# Properties

 Label 720.2.q.i.241.1 Level $720$ Weight $2$ Character 720.241 Analytic conductor $5.749$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 720.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.74922894553$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.954288.1 Defining polynomial: $$x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27$$ x^6 - x^5 - 2*x^4 + 3*x^3 - 6*x^2 - 9*x + 27 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 45) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 241.1 Root $$0.403374 - 1.68443i$$ of defining polynomial Character $$\chi$$ $$=$$ 720.241 Dual form 720.2.q.i.481.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.25707 - 1.19154i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.257068 + 0.445256i) q^{7} +(0.160442 + 2.99571i) q^{9} +O(q^{10})$$ $$q+(-1.25707 - 1.19154i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.257068 + 0.445256i) q^{7} +(0.160442 + 2.99571i) q^{9} +(-1.66044 + 2.87597i) q^{11} +(0.660442 + 1.14392i) q^{13} +(-0.403374 + 1.68443i) q^{15} -3.32088 q^{17} +1.32088 q^{19} +(0.853695 - 0.253408i) q^{21} +(2.06382 + 3.57463i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.36783 - 3.95698i) q^{27} +(0.693252 - 1.20075i) q^{29} +(4.36783 + 7.56531i) q^{31} +(5.51414 - 1.63680i) q^{33} +0.514137 q^{35} +0.292611 q^{37} +(0.532810 - 2.22493i) q^{39} +(5.67458 + 9.82866i) q^{41} +(5.17458 - 8.96263i) q^{43} +(2.51414 - 1.63680i) q^{45} +(-2.43165 + 4.21174i) q^{47} +(3.36783 + 5.83326i) q^{49} +(4.17458 + 3.95698i) q^{51} -5.02827 q^{53} +3.32088 q^{55} +(-1.66044 - 1.57389i) q^{57} +(-2.51414 - 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} +(-1.37510 - 0.698664i) q^{63} +(0.660442 - 1.14392i) q^{65} +(4.72426 + 8.18266i) q^{67} +(1.66498 - 6.95269i) q^{69} -8.99093 q^{71} +6.05655 q^{73} +(1.66044 - 0.492881i) q^{75} +(-0.853695 - 1.47864i) q^{77} +(-4.02827 + 6.97717i) q^{79} +(-8.94852 + 0.961276i) q^{81} +(0.771205 - 1.33577i) q^{83} +(1.66044 + 2.87597i) q^{85} +(-2.30221 + 0.683382i) q^{87} -3.00000 q^{89} -0.679116 q^{91} +(3.52374 - 14.7146i) q^{93} +(-0.660442 - 1.14392i) q^{95} +(6.12763 - 10.6134i) q^{97} +(-8.88197 - 4.51277i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9}+O(q^{10})$$ 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9 $$6 q - q^{3} - 3 q^{5} + 5 q^{7} - 7 q^{9} - 2 q^{11} - 4 q^{13} - q^{15} - 4 q^{17} - 8 q^{19} + 3 q^{23} - 3 q^{25} + 2 q^{27} + 7 q^{29} + 8 q^{31} + 20 q^{33} - 10 q^{35} + 12 q^{37} + 14 q^{39} + 13 q^{41} + 10 q^{43} + 2 q^{45} + 13 q^{47} + 2 q^{49} + 4 q^{51} - 4 q^{53} + 4 q^{55} - 2 q^{57} - 2 q^{59} - q^{61} - 33 q^{63} - 4 q^{65} + 11 q^{67} + 39 q^{69} + 20 q^{71} - 16 q^{73} + 2 q^{75} + 2 q^{79} - 19 q^{81} - 15 q^{83} + 2 q^{85} + 26 q^{87} - 18 q^{89} - 20 q^{91} - 42 q^{93} + 4 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100})$$ 6 * q - q^3 - 3 * q^5 + 5 * q^7 - 7 * q^9 - 2 * q^11 - 4 * q^13 - q^15 - 4 * q^17 - 8 * q^19 + 3 * q^23 - 3 * q^25 + 2 * q^27 + 7 * q^29 + 8 * q^31 + 20 * q^33 - 10 * q^35 + 12 * q^37 + 14 * q^39 + 13 * q^41 + 10 * q^43 + 2 * q^45 + 13 * q^47 + 2 * q^49 + 4 * q^51 - 4 * q^53 + 4 * q^55 - 2 * q^57 - 2 * q^59 - q^61 - 33 * q^63 - 4 * q^65 + 11 * q^67 + 39 * q^69 + 20 * q^71 - 16 * q^73 + 2 * q^75 + 2 * q^79 - 19 * q^81 - 15 * q^83 + 2 * q^85 + 26 * q^87 - 18 * q^89 - 20 * q^91 - 42 * q^93 + 4 * q^95 + 18 * q^97 - 22 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$$.

 $$n$$ $$181$$ $$271$$ $$577$$ $$641$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.25707 1.19154i −0.725769 0.687939i
$$4$$ 0 0
$$5$$ −0.500000 0.866025i −0.223607 0.387298i
$$6$$ 0 0
$$7$$ −0.257068 + 0.445256i −0.0971627 + 0.168291i −0.910509 0.413489i $$-0.864310\pi$$
0.813346 + 0.581780i $$0.197643\pi$$
$$8$$ 0 0
$$9$$ 0.160442 + 2.99571i 0.0534807 + 0.998569i
$$10$$ 0 0
$$11$$ −1.66044 + 2.87597i −0.500642 + 0.867138i 0.499358 + 0.866396i $$0.333569\pi$$
−1.00000 0.000741679i $$0.999764\pi$$
$$12$$ 0 0
$$13$$ 0.660442 + 1.14392i 0.183174 + 0.317266i 0.942960 0.332907i $$-0.108030\pi$$
−0.759786 + 0.650173i $$0.774696\pi$$
$$14$$ 0 0
$$15$$ −0.403374 + 1.68443i −0.104151 + 0.434917i
$$16$$ 0 0
$$17$$ −3.32088 −0.805433 −0.402716 0.915325i $$-0.631934\pi$$
−0.402716 + 0.915325i $$0.631934\pi$$
$$18$$ 0 0
$$19$$ 1.32088 0.303032 0.151516 0.988455i $$-0.451585\pi$$
0.151516 + 0.988455i $$0.451585\pi$$
$$20$$ 0 0
