# Properties

 Label 1008.3.cg.i.145.2 Level $1008$ Weight $3$ Character 1008.145 Analytic conductor $27.466$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1008.cg (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$27.4660106475$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}\cdot 3$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 145.2 Root $$0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1008.145 Dual form 1008.3.cg.i.577.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(4.24264 + 2.44949i) q^{5} +(-3.50000 + 6.06218i) q^{7} +O(q^{10})$$ $$q+(4.24264 + 2.44949i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(-8.48528 - 14.6969i) q^{11} +1.73205i q^{13} +(-4.24264 + 2.44949i) q^{17} +(-25.5000 - 14.7224i) q^{19} +(-4.24264 + 7.34847i) q^{23} +(-0.500000 - 0.866025i) q^{25} -33.9411 q^{29} +(10.5000 - 6.06218i) q^{31} +(-29.6985 + 17.1464i) q^{35} +(23.5000 - 40.7032i) q^{37} -68.5857i q^{41} -31.0000 q^{43} +(72.1249 + 41.6413i) q^{47} +(-24.5000 - 42.4352i) q^{49} +(38.1838 + 66.1362i) q^{53} -83.1384i q^{55} +(72.1249 - 41.6413i) q^{59} +(-72.0000 - 41.5692i) q^{61} +(-4.24264 + 7.34847i) q^{65} +(-15.5000 - 26.8468i) q^{67} -59.3970 q^{71} +(-70.5000 + 40.7032i) q^{73} +118.794 q^{77} +(20.5000 - 35.5070i) q^{79} -4.89898i q^{83} -24.0000 q^{85} +(50.9117 + 29.3939i) q^{89} +(-10.5000 - 6.06218i) q^{91} +(-72.1249 - 124.924i) q^{95} -41.5692i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 14 q^{7} + O(q^{10})$$ $$4 q - 14 q^{7} - 102 q^{19} - 2 q^{25} + 42 q^{31} + 94 q^{37} - 124 q^{43} - 98 q^{49} - 288 q^{61} - 62 q^{67} - 282 q^{73} + 82 q^{79} - 96 q^{85} - 42 q^{91} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$577$$ $$757$$ $$785$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$

## 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 0
$$4$$ 0 0
$$5$$ 4.24264 + 2.44949i 0.848528 + 0.489898i 0.860154 0.510034i $$-0.170367\pi$$
−0.0116258 + 0.999932i $$0.503701\pi$$
$$6$$ 0 0
$$7$$ −3.50000 + 6.06218i −0.500000 + 0.866025i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −8.48528 14.6969i −0.771389 1.33609i −0.936802 0.349861i $$-0.886229\pi$$
0.165412 0.986224i $$-0.447104\pi$$
$$12$$ 0 0
$$13$$ 1.73205i 0.133235i 0.997779 + 0.0666173i $$0.0212207\pi$$
−0.997779 + 0.0666173i $$0.978779\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −4.24264 + 2.44949i −0.249567 + 0.144088i −0.619566 0.784945i $$-0.712691\pi$$
0.369999 + 0.929032i $$0.379358\pi$$
$$18$$ 0 0
$$19$$ −25.5000 14.7224i −1.34211 0.774865i −0.354989 0.934870i $$-0.615515\pi$$
−0.987116 + 0.160006i $$0.948849\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4.24264 + 7.34847i −0.184463 + 0.319499i −0.943395 0.331670i $$-0.892388\pi$$
0.758933 + 0.651169i $$0.225721\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −33.9411 −1.17038 −0.585192 0.810895i $$-0.698981\pi$$
−0.585192 + 0.810895i $$0.698981\pi$$
$$30$$ 0 0
$$31$$ 10.5000 6.06218i 0.338710 0.195554i −0.320992 0.947082i $$-0.604016\pi$$
0.659701 + 0.751528i $$0.270683\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −29.6985 + 17.1464i −0.848528 + 0.489898i
$$36$$ 0 0
$$37$$ 23.5000 40.7032i 0.635135 1.10009i −0.351351 0.936244i $$-0.614278\pi$$
0.986486 0.163843i $$-0.0523889\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 68.5857i 1.67282i −0.548103 0.836411i $$-0.684650\pi$$
0.548103 0.836411i $$-0.315350\pi$$
$$42$$ 0 0
$$43$$ −31.0000 −0.720930 −0.360465 0.932773i $$-0.617382\pi$$
−0.360465 + 0.932773i $$0.617382\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 72.1249 + 41.6413i 1.53457 + 0.885986i 0.999142 + 0.0414059i $$0.0131837\pi$$
0.535430 + 0.844580i $$0.320150\pi$$
$$48$$ 0 0
