# Properties

 Label 1728.3.q.g.449.1 Level $1728$ Weight $3$ Character 1728.449 Analytic conductor $47.085$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1728 = 2^{6} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1728.q (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$47.0845896815$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-11})$$ Defining polynomial: $$x^{4} - x^{3} - 2x^{2} - 3x + 9$$ x^4 - x^3 - 2*x^2 - 3*x + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$3^{2}$$ Twist minimal: no (minimal twist has level 36) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 449.1 Root $$1.68614 + 0.396143i$$ of defining polynomial Character $$\chi$$ $$=$$ 1728.449 Dual form 1728.3.q.g.1601.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.05842 - 1.18843i) q^{5} +(4.05842 + 7.02939i) q^{7} +O(q^{10})$$ $$q+(-2.05842 - 1.18843i) q^{5} +(4.05842 + 7.02939i) q^{7} +(-17.6168 + 10.1711i) q^{11} +(3.05842 - 5.29734i) q^{13} +17.9653i q^{17} -9.11684 q^{19} +(-29.0584 - 16.7769i) q^{23} +(-9.67527 - 16.7581i) q^{25} +(14.4090 - 8.31901i) q^{29} +(11.1753 - 19.3561i) q^{31} -19.2926i q^{35} +50.4674 q^{37} +(-29.9674 - 17.3017i) q^{41} +(11.5000 + 19.9186i) q^{43} +(33.1753 - 19.1537i) q^{47} +(-8.44158 + 14.6212i) q^{49} -19.0149i q^{53} +48.3505 q^{55} +(-2.96738 - 1.71322i) q^{59} +(-23.1753 - 40.1407i) q^{61} +(-12.5910 + 7.26944i) q^{65} +(-3.14947 + 5.45504i) q^{67} -35.9306i q^{71} +47.3505 q^{73} +(-142.993 - 82.5571i) q^{77} +(42.2921 + 73.2521i) q^{79} +(-33.1753 + 19.1537i) q^{83} +(21.3505 - 36.9802i) q^{85} -143.723i q^{89} +49.6495 q^{91} +(18.7663 + 10.8347i) q^{95} +(-40.3832 - 69.9457i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 9 q^{5} - q^{7}+O(q^{10})$$ 4 * q + 9 * q^5 - q^7 $$4 q + 9 q^{5} - q^{7} - 36 q^{11} - 5 q^{13} - 2 q^{19} - 99 q^{23} + 13 q^{25} - 63 q^{29} - 7 q^{31} + 64 q^{37} + 18 q^{41} + 46 q^{43} + 81 q^{47} - 51 q^{49} + 90 q^{55} + 126 q^{59} - 41 q^{61} - 171 q^{65} - 116 q^{67} + 86 q^{73} - 279 q^{77} + 83 q^{79} - 81 q^{83} - 18 q^{85} + 302 q^{91} + 144 q^{95} - 196 q^{97}+O(q^{100})$$ 4 * q + 9 * q^5 - q^7 - 36 * q^11 - 5 * q^13 - 2 * q^19 - 99 * q^23 + 13 * q^25 - 63 * q^29 - 7 * q^31 + 64 * q^37 + 18 * q^41 + 46 * q^43 + 81 * q^47 - 51 * q^49 + 90 * q^55 + 126 * q^59 - 41 * q^61 - 171 * q^65 - 116 * q^67 + 86 * q^73 - 279 * q^77 + 83 * q^79 - 81 * q^83 - 18 * q^85 + 302 * q^91 + 144 * q^95 - 196 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$703$$ $$1217$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −2.05842 1.18843i −0.411684 0.237686i 0.279829 0.960050i $$-0.409722\pi$$
−0.691513 + 0.722364i $$0.743056\pi$$
$$6$$ 0 0
$$7$$ 4.05842 + 7.02939i 0.579775 + 1.00420i 0.995505 + 0.0947110i $$0.0301927\pi$$
−0.415730 + 0.909488i $$0.636474\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −17.6168 + 10.1711i −1.60153 + 0.924645i −0.610350 + 0.792132i $$0.708971\pi$$
−0.991181 + 0.132513i $$0.957695\pi$$
$$12$$ 0 0
$$13$$ 3.05842 5.29734i 0.235263 0.407488i −0.724086 0.689710i $$-0.757738\pi$$
0.959349 + 0.282222i $$0.0910714\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 17.9653i 1.05678i 0.849001 + 0.528392i $$0.177205\pi$$
−0.849001 + 0.528392i $$0.822795\pi$$
$$18$$ 0 0
$$19$$ −9.11684 −0.479834 −0.239917 0.970793i $$-0.577120\pi$$
−0.239917 + 0.970793i $$0.577120\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −29.0584 16.7769i −1.26341 0.729430i −0.289677 0.957124i $$-0.593548\pi$$
−0.973733 + 0.227695i $$0.926881\pi$$
$$24$$ 0 0
$$25$$ −9.67527 16.7581i −0.387011 0.670322i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 14.4090 8.31901i 0.496860 0.286863i −0.230556 0.973059i $$-0.574054\pi$$
0.727416 + 0.686197i $$0.240721\pi$$
$$30$$ 0 0
$$31$$ 11.1753 19.3561i 0.360492 0.624391i −0.627549 0.778577i $$-0.715942\pi$$