$$21$$ 0.853695 0.253408i 0.186291 0.0552982i
$$22$$ 0 0
$$23$$ 2.06382 + 3.57463i 0.430335 + 0.745363i 0.996902 0.0786532i $$-0.0250620\pi$$
−0.566567 + 0.824016i $$0.691729\pi$$
$$24$$ 0 0
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 0 0
$$27$$ 3.36783 3.95698i 0.648139 0.761522i
$$28$$ 0 0
$$29$$ 0.693252 1.20075i 0.128734 0.222973i −0.794453 0.607326i $$-0.792242\pi$$
0.923186 + 0.384353i $$0.125575\pi$$
$$30$$ 0 0
$$31$$ 4.36783 + 7.56531i 0.784486 + 1.35877i 0.929306 + 0.369311i $$0.120406\pi$$
−0.144820 + 0.989458i $$0.546260\pi$$
$$32$$ 0 0
$$33$$ 5.51414 1.63680i 0.959888 0.284930i
$$34$$ 0 0
$$35$$ 0.514137 0.0869050
$$36$$ 0 0
$$37$$ 0.292611 0.0481049 0.0240524 0.999711i $$-0.492343\pi$$
0.0240524 + 0.999711i $$0.492343\pi$$
$$38$$ 0 0
$$39$$ 0.532810 2.22493i 0.0853179 0.356274i
$$40$$ 0 0
$$41$$ 5.67458 + 9.82866i 0.886220 + 1.53498i 0.844308 + 0.535857i $$0.180012\pi$$
0.0419119 + 0.999121i $$0.486655\pi$$
$$42$$ 0 0
$$43$$ 5.17458 8.96263i 0.789116 1.36679i −0.137393 0.990517i $$-0.543872\pi$$
0.926509 0.376272i $$-0.122794\pi$$
$$44$$ 0 0
$$45$$ 2.51414 1.63680i 0.374785 0.244000i
$$46$$ 0 0
$$47$$ −2.43165 + 4.21174i −0.354692 + 0.614345i −0.987065 0.160319i $$-0.948748\pi$$
0.632373 + 0.774664i $$0.282081\pi$$
$$48$$ 0 0
$$49$$ 3.36783 + 5.83326i 0.481119 + 0.833322i
$$50$$ 0 0
$$51$$ 4.17458 + 3.95698i 0.584558 + 0.554088i
$$52$$ 0 0
$$53$$ −5.02827 −0.690687 −0.345343 0.938476i $$-0.612238\pi$$
−0.345343 + 0.938476i $$0.612238\pi$$
$$54$$ 0 0
$$55$$ 3.32088 0.447788
$$56$$ 0 0
$$57$$ −1.66044 1.57389i −0.219931 0.208467i
$$58$$ 0 0
$$59$$ −2.51414 4.35461i −0.327313 0.566922i 0.654665 0.755919i $$-0.272810\pi$$
−0.981978 + 0.188997i $$0.939476\pi$$
$$60$$ 0 0
$$61$$ −3.67458 + 6.36456i −0.470482 + 0.814898i −0.999430 0.0337558i $$-0.989253\pi$$
0.528948 + 0.848654i $$0.322586\pi$$
$$62$$ 0 0
$$63$$ −1.37510 0.698664i −0.173246 0.0880234i
$$64$$ 0 0
$$65$$ 0.660442 1.14392i 0.0819178 0.141886i
$$66$$ 0 0
$$67$$ 4.72426 + 8.18266i 0.577160 + 0.999670i 0.995803 + 0.0915197i $$0.0291724\pi$$
−0.418643 + 0.908151i $$0.637494\pi$$
$$68$$ 0 0
$$69$$ 1.66498 6.95269i 0.200440 0.837005i
$$70$$ 0 0
$$71$$ −8.99093 −1.06703 −0.533513 0.845792i $$-0.679129\pi$$
−0.533513 + 0.845792i $$0.679129\pi$$
$$72$$ 0 0
$$73$$ 6.05655 0.708865 0.354433 0.935082i $$-0.384674\pi$$
0.354433 + 0.935082i $$0.384674\pi$$
$$74$$ 0 0
$$75$$ 1.66044 0.492881i 0.191731 0.0569130i
$$76$$ 0 0
$$77$$ −0.853695 1.47864i −0.0972875 0.168507i
$$78$$ 0 0
$$79$$ −4.02827 + 6.97717i −0.453216 + 0.784994i −0.998584 0.0532036i $$-0.983057\pi$$
0.545367 + 0.838197i $$0.316390\pi$$
$$80$$ 0 0
$$81$$ −8.94852 + 0.961276i −0.994280 + 0.106808i
$$82$$ 0 0
$$83$$ 0.771205 1.33577i 0.0846508 0.146619i −0.820592 0.571515i $$-0.806356\pi$$
0.905242 + 0.424896i $$0.139689\pi$$
$$84$$ 0 0
$$85$$ 1.66044 + 2.87597i 0.180100 + 0.311943i
$$86$$ 0 0
$$87$$ −2.30221 + 0.683382i −0.246823 + 0.0732662i
$$88$$ 0 0
$$89$$ −3.00000 −0.317999 −0.159000 0.987279i $$-0.550827\pi$$
−0.159000 + 0.987279i $$0.550827\pi$$
$$90$$ 0 0
$$91$$ −0.679116 −0.0711906
$$92$$ 0 0
$$93$$ 3.52374 14.7146i 0.365395 1.52583i
$$94$$ 0 0
$$95$$ −0.660442 1.14392i −0.0677599 0.117364i
$$96$$ 0 0
$$97$$ 6.12763 10.6134i 0.622167 1.07762i −0.366915 0.930255i $$-0.619586\pi$$
0.989081 0.147370i $$-0.0470808\pi$$
$$98$$ 0 0
$$99$$ −8.88197 4.51277i −0.892671 0.453551i
$$100$$ 0 0
$$101$$ −5.83502 + 10.1066i −0.580606 + 1.00564i 0.414801 + 0.909912i $$0.363851\pi$$
−0.995408 + 0.0957276i $$0.969482\pi$$
$$102$$ 0 0
$$103$$ 0.146305 + 0.253408i 0.0144159 + 0.0249691i 0.873143 0.487464i $$-0.162078\pi$$
−0.858727 + 0.512433i $$0.828744\pi$$
$$104$$ 0 0
$$105$$ −0.646305 0.612617i −0.0630729 0.0597853i
$$106$$ 0 0
$$107$$ −1.87237 −0.181009 −0.0905043 0.995896i $$-0.528848\pi$$
−0.0905043 + 0.995896i $$0.528848\pi$$
$$108$$ 0 0
$$109$$ 5.54787 0.531390 0.265695 0.964057i $$-0.414399\pi$$
0.265695 + 0.964057i $$0.414399\pi$$
$$110$$ 0 0
$$111$$ −0.367832 0.348659i −0.0349130 0.0330932i
$$112$$ 0 0
$$113$$ −3.90064 6.75611i −0.366942 0.635561i 0.622144 0.782903i $$-0.286262\pi$$
−0.989086 + 0.147341i $$0.952928\pi$$
$$114$$ 0 0
$$115$$ 2.06382 3.57463i 0.192452 0.333336i
$$116$$ 0 0
$$117$$ −3.32088 + 2.16202i −0.307016 + 0.199879i
$$118$$ 0 0
$$119$$ 0.853695 1.47864i 0.0782581 0.135547i
$$120$$ 0 0
$$121$$ −0.0141369 0.0244859i −0.00128518 0.00222599i
$$122$$ 0 0
$$123$$ 4.57795 19.1168i 0.412780 1.72370i