$$49$$ −24.5000 42.4352i −0.500000 0.866025i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 38.1838 + 66.1362i 0.720448 + 1.24785i 0.960820 + 0.277172i $$0.0893973\pi$$
−0.240372 + 0.970681i $$0.577269\pi$$
$$54$$ 0 0
$$55$$ 83.1384i 1.51161i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 72.1249 41.6413i 1.22246 0.705785i 0.257015 0.966407i $$-0.417261\pi$$
0.965441 + 0.260622i $$0.0839277\pi$$
$$60$$ 0 0
$$61$$ −72.0000 41.5692i −1.18033 0.681463i −0.224237 0.974535i $$-0.571989\pi$$
−0.956090 + 0.293072i $$0.905322\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −4.24264 + 7.34847i −0.0652714 + 0.113053i
$$66$$ 0 0
$$67$$ −15.5000 26.8468i −0.231343 0.400698i 0.726860 0.686785i $$-0.240979\pi$$
−0.958204 + 0.286087i $$0.907645\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −59.3970 −0.836577 −0.418289 0.908314i $$-0.637370\pi$$
−0.418289 + 0.908314i $$0.637370\pi$$
$$72$$ 0 0
$$73$$ −70.5000 + 40.7032i −0.965753 + 0.557578i −0.897939 0.440120i $$-0.854936\pi$$
−0.0678144 + 0.997698i $$0.521603\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 118.794 1.54278
$$78$$ 0 0
$$79$$ 20.5000 35.5070i 0.259494 0.449456i −0.706613 0.707601i $$-0.749778\pi$$
0.966106 + 0.258144i $$0.0831110\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 4.89898i 0.0590238i −0.999564 0.0295119i $$-0.990605\pi$$
0.999564 0.0295119i $$-0.00939530\pi$$
$$84$$ 0 0
$$85$$ −24.0000 −0.282353
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 50.9117 + 29.3939i 0.572041 + 0.330268i 0.757964 0.652296i $$-0.226194\pi$$
−0.185923 + 0.982564i $$0.559527\pi$$
$$90$$ 0 0
$$91$$ −10.5000 6.06218i −0.115385 0.0666173i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −72.1249 124.924i −0.759209 1.31499i
$$96$$ 0 0
$$97$$ 41.5692i 0.428549i −0.976774 0.214274i $$-0.931261\pi$$
0.976774 0.214274i $$-0.0687387\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −152.735 + 88.1816i −1.51223 + 0.873085i −0.512331 + 0.858788i $$0.671218\pi$$
−0.999898 + 0.0142971i $$0.995449\pi$$
$$102$$ 0 0
$$103$$ 25.5000 + 14.7224i 0.247573 + 0.142936i 0.618652 0.785665i $$-0.287679\pi$$
−0.371080 + 0.928601i $$0.621012\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −72.1249 + 124.924i −0.674064 + 1.16751i 0.302677 + 0.953093i $$0.402120\pi$$
−0.976741 + 0.214421i $$0.931214\pi$$
$$108$$ 0 0
$$109$$ −84.5000 146.358i −0.775229 1.34274i −0.934665 0.355528i $$-0.884301\pi$$
0.159436 0.987208i $$-0.449032\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −59.3970 −0.525637 −0.262818 0.964845i $$-0.584652\pi$$
−0.262818 + 0.964845i $$0.584652\pi$$
$$114$$ 0 0
$$115$$ −36.0000 + 20.7846i −0.313043 + 0.180736i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 34.2929i 0.288175i
$$120$$ 0 0
$$121$$ −83.5000 + 144.626i −0.690083 + 1.19526i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 127.373i 1.01899i
$$126$$ 0 0
$$127$$ −209.000 −1.64567 −0.822835 0.568281i $$-0.807609\pi$$
−0.822835 + 0.568281i $$0.807609\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 50.9117 + 29.3939i 0.388639 + 0.224381i 0.681570 0.731753i $$-0.261297\pi$$
−0.292931 + 0.956133i $$0.594631\pi$$
$$132$$ 0 0
$$133$$ 178.500 103.057i 1.34211 0.774865i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −76.3675 132.272i −0.557427 0.965492i −0.997710 0.0676333i $$-0.978455\pi$$
0.440283 0.897859i $$-0.354878\pi$$
$$138$$ 0 0
$$139$$ 195.722i 1.40807i −0.710165 0.704035i $$-0.751380\pi$$
0.710165 0.704035i $$-0.248620\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 25.4558 14.6969i 0.178013 0.102776i
$$144$$ 0 0
$$145$$ −144.000 83.1384i −0.993103 0.573369i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −25.4558 + 44.0908i −0.170845 + 0.295912i −0.938715 0.344693i $$-0.887983\pi$$
0.767871 + 0.640605i $$0.221316\pi$$
