.787113\pi$$
−0.784563 + 0.620049i $$0.787113\pi$$
$$350$$ 0 0
$$351$$ 5.82843 0.311098
$$352$$ 0 0
$$353$$ 6.10660 10.5769i 0.325022 0.562954i −0.656495 0.754330i $$-0.727962\pi$$
0.981517 + 0.191376i $$0.0612951\pi$$
$$354$$ 0 0
$$355$$ 7.24264 + 12.5446i 0.384399 + 0.665799i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 9.17157 + 15.8856i 0.484057 + 0.838411i 0.999832 0.0183125i $$-0.00582936\pi$$
−0.515775 + 0.856724i $$0.672496\pi$$
$$360$$ 0 0
$$361$$ 7.50000 12.9904i 0.394737 0.683704i
$$362$$ 0 0
$$363$$ 4.14214 0.217406
$$364$$ 0 0
$$365$$ 5.17157 0.270692
$$366$$ 0 0
$$367$$ −1.37868 + 2.38794i −0.0719665 + 0.124650i −0.899763 0.436379i $$-0.856261\pi$$
0.827797 + 0.561028i $$0.189594\pi$$
$$368$$ 0 0
$$369$$ 10.4853 + 18.1610i 0.545842 + 0.945426i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −8.58579 14.8710i −0.444555 0.769992i 0.553466 0.832872i $$-0.313305\pi$$
−0.998021 + 0.0628797i $$0.979972\pi$$
$$374$$ 0 0
$$375$$ −0.207107 + 0.358719i −0.0106949 + 0.0185242i
$$376$$ 0 0
$$377$$ 2.41421 0.124338
$$378$$ 0 0
$$379$$ −16.6274 −0.854093 −0.427047 0.904230i $$-0.640446\pi$$
−0.427047 + 0.904230i $$0.640446\pi$$
$$380$$ 0 0
$$381$$ 2.53553 4.39167i 0.129899 0.224992i
$$382$$ 0 0
$$383$$ −8.58579 14.8710i −0.438713 0.759874i 0.558877 0.829250i $$-0.311232\pi$$
−0.997591 + 0.0693768i $$0.977899\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −0.485281 0.840532i −0.0246682 0.0427266i
$$388$$ 0 0
$$389$$ 14.3995 24.9407i 0.730083 1.26454i −0.226764 0.973950i $$-0.572815\pi$$
0.956847 0.290592i $$-0.0938521\pi$$
$$390$$ 0 0
$$391$$ 0.928932 0.0469781
$$392$$ 0 0
$$393$$ −4.87006 −0.245662
$$394$$ 0 0
$$395$$ −7.32843 + 12.6932i −0.368733 + 0.638665i
$$396$$ 0 0
$$397$$ 4.20711 + 7.28692i 0.211149 + 0.365720i 0.952074 0.305867i $$-0.0989463\pi$$
−0.740926 + 0.671587i $$0.765613\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −13.2279 22.9114i −0.660571 1.14414i −0.980466 0.196689i $$-0.936981\pi$$
0.319895 0.947453i $$-0.396352\pi$$
$$402$$ 0 0
$$403$$ −2.12132 + 3.67423i −0.105670 + 0.183027i
$$404$$ 0 0
$$405$$ −7.48528 −0.371947
$$406$$ 0 0
$$407$$ 7.89949 0.391563
$$408$$ 0 0
$$409$$ −14.5563 + 25.2123i −0.719765 + 1.24667i 0.241328 + 0.970444i $$0.422417\pi$$
−0.961093 + 0.276226i $$0.910916\pi$$
$$410$$ 0 0
$$411$$ 0.686292 + 1.18869i 0.0338523 + 0.0586338i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 5.65685 + 9.79796i 0.277684 + 0.480963i
$$416$$ 0 0
$$417$$ −0.292893 + 0.507306i −0.0143430 + 0.0248429i
$$418$$ 0 0
$$419$$ −31.4142 −1.53468 −0.767342 0.641238i $$-0.778421\pi$$
−0.767342 + 0.641238i $$0.778421\pi$$
$$420$$ 0 0
$$421$$ −3.68629 −0.179659 −0.0898294 0.995957i $$-0.528632\pi$$
−0.0898294 + 0.995957i $$0.528632\pi$$