0.988042 + 0.154185i $$0.0492753\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 19.2926i 0.551217i
$$36$$ 0 0
$$37$$ 50.4674 1.36398 0.681992 0.731360i $$-0.261114\pi$$
0.681992 + 0.731360i $$0.261114\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −29.9674 17.3017i −0.730912 0.421992i 0.0878440 0.996134i $$-0.472002\pi$$
−0.818756 + 0.574142i $$0.805336\pi$$
$$42$$ 0 0
$$43$$ 11.5000 + 19.9186i 0.267442 + 0.463223i 0.968200 0.250176i $$-0.0804883\pi$$
−0.700759 + 0.713398i $$0.747155\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 33.1753 19.1537i 0.705857 0.407527i −0.103668 0.994612i $$-0.533058\pi$$
0.809525 + 0.587085i $$0.199725\pi$$
$$48$$ 0 0
$$49$$ −8.44158 + 14.6212i −0.172277 + 0.298393i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 19.0149i 0.358771i −0.983779 0.179386i $$-0.942589\pi$$
0.983779 0.179386i $$-0.0574110\pi$$
$$54$$ 0 0
$$55$$ 48.3505 0.879101
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −2.96738 1.71322i −0.0502945 0.0290375i 0.474642 0.880179i $$-0.342578\pi$$
−0.524936 + 0.851141i $$0.675911\pi$$
$$60$$ 0 0
$$61$$ −23.1753 40.1407i −0.379922 0.658045i 0.611128 0.791532i $$-0.290716\pi$$
−0.991051 + 0.133487i $$0.957383\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −12.5910 + 7.26944i −0.193708 + 0.111838i
$$66$$ 0 0
$$67$$ −3.14947 + 5.45504i −0.0470070 + 0.0814185i −0.888572 0.458738i $$-0.848302\pi$$
0.841565 + 0.540157i $$0.181635\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 35.9306i 0.506065i −0.967458 0.253033i $$-0.918572\pi$$
0.967458 0.253033i $$-0.0814280\pi$$
$$72$$ 0 0
$$73$$ 47.3505 0.648637 0.324319 0.945948i $$-0.394865\pi$$
0.324319 + 0.945948i $$0.394865\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −142.993 82.5571i −1.85705 1.07217i
$$78$$ 0 0
$$79$$ 42.2921 + 73.2521i 0.535343 + 0.927242i 0.999147 + 0.0413035i $$0.0131510\pi$$
−0.463803 + 0.885938i $$0.653516\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −33.1753 + 19.1537i −0.399702 + 0.230768i −0.686355 0.727266i $$-0.740791\pi$$
0.286653 + 0.958034i $$0.407457\pi$$
$$84$$ 0 0
$$85$$ 21.3505 36.9802i 0.251183 0.435061i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 143.723i 1.61486i −0.589963 0.807430i $$-0.700858\pi$$
0.589963 0.807430i $$-0.299142\pi$$
$$90$$ 0 0
$$91$$ 49.6495 0.545599
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 18.7663 + 10.8347i 0.197540 + 0.114050i
$$96$$ 0 0
$$97$$ −40.3832 69.9457i −0.416321 0.721089i 0.579245 0.815154i $$-0.303347\pi$$
−0.995566 + 0.0940641i $$0.970014\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 105.942 61.1654i 1.04893 0.605598i 0.126578 0.991957i $$-0.459601\pi$$
0.922349 + 0.386359i $$0.126267\pi$$
$$102$$ 0 0
$$103$$ −36.8247 + 63.7823i −0.357522 + 0.619246i −0.987546 0.157330i $$-0.949712\pi$$
0.630024 + 0.776575i $$0.283045\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 72.9108i 0.681410i −0.940170 0.340705i $$-0.889334\pi$$
0.940170 0.340705i $$-0.110666\pi$$
$$108$$ 0 0
$$109$$ −31.2989 −0.287146 −0.143573 0.989640i $$-0.545859\pi$$
−0.143573 + 0.989640i $$0.545859\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −16.2269 9.36858i −0.143601 0.0829078i 0.426478 0.904498i $$-0.359754\pi$$
−0.570079 + 0.821590i $$0.693087\pi$$
$$114$$ 0 0
$$115$$ 39.8763 + 69.0678i 0.346751 + 0.600590i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −126.285 + 72.9108i −1.06122 + 0.612696i
$$120$$ 0 0
$$121$$ 146.402 253.576i 1.20993 2.09567i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 105.415i 0.843320i
$$126$$ 0 0
$$127$$ −126.103 −0.992939 −0.496469 0.868054i $$-0.665370\pi$$
−0.496469 + 0.868054i $$0.665370\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 140.694 + 81.2299i 1.07400 + 0.620075i 0.929272 0.369396i $$-0.120435\pi$$
0.144730 + 0.989471i $$0.453769\pi$$
$$132$$ 0 0