$$150$$ 0 0
$$151$$ 5.00000 + 8.66025i 0.0331126 + 0.0573527i 0.882107 0.471049i $$-0.156125\pi$$
−0.848994 + 0.528402i $$0.822791\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 59.3970 0.383206
$$156$$ 0 0
$$157$$ 36.0000 20.7846i 0.229299 0.132386i −0.380949 0.924596i $$-0.624403\pi$$
0.610249 + 0.792210i $$0.291069\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −29.6985 51.4393i −0.184463 0.319499i
$$162$$ 0 0
$$163$$ 43.0000 74.4782i 0.263804 0.456921i −0.703446 0.710749i $$-0.748356\pi$$
0.967250 + 0.253828i $$0.0816896\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 181.262i 1.08540i 0.839926 + 0.542701i $$0.182598\pi$$
−0.839926 + 0.542701i $$0.817402\pi$$
$$168$$ 0 0
$$169$$ 166.000 0.982249
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −38.1838 22.0454i −0.220715 0.127430i 0.385566 0.922680i $$-0.374006\pi$$
−0.606281 + 0.795250i $$0.707340\pi$$
$$174$$ 0 0
$$175$$ 7.00000 0.0400000
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −4.24264 7.34847i −0.0237019 0.0410529i 0.853931 0.520386i $$-0.174212\pi$$
−0.877633 + 0.479333i $$0.840879\pi$$
$$180$$ 0 0
$$181$$ 43.3013i 0.239234i −0.992820 0.119617i $$-0.961833\pi$$
0.992820 0.119617i $$-0.0381666\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 199.404 115.126i 1.07786 0.622303i
$$186$$ 0 0
$$187$$ 72.0000 + 41.5692i 0.385027 + 0.222295i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 38.1838 66.1362i 0.199915 0.346263i −0.748586 0.663038i $$-0.769267\pi$$
0.948501 + 0.316775i $$0.102600\pi$$
$$192$$ 0 0
$$193$$ 143.500 + 248.549i 0.743523 + 1.28782i 0.950882 + 0.309555i $$0.100180\pi$$
−0.207358 + 0.978265i $$0.566487\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 127.279 0.646087 0.323044 0.946384i $$-0.395294\pi$$
0.323044 + 0.946384i $$0.395294\pi$$
$$198$$ 0 0
$$199$$ −180.000 + 103.923i −0.904523 + 0.522226i −0.878665 0.477439i $$-0.841565\pi$$
−0.0258579 + 0.999666i $$0.508232\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 118.794 205.757i 0.585192 1.01358i
$$204$$ 0 0
$$205$$ 168.000 290.985i 0.819512 1.41944i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 499.696i 2.39089i
$$210$$ 0 0
$$211$$ −82.0000 −0.388626 −0.194313 0.980940i $$-0.562248\pi$$
−0.194313 + 0.980940i $$0.562248\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −131.522 75.9342i −0.611730 0.353182i
$$216$$ 0 0
$$217$$ 84.8705i 0.391108i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −4.24264 7.34847i −0.0191975 0.0332510i
$$222$$ 0 0
$$223$$ 41.5692i 0.186409i −0.995647 0.0932045i $$-0.970289\pi$$
0.995647 0.0932045i $$-0.0297110\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −330.926 + 191.060i −1.45782 + 0.841675i −0.998904 0.0468029i $$-0.985097\pi$$
−0.458920 + 0.888478i $$0.651763\pi$$
$$228$$ 0 0
$$229$$ −70.5000 40.7032i −0.307860 0.177743i 0.338108 0.941107i $$-0.390213\pi$$
−0.645969 + 0.763364i $$0.723546\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −114.551 + 198.409i −0.491636 + 0.851539i −0.999954 0.00963059i $$-0.996934\pi$$
0.508317 + 0.861170i $$0.330268\pi$$
$$234$$ 0 0
$$235$$ 204.000 + 353.338i 0.868085 + 1.50357i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 67.8823 0.284026 0.142013 0.989865i $$-0.454642\pi$$
0.142013 + 0.989865i $$0.454642\pi$$
$$240$$ 0 0
$$241$$ −396.000 + 228.631i −1.64315 + 0.948675i −0.663451 + 0.748220i $$0.730909\pi$$
−0.979703 + 0.200455i $$0.935758\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 240.050i 0.979796i
$$246$$ 0 0
$$247$$ 25.5000 44.1673i 0.103239 0.178815i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 347.828i 1.38577i −0.721050 0.692884i $$-0.756340\pi$$
0.721050 0.692884i $$-0.243660\pi$$
$$252$$ 0 0
$$253$$ 144.000 0.569170