$$422$$ 0 0
$$423$$ 14.7279 25.5095i 0.716096 1.24031i
$$424$$ 0 0
$$425$$ 0.207107 + 0.358719i 0.0100462 + 0.0174005i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −0.500000 0.866025i −0.0241402 0.0418121i
$$430$$ 0 0
$$431$$ −5.67157 + 9.82345i −0.273190 + 0.473179i −0.969677 0.244391i $$-0.921412\pi$$
0.696487 + 0.717570i $$0.254745\pi$$
$$432$$ 0 0
$$433$$ −26.9706 −1.29612 −0.648061 0.761588i $$-0.724420\pi$$
−0.648061 + 0.761588i $$0.724420\pi$$
$$434$$ 0 0
$$435$$ 0.414214 0.0198600
$$436$$ 0 0
$$437$$ 2.24264 3.88437i 0.107280 0.185815i
$$438$$ 0 0
$$439$$ 6.12132 + 10.6024i 0.292155 + 0.506027i 0.974319 0.225172i $$-0.0722945\pi$$
−0.682164 + 0.731199i $$0.738961\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −19.3848 33.5754i −0.920999 1.59522i −0.797873 0.602825i $$-0.794042\pi$$
−0.123125 0.992391i $$-0.539292\pi$$
$$444$$ 0 0
$$445$$ −0.828427 + 1.43488i −0.0392712 + 0.0680197i
$$446$$ 0 0
$$447$$ 6.14214 0.290513
$$448$$ 0 0
$$449$$ −10.5147 −0.496220 −0.248110 0.968732i $$-0.579809\pi$$
−0.248110 + 0.968732i $$0.579809\pi$$
$$450$$ 0 0
$$451$$ 3.70711 6.42090i 0.174561 0.302348i
$$452$$ 0 0
$$453$$ 0.964466 + 1.67050i 0.0453146 + 0.0784871i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −9.53553 16.5160i −0.446053 0.772587i 0.552071 0.833797i $$-0.313838\pi$$
−0.998125 + 0.0612095i $$0.980504\pi$$
$$458$$ 0 0
$$459$$ 0.500000 0.866025i 0.0233380 0.0404226i
$$460$$ 0 0
$$461$$ 24.2843 1.13103 0.565516 0.824738i $$-0.308677\pi$$
0.565516 + 0.824738i $$0.308677\pi$$
$$462$$ 0 0
$$463$$ −25.4558 −1.18303 −0.591517 0.806293i $$-0.701471\pi$$
−0.591517 + 0.806293i $$0.701471\pi$$
$$464$$ 0 0
$$465$$ −0.363961 + 0.630399i −0.0168783 + 0.0292341i
$$466$$ 0 0
$$467$$ −2.79289 4.83743i −0.129240 0.223850i 0.794143 0.607732i $$-0.207920\pi$$
−0.923382 + 0.383882i $$0.874587\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −1.34315 2.32640i −0.0618889 0.107195i
$$472$$ 0 0
$$473$$ −0.171573 + 0.297173i −0.00788893 + 0.0136640i
$$474$$ 0 0
$$475$$ 2.00000 0.0917663
$$476$$ 0 0
$$477$$ −26.6274 −1.21919
$$478$$ 0 0
$$479$$ −12.2635 + 21.2409i −0.560332 + 0.970523i 0.437136 + 0.899396i $$0.355993\pi$$
−0.997467 + 0.0711272i $$0.977340\pi$$
$$480$$ 0 0
$$481$$ 9.53553 + 16.5160i 0.434783 + 0.753066i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −0.0355339 0.0615465i −0.00161351 0.00279468i
$$486$$ 0 0
$$487$$ −13.3640 + 23.1471i −0.605579 + 1.04889i 0.386381 + 0.922339i $$0.373725\pi$$
−0.991960 + 0.126554i $$0.959608\pi$$
$$488$$ 0 0
$$489$$ −7.07107 −0.319765
$$490$$ 0 0
$$491$$ 5.48528 0.247547 0.123774 0.992310i $$-0.460500\pi$$
0.123774 + 0.992310i $$0.460500\pi$$
$$492$$ 0 0
$$493$$ 0.207107 0.358719i 0.00932762 0.0161559i