$$133$$ −37.0000 64.0859i −0.278195 0.481849i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −90.3832 + 52.1827i −0.659731 + 0.380896i −0.792174 0.610295i $$-0.791051\pi$$
0.132443 + 0.991191i $$0.457718\pi$$
$$138$$ 0 0
$$139$$ 30.6168 53.0299i 0.220265 0.381510i −0.734623 0.678475i $$-0.762641\pi$$
0.954888 + 0.296965i $$0.0959744\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 124.430i 0.870139i
$$144$$ 0 0
$$145$$ −39.5463 −0.272733
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −128.344 74.0993i −0.861367 0.497311i 0.00310272 0.999995i $$-0.499012\pi$$
−0.864470 + 0.502685i $$0.832346\pi$$
$$150$$ 0 0
$$151$$ −127.526 220.881i −0.844542 1.46279i −0.886019 0.463650i $$-0.846540\pi$$
0.0414769 0.999139i $$-0.486794\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −46.0068 + 26.5621i −0.296818 + 0.171368i
$$156$$ 0 0
$$157$$ 146.227 253.272i 0.931381 1.61320i 0.150418 0.988622i $$-0.451938\pi$$
0.780963 0.624577i $$-0.214729\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 272.351i 1.69162i
$$162$$ 0 0
$$163$$ −93.5326 −0.573820 −0.286910 0.957958i $$-0.592628\pi$$
−0.286910 + 0.957958i $$0.592628\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 97.2269 + 56.1340i 0.582197 + 0.336131i 0.762006 0.647570i $$-0.224215\pi$$
−0.179809 + 0.983702i $$0.557548\pi$$
$$168$$ 0 0
$$169$$ 65.7921 + 113.955i 0.389302 + 0.674292i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −205.227 + 118.488i −1.18628 + 0.684900i −0.957460 0.288568i $$-0.906821\pi$$
−0.228823 + 0.973468i $$0.573488\pi$$
$$174$$ 0 0
$$175$$ 78.5326 136.022i 0.448758 0.777271i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 234.599i 1.31061i −0.755366 0.655304i $$-0.772541\pi$$
0.755366 0.655304i $$-0.227459\pi$$
$$180$$ 0 0
$$181$$ −221.636 −1.22451 −0.612254 0.790661i $$-0.709737\pi$$
−0.612254 + 0.790661i $$0.709737\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −103.883 59.9770i −0.561531 0.324200i
$$186$$ 0 0
$$187$$ −182.727 316.492i −0.977149 1.69247i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 130.162 75.1488i 0.681474 0.393449i −0.118936 0.992902i $$-0.537948\pi$$
0.800410 + 0.599452i $$0.204615\pi$$
$$192$$ 0 0
$$193$$ 24.5000 42.4352i 0.126943 0.219872i −0.795548 0.605891i $$-0.792817\pi$$
0.922491 + 0.386019i $$0.126150\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 276.827i 1.40521i −0.711579 0.702606i $$-0.752020\pi$$
0.711579 0.702606i $$-0.247980\pi$$
$$198$$ 0 0
$$199$$ −198.935 −0.999672 −0.499836 0.866120i $$-0.666606\pi$$
−0.499836 + 0.866120i $$0.666606\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 116.955 + 67.5241i 0.576134 + 0.332631i
$$204$$ 0 0
$$205$$ 41.1237 + 71.2283i 0.200603 + 0.347455i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 160.610 92.7282i 0.768469 0.443676i
$$210$$ 0 0
$$211$$ 47.0068 81.4182i 0.222781 0.385868i −0.732870 0.680368i $$-0.761820\pi$$
0.955651 + 0.294500i $$0.0951531\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 54.6678i 0.254269i
$$216$$ 0 0
$$217$$ 181.416 0.836017
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 95.1684 + 54.9455i 0.430626 + 0.248622i
$$222$$ 0 0
$$223$$ 77.8763 + 134.886i 0.349221 + 0.604869i 0.986111 0.166086i $$-0.0531128\pi$$
−0.636890 + 0.770955i $$0.719780\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −138.448 + 79.9332i −0.609905 + 0.352129i −0.772928 0.634493i $$-0.781209\pi$$
0.163023 + 0.986622i $$0.447875\pi$$
$$228$$ 0 0
$$229$$ −19.1237 + 33.1232i −0.0835095 + 0.144643i −0.904755 0.425932i $$-0.859946\pi$$
0.821246 + 0.570575i $$0.193280\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 157.490i 0.675921i 0.941160 + 0.337960i $$0.109737\pi$$
−0.941160 + 0.337960i $$0.890263\pi$$
$$234$$ 0 0
$$235$$ −91.0516 −0.387454
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 62.4742 + 36.0695i 0.261398 + 0.150918i 0.624972 0.780647i $$-0.285110\pi$$
−0.363574 + 0.931565i $$0.618444\pi$$