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 140.007 + 80.8332i 0.544775 + 0.314526i 0.747012 0.664811i $$-0.231488\pi$$
−0.202237 + 0.979337i $$0.564821\pi$$
$$258$$ 0 0
$$259$$ 164.500 + 284.922i 0.635135 + 1.10009i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 127.279 + 220.454i 0.483951 + 0.838228i 0.999830 0.0184332i $$-0.00586781\pi$$
−0.515879 + 0.856662i $$0.672534\pi$$
$$264$$ 0 0
$$265$$ 374.123i 1.41178i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 16.9706 9.79796i 0.0630876 0.0364236i −0.468124 0.883663i $$-0.655070\pi$$
0.531212 + 0.847239i $$0.321737\pi$$
$$270$$ 0 0
$$271$$ −36.0000 20.7846i −0.132841 0.0766960i 0.432107 0.901823i $$-0.357770\pi$$
−0.564948 + 0.825127i $$0.691104\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −8.48528 + 14.6969i −0.0308556 + 0.0534434i
$$276$$ 0 0
$$277$$ 168.500 + 291.851i 0.608303 + 1.05361i 0.991520 + 0.129954i $$0.0414829\pi$$
−0.383217 + 0.923658i $$0.625184\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 246.073 0.875705 0.437853 0.899047i $$-0.355739\pi$$
0.437853 + 0.899047i $$0.355739\pi$$
$$282$$ 0 0
$$283$$ 169.500 97.8609i 0.598940 0.345798i −0.169685 0.985498i $$-0.554275\pi$$
0.768624 + 0.639700i $$0.220942\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 415.779 + 240.050i 1.44871 + 0.836411i
$$288$$ 0 0
$$289$$ −132.500 + 229.497i −0.458478 + 0.794106i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 97.9796i 0.334401i −0.985923 0.167201i $$-0.946527\pi$$
0.985923 0.167201i $$-0.0534728\pi$$
$$294$$ 0 0
$$295$$ 408.000 1.38305
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −12.7279 7.34847i −0.0425683 0.0245768i
$$300$$ 0 0
$$301$$ 108.500 187.928i 0.360465 0.624344i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −203.647 352.727i −0.667694 1.15648i
$$306$$ 0 0
$$307$$ 71.0141i 0.231316i −0.993289 0.115658i $$-0.963102\pi$$
0.993289 0.115658i $$-0.0368977\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −186.676 + 107.778i −0.600245 + 0.346552i −0.769138 0.639083i $$-0.779314\pi$$
0.168893 + 0.985634i $$0.445981\pi$$
$$312$$ 0 0
$$313$$ 253.500 + 146.358i 0.809904 + 0.467598i 0.846923 0.531716i $$-0.178453\pi$$
−0.0370184 + 0.999315i $$0.511786\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 118.794 205.757i 0.374744 0.649076i −0.615544 0.788102i $$-0.711064\pi$$
0.990289 + 0.139026i $$0.0443972\pi$$
$$318$$ 0 0
$$319$$ 288.000 + 498.831i 0.902821 + 1.56373i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 144.250 0.446594
$$324$$ 0 0
$$325$$ 1.50000 0.866025i 0.00461538 0.00266469i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −504.874 + 291.489i −1.53457 + 0.885986i
$$330$$ 0 0
$$331$$ −92.5000 + 160.215i −0.279456 + 0.484032i −0.971250 0.238063i $$-0.923488\pi$$
0.691794 + 0.722095i $$0.256821\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 151.868i 0.453338i
$$336$$ 0 0
$$337$$ −359.000 −1.06528 −0.532641 0.846341i $$-0.678800\pi$$
−0.532641 + 0.846341i $$0.678800\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −178.191 102.879i −0.522554 0.301697i
$$342$$ 0 0
$$343$$ 343.000 1.00000
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 233.345 + 404.166i 0.672465 + 1.16474i 0.977203 + 0.212307i $$0.0680976\pi$$
−0.304738 + 0.952436i $$0.598569\pi$$
$$348$$ 0 0
$$349$$ 581.969i 1.66753i −0.552117 0.833767i $$-0.686180\pi$$
0.552117 0.833767i $$-0.313820\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 250.316 144.520i 0.709110 0.409405i −0.101621 0.994823i $$-0.532403\pi$$
0.810731 + 0.585418i $$0.199070\pi$$
$$354$$ 0 0
$$355$$ −252.000 145.492i −0.709859 0.409837i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 169.706 293.939i 0.472718 0.818771i −0.526795 0.849992i $$-0.676606\pi$$