$$494$$ 0 0
$$495$$ 1.41421 + 2.44949i 0.0635642 + 0.110096i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −6.39949 11.0843i −0.286481 0.496199i 0.686486 0.727143i $$-0.259152\pi$$
−0.972967 + 0.230943i $$0.925819\pi$$
$$500$$ 0 0
$$501$$ 2.15685 3.73578i 0.0963611 0.166902i
$$502$$ 0 0
$$503$$ 31.0416 1.38408 0.692039 0.721860i $$-0.256713\pi$$
0.692039 + 0.721860i $$0.256713\pi$$
$$504$$ 0 0
$$505$$ 6.48528 0.288591
$$506$$ 0 0
$$507$$ −1.48528 + 2.57258i −0.0659637 + 0.114252i
$$508$$ 0 0
$$509$$ −3.87868 6.71807i −0.171919 0.297773i 0.767171 0.641442i $$-0.221664\pi$$
−0.939091 + 0.343669i $$0.888330\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −2.41421 4.18154i −0.106590 0.184620i
$$514$$ 0 0
$$515$$ 7.62132 13.2005i 0.335836 0.581684i
$$516$$ 0 0
$$517$$ −10.4142 −0.458017
$$518$$ 0 0
$$519$$ −4.85786 −0.213237
$$520$$ 0 0
$$521$$ −3.00000 + 5.19615i −0.131432 + 0.227648i −0.924229 0.381839i $$-0.875291\pi$$
0.792797 + 0.609486i $$0.208624\pi$$
$$522$$ 0 0
$$523$$ 16.2426 + 28.1331i 0.710241 + 1.23017i 0.964767 + 0.263108i $$0.0847474\pi$$
−0.254525 + 0.967066i $$0.581919\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0.363961 + 0.630399i 0.0158544 + 0.0274606i
$$528$$ 0 0
$$529$$ 8.98528 15.5630i 0.390664 0.676651i
$$530$$ 0 0
$$531$$ −28.9706 −1.25722
$$532$$ 0 0
$$533$$ 17.8995 0.775313
$$534$$ 0 0
$$535$$ 1.24264 2.15232i 0.0537240 0.0930528i
$$536$$ 0 0
$$537$$ −5.00000 8.66025i −0.215766 0.373718i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −5.15685 8.93193i −0.221710 0.384014i 0.733617 0.679563i $$-0.237831\pi$$
−0.955327 + 0.295549i $$0.904497\pi$$
$$542$$ 0 0
$$543$$ 1.15076 1.99317i 0.0493837 0.0855351i
$$544$$ 0 0
$$545$$ −4.31371 −0.184779
$$546$$ 0 0
$$547$$ −27.1127 −1.15926 −0.579628 0.814881i $$-0.696802\pi$$
−0.579628 + 0.814881i $$0.696802\pi$$
$$548$$ 0 0
$$549$$ −1.65685 + 2.86976i −0.0707128 + 0.122478i
$$550$$ 0 0
$$551$$ −1.00000 1.73205i −0.0426014 0.0737878i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 1.63604 + 2.83370i 0.0694460 + 0.120284i
$$556$$ 0 0
$$557$$ 13.0711 22.6398i 0.553839 0.959277i −0.444154 0.895950i $$-0.646496\pi$$
0.997993 0.0633267i $$-0.0201710\pi$$
$$558$$ 0 0
$$559$$ −0.828427 −0.0350387
$$560$$ 0 0
$$561$$ −0.171573 −0.00724381
$$562$$ 0 0
$$563$$ 19.9706 34.5900i 0.841659 1.45780i −0.0468326 0.998903i $$-0.514913\pi$$
0.888491 0.458893i $$-0.151754\pi$$
$$564$$ 0 0
$$565$$ 2.53553 + 4.39167i 0.106671 + 0.184759i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 2.92893 + 5.07306i 0.122787 + 0.212674i 0.920866 0.389880i $$-0.127483\pi$$
−0.798079 + 0.602553i $$0.794150\pi$$
$$570$$ 0 0
$$571$$ −13.7279 + 23.7775i −0.574496 + 0.995056i 0.421601 + 0.906782i $$0.361468\pi$$