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −17.8916 −1.58762 −0.793810 0.608166i $$-0.791906\pi$$
−0.793810 + 0.608166i $$0.791906\pi$$
$$128$$ 0 0
$$129$$ −17.1842 + 5.10090i −1.51298 + 0.449109i
$$130$$ 0 0
$$131$$ −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i $$-0.251085\pi$$
−0.966803 + 0.255524i $$0.917752\pi$$
$$132$$ 0 0
$$133$$ −0.339558 + 0.588131i −0.0294434 + 0.0509974i
$$134$$ 0 0
$$135$$ −5.11076 0.938136i −0.439864 0.0807419i
$$136$$ 0 0
$$137$$ −2.83502 + 4.91040i −0.242212 + 0.419524i −0.961344 0.275350i $$-0.911206\pi$$
0.719132 + 0.694874i $$0.244540\pi$$
$$138$$ 0 0
$$139$$ 4.00000 + 6.92820i 0.339276 + 0.587643i 0.984297 0.176522i $$-0.0564848\pi$$
−0.645021 + 0.764165i $$0.723151\pi$$
$$140$$ 0 0
$$141$$ 8.07522 2.39703i 0.680056 0.201866i
$$142$$ 0 0
$$143$$ −4.38650 −0.366818
$$144$$ 0 0
$$145$$ −1.38650 −0.115143
$$146$$ 0 0
$$147$$ 2.71699 11.3457i 0.224094 0.935780i
$$148$$ 0 0
$$149$$ −8.83049 15.2948i −0.723422 1.25300i −0.959620 0.281298i $$-0.909235\pi$$
0.236199 0.971705i $$-0.424098\pi$$
$$150$$ 0 0
$$151$$ 0.632168 1.09495i 0.0514451 0.0891056i −0.839156 0.543891i $$-0.816951\pi$$
0.890601 + 0.454785i $$0.150284\pi$$
$$152$$ 0 0
$$153$$ −0.532810 9.94840i −0.0430752 0.804280i
$$154$$ 0 0
$$155$$ 4.36783 7.56531i 0.350833 0.607660i
$$156$$ 0 0
$$157$$ 7.83502 + 13.5707i 0.625303 + 1.08306i 0.988482 + 0.151337i $$0.0483579\pi$$
−0.363179 + 0.931719i $$0.618309\pi$$
$$158$$ 0 0
$$159$$ 6.32088 + 5.99141i 0.501279 + 0.475150i
$$160$$ 0 0
$$161$$ −2.12217 −0.167250
$$162$$ 0 0
$$163$$ −15.7074 −1.23030 −0.615149 0.788411i $$-0.710904\pi$$
−0.615149 + 0.788411i $$0.710904\pi$$
$$164$$ 0 0
$$165$$ −4.17458 3.95698i −0.324991 0.308051i
$$166$$ 0 0
$$167$$ 3.08249 + 5.33903i 0.238530 + 0.413146i 0.960293 0.278994i $$-0.0900011\pi$$
−0.721763 + 0.692141i $$0.756668\pi$$
$$168$$ 0 0
$$169$$ 5.62763 9.74734i 0.432895 0.749796i
$$170$$ 0 0
$$171$$ 0.211926 + 3.95698i 0.0162064 + 0.302598i
$$172$$ 0 0
$$173$$ −4.29261 + 7.43502i −0.326361 + 0.565274i −0.981787 0.189986i $$-0.939156\pi$$
0.655426 + 0.755260i $$0.272489\pi$$
$$174$$ 0 0
$$175$$ −0.257068 0.445256i −0.0194325 0.0336582i
$$176$$ 0 0
$$177$$ −2.02827 + 8.46975i −0.152454 + 0.636626i
$$178$$ 0 0
$$179$$ 1.06562 0.0796482 0.0398241 0.999207i $$-0.487320\pi$$
0.0398241 + 0.999207i $$0.487320\pi$$
$$180$$ 0 0
$$181$$ −12.6700 −0.941757 −0.470878 0.882198i $$-0.656063\pi$$
−0.470878 + 0.882198i $$0.656063\pi$$
$$182$$ 0 0
$$183$$ 12.2029 3.62226i 0.902061 0.267765i
$$184$$ 0 0
$$185$$ −0.146305 0.253408i −0.0107566 0.0186309i
$$186$$ 0 0
$$187$$ 5.51414 9.55077i 0.403234 0.698421i
$$188$$ 0 0
$$189$$ 0.896105 + 2.51676i 0.0651821 + 0.183067i
$$190$$ 0 0
$$191$$ −8.46719 + 14.6656i −0.612664 + 1.06117i 0.378125 + 0.925754i $$0.376569\pi$$
−0.990789 + 0.135411i $$0.956764\pi$$
$$192$$ 0 0
$$193$$ −13.3588 23.1380i −0.961585 1.66551i −0.718524 0.695502i $$-0.755182\pi$$
−0.243060 0.970011i $$-0.578151\pi$$
$$194$$ 0 0
$$195$$ −2.19325 + 0.651039i −0.157062 + 0.0466218i
$$196$$ 0 0
$$197$$ −14.2553 −1.01565 −0.507823 0.861462i $$-0.669550\pi$$
−0.507823 + 0.861462i $$0.669550\pi$$
$$198$$ 0 0
$$199$$ 24.6610 1.74817 0.874085 0.485773i $$-0.161462\pi$$
0.874085 + 0.485773i $$0.161462\pi$$
$$200$$ 0 0
$$201$$ 3.81128 15.9153i 0.268827 1.12258i
$$202$$ 0 0
$$203$$ 0.356427 + 0.617349i 0.0250162 + 0.0433294i
$$204$$ 0 0
$$205$$ 5.67458 9.82866i 0.396330 0.686463i
$$206$$ 0 0
$$207$$ −10.3774 + 6.75611i −0.721281 + 0.469582i
$$208$$ 0 0
$$209$$ −2.19325 + 3.79882i −0.151710 + 0.262770i
$$210$$ 0 0
$$211$$ −2.68872 4.65699i −0.185099 0.320601i 0.758511 0.651660i $$-0.225927\pi$$
−0.943610 + 0.331060i $$0.892594\pi$$
$$212$$ 0 0
$$213$$ 11.3022 + 10.7131i 0.774415 + 0.734049i
$$214$$ 0 0
$$215$$ −10.3492 −0.705807
$$216$$ 0 0
$$217$$ −4.49133 −0.304891
$$218$$ 0 0
$$219$$ −7.61350 7.21665i −0.514472 0.487656i
$$220$$ 0 0
$$221$$ −2.19325 3.79882i −0.147534 0.255537i
$$222$$ 0 0
$$223$$ 4.33229 7.50375i 0.290112 0.502488i −0.683724 0.729740i $$-0.739641\pi$$
0.973836 + 0.227252i $$0.0729743\pi$$
$$224$$ 0 0
$$225$$ −2.67458 1.35891i −0.178305 0.0905938i
$$226$$ 0 0
$$227$$ 1.66044 2.87597i 0.110207 0.190885i −0.805646 0.592397i $$-0.798182\pi$$
0.915854 + 0.401512i $$0.131515\pi$$
$$228$$ 0 0
$$229$$ 12.6559 + 21.9207i 0.836326 + 1.44856i 0.892946 + 0.450163i $$0.148634\pi$$
−0.0566206 + 0.998396i $$0.518033\pi$$
$$230$$ 0 0