0.999512 + 0.0312215i $$0.00993973\pi$$
$$360$$ 0 0
$$361$$ 253.000 + 438.209i 0.700831 + 1.21387i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −398.808 −1.09263
$$366$$ 0 0
$$367$$ −133.500 + 77.0763i −0.363760 + 0.210017i −0.670729 0.741703i $$-0.734019\pi$$
0.306969 + 0.951720i $$0.400685\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −534.573 −1.44090
$$372$$ 0 0
$$373$$ 144.500 250.281i 0.387399 0.670996i −0.604699 0.796454i $$-0.706707\pi$$
0.992099 + 0.125458i $$0.0400401\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 58.7878i 0.155936i
$$378$$ 0 0
$$379$$ −7.00000 −0.0184697 −0.00923483 0.999957i $$-0.502940\pi$$
−0.00923483 + 0.999957i $$0.502940\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −428.507 247.398i −1.11882 0.645949i −0.177718 0.984081i $$-0.556871\pi$$
−0.941099 + 0.338132i $$0.890205\pi$$
$$384$$ 0 0
$$385$$ 504.000 + 290.985i 1.30909 + 0.755804i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 114.551 + 198.409i 0.294476 + 0.510048i 0.974863 0.222805i $$-0.0715214\pi$$
−0.680387 + 0.732853i $$0.738188\pi$$
$$390$$ 0 0
$$391$$ 41.5692i 0.106315i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 173.948 100.429i 0.440375 0.254251i
$$396$$ 0 0
$$397$$ 70.5000 + 40.7032i 0.177582 + 0.102527i 0.586156 0.810198i $$-0.300641\pi$$
−0.408574 + 0.912725i $$0.633974\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 46.6690 80.8332i 0.116382 0.201579i −0.801950 0.597392i $$-0.796204\pi$$
0.918331 + 0.395813i $$0.129537\pi$$
$$402$$ 0 0
$$403$$ 10.5000 + 18.1865i 0.0260546 + 0.0451279i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −797.616 −1.95975
$$408$$ 0 0
$$409$$ −361.500 + 208.712i −0.883863 + 0.510299i −0.871930 0.489630i $$-0.837132\pi$$
−0.0119329 + 0.999929i $$0.503798\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 582.979i 1.41157i
$$414$$ 0 0
$$415$$ 12.0000 20.7846i 0.0289157 0.0500834i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 19.5959i 0.0467683i 0.999727 + 0.0233842i $$0.00744408\pi$$
−0.999727 + 0.0233842i $$0.992556\pi$$
$$420$$ 0 0
$$421$$ 407.000 0.966746 0.483373 0.875415i $$-0.339412\pi$$
0.483373 + 0.875415i $$0.339412\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 4.24264 + 2.44949i 0.00998268 + 0.00576351i
$$426$$ 0 0
$$427$$ 504.000 290.985i 1.18033 0.681463i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −80.6102 139.621i −0.187031 0.323946i 0.757228 0.653150i $$-0.226553\pi$$
−0.944259 + 0.329204i $$0.893220\pi$$
$$432$$ 0 0
$$433$$ 168.009i 0.388011i 0.981000 + 0.194006i $$0.0621480\pi$$
−0.981000 + 0.194006i $$0.937852\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 216.375 124.924i 0.495137 0.285867i
$$438$$ 0 0
$$439$$ 468.000 + 270.200i 1.06606 + 0.615490i 0.927102 0.374809i $$-0.122292\pi$$
0.138957 + 0.990298i $$0.455625\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 63.6396 110.227i 0.143656 0.248819i −0.785215 0.619224i $$-0.787447\pi$$
0.928871 + 0.370404i $$0.120781\pi$$
$$444$$ 0 0
$$445$$ 144.000 + 249.415i 0.323596 + 0.560484i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 110.309 0.245676 0.122838 0.992427i $$-0.460800\pi$$
0.122838 + 0.992427i $$0.460800\pi$$
$$450$$ 0 0
$$451$$ −1008.00 + 581.969i −2.23503 + 1.29040i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −29.6985 51.4393i −0.0652714 0.113053i
$$456$$ 0 0
$$457$$ −12.5000 + 21.6506i −0.0273523 + 0.0473756i −0.879378 0.476125i $$-0.842041\pi$$
0.852025 + 0.523501i $$0.175374\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 78.3837i 0.170030i 0.996380 + 0.0850148i $$0.0270938\pi$$
−0.996380 + 0.0850148i $$0.972906\pi$$
$$462$$ 0 0
$$463$$ −521.000 −1.12527 −0.562635 0.826705i $$-0.690212\pi$$