−0.996096 + 0.0882740i $$0.971865\pi$$
$$572$$ 0 0
$$573$$ −3.38478 −0.141401
$$574$$ 0 0
$$575$$ −2.24264 −0.0935246
$$576$$ 0 0
$$577$$ 16.7929 29.0861i 0.699097 1.21087i −0.269683 0.962949i $$-0.586919\pi$$
0.968780 0.247923i $$-0.0797479\pi$$
$$578$$ 0 0
$$579$$ 4.82843 + 8.36308i 0.200663 + 0.347558i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 4.70711 + 8.15295i 0.194948 + 0.337661i
$$584$$ 0 0
$$585$$ −3.41421 + 5.91359i −0.141160 + 0.244497i
$$586$$ 0 0
$$587$$ −42.1421 −1.73939 −0.869696 0.493588i $$-0.835685\pi$$
−0.869696 + 0.493588i $$0.835685\pi$$
$$588$$ 0 0
$$589$$ 3.51472 0.144821
$$590$$ 0 0
$$591$$ −0.778175 + 1.34784i −0.0320098 + 0.0554426i
$$592$$ 0 0
$$593$$ −20.2782 35.1228i −0.832725 1.44232i −0.895869 0.444317i $$-0.853446\pi$$
0.0631447 0.998004i $$-0.479887\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 5.05025 + 8.74729i 0.206693 + 0.358003i
$$598$$ 0 0
$$599$$ 6.84315 11.8527i 0.279603 0.484287i −0.691683 0.722201i $$-0.743130\pi$$
0.971286 + 0.237914i $$0.0764637\pi$$
$$600$$ 0 0
$$601$$ 38.2843 1.56165 0.780824 0.624751i $$-0.214800\pi$$
0.780824 + 0.624751i $$0.214800\pi$$
$$602$$ 0 0
$$603$$ −4.00000 −0.162893
$$604$$ 0 0
$$605$$ −5.00000 + 8.66025i −0.203279 + 0.352089i
$$606$$ 0 0
$$607$$ −2.96447 5.13461i −0.120324 0.208407i 0.799571 0.600571i $$-0.205060\pi$$
−0.919895 + 0.392164i $$0.871727\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −12.5711 21.7737i −0.508571 0.880871i
$$612$$ 0 0
$$613$$ −3.34315 + 5.79050i −0.135028 + 0.233876i −0.925608 0.378483i $$-0.876446\pi$$
0.790580 + 0.612359i $$0.209779\pi$$
$$614$$ 0 0
$$615$$ 3.07107 0.123837
$$616$$ 0 0
$$617$$ −8.58579 −0.345651 −0.172825 0.984952i $$-0.555290\pi$$
−0.172825 + 0.984952i $$0.555290\pi$$
$$618$$ 0 0
$$619$$ 0.464466 0.804479i 0.0186685 0.0323347i −0.856540 0.516080i $$-0.827391\pi$$
0.875209 + 0.483745i $$0.160724\pi$$
$$620$$ 0 0
$$621$$ 2.70711 + 4.68885i 0.108632 + 0.188157i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ 0 0
$$627$$ −0.414214 + 0.717439i −0.0165421 + 0.0286518i
$$628$$ 0 0
$$629$$ 3.27208 0.130466
$$630$$ 0 0
$$631$$ 7.62742 0.303643 0.151821 0.988408i $$-0.451486\pi$$
0.151821 + 0.988408i $$0.451486\pi$$
$$632$$ 0 0
$$633$$ −2.30761 + 3.99690i −0.0917193 + 0.158863i
$$634$$ 0 0
$$635$$ 6.12132 + 10.6024i 0.242917 + 0.420745i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 20.4853 + 35.4815i 0.810385 + 1.40363i
$$640$$ 0 0
$$641$$ 12.1421 21.0308i 0.479586 0.830666i −0.520140 0.854081i $$-0.674120\pi$$
0.999726 + 0.0234143i $$0.00745369\pi$$
$$642$$ 0 0
$$643$$ 12.2132 0.481642 0.240821 0.970570i $$-0.422583\pi$$
0.240821 + 0.970570i $$0.422583\pi$$
$$644$$ 0 0
$$645$$ −0.142136 −0.00559658
$$646$$ 0 0