$$240$$ 0 0
$$241$$ −113.370 196.362i −0.470413 0.814779i 0.529015 0.848613i $$-0.322562\pi$$
−0.999427 + 0.0338337i $$0.989228\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 34.7527 20.0645i 0.141848 0.0818957i
$$246$$ 0 0
$$247$$ −27.8832 + 48.2950i −0.112887 + 0.195526i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 222.931i 0.888171i 0.895985 + 0.444085i $$0.146471\pi$$
−0.895985 + 0.444085i $$0.853529\pi$$
$$252$$ 0 0
$$253$$ 682.557 2.69785
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −92.2011 53.2323i −0.358759 0.207130i 0.309777 0.950809i $$-0.399746\pi$$
−0.668536 + 0.743680i $$0.733079\pi$$
$$258$$ 0 0
$$259$$ 204.818 + 354.755i 0.790803 + 1.36971i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −155.344 + 89.6877i −0.590660 + 0.341018i −0.765359 0.643604i $$-0.777438\pi$$
0.174698 + 0.984622i $$0.444105\pi$$
$$264$$ 0 0
$$265$$ −22.5979 + 39.1407i −0.0852750 + 0.147701i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 416.351i 1.54777i −0.633324 0.773887i $$-0.718310\pi$$
0.633324 0.773887i $$-0.281690\pi$$
$$270$$ 0 0
$$271$$ 396.907 1.46460 0.732302 0.680980i $$-0.238446\pi$$
0.732302 + 0.680980i $$0.238446\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 340.895 + 196.816i 1.23962 + 0.715695i
$$276$$ 0 0
$$277$$ −57.7731 100.066i −0.208567 0.361249i 0.742696 0.669629i $$-0.233547\pi$$
−0.951263 + 0.308379i $$0.900213\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −422.564 + 243.967i −1.50379 + 0.868211i −0.503795 + 0.863823i $$0.668063\pi$$
−0.999990 + 0.00438786i $$0.998603\pi$$
$$282$$ 0 0
$$283$$ −169.825 + 294.145i −0.600087 + 1.03938i 0.392720 + 0.919658i $$0.371534\pi$$
−0.992807 + 0.119724i $$0.961799\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 280.870i 0.978641i
$$288$$ 0 0
$$289$$ −33.7527 −0.116791
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 122.409 + 70.6728i 0.417778 + 0.241204i 0.694126 0.719853i $$-0.255791\pi$$
−0.276348 + 0.961058i $$0.589124\pi$$
$$294$$ 0 0
$$295$$ 4.07207 + 7.05304i 0.0138036 + 0.0239086i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −177.746 + 102.622i −0.594468 + 0.343216i
$$300$$ 0 0
$$301$$ −93.3437 + 161.676i −0.310112 + 0.537130i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 110.169i 0.361209i
$$306$$ 0 0
$$307$$ 120.649 0.392995 0.196498 0.980504i $$-0.437043\pi$$
0.196498 + 0.980504i $$0.437043\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 119.254 + 68.8514i 0.383454 + 0.221387i 0.679320 0.733842i $$-0.262275\pi$$
−0.295866 + 0.955229i $$0.595608\pi$$
$$312$$ 0 0
$$313$$ −129.266 223.896i −0.412991 0.715322i 0.582224 0.813029i $$-0.302183\pi$$
−0.995215 + 0.0977064i $$0.968849\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −16.7079 + 9.64630i −0.0527063 + 0.0304300i −0.526122 0.850409i $$-0.676354\pi$$
0.473415 + 0.880839i $$0.343021\pi$$
$$318$$ 0 0
$$319$$ −169.227 + 293.110i −0.530492 + 0.918839i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 163.787i 0.507081i
$$324$$ 0 0
$$325$$ −118.364 −0.364197
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 269.278 + 155.468i 0.818476 + 0.472547i
$$330$$ 0 0
$$331$$ −98.3953 170.426i −0.297267 0.514881i 0.678243 0.734838i $$-0.262742\pi$$
−0.975510 + 0.219957i $$0.929408\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 12.9659 7.48585i 0.0387041 0.0223458i
$$336$$ 0 0
$$337$$ −158.720 + 274.911i −0.470979 + 0.815760i −0.999449 0.0331921i $$-0.989433\pi$$
0.528470 + 0.848952i $$0.322766\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 454.659i 1.33331i
$$342$$ 0 0
$$343$$ 260.687 0.760022
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −537.407 310.272i −1.54872 0.894157i −0.998240 0.0593116i $$-0.981109\pi$$
−0.550485 0.834845i $$-0.685557\pi$$
$$348$$ 0 0
$$349$$ −189.512 328.245i −0.543015 0.940529i −0.998729 0.0504030i $$-0.983949\pi$$