−0.562635 + 0.826705i $$0.690212\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 190.919 + 110.227i 0.408820 + 0.236032i 0.690283 0.723540i $$-0.257486\pi$$
−0.281463 + 0.959572i $$0.590820\pi$$
$$468$$ 0 0
$$469$$ 217.000 0.462687
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 263.044 + 455.605i 0.556118 + 0.963224i
$$474$$ 0 0
$$475$$ 29.4449i 0.0619892i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 759.433 438.459i 1.58545 0.915363i 0.591412 0.806370i $$-0.298571\pi$$
0.994043 0.108993i $$-0.0347626\pi$$
$$480$$ 0 0
$$481$$ 70.5000 + 40.7032i 0.146570 + 0.0846220i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 101.823 176.363i 0.209945 0.363636i
$$486$$ 0 0
$$487$$ 63.5000 + 109.985i 0.130390 + 0.225842i 0.923827 0.382810i $$-0.125044\pi$$
−0.793437 + 0.608653i $$0.791710\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 627.911 1.27884 0.639420 0.768857i $$-0.279174\pi$$
0.639420 + 0.768857i $$0.279174\pi$$
$$492$$ 0 0
$$493$$ 144.000 83.1384i 0.292089 0.168638i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 207.889 360.075i 0.418289 0.724497i
$$498$$ 0 0
$$499$$ −116.500 + 201.784i −0.233467 + 0.404377i −0.958826 0.283994i $$-0.908340\pi$$
0.725359 + 0.688371i $$0.241674\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 538.888i 1.07135i 0.844425 + 0.535674i $$0.179942\pi$$
−0.844425 + 0.535674i $$0.820058\pi$$
$$504$$ 0 0
$$505$$ −864.000 −1.71089
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 275.772 + 159.217i 0.541791 + 0.312803i 0.745805 0.666165i $$-0.232065\pi$$
−0.204013 + 0.978968i $$0.565399\pi$$
$$510$$ 0 0
$$511$$ 569.845i 1.11516i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 72.1249 + 124.924i 0.140048 + 0.242571i
$$516$$ 0 0
$$517$$ 1413.35i 2.73376i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −492.146 + 284.141i −0.944619 + 0.545376i −0.891405 0.453207i $$-0.850280\pi$$
−0.0532135 + 0.998583i $$0.516946\pi$$
$$522$$ 0 0
$$523$$ −457.500 264.138i −0.874761 0.505043i −0.00583355 0.999983i $$-0.501857\pi$$
−0.868927 + 0.494939i $$0.835190\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −29.6985 + 51.4393i −0.0563539 + 0.0976078i
$$528$$ 0 0
$$529$$ 228.500 + 395.774i 0.431947 + 0.748154i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 118.794 0.222878
$$534$$ 0 0
$$535$$ −612.000 + 353.338i −1.14393 + 0.660446i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −415.779 + 720.150i −0.771389 + 1.33609i
$$540$$ 0 0
$$541$$ −167.500 + 290.119i −0.309612 + 0.536263i −0.978277 0.207300i $$-0.933532\pi$$
0.668666 + 0.743563i $$0.266866\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 827.928i 1.51913i
$$546$$ 0 0
$$547$$ 658.000 1.20293 0.601463 0.798901i $$-0.294585\pi$$
0.601463 + 0.798901i $$0.294585\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 865.499 + 499.696i 1.57078 + 0.906889i
$$552$$ 0 0
$$553$$ 143.500 + 248.549i 0.259494 + 0.449456i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 135.765 + 235.151i 0.243742 + 0.422174i 0.961777 0.273833i $$-0.0882915\pi$$
−0.718035 + 0.696007i $$0.754958\pi$$
$$558$$ 0 0
$$559$$ 53.6936i 0.0960529i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 12.7279 7.34847i 0.0226073 0.0130523i −0.488654 0.872478i $$-0.662512\pi$$
0.511261 + 0.859425i $$0.329179\pi$$
$$564$$ 0 0
$$565$$ −252.000 145.492i −0.446018 0.257508i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 424.264 734.847i 0.745631 1.29147i −0.204268 0.978915i $$-0.565481\pi$$
0.949899 0.312556i $$-0.101185\pi$$
$$570$$ 0 0
$$571$$ 224.500 + 388.845i 0.393170 + 0.680990i 0.992866 0.119238i $$-0.0380451\pi$$
−0.599696 + 0.800228i $$0.704712\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 8.48528 0.0147570
$$576$$ 0 0
$$577$$ −253.500 + 146.358i −0.439341 + 0.253654i −0.703318 0.710875i $$-0.748299\pi$$