$$647$$ 5.07107 8.78335i 0.199364 0.345309i −0.748958 0.662617i $$-0.769446\pi$$
0.948322 + 0.317308i $$0.102779\pi$$
$$648$$ 0 0
$$649$$ 5.12132 + 8.87039i 0.201029 + 0.348193i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −17.1421 29.6910i −0.670824 1.16190i −0.977671 0.210142i $$-0.932607\pi$$
0.306847 0.951759i $$-0.400726\pi$$
$$654$$ 0 0
$$655$$ 5.87868 10.1822i 0.229699 0.397850i
$$656$$ 0 0
$$657$$ 14.6274 0.570670
$$658$$ 0 0
$$659$$ 0.514719 0.0200506 0.0100253 0.999950i $$-0.496809\pi$$
0.0100253 + 0.999950i $$0.496809\pi$$
$$660$$ 0 0
$$661$$ 12.5858 21.7992i 0.489530 0.847891i −0.510397 0.859939i $$-0.670502\pi$$
0.999927 + 0.0120474i $$0.00383490\pi$$
$$662$$ 0 0
$$663$$ −0.207107 0.358719i −0.00804336 0.0139315i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.12132 + 1.94218i 0.0434177 + 0.0752017i
$$668$$ 0 0
$$669$$ 4.01472 6.95370i 0.155218 0.268845i
$$670$$ 0 0
$$671$$ 1.17157 0.0452281
$$672$$ 0 0
$$673$$ 45.1716 1.74124 0.870618 0.491959i $$-0.163719\pi$$
0.870618 + 0.491959i $$0.163719\pi$$
$$674$$ 0 0
$$675$$ −1.20711 + 2.09077i −0.0464616 + 0.0804738i
$$676$$ 0 0
$$677$$ −10.9645 18.9910i −0.421399 0.729884i 0.574678 0.818380i $$-0.305127\pi$$
−0.996077 + 0.0884958i $$0.971794\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0.914214 + 1.58346i 0.0350327 + 0.0606785i
$$682$$ 0 0
$$683$$ 9.41421 16.3059i 0.360225 0.623928i −0.627773 0.778397i $$-0.716033\pi$$
0.987998 + 0.154469i $$0.0493666\pi$$
$$684$$ 0 0
$$685$$ −3.31371 −0.126610
$$686$$ 0 0
$$687$$ 9.89949 0.377689
$$688$$ 0 0
$$689$$ −11.3640 + 19.6830i −0.432932 + 0.749861i
$$690$$ 0 0
$$691$$ 9.07107 + 15.7116i 0.345080 + 0.597696i 0.985368 0.170439i $$-0.0545186\pi$$
−0.640289 + 0.768134i $$0.721185\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −0.707107 1.22474i −0.0268221 0.0464572i
$$696$$ 0 0
$$697$$ 1.53553 2.65962i 0.0581625 0.100740i
$$698$$ 0 0
$$699$$ −8.48528 −0.320943
$$700$$ 0 0
$$701$$ −8.85786 −0.334557 −0.167278 0.985910i $$-0.553498\pi$$
−0.167278 + 0.985910i $$0.553498\pi$$
$$702$$ 0 0
$$703$$ 7.89949 13.6823i 0.297935 0.516039i
$$704$$ 0 0
$$705$$ −2.15685 3.73578i −0.0812318 0.140698i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 16.3284 + 28.2817i 0.613227 + 1.06214i 0.990693 + 0.136117i $$0.0434622\pi$$
−0.377466 + 0.926024i $$0.623204\pi$$
$$710$$ 0 0
$$711$$ −20.7279 + 35.9018i −0.777358 + 1.34642i
$$712$$ 0 0
$$713$$ −3.94113 −0.147596
$$714$$ 0 0
$$715$$ 2.41421 0.0902865
$$716$$ 0 0
$$717$$ 1.37868 2.38794i 0.0514877 0.0891794i
$$718$$ 0 0
$$719$$ 4.84924 + 8.39913i 0.180846 + 0.313235i 0.942169 0.335138i $$-0.108783\pi$$
−0.761323 + 0.648373i $$0.775450\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −5.46447 9.46473i −0.203226 0.351997i