$$231$$ −0.688716 + 2.87597i −0.0453142 + 0.189225i
$$232$$ 0 0
$$233$$ 27.6327 1.81028 0.905139 0.425116i $$-0.139767\pi$$
0.905139 + 0.425116i $$0.139767\pi$$
$$234$$ 0 0
$$235$$ 4.86330 0.317246
$$236$$ 0 0
$$237$$ 13.3774 3.97092i 0.868958 0.257939i
$$238$$ 0 0
$$239$$ −2.09936 3.63620i −0.135796 0.235206i 0.790105 0.612971i $$-0.210026\pi$$
−0.925901 + 0.377765i $$0.876693\pi$$
$$240$$ 0 0
$$241$$ −1.80221 + 3.12152i −0.116091 + 0.201075i −0.918215 0.396082i $$-0.870370\pi$$
0.802125 + 0.597157i $$0.203703\pi$$
$$242$$ 0 0
$$243$$ 12.3943 + 9.45417i 0.795095 + 0.606485i
$$244$$ 0 0
$$245$$ 3.36783 5.83326i 0.215163 0.372673i
$$246$$ 0 0
$$247$$ 0.872368 + 1.51099i 0.0555074 + 0.0961417i
$$248$$ 0 0
$$249$$ −2.56108 + 0.760225i −0.162302 + 0.0481773i
$$250$$ 0 0
$$251$$ 6.87783 0.434125 0.217062 0.976158i $$-0.430352\pi$$
0.217062 + 0.976158i $$0.430352\pi$$
$$252$$ 0 0
$$253$$ −13.7074 −0.861776
$$254$$ 0 0
$$255$$ 1.33956 5.59378i 0.0838864 0.350296i
$$256$$ 0 0
$$257$$ 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i $$0.0230722\pi$$
−0.435970 + 0.899961i $$0.643595\pi$$
$$258$$ 0 0
$$259$$ −0.0752210 + 0.130287i −0.00467400 + 0.00809561i
$$260$$ 0 0
$$261$$ 3.70832 + 1.88413i 0.229539 + 0.116625i
$$262$$ 0 0
$$263$$ 3.11803 5.40059i 0.192266 0.333015i −0.753735 0.657179i $$-0.771750\pi$$
0.946001 + 0.324164i $$0.105083\pi$$
$$264$$ 0 0
$$265$$ 2.51414 + 4.35461i 0.154442 + 0.267502i
$$266$$ 0 0
$$267$$ 3.77121 + 3.57463i 0.230794 + 0.218764i
$$268$$ 0 0
$$269$$ 9.92345 0.605044 0.302522 0.953142i $$-0.402172\pi$$
0.302522 + 0.953142i $$0.402172\pi$$
$$270$$ 0 0
$$271$$ −6.60442 −0.401190 −0.200595 0.979674i $$-0.564288\pi$$
−0.200595 + 0.979674i $$0.564288\pi$$
$$272$$ 0 0
$$273$$ 0.853695 + 0.809197i 0.0516680 + 0.0489748i
$$274$$ 0 0
$$275$$ −1.66044 2.87597i −0.100128 0.173428i
$$276$$ 0 0
$$277$$ −11.3305 + 19.6250i −0.680783 + 1.17915i 0.293959 + 0.955818i $$0.405027\pi$$
−0.974742 + 0.223333i $$0.928306\pi$$
$$278$$ 0 0
$$279$$ −21.9627 + 14.2985i −1.31487 + 0.856031i
$$280$$ 0 0
$$281$$ 7.77394 13.4649i 0.463754 0.803246i −0.535390 0.844605i $$-0.679835\pi$$
0.999144 + 0.0413590i $$0.0131687\pi$$
$$282$$ 0 0
$$283$$ 0.322689 + 0.558913i 0.0191819 + 0.0332240i 0.875457 0.483296i $$-0.160561\pi$$
−0.856275 + 0.516520i $$0.827227\pi$$
$$284$$ 0 0
$$285$$ −0.532810 + 2.22493i −0.0315610 + 0.131794i
$$286$$ 0 0
$$287$$ −5.83502 −0.344430
$$288$$ 0 0
$$289$$ −5.97173 −0.351278
$$290$$ 0 0
$$291$$ −20.3492 + 6.04039i −1.19289 + 0.354094i
$$292$$ 0 0
$$293$$ 0.688716 + 1.19289i 0.0402352 + 0.0696895i 0.885442 0.464750i $$-0.153856\pi$$
−0.845207 + 0.534440i $$0.820523\pi$$
$$294$$ 0 0
$$295$$ −2.51414 + 4.35461i −0.146379 + 0.253535i
$$296$$ 0 0
$$297$$ 5.78807 + 16.2561i 0.335858 + 0.943276i
$$298$$ 0 0
$$299$$ −2.72606 + 4.72168i −0.157652 + 0.273062i
$$300$$ 0 0
$$301$$ 2.66044 + 4.60802i 0.153345 + 0.265602i
$$302$$ 0 0
$$303$$ 19.3774 5.75194i 1.11320 0.330440i
$$304$$ 0 0
$$305$$ 7.34916 0.420812
$$306$$ 0 0
$$307$$ 7.98546 0.455754 0.227877 0.973690i $$-0.426822\pi$$
0.227877 + 0.973690i $$0.426822\pi$$
$$308$$ 0 0
$$309$$ 0.118031 0.492881i 0.00671458 0.0280390i
$$310$$ 0 0
$$311$$ 4.81635 + 8.34216i 0.273110 + 0.473040i 0.969657 0.244471i $$-0.0786143\pi$$
−0.696547 + 0.717512i $$0.745281\pi$$
$$312$$ 0 0
$$313$$ 12.2685 21.2496i 0.693455 1.20110i −0.277244 0.960800i $$-0.589421\pi$$
0.970699 0.240300i $$-0.0772458\pi$$
$$314$$ 0 0
$$315$$ 0.0824893 + 1.54020i 0.00464774 + 0.0867806i
$$316$$ 0 0
$$317$$ 10.1746 17.6229i 0.571461 0.989800i −0.424955 0.905215i $$-0.639710\pi$$
0.996416 0.0845855i $$-0.0269566\pi$$
$$318$$ 0 0
$$319$$ 2.30221 + 3.98755i 0.128899 + 0.223260i
$$320$$ 0 0
$$321$$ 2.35369 + 2.23101i 0.131370 + 0.124523i
$$322$$ 0 0
$$323$$ −4.38650 −0.244072
$$324$$ 0 0
$$325$$ −1.32088 −0.0732695
$$326$$ 0 0
$$327$$ −6.97406 6.61054i −0.385666 0.365564i
$$328$$ 0 0
$$329$$ −1.25020 2.16541i −0.0689257 0.119383i
$$330$$ 0 0
$$331$$ 8.22153 14.2401i 0.451896 0.782707i −0.546608 0.837389i $$-0.684081\pi$$
0.998504 + 0.0546819i $$0.0174145\pi$$
$$332$$ 0 0
$$333$$ 0.0469471 + 0.876576i 0.00257269 + 0.0480360i
$$334$$ 0 0
$$335$$ 4.72426 8.18266i 0.258114 0.447066i
$$336$$ 0 0
$$337$$ −2.44852 4.24096i −0.133379 0.231020i 0.791598 0.611042i $$-0.209249\pi$$
−0.924977 + 0.380023i $$0.875916\pi$$
$$338$$ 0 0
$$339$$ −3.14683 + 13.1407i −0.170913 + 0.713704i
$$340$$ 0 0
$$341$$ −29.0101 −1.57099