0.263977 + 0.964529i $$0.414966\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 29.6985 + 17.1464i 0.0511162 + 0.0295119i
$$582$$ 0 0
$$583$$ 648.000 1122.37i 1.11149 1.92516i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 529.090i 0.901345i −0.892689 0.450673i $$-0.851184\pi$$
0.892689 0.450673i $$-0.148816\pi$$
$$588$$ 0 0
$$589$$ −357.000 −0.606112
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −907.925 524.191i −1.53107 0.883964i −0.999313 0.0370681i $$-0.988198\pi$$
−0.531758 0.846896i $$-0.678469\pi$$
$$594$$ 0 0
$$595$$ 84.0000 145.492i 0.141176 0.244525i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −322.441 558.484i −0.538298 0.932360i −0.998996 0.0448028i $$-0.985734\pi$$
0.460698 0.887557i $$-0.347599\pi$$
$$600$$ 0 0
$$601$$ 458.993i 0.763716i −0.924221 0.381858i $$-0.875284\pi$$
0.924221 0.381858i $$-0.124716\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −708.521 + 409.065i −1.17111 + 0.676140i
$$606$$ 0 0
$$607$$ −910.500 525.677i −1.50000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −72.1249 + 124.924i −0.118044 + 0.204458i
$$612$$ 0 0
$$613$$ −145.000 251.147i −0.236542 0.409702i 0.723178 0.690662i $$-0.242681\pi$$
−0.959720 + 0.280960i $$0.909347\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −729.734 −1.18271 −0.591357 0.806410i $$-0.701407\pi$$
−0.591357 + 0.806410i $$0.701407\pi$$
$$618$$ 0 0
$$619$$ 709.500 409.630i 1.14620 0.661761i 0.198244 0.980153i $$-0.436476\pi$$
0.947959 + 0.318392i $$0.103143\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −356.382 + 205.757i −0.572041 + 0.330268i
$$624$$ 0 0
$$625$$ 299.500 518.749i 0.479200 0.829999i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 230.252i 0.366060i
$$630$$ 0 0
$$631$$ 58.0000 0.0919176 0.0459588 0.998943i $$-0.485366\pi$$
0.0459588 + 0.998943i $$0.485366\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −886.712 511.943i −1.39640 0.806210i
$$636$$ 0 0
$$637$$ 73.5000 42.4352i 0.115385 0.0666173i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 479.418 + 830.377i 0.747923 + 1.29544i 0.948817 + 0.315827i $$0.102282\pi$$
−0.200894 + 0.979613i $$0.564385\pi$$
$$642$$ 0 0
$$643$$ 760.370i 1.18254i −0.806475 0.591268i $$-0.798628\pi$$
0.806475 0.591268i $$-0.201372\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −305.470 + 176.363i −0.472133 + 0.272586i −0.717132 0.696937i $$-0.754546\pi$$
0.244999 + 0.969523i $$0.421212\pi$$
$$648$$ 0 0
$$649$$ −1224.00 706.677i −1.88598 1.08887i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −220.617 + 382.120i −0.337852 + 0.585177i −0.984028 0.178011i $$-0.943034\pi$$
0.646177 + 0.763188i $$0.276367\pi$$
$$654$$ 0 0
$$655$$ 144.000 + 249.415i 0.219847 + 0.380787i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 161.220 0.244644 0.122322 0.992490i $$-0.460966\pi$$
0.122322 + 0.992490i $$0.460966\pi$$
$$660$$ 0 0
$$661$$ −721.500 + 416.558i −1.09153 + 0.630194i −0.933983 0.357318i $$-0.883691\pi$$
−0.157545 + 0.987512i $$0.550358\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 1009.75 1.51842
$$666$$ 0 0
$$667$$ 144.000 249.415i 0.215892 0.373936i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 1410.91i 2.10269i
$$672$$ 0 0
$$673$$ −263.000 −0.390788 −0.195394 0.980725i $$-0.562598\pi$$
−0.195394 + 0.980725i $$0.562598\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −432.749 249.848i −0.639216 0.369052i 0.145096 0.989418i $$-0.453651\pi$$
−0.784313 + 0.620366i $$0.786984\pi$$
$$678$$ 0 0
$$679$$ 252.000 + 145.492i 0.371134 + 0.214274i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −479.418 830.377i −0.701930 1.21578i −0.967788 0.251767i $$-0.918988\pi$$
0.265858 0.964012i $$-0.414345\pi$$
$$684$$ 0 0