$$724$$ 0 0
$$725$$ −0.500000 + 0.866025i −0.0185695 + 0.0321634i
$$726$$ 0 0
$$727$$ 18.6863 0.693036 0.346518 0.938043i $$-0.387364\pi$$
0.346518 + 0.938043i $$0.387364\pi$$
$$728$$ 0 0
$$729$$ −18.1716 −0.673021
$$730$$ 0 0
$$731$$ −0.0710678 + 0.123093i −0.00262854 + 0.00455276i
$$732$$ 0 0
$$733$$ −16.3492 28.3177i −0.603873 1.04594i −0.992228 0.124429i $$-0.960290\pi$$
0.388355 0.921510i $$-0.373043\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0.707107 + 1.22474i 0.0260466 + 0.0451141i
$$738$$ 0 0
$$739$$ −17.3995 + 30.1368i −0.640051 + 1.10860i 0.345370 + 0.938467i $$0.387753\pi$$
−0.985421 + 0.170134i $$0.945580\pi$$
$$740$$ 0 0
$$741$$ −2.00000 −0.0734718
$$742$$ 0 0
$$743$$ 13.8995 0.509923 0.254962 0.966951i $$-0.417937\pi$$
0.254962 + 0.966951i $$0.417937\pi$$
$$744$$ 0 0
$$745$$ −7.41421 + 12.8418i −0.271636 + 0.470487i
$$746$$ 0 0
$$747$$ 16.0000 + 27.7128i 0.585409 + 1.01396i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 9.81371 + 16.9978i 0.358107 + 0.620260i 0.987645 0.156710i $$-0.0500889\pi$$
−0.629537 + 0.776970i $$0.716756\pi$$
$$752$$ 0 0
$$753$$ −4.87868 + 8.45012i −0.177789 + 0.307940i
$$754$$ 0 0
$$755$$ −4.65685 −0.169480
$$756$$ 0 0
$$757$$ 36.7696 1.33641 0.668206 0.743976i $$-0.267062\pi$$
0.668206 + 0.743976i $$0.267062\pi$$
$$758$$ 0 0
$$759$$ 0.464466 0.804479i 0.0168591 0.0292007i
$$760$$ 0 0
$$761$$ −17.7782 30.7927i −0.644458 1.11623i −0.984426 0.175798i $$-0.943750\pi$$
0.339968 0.940437i $$-0.389584\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0.585786 + 1.01461i 0.0211792 + 0.0366834i
$$766$$ 0 0
$$767$$ −12.3640 + 21.4150i −0.446437 + 0.773251i
$$768$$ 0 0
$$769$$ −1.51472 −0.0546222 −0.0273111 0.999627i $$-0.508694\pi$$
−0.0273111 + 0.999627i $$0.508694\pi$$
$$770$$ 0 0
$$771$$ 2.68629 0.0967444
$$772$$ 0 0
$$773$$ −7.69239 + 13.3236i −0.276676 + 0.479217i −0.970557 0.240873i $$-0.922566\pi$$
0.693881 + 0.720090i $$0.255900\pi$$
$$774$$ 0 0
$$775$$ −0.878680 1.52192i −0.0315631 0.0546689i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −7.41421 12.8418i −0.265642 0.460105i
$$780$$ 0 0
$$781$$ 7.24264 12.5446i 0.259162 0.448882i
$$782$$ 0 0
$$783$$ 2.41421 0.0862770
$$784$$ 0 0
$$785$$ 6.48528 0.231470
$$786$$ 0 0
$$787$$ −22.4203 + 38.8331i −0.799198 + 1.38425i 0.120941 + 0.992660i $$0.461409\pi$$
−0.920139 + 0.391591i $$0.871925\pi$$
$$788$$ 0 0
$$789$$ −3.10051 5.37023i −0.110381 0.191185i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 1.41421 + 2.44949i 0.0502202 + 0.0869839i
$$794$$ 0 0
$$795$$ −1.94975 + 3.37706i −0.0691504 + 0.119772i
$$796$$ 0 0
$$797$$ 50.0711 1.77361 0.886804 0.462146i $$-0.152920\pi$$
0.886804 + 0.462146i $$0.152920\pi$$
$$798$$ 0 0
$$799$$ −4.31371 −0.152608
$$800$$ 0