0.455714 0.890126i $$-0.349384\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 213.514 123.272i 0.604855 0.349213i −0.166094 0.986110i $$-0.553116\pi$$
0.770949 + 0.636897i $$0.219782\pi$$
$$354$$ 0 0
$$355$$ −42.7011 + 73.9604i −0.120285 + 0.208339i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 572.791i 1.59552i −0.602976 0.797759i $$-0.706019\pi$$
0.602976 0.797759i $$-0.293981\pi$$
$$360$$ 0 0
$$361$$ −277.883 −0.769759
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −97.4674 56.2728i −0.267034 0.154172i
$$366$$ 0 0
$$367$$ 93.9279 + 162.688i 0.255934 + 0.443291i 0.965149 0.261701i $$-0.0842836\pi$$
−0.709214 + 0.704993i $$0.750950\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 133.663 77.1704i 0.360278 0.208007i
$$372$$ 0 0
$$373$$ 75.0584 130.005i 0.201229 0.348539i −0.747696 0.664042i $$-0.768840\pi$$
0.948925 + 0.315503i $$0.102173\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 101.772i 0.269953i
$$378$$ 0 0
$$379$$ 26.6222 0.0702432 0.0351216 0.999383i $$-0.488818\pi$$
0.0351216 + 0.999383i $$0.488818\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 444.966 + 256.901i 1.16179 + 0.670760i 0.951733 0.306929i $$-0.0993013\pi$$
0.210058 + 0.977689i $$0.432635\pi$$
$$384$$ 0 0
$$385$$ 196.227 + 339.875i 0.509680 + 0.882792i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −22.1616 + 12.7950i −0.0569707 + 0.0328921i −0.528215 0.849111i $$-0.677138\pi$$
0.471244 + 0.882003i $$0.343805\pi$$
$$390$$ 0 0
$$391$$ 301.402 522.044i 0.770849 1.33515i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 201.045i 0.508975i
$$396$$ 0 0
$$397$$ −388.804 −0.979356 −0.489678 0.871903i $$-0.662886\pi$$
−0.489678 + 0.871903i $$0.662886\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 34.0842 + 19.6785i 0.0849981 + 0.0490736i 0.541897 0.840445i $$-0.317706\pi$$
−0.456899 + 0.889519i $$0.651040\pi$$
$$402$$ 0 0
$$403$$ −68.3574 118.398i −0.169621 0.293793i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −889.076 + 513.308i −2.18446 + 1.26120i
$$408$$ 0 0
$$409$$ −86.7200 + 150.204i −0.212029 + 0.367246i −0.952350 0.305009i $$-0.901341\pi$$
0.740320 + 0.672255i $$0.234674\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 27.8118i 0.0673409i
$$414$$ 0 0
$$415$$ 91.0516 0.219401
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 115.031 + 66.4132i 0.274537 + 0.158504i 0.630948 0.775825i $$-0.282666\pi$$
−0.356411 + 0.934329i $$0.616000\pi$$
$$420$$ 0 0
$$421$$ 317.447 + 549.834i 0.754031 + 1.30602i 0.945855 + 0.324590i $$0.105226\pi$$
−0.191824 + 0.981429i $$0.561440\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 301.064 173.819i 0.708385 0.408986i
$$426$$ 0 0
$$427$$ 188.110 325.816i 0.440539 0.763035i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 602.424i 1.39774i −0.715251 0.698868i $$-0.753687\pi$$
0.715251 0.698868i $$-0.246313\pi$$
$$432$$ 0 0
$$433$$ 266.155 0.614676 0.307338 0.951600i $$-0.400562\pi$$
0.307338 + 0.951600i $$0.400562\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 264.921 + 152.952i 0.606227 + 0.350005i
$$438$$ 0 0
$$439$$ −250.330 433.584i −0.570228 0.987664i −0.996542 0.0830886i $$-0.973522\pi$$
0.426314 0.904575i $$-0.359812\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −261.098 + 150.745i −0.589386 + 0.340282i −0.764855 0.644203i $$-0.777189\pi$$
0.175469 + 0.984485i $$0.443856\pi$$
$$444$$ 0 0
$$445$$ −170.804 + 295.842i −0.383830 + 0.664813i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 565.321i 1.25907i 0.776973 + 0.629534i $$0.216754\pi$$
−0.776973 + 0.629534i $$0.783246\pi$$
$$450$$ 0 0
$$451$$ 703.907 1.56077
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −102.200 59.0049i −0.224614 0.129681i
$$456$$ 0 0
$$457$$ −26.1495 45.2922i −0.0572198 0.0991077i 0.835997 0.548735i $$-0.184890\pi$$