$$342$$ 0 0
$$343$$ −7.06201 −0.381313
$$344$$ 0 0
$$345$$ −6.85369 + 2.03443i −0.368991 + 0.109530i
$$346$$ 0 0
$$347$$ 11.1372 + 19.2903i 0.597878 + 1.03556i 0.993134 + 0.116984i $$0.0373226\pi$$
−0.395256 + 0.918571i $$0.629344\pi$$
$$348$$ 0 0
$$349$$ 1.47173 2.54910i 0.0787797 0.136450i −0.823944 0.566671i $$-0.808231\pi$$
0.902724 + 0.430221i $$0.141564\pi$$
$$350$$ 0 0
$$351$$ 6.75073 + 1.23917i 0.360327 + 0.0661420i
$$352$$ 0 0
$$353$$ −9.41478 + 16.3069i −0.501098 + 0.867927i 0.498901 + 0.866659i $$0.333737\pi$$
−0.999999 + 0.00126845i $$0.999596\pi$$
$$354$$ 0 0
$$355$$ 4.49546 + 7.78637i 0.238594 + 0.413258i
$$356$$ 0 0
$$357$$ −2.83502 + 0.841540i −0.150045 + 0.0445390i
$$358$$ 0 0
$$359$$ 31.8770 1.68241 0.841203 0.540720i $$-0.181848\pi$$
0.841203 + 0.540720i $$0.181848\pi$$
$$360$$ 0 0
$$361$$ −17.2553 −0.908172
$$362$$ 0 0
$$363$$ −0.0114049 + 0.0476252i −0.000598604 + 0.00249968i
$$364$$ 0 0
$$365$$ −3.02827 5.24512i −0.158507 0.274542i
$$366$$ 0 0
$$367$$ −9.17458 + 15.8908i −0.478909 + 0.829495i −0.999708 0.0241848i $$-0.992301\pi$$
0.520798 + 0.853680i $$0.325634\pi$$
$$368$$ 0 0
$$369$$ −28.5333 + 18.5763i −1.48539 + 0.967044i
$$370$$ 0 0
$$371$$ 1.29261 2.23887i 0.0671090 0.116236i
$$372$$ 0 0
$$373$$ 1.09936 + 1.90414i 0.0569226 + 0.0985929i 0.893083 0.449893i $$-0.148538\pi$$
−0.836160 + 0.548486i $$0.815205\pi$$
$$374$$ 0 0
$$375$$ −1.25707 1.19154i −0.0649147 0.0615311i
$$376$$ 0 0
$$377$$ 1.83141 0.0943226
$$378$$ 0 0
$$379$$ −15.4713 −0.794709 −0.397354 0.917665i $$-0.630072\pi$$
−0.397354 + 0.917665i $$0.630072\pi$$
$$380$$ 0 0
$$381$$ 22.4909 + 21.3186i 1.15225 + 1.09219i
$$382$$ 0 0
$$383$$ 3.85369 + 6.67479i 0.196915 + 0.341066i 0.947526 0.319677i $$-0.103574\pi$$
−0.750612 + 0.660743i $$0.770241\pi$$
$$384$$ 0 0
$$385$$ −0.853695 + 1.47864i −0.0435083 + 0.0753586i
$$386$$ 0 0
$$387$$ 27.6796 + 14.0635i 1.40704 + 0.714890i
$$388$$ 0 0
$$389$$ 12.3163 21.3325i 0.624464 1.08160i −0.364181 0.931328i $$-0.618651\pi$$
0.988644 0.150274i $$-0.0480157\pi$$
$$390$$ 0 0
$$391$$ −6.85369 11.8709i −0.346606 0.600340i
$$392$$ 0 0
$$393$$ −2.42024 + 10.1066i −0.122085 + 0.509808i
$$394$$ 0 0
$$395$$ 8.05655 0.405369
$$396$$ 0 0
$$397$$ −6.77301 −0.339928 −0.169964 0.985450i $$-0.554365\pi$$
−0.169964 + 0.985450i $$0.554365\pi$$
$$398$$ 0 0
$$399$$ 1.12763 0.334723i 0.0564522 0.0167571i
$$400$$ 0 0
$$401$$ 9.24980 + 16.0211i 0.461913 + 0.800057i 0.999056 0.0434343i $$-0.0138299\pi$$
−0.537143 + 0.843491i $$0.680497\pi$$
$$402$$ 0 0
$$403$$ −5.76940 + 9.99290i −0.287394 + 0.497782i
$$404$$ 0 0
$$405$$ 5.30675 + 7.26900i 0.263694 + 0.361200i
$$406$$ 0 0
$$407$$ −0.485863 + 0.841540i −0.0240833 + 0.0417136i
$$408$$ 0 0
$$409$$ 6.70739 + 11.6175i 0.331659 + 0.574450i 0.982837 0.184474i $$-0.0590583\pi$$
−0.651178 + 0.758925i $$0.725725\pi$$
$$410$$ 0 0
$$411$$ 9.41478 2.79466i 0.464397 0.137850i
$$412$$ 0 0
$$413$$ 2.58522 0.127210
$$414$$ 0 0
$$415$$ −1.54241 −0.0757140
$$416$$ 0 0
$$417$$ 3.22699 13.4754i 0.158026 0.659893i
$$418$$ 0 0
$$419$$ −16.5575 28.6784i −0.808886 1.40103i −0.913636 0.406532i $$-0.866738\pi$$
0.104751 0.994499i $$-0.466596\pi$$
$$420$$ 0 0
$$421$$ 7.34916 12.7291i 0.358176 0.620379i −0.629480 0.777017i $$-0.716732\pi$$
0.987656 + 0.156637i $$0.0500654\pi$$
$$422$$ 0 0
$$423$$ −13.0073 6.60876i −0.632435 0.321329i
$$424$$ 0 0
$$425$$ 1.66044 2.87597i 0.0805433 0.139505i
$$426$$ 0 0
$$427$$ −1.88924 3.27225i −0.0914266 0.158355i
$$428$$ 0 0
$$429$$ 5.51414 + 5.22672i 0.266225 + 0.252348i
$$430$$ 0 0
$$431$$ 32.7549 1.57775 0.788873 0.614556i $$-0.210665\pi$$
0.788873 + 0.614556i $$0.210665\pi$$
$$432$$ 0 0
$$433$$ −11.8314 −0.568581 −0.284291 0.958738i $$-0.591758\pi$$
−0.284291 + 0.958738i $$0.591758\pi$$
$$434$$ 0 0
$$435$$ 1.74293 + 1.65208i 0.0835672 + 0.0792113i
$$436$$ 0 0
$$437$$ 2.72606 + 4.72168i 0.130405 + 0.225869i
$$438$$ 0 0
$$439$$ 4.15591 7.19824i 0.198351 0.343553i −0.749643 0.661842i $$-0.769775\pi$$
0.947994 + 0.318289i $$0.103108\pi$$
$$440$$ 0 0
$$441$$ −16.9344 + 11.0249i −0.806399 + 0.524997i
$$442$$ 0 0
$$443$$ −14.5876 + 25.2664i −0.693076 + 1.20044i 0.277750 + 0.960654i $$0.410411\pi$$
−0.970825 + 0.239789i $$0.922922\pi$$
$$444$$ 0 0
$$445$$ 1.50000 + 2.59808i 0.0711068 + 0.123161i
$$446$$ 0 0
$$447$$ −7.12397 + 29.7486i −0.336952 + 1.40706i
$$448$$ 0 0
$$449$$ 18.9717 0.895331 0.447666 0.894201i $$-0.352256\pi$$
0.447666 + 0.894201i $$0.352256\pi$$