$$685$$ 748.246i 1.09233i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −114.551 + 66.1362i −0.166257 + 0.0959887i
$$690$$ 0 0
$$691$$ −1069.50 617.476i −1.54776 0.893598i −0.998313 0.0580674i $$-0.981506\pi$$
−0.549444 0.835530i $$-0.685161\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 479.418 830.377i 0.689811 1.19479i
$$696$$ 0 0
$$697$$ 168.000 + 290.985i 0.241033 + 0.417481i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 975.807 1.39202 0.696011 0.718031i $$-0.254956\pi$$
0.696011 + 0.718031i $$0.254956\pi$$
$$702$$ 0 0
$$703$$ −1198.50 + 691.954i −1.70484 + 0.984288i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1234.54i 1.74617i
$$708$$ 0 0
$$709$$ 553.000 957.824i 0.779972 1.35095i −0.151986 0.988383i $$-0.548567\pi$$
0.931957 0.362568i $$-0.118100\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 102.879i 0.144290i
$$714$$ 0 0
$$715$$ 144.000 0.201399
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −593.970 342.929i −0.826105 0.476952i 0.0264120 0.999651i $$-0.491592\pi$$
−0.852517 + 0.522699i $$0.824925\pi$$
$$720$$ 0 0
$$721$$ −178.500 + 103.057i −0.247573 + 0.142936i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 16.9706 + 29.3939i 0.0234077 + 0.0405433i
$$726$$ 0 0
$$727$$ 427.817i 0.588468i −0.955733 0.294234i $$-0.904935\pi$$
0.955733 0.294234i $$-0.0950646\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 131.522 75.9342i 0.179920 0.103877i
$$732$$ 0 0
$$733$$ 34.5000 + 19.9186i 0.0470668 + 0.0271741i 0.523349 0.852119i $$-0.324682\pi$$
−0.476282 + 0.879293i $$0.658016\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −263.044 + 455.605i −0.356911 + 0.618189i
$$738$$ 0 0
$$739$$ −243.500 421.754i −0.329499 0.570710i 0.652913 0.757433i $$-0.273547\pi$$
−0.982413 + 0.186723i $$0.940213\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 509.117 0.685218 0.342609 0.939478i $$-0.388689\pi$$
0.342609 + 0.939478i $$0.388689\pi$$
$$744$$ 0 0
$$745$$ −216.000 + 124.708i −0.289933 + 0.167393i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −504.874 874.468i −0.674064 1.16751i
$$750$$ 0 0
$$751$$ −272.500 + 471.984i −0.362850 + 0.628474i −0.988429 0.151687i $$-0.951529\pi$$
0.625579 + 0.780161i $$0.284863\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 48.9898i 0.0648871i
$$756$$ 0 0
$$757$$ −770.000 −1.01717 −0.508587 0.861011i $$-0.669832\pi$$
−0.508587 + 0.861011i $$0.669832\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 148.492 + 85.7321i 0.195128 + 0.112657i 0.594381 0.804184i $$-0.297397\pi$$
−0.399253 + 0.916841i $$0.630730\pi$$
$$762$$ 0 0
$$763$$ 1183.00 1.55046
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 72.1249 + 124.924i 0.0940351 + 0.162874i
$$768$$ 0 0
$$769$$ 704.945i 0.916703i −0.888771 0.458352i $$-0.848440\pi$$
0.888771 0.458352i $$-0.151560\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 797.616 460.504i 1.03185 0.595736i 0.114333 0.993443i $$-0.463527\pi$$
0.917513 + 0.397706i $$0.130194\pi$$
$$774$$ 0 0
$$775$$ −10.5000 6.06218i −0.0135484 0.00782216i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1009.75 + 1748.94i −1.29621 + 2.24510i
$$780$$ 0 0
$$781$$ 504.000 + 872.954i 0.645327 + 1.11774i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 203.647 0.259423
$$786$$ 0 0
$$787$$ −396.000 + 228.631i −0.503177 + 0.290509i −0.730024 0.683421i $$-0.760491\pi$$
0.226848 + 0.973930i $$0.427158\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 207.889 360.075i 0.262818 0.455215i
$$792$$ 0 0
$$793$$ 72.0000 124.708i 0.0907945 0.157261i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 14.6969i 0.0184403i 0.999957 + 0.00922016i $$0.00293491\pi$$
−0.999957 + 0.00922016i $$0.997065\pi$$
$$798$$ 0 0
$$799$$ −408.000 −0.510638
$$800$$ 0 0