−0.893216 + 0.449627i $$0.851557\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 166.357 96.0465i 0.360862 0.208344i −0.308597 0.951193i $$-0.599859\pi$$
0.669459 + 0.742849i $$0.266526\pi$$
$$462$$ 0 0
$$463$$ −283.110 + 490.361i −0.611469 + 1.05909i 0.379524 + 0.925182i $$0.376088\pi$$
−0.990993 + 0.133913i $$0.957246\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 174.405i 0.373459i −0.982411 0.186729i $$-0.940211\pi$$
0.982411 0.186729i $$-0.0597888\pi$$
$$468$$ 0 0
$$469$$ −51.1275 −0.109014
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −405.187 233.935i −0.856633 0.494577i
$$474$$ 0 0
$$475$$ 88.2079 + 152.781i 0.185701 + 0.321643i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −473.784 + 273.539i −0.989110 + 0.571063i −0.905008 0.425394i $$-0.860135\pi$$
−0.0841020 + 0.996457i $$0.526802\pi$$
$$480$$ 0 0
$$481$$ 154.351 267.343i 0.320895 0.555807i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 191.970i 0.395815i
$$486$$ 0 0
$$487$$ −769.945 −1.58100 −0.790498 0.612464i $$-0.790178\pi$$
−0.790498 + 0.612464i $$0.790178\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −154.916 89.4407i −0.315511 0.182160i 0.333879 0.942616i $$-0.391642\pi$$
−0.649390 + 0.760456i $$0.724976\pi$$
$$492$$ 0 0
$$493$$ 149.454 + 258.861i 0.303152 + 0.525074i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 252.571 145.822i 0.508190 0.293404i
$$498$$ 0 0
$$499$$ −192.655 + 333.688i −0.386082 + 0.668713i −0.991919 0.126876i $$-0.959505\pi$$
0.605837 + 0.795589i $$0.292838\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 67.6630i 0.134519i 0.997736 + 0.0672594i $$0.0214255\pi$$
−0.997736 + 0.0672594i $$0.978574\pi$$
$$504$$ 0 0
$$505$$ −290.763 −0.575769
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 523.292 + 302.123i 1.02808 + 0.593562i 0.916434 0.400187i $$-0.131055\pi$$
0.111645 + 0.993748i $$0.464388\pi$$
$$510$$ 0 0
$$511$$ 192.168 + 332.846i 0.376063 + 0.651361i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 151.602 87.5273i 0.294372 0.169956i
$$516$$ 0 0
$$517$$ −389.629 + 674.857i −0.753634 + 1.30533i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 273.678i 0.525294i 0.964892 + 0.262647i $$0.0845954\pi$$
−0.964892 + 0.262647i $$0.915405\pi$$
$$522$$ 0 0
$$523$$ −687.402 −1.31434 −0.657172 0.753740i $$-0.728248\pi$$
−0.657172 + 0.753740i $$0.728248\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 347.739 + 200.767i 0.659846 + 0.380962i
$$528$$ 0 0
$$529$$ 298.428 + 516.892i 0.564136 + 0.977112i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −183.306 + 105.832i −0.343913 + 0.198558i
$$534$$ 0 0
$$535$$ −86.6495 + 150.081i −0.161962 + 0.280526i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 343.440i 0.637180i
$$540$$ 0 0
$$541$$ −664.543 −1.22836 −0.614180 0.789166i $$-0.710513\pi$$
−0.614180 + 0.789166i $$0.710513\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 64.4264 + 37.1966i 0.118214 + 0.0682507i
$$546$$ 0 0
$$547$$ 259.603 + 449.646i 0.474594 + 0.822022i 0.999577 0.0290914i $$-0.00926138\pi$$
−0.524982 + 0.851113i $$0.675928\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −131.364 + 75.8431i −0.238410 + 0.137646i
$$552$$ 0 0
$$553$$ −343.278 + 594.576i −0.620757 + 1.07518i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 422.648i 0.758794i 0.925234 + 0.379397i $$0.123869\pi$$
−0.925234 + 0.379397i $$0.876131\pi$$
$$558$$ 0 0
$$559$$ 140.687 0.251677
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 798.799 + 461.187i 1.41883 + 0.819159i 0.996196 0.0871428i $$-0.0277737\pi$$
0.422630 + 0.906302i $$0.361107\pi$$
$$564$$ 0 0
$$565$$ 22.2678 + 38.5690i 0.0394121 + 0.0682637i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 914.445 527.955i 1.60711 0.927865i 0.617097 0.786887i $$-0.288309\pi$$
0.990013 0.140978i $$-0.0450247\pi$$
$$570$$ 0 0
$$571$$ 401.524 695.460i 0.703195 1.21797i −0.264144 0.964483i $$-0.585089\pi$$