$$450$$ 0 0
$$451$$ −37.6892 −1.77472
$$452$$ 0 0
$$453$$ −2.09936 + 0.623167i −0.0986365 + 0.0292790i
$$454$$ 0 0
$$455$$ 0.339558 + 0.588131i 0.0159187 + 0.0275720i
$$456$$ 0 0
$$457$$ 11.6176 20.1223i 0.543450 0.941283i −0.455253 0.890362i $$-0.650451\pi$$
0.998703 0.0509206i $$-0.0162155\pi$$
$$458$$ 0 0
$$459$$ −11.1842 + 13.1407i −0.522033 + 0.613354i
$$460$$ 0 0
$$461$$ −2.21285 + 3.83277i −0.103063 + 0.178510i −0.912945 0.408082i $$-0.866198\pi$$
0.809882 + 0.586592i $$0.199531\pi$$
$$462$$ 0 0
$$463$$ −9.75434 16.8950i −0.453322 0.785178i 0.545268 0.838262i $$-0.316428\pi$$
−0.998590 + 0.0530845i $$0.983095\pi$$
$$464$$ 0 0
$$465$$ −14.5051 + 4.30564i −0.672656 + 0.199669i
$$466$$ 0 0
$$467$$ 24.5935 1.13805 0.569026 0.822320i $$-0.307321\pi$$
0.569026 + 0.822320i $$0.307321\pi$$
$$468$$ 0 0
$$469$$ −4.85783 −0.224314
$$470$$ 0 0
$$471$$ 6.32088 26.3950i 0.291251 1.21622i
$$472$$ 0 0
$$473$$ 17.1842 + 29.7639i 0.790129 + 1.36854i
$$474$$ 0 0
$$475$$ −0.660442 + 1.14392i −0.0303032 + 0.0524866i
$$476$$ 0 0
$$477$$ −0.806748 15.0632i −0.0369384 0.689698i
$$478$$ 0 0
$$479$$ 16.3774 28.3665i 0.748304 1.29610i −0.200331 0.979728i $$-0.564202\pi$$
0.948635 0.316372i $$-0.102465\pi$$
$$480$$ 0 0
$$481$$ 0.193252 + 0.334723i 0.00881155 + 0.0152621i
$$482$$ 0 0
$$483$$ 2.66771 + 2.52866i 0.121385 + 0.115058i
$$484$$ 0 0
$$485$$ −12.2553 −0.556483
$$486$$ 0 0
$$487$$ 6.03735 0.273578 0.136789 0.990600i $$-0.456322\pi$$
0.136789 + 0.990600i $$0.456322\pi$$
$$488$$ 0 0
$$489$$ 19.7453 + 18.7161i 0.892912 + 0.846369i
$$490$$ 0 0
$$491$$ 7.22153 + 12.5081i 0.325903 + 0.564480i 0.981695 0.190461i $$-0.0609984\pi$$
−0.655792 + 0.754942i $$0.727665\pi$$
$$492$$ 0 0
$$493$$ −2.30221 + 3.98755i −0.103686 + 0.179590i
$$494$$ 0 0
$$495$$ 0.532810 + 9.94840i 0.0239480 + 0.447147i
$$496$$ 0 0
$$497$$ 2.31128 4.00326i 0.103675 0.179571i
$$498$$ 0 0
$$499$$ 10.4859 + 18.1620i 0.469412 + 0.813045i 0.999388 0.0349673i $$-0.0111327\pi$$
−0.529977 + 0.848012i $$0.677799\pi$$
$$500$$ 0 0
$$501$$ 2.48679 10.3844i 0.111102 0.463943i
$$502$$ 0 0
$$503$$ 5.31728 0.237086 0.118543 0.992949i $$-0.462178\pi$$
0.118543 + 0.992949i $$0.462178\pi$$
$$504$$ 0 0
$$505$$ 11.6700 0.519310
$$506$$ 0 0
$$507$$ −18.6887 + 5.54750i −0.829995 + 0.246373i
$$508$$ 0 0
$$509$$ −9.11350 15.7850i −0.403949 0.699659i 0.590250 0.807221i $$-0.299029\pi$$
−0.994198 + 0.107561i $$0.965696\pi$$
$$510$$ 0 0
$$511$$ −1.55695 + 2.69671i −0.0688753 + 0.119296i
$$512$$ 0 0
$$513$$ 4.44852 5.22672i 0.196407 0.230765i
$$514$$ 0 0
$$515$$ 0.146305 0.253408i 0.00644698 0.0111665i
$$516$$ 0 0
$$517$$ −8.07522 13.9867i −0.355148 0.615134i
$$518$$ 0 0
$$519$$ 14.2553 4.23149i 0.625737 0.185742i
$$520$$ 0 0
$$521$$ 40.1232 1.75783 0.878915 0.476978i $$-0.158268\pi$$
0.878915 + 0.476978i $$0.158268\pi$$
$$522$$ 0 0
$$523$$ −18.9873 −0.830257 −0.415129 0.909763i $$-0.636263\pi$$
−0.415129 + 0.909763i $$0.636263\pi$$
$$524$$ 0 0
$$525$$ −0.207389 + 0.866025i −0.00905121 + 0.0377964i
$$526$$ 0 0
$$527$$ −14.5051 25.1235i −0.631851 1.09440i
$$528$$ 0 0
$$529$$ 2.98133 5.16381i 0.129623 0.224513i
$$530$$ 0 0
$$531$$ 12.6418 8.23028i 0.548606 0.357164i
$$532$$ 0 0
$$533$$ −7.49546 + 12.9825i −0.324665 + 0.562336i
$$534$$ 0 0
$$535$$ 0.936184 + 1.62152i 0.0404748 + 0.0701043i
$$536$$ 0 0
$$537$$ −1.33956 1.26973i −0.0578062 0.0547931i
$$538$$ 0 0
$$539$$ −22.3684 −0.963473
$$540$$ 0 0
$$541$$ 16.5279 0.710589 0.355294 0.934754i $$-0.384381\pi$$
0.355294 + 0.934754i $$0.384381\pi$$
$$542$$ 0 0
$$543$$ 15.9271 + 15.0969i 0.683498 + 0.647871i
$$544$$ 0 0
$$545$$ −2.77394 4.80460i −0.118822 0.205806i
$$546$$ 0 0
$$547$$ 8.83683 15.3058i 0.377835 0.654430i −0.612912 0.790151i $$-0.710002\pi$$
0.990747 + 0.135721i $$0.0433352\pi$$
$$548$$ 0 0
$$549$$ −19.6559 9.98682i −0.838894 0.426227i
$$550$$ 0 0
$$551$$ 0.915706 1.58605i 0.0390104 0.0675680i
$$552$$ 0 0
$$553$$ −2.07108 3.58722i −0.0880715 0.152544i
$$554$$ 0 0
$$555$$ −0.118031 + 0.492881i −0.00501016 + 0.0209216i
$$556$$ 0 0
$$557$$ 17.3401 0.734723 0.367362 0.930078i $$-0.380261\pi$$
0.367362 + 0.930078i $$0.380261\pi$$
$$558$$ 0 0
$$559$$ 13.6700 0.578181
$$560$$ 0 0
$$561$$ −18.3118 + 5.43563i −0.773125 + 0.229492i
$$562$$ 0 0
$$563$$ 6.49727 + 11.2536i 0.273827 + 0.474283i 0.969839 0.243748i $$-0.0783770\pi$$
−0.696011 + 0.718031i $$0.745044\pi$$
$$564$$ 0 0
$$565$$ −3.90064 + 6.75611i −0.164101 + 0.284232i
$$566$$ 0 0
$$567$$ 1.87237 4.23149i 0.0786321 0.177706i
$$568$$ 0 0
$$569$$ 8.34009 14.4455i 0.349635 0.605585i −0.636550 0.771236i $$-0.719639\pi$$
0.986184 + 0.165651i $$0.0529724\pi$$
$$570$$ 0 0
$$571$$ 10.0000 + 17.3205i 0.418487 + 0.724841i 0.995788 0.0916910i $$-0.0292272\pi$$
−0.577301 + 0.816532i $$0.695894\pi$$
$$572$$ 0 0
$$573$$ 28.1186 8.34663i 1.17467 0.348686i
$$574$$ 0 0
$$575$$ −4.12763 −0.172134
$$576$$ 0 0
$$577$$ −23.5953 −0.982287 −0.491144 0.871079i $$-0.663421\pi$$
−0.491144 + 0.871079i $$0.663421\pi$$
$$578$$ 0 0
$$579$$ −10.7771 + 45.0037i −0.447883 + 1.87029i
$$580$$ 0 0
$$581$$ 0.396505 + 0.686767i 0.0164498 + 0.0284919i
$$582$$ 0 0
$$583$$ 8.34916 14.4612i 0.345787 0.598920i
$$584$$ 0 0
$$585$$ 3.53281 + 1.79496i 0.146064 + 0.0742124i
$$586$$ 0 0
$$587$$ 14.0638 24.3592i 0.580476 1.00541i −0.414947 0.909846i $$-0.636200\pi$$
0.995423 0.0955681i $$-0.0304668\pi$$
$$588$$ 0 0
$$589$$ 5.76940 + 9.99290i 0.237724 + 0.411750i
$$590$$ 0 0
$$591$$ 17.9198 + 16.9858i 0.737124 + 0.698702i
$$592$$ 0 0
$$593$$ −9.17872 −0.376925 −0.188462 0.982080i $$-0.560350\pi$$
−0.188462 + 0.982080i $$0.560350\pi$$
$$594$$ 0 0
$$595$$ −1.70739 −0.0699961
$$596$$ 0 0
$$597$$ −31.0005 29.3846i −1.26877 1.20263i
$$598$$ 0 0
$$599$$ −15.7357 27.2550i −0.642942 1.11361i −0.984773 0.173846i $$-0.944380\pi$$
0.341831 0.939761i $$-0.388953\pi$$
$$600$$ 0 0
$$601$$ 14.6327 25.3446i 0.596880 1.03383i −0.396398 0.918079i $$-0.629740\pi$$
0.993279 0.115748i $$-0.0369265\pi$$
$$602$$ 0 0
$$603$$ −23.7549 + 15.4653i −0.967373 + 0.629797i
$$604$$ 0 0
$$605$$ −0.0141369 + 0.0244859i −0.000574748 + 0.000995493i
$$606$$ 0 0
$$607$$ −22.1017 38.2813i −0.897080 1.55379i −0.831209 0.555960i $$-0.812351\pi$$
−0.0658708 0.997828i $$-0.520983\pi$$
$$608$$ 0 0
$$609$$ 0.287546 1.20075i 0.0116520 0.0486568i
$$610$$ 0 0
$$611$$ −6.42385 −0.259881
$$612$$ 0 0
$$613$$ −35.1715 −1.42056 −0.710282 0.703918i $$-0.751432\pi$$
−0.710282 + 0.703918i $$0.751432\pi$$
$$614$$ 0 0
$$615$$ −18.8446 + 5.59378i −0.759889 + 0.225563i
$$616$$ 0 0
$$617$$ 3.71285 + 6.43085i 0.149474 + 0.258896i 0.931033 0.364935i $$-0.118909\pi$$
−0.781559 + 0.623831i $$0.785575\pi$$
$$618$$ 0 0
$$619$$ 4.27394 7.40268i 0.171784 0.297539i −0.767260 0.641337i $$-0.778380\pi$$
0.939044 + 0.343798i $$0.111714\pi$$
$$620$$ 0 0
$$621$$ 21.0953 + 3.87228i 0.846527 + 0.155389i
$$622$$ 0 0
$$623$$ 0.771205 1.33577i 0.0308977 0.0535164i
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ 0 0
$$627$$ 7.28354 2.16202i 0.290876 0.0863429i
$$628$$ 0 0
$$629$$ −0.971726 −0.0387453
$$630$$ 0 0
$$631$$ 2.36836 0.0942829 0.0471415 0.998888i $$-0.484989\pi$$
0.0471415 + 0.998888i $$0.484989\pi$$
$$632$$ 0 0
$$633$$ −2.16912 + 9.05788i −0.0862146 + 0.360019i
$$634$$ 0 0
$$635$$ 8.94578 + 15.4946i 0.355003 + 0.614883i
$$636$$ 0 0
$$637$$ −4.44852 + 7.70506i −0.176257 + 0.305285i
$$638$$ 0 0
$$639$$ −1.44252 26.9342i −0.0570654 1.06550i
$$640$$ 0 0
$$641$$ 0.0665480 0.115265i 0.00262849 0.00455268i −0.864708 0.502275i $$-0.832497\pi$$
0.867337 + 0.497722i $$0.165830\pi$$
$$642$$ 0 0
$$643$$ −11.3232 19.6124i −0.446544 0.773437i 0.551614 0.834099i $$-0.314012\pi$$
−0.998158 + 0.0606623i $$0.980679\pi$$
$$644$$ 0 0
$$645$$ 13.0096 + 12.3315i 0.512253 + 0.485552i
$$646$$ 0 0
$$647$$ −46.3912 −1.82383 −0.911913 0.410385i $$-0.865394\pi$$
−0.911913 + 0.410385i $$0.865394\pi$$
$$648$$ 0 0
$$649$$ 16.6983 0.655466
$$650$$ 0 0
$$651$$ 5.64591 + 5.35162i 0.221280 + 0.209746i
$$652$$ 0 0
$$653$$ −18.2029 31.5283i −0.712333 1.23380i −0.963979 0.265977i $$-0.914305\pi$$
0.251647 0.967819i $$-0.419028\pi$$
$$654$$ 0 0
$$655$$ −3.00000 + 5.19615i −0.117220 + 0.203030i
$$656$$ 0 0
$$657$$ 0.971726 + 18.1436i 0.0379106 + 0.707851i
$$658$$ 0 0
$$659$$ 9.57068 16.5769i 0.372821 0.645745i −0.617177 0.786824i $$-0.711724\pi$$
0.989998 + 0.141079i $$0.0450572\pi$$
$$660$$ 0 0
$$661$$ −19.9536 34.5606i −0.776104 1.34425i −0.934172 0.356824i $$-0.883860\pi$$
0.158067 0.987428i $$-0.449474\pi$$
$$662$$ 0 0
$$663$$ −1.76940 + 7.38874i −0.0687178 + 0.286955i
$$664$$ 0 0
$$665$$ 0.679116 0.0263350
$$666$$ 0 0
$$667$$ 5.72298 0.221595
$$668$$ 0 0
$$669$$ −14.3870 + 4.27061i −0.556235 + 0.165111i
$$670$$ 0 0
$$671$$ −12.2029 21.1360i −0.471086 0.815945i
$$672$$ 0 0
$$673$$ −11.8254 + 20.4822i −0.455836 + 0.789532i −0.998736 0.0502658i $$-0.983993\pi$$
0.542899 + 0.839798i $$0.317326\pi$$
$$674$$ 0 0
$$675$$ 1.74293 + 4.89512i 0.0670855 + 0.188413i