0.967339 0.253486i $$-0.0815772\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 649.283i 1.12919i
$$576$$ 0 0
$$577$$ −96.6495 −0.167503 −0.0837517 0.996487i $$-0.526690\pi$$
−0.0837517 + 0.996487i $$0.526690\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −269.278 155.468i −0.463474 0.267587i
$$582$$ 0 0
$$583$$ 193.402 + 334.982i 0.331736 + 0.574584i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −870.497 + 502.582i −1.48296 + 0.856187i −0.999813 0.0193528i $$-0.993839\pi$$
−0.483146 + 0.875540i $$0.660506\pi$$
$$588$$ 0 0
$$589$$ −101.883 + 176.467i −0.172976 + 0.299604i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 752.444i 1.26888i 0.772973 + 0.634439i $$0.218769\pi$$
−0.772973 + 0.634439i $$0.781231\pi$$
$$594$$ 0 0
$$595$$ 346.598 0.582517
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 24.0857 + 13.9059i 0.0402099 + 0.0232152i 0.519970 0.854184i $$-0.325943\pi$$
−0.479760 + 0.877400i $$0.659276\pi$$
$$600$$ 0 0
$$601$$ 475.356 + 823.340i 0.790942 + 1.36995i 0.925385 + 0.379030i $$0.123742\pi$$
−0.134443 + 0.990921i $$0.542925\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −602.715 + 347.978i −0.996223 + 0.575169i
$$606$$ 0 0
$$607$$ 161.306 279.390i 0.265743 0.460280i −0.702015 0.712162i $$-0.747716\pi$$
0.967758 + 0.251882i $$0.0810495\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 234.321i 0.383504i
$$612$$ 0 0
$$613$$ −138.206 −0.225459 −0.112730 0.993626i $$-0.535959\pi$$
−0.112730 + 0.993626i $$0.535959\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 682.084 + 393.802i 1.10548 + 0.638252i 0.937656 0.347564i $$-0.112991\pi$$
0.167829 + 0.985816i $$0.446324\pi$$
$$618$$ 0 0
$$619$$ −121.747 210.873i −0.196684 0.340667i 0.750767 0.660567i $$-0.229684\pi$$
−0.947451 + 0.319900i $$0.896351\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 1010.28 583.287i 1.62164 0.936255i
$$624$$ 0 0
$$625$$ −116.603 + 201.963i −0.186565 + 0.323140i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 906.662i 1.44143i
$$630$$ 0 0
$$631$$ 111.924 0.177376 0.0886879 0.996059i $$-0.471733\pi$$
0.0886879 + 0.996059i $$0.471733\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 259.574 + 149.865i 0.408777 + 0.236008i
$$636$$ 0 0
$$637$$ 51.6358 + 89.4359i 0.0810609 + 0.140402i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −632.095 + 364.940i −0.986107 + 0.569329i −0.904108 0.427303i $$-0.859464\pi$$
−0.0819990 + 0.996632i $$0.526130\pi$$
$$642$$ 0 0
$$643$$ −288.500 + 499.697i −0.448678 + 0.777133i −0.998300 0.0582801i $$-0.981438\pi$$
0.549622 + 0.835413i $$0.314772\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 129.029i 0.199426i 0.995016 + 0.0997130i $$0.0317925\pi$$
−0.995016 + 0.0997130i $$0.968208\pi$$
$$648$$ 0 0
$$649$$ 69.7011 0.107398
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1026.62 + 592.717i 1.57215 + 0.907682i 0.995905 + 0.0904070i $$0.0288168\pi$$
0.576247 + 0.817275i $$0.304517\pi$$
$$654$$ 0 0
$$655$$ −193.072 334.411i −0.294767 0.510551i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 947.808 547.217i 1.43825 0.830375i 0.440524 0.897741i $$-0.354793\pi$$
0.997728 + 0.0673658i $$0.0214595\pi$$
$$660$$ 0 0
$$661$$ 604.876 1047.68i 0.915093 1.58499i 0.108327 0.994115i $$-0.465451\pi$$
0.806765 0.590872i $$-0.201216\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 175.888i 0.264493i
$$666$$ 0 0
$$667$$ −558.269 −0.836984
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 816.550 + 471.435i 1.21692 + 0.702586i
$$672$$ 0 0
$$673$$ −508.615 880.948i −0.755743 1.30899i −0.945004 0.327059i $$-0.893942\pi$$
0.189260 0.981927i $$-0.439391\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 689.890 398.308i 1.01904 0.588343i 0.105214 0.994450i $$-0.466447\pi$$
0.913826 + 0.406107i $$0.133114\pi$$
$$678$$ 0 0
$$679$$ 327.784 567.738i 0.482745 0.836139i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 400.485i 0.586361i −0.956057 0.293181i $$-0.905286\pi$$