$$676$$ 0 0
$$677$$ 7.40157 12.8199i 0.284465 0.492709i −0.688014 0.725697i $$-0.741517\pi$$
0.972479 + 0.232989i $$0.0748506\pi$$
$$678$$ 0 0
$$679$$ 3.15044 + 5.45673i 0.120903 + 0.209410i
$$680$$ 0 0
$$681$$ −5.51414 + 1.63680i −0.211302 + 0.0627223i
$$682$$ 0 0
$$683$$ 4.95252 0.189503 0.0947515 0.995501i $$-0.469794\pi$$
0.0947515 + 0.995501i $$0.469794\pi$$
$$684$$ 0 0
$$685$$ 5.67004 0.216641
$$686$$ 0 0
$$687$$ 10.2101 42.6359i 0.389540 1.62666i
$$688$$ 0 0
$$689$$ −3.32088 5.75194i −0.126516 0.219131i
$$690$$ 0 0
$$691$$ −9.60442 + 16.6353i −0.365369 + 0.632838i −0.988835 0.149012i $$-0.952391\pi$$
0.623466 + 0.781851i $$0.285724\pi$$
$$692$$ 0 0
$$693$$ 4.29261 2.79466i 0.163063 0.106160i
$$694$$ 0 0
$$695$$ 4.00000 6.92820i 0.151729 0.262802i
$$696$$ 0 0
$$697$$ −18.8446 32.6398i −0.713791 1.23632i
$$698$$ 0 0
$$699$$ −34.7362 32.9256i −1.31384 1.24536i
$$700$$ 0 0
$$701$$ −29.3492 −1.10850 −0.554251 0.832349i $$-0.686995\pi$$
−0.554251 + 0.832349i $$0.686995\pi$$
$$702$$ 0 0
$$703$$ 0.386505 0.0145773
$$704$$ 0 0
$$705$$ −6.11350 5.79483i −0.230248 0.218246i
$$706$$ 0 0
$$707$$ −3.00000 5.19615i −0.112827 0.195421i
$$708$$ 0 0
$$709$$ −19.3633 + 33.5382i −0.727204 + 1.25955i 0.230857 + 0.972988i $$0.425847\pi$$
−0.958060 + 0.286566i $$0.907486\pi$$
$$710$$ 0 0
$$711$$ −21.5479 10.9481i −0.808108 0.410586i
$$712$$ 0 0
$$713$$ −18.0288 + 31.2268i −0.675184 + 1.16945i
$$714$$ 0 0
$$715$$ 2.19325 + 3.79882i 0.0820230 + 0.142068i
$$716$$ 0 0
$$717$$ −1.69365 + 7.07243i −0.0632506 + 0.264125i
$$718$$ 0 0
$$719$$ 15.0848 0.562569 0.281284 0.959624i $$-0.409240\pi$$
0.281284 + 0.959624i $$0.409240\pi$$
$$720$$ 0 0
$$721$$ −0.150442 −0.00560275
$$722$$ 0 0
$$723$$ 5.98494 1.77655i 0.222582 0.0660706i
$$724$$ 0 0
$$725$$ 0.693252 + 1.20075i 0.0257467 + 0.0445947i
$$726$$ 0 0
$$727$$ 6.17277 10.6916i 0.228936 0.396528i −0.728557 0.684985i $$-0.759809\pi$$
0.957493 + 0.288457i $$0.0931422\pi$$
$$728$$ 0 0
$$729$$ −4.31542 26.6529i −0.159830 0.987144i
$$730$$ 0 0
$$731$$ −17.1842 + 29.7639i −0.635580 + 1.10086i
$$732$$ 0 0
$$733$$ 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i $$-0.0334875\pi$$
−0.588177 + 0.808732i $$0.700154\pi$$
$$734$$ 0 0
$$735$$ −11.1842 + 3.31988i −0.412535 + 0.122456i
$$736$$ 0 0
$$737$$ −31.3774 −1.15580
$$738$$ 0 0
$$739$$ −29.7266 −1.09351 −0.546755 0.837293i $$-0.684137\pi$$
−0.546755 + 0.837293i $$0.684137\pi$$
$$740$$ 0 0
$$741$$ 0.703781 2.93888i 0.0258540 0.107962i
$$742$$ 0 0
$$743$$ 24.1824 + 41.8851i 0.887165 + 1.53662i 0.843212 + 0.537582i $$0.180662\pi$$
0.0439537 + 0.999034i $$0.486005\pi$$
$$744$$ 0 0
$$745$$ −8.83049 + 15.2948i −0.323524 + 0.560360i
$$746$$ 0 0
$$747$$ 4.12530 + 2.09599i 0.150937 + 0.0766883i
$$748$$ 0 0
$$749$$ 0.481327 0.833682i 0.0175873 0.0304621i
$$750$$ 0 0
$$751$$ −15.9102 27.5573i −0.580573 1.00558i −0.995411 0.0956869i $$-0.969495\pi$$
0.414838 0.909895i $$-0.363838\pi$$
$$752$$ 0 0
$$753$$ −8.64591 8.19524i −0.315074 0.298651i
$$754$$ 0 0
$$755$$ −1.26434 −0.0460139
$$756$$ 0 0
$$757$$ 4.94531 0.179740 0.0898701 0.995953i $$-0.471355\pi$$
0.0898701 + 0.995953i $$0.471355\pi$$
$$758$$ 0 0
$$759$$ 17.2311 + 16.3330i 0.625450 + 0.592849i
$$760$$ 0 0
$$761$$ −17.7125 30.6789i −0.642076 1.11211i −0.984969 0.172734i $$-0.944740\pi$$
0.342893 0.939375i $$-0.388593\pi$$
$$762$$ 0 0
$$763$$ −1.42618 + 2.47022i −0.0516313 + 0.0894281i
$$764$$ 0 0
$$765$$ −8.34916 + 5.43563i −0.301864 + 0.196525i
$$766$$ 0 0
$$767$$ 3.32088 5.75194i 0.119910 0.207691i
$$768$$ 0 0
$$769$$ −24.7125 42.8032i −0.891154 1.54352i −0.838494 0.544911i $$-0.816563\pi$$
−0.0526602 0.998612i $$-0.516770\pi$$
$$770$$ 0 0
$$771$$ 7.26073 30.3197i 0.261489 1.09194i
$$772$$ 0 0
$$773$$ 12.6599 0.455345 0.227673 0.973738i $$-0.426888\pi$$
0.227673 + 0.973738i $$0.426888\pi$$
$$774$$ 0 0
$$775$$ −8.73566 −0.313794
$$776$$ 0 0
$$777$$ 0.249800 0.0741499i 0.00896153 0.00266011i
$$778$$ 0 0
$$779$$ 7.49546 + 12.9825i 0.268553 + 0.465147i
$$780$$ 0 0
$$781$$ 14.9289 25.8576i 0.534199 0.925259i
$$782$$ 0 0
$$783$$ −2.41658 6.78711i −0.0863616 0.242551i
$$784$$ 0 0
$$785$$ 7.83502 13.5707i 0.279644 0.484357i
$$786$$ 0 0
$$787$$ 15.4672 + 26.7900i 0.551346 + 0.954959i 0.998178 + 0.0603410i $$0.0192188\pi$$
−0.446832 + 0.894618i $$0.647448\pi$$
$$788$$ 0 0
$$789$$ −10.3546 + 3.07364i −0.368634 + 0.109424i
$$790$$ 0 0
$$791$$ 4.01093 0.142612
$$792$$ 0 0
$$793$$ −9.70739 −0.344720
$$794$$ 0