0.956057 0.293181i $$-0.0947138\pi$$
$$684$$ 0 0
$$685$$ 248.062 0.362135
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −100.728 58.1556i −0.146195 0.0844057i
$$690$$ 0 0
$$691$$ −216.423 374.855i −0.313202 0.542482i 0.665852 0.746084i $$-0.268068\pi$$
−0.979054 + 0.203602i $$0.934735\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −126.045 + 72.7720i −0.181359 + 0.104708i
$$696$$ 0 0
$$697$$ 310.830 538.373i 0.445954 0.772415i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 65.4412i 0.0933541i −0.998910 0.0466770i $$-0.985137\pi$$
0.998910 0.0466770i $$-0.0148632\pi$$
$$702$$ 0 0
$$703$$ −460.103 −0.654485
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 859.911 + 496.470i 1.21628 + 0.702221i
$$708$$ 0 0
$$709$$ 100.461 + 174.003i 0.141693 + 0.245420i 0.928134 0.372245i $$-0.121412\pi$$
−0.786441 + 0.617665i $$0.788079\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −649.471 + 374.972i −0.910899 + 0.525908i
$$714$$ 0 0
$$715$$ 147.876 256.129i 0.206820 0.358223i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1062.98i 1.47841i −0.673478 0.739207i $$-0.735200\pi$$
0.673478 0.739207i $$-0.264800\pi$$
$$720$$ 0 0
$$721$$ −597.801 −0.829128
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −278.821 160.977i −0.384581 0.222038i
$$726$$ 0 0
$$727$$ −495.629 858.455i −0.681746 1.18082i −0.974448 0.224614i $$-0.927888\pi$$
0.292702 0.956204i $$-0.405446\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −357.844 + 206.601i −0.489526 + 0.282628i
$$732$$ 0 0
$$733$$ −590.134 + 1022.14i −0.805095 + 1.39446i 0.111133 + 0.993806i $$0.464552\pi$$
−0.916227 + 0.400659i $$0.868781\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 128.134i 0.173859i
$$738$$ 0 0
$$739$$ −599.351 −0.811029 −0.405515 0.914089i $$-0.632908\pi$$
−0.405515 + 0.914089i $$0.632908\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −287.083 165.747i −0.386383 0.223078i 0.294209 0.955741i $$-0.404944\pi$$
−0.680592 + 0.732663i $$0.738277\pi$$
$$744$$ 0 0
$$745$$ 176.124 + 305.055i 0.236408 + 0.409470i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 512.519 295.903i 0.684271 0.395064i
$$750$$ 0 0
$$751$$ −76.0448 + 131.713i −0.101258 + 0.175384i −0.912203 0.409738i $$-0.865620\pi$$
0.810945 + 0.585122i $$0.198953\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 606.222i 0.802943i
$$756$$ 0 0
$$757$$ 1179.61 1.55827 0.779134 0.626858i $$-0.215659\pi$$
0.779134 + 0.626858i $$0.215659\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1162.58 + 671.214i 1.52770 + 0.882016i 0.999458 + 0.0329205i $$0.0104808\pi$$
0.528239 + 0.849096i $$0.322853\pi$$
$$762$$ 0 0
$$763$$ −127.024 220.013i −0.166480 0.288352i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −18.1510 + 10.4795i −0.0236649 + 0.0136629i
$$768$$ 0 0
$$769$$ −548.512 + 950.051i −0.713280 + 1.23544i 0.250339 + 0.968158i $$0.419458\pi$$
−0.963619 + 0.267279i $$0.913876\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1181.39i 1.52832i −0.645028 0.764159i $$-0.723154\pi$$
0.645028 0.764159i $$-0.276846\pi$$
$$774$$ 0 0
$$775$$ −432.495 −0.558058
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 273.208 + 157.737i 0.350716 + 0.202486i
$$780$$ 0 0
$$781$$ 365.454 + 632.984i 0.467931 + 0.810479i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −601.993 + 347.561i −0.766870 + 0.442753i
$$786$$ 0 0
$$787$$ −18.0311 + 31.2308i −0.0229112 + 0.0396834i −0.877254 0.480027i $$-0.840627\pi$$
0.854342 + 0.519710i $$0.173960\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 152.087i 0.192271i
$$792$$ 0 0
$$793$$ −283.519 −0.357527
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −115.618 66.7523i −0.145067 0.0837544i 0.425710 0.904860i $$-0.360024\pi$$
−0.570777 + 0.821105i $$0.693358\pi$$
$$798$$ 0 0
$$799$$ 344.103