# Properties

 Label 1728.3.q.f.1601.2 Level $1728$ Weight $3$ Character 1728.1601 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: $$\Q(\sqrt{-2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} - 2x^{2} + 4$$ x^4 - 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 72) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 1601.2 Root $$-1.22474 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 1728.1601 Dual form 1728.3.q.f.449.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(6.39898 - 3.69445i) q^{5} +(-3.39898 + 5.88721i) q^{7} +O(q^{10})$$ $$q+(6.39898 - 3.69445i) q^{5} +(-3.39898 + 5.88721i) q^{7} +(-5.29796 - 3.05878i) q^{11} +(8.39898 + 14.5475i) q^{13} -25.1701i q^{17} -17.5959 q^{19} +(12.3990 - 7.15855i) q^{23} +(14.7980 - 25.6308i) q^{25} +(16.1969 + 9.35131i) q^{29} +(-23.3990 - 40.5282i) q^{31} +50.2295i q^{35} +49.5959 q^{37} +(34.5000 - 19.9186i) q^{41} +(22.0959 - 38.2713i) q^{43} +(28.8031 + 16.6295i) q^{47} +(1.39388 + 2.41427i) q^{49} +10.1708i q^{53} -45.2020 q^{55} +(14.2980 - 8.25493i) q^{59} +(10.6010 - 18.3615i) q^{61} +(107.490 + 62.0593i) q^{65} +(43.4898 + 75.3265i) q^{67} -30.2555i q^{71} -48.7878 q^{73} +(36.0153 - 20.7934i) q^{77} +(55.7929 - 96.6361i) q^{79} +(85.0857 + 49.1243i) q^{83} +(-92.9898 - 161.063i) q^{85} -75.5103i q^{89} -114.192 q^{91} +(-112.596 + 65.0073i) q^{95} +(70.2980 - 121.760i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 6 q^{5} + 6 q^{7}+O(q^{10})$$ 4 * q + 6 * q^5 + 6 * q^7 $$4 q + 6 q^{5} + 6 q^{7} + 18 q^{11} + 14 q^{13} + 8 q^{19} + 30 q^{23} + 20 q^{25} + 6 q^{29} - 74 q^{31} + 120 q^{37} + 138 q^{41} + 10 q^{43} + 174 q^{47} - 112 q^{49} - 220 q^{55} + 18 q^{59} + 62 q^{61} + 234 q^{65} - 22 q^{67} + 40 q^{73} + 438 q^{77} + 86 q^{79} + 66 q^{83} - 176 q^{85} - 300 q^{91} - 372 q^{95} + 242 q^{97}+O(q^{100})$$ 4 * q + 6 * q^5 + 6 * q^7 + 18 * q^11 + 14 * q^13 + 8 * q^19 + 30 * q^23 + 20 * q^25 + 6 * q^29 - 74 * q^31 + 120 * q^37 + 138 * q^41 + 10 * q^43 + 174 * q^47 - 112 * q^49 - 220 * q^55 + 18 * q^59 + 62 * q^61 + 234 * q^65 - 22 * q^67 + 40 * q^73 + 438 * q^77 + 86 * q^79 + 66 * q^83 - 176 * q^85 - 300 * q^91 - 372 * q^95 + 242 * q^97

## Character values

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

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

## 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
$$5$$ 6.39898 3.69445i 1.27980 0.738891i 0.302985 0.952995i $$-0.402017\pi$$
0.976811 + 0.214105i $$0.0686834\pi$$
$$6$$ 0 0
$$7$$ −3.39898 + 5.88721i −0.485568 + 0.841029i −0.999862 0.0165847i $$-0.994721\pi$$
0.514294 + 0.857614i $$0.328054\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −5.29796 3.05878i −0.481633 0.278071i 0.239464 0.970905i $$-0.423028\pi$$
−0.721097 + 0.692835i $$0.756362\pi$$
$$12$$ 0 0
$$13$$ 8.39898 + 14.5475i 0.646075 + 1.11904i 0.984052 + 0.177881i $$0.0569242\pi$$
−0.337977 + 0.941154i $$0.609743\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 25.1701i 1.48059i −0.672279 0.740297i $$-0.734685\pi$$
0.672279 0.740297i $$-0.265315\pi$$
$$18$$ 0 0
$$19$$ −17.5959 −0.926101 −0.463050 0.886332i $$-0.653245\pi$$
−0.463050 + 0.886332i $$0.653245\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 12.3990 7.15855i 0.539086 0.311241i −0.205622 0.978631i $$-0.565922\pi$$
0.744708 + 0.667390i $$0.232589\pi$$
$$24$$ 0 0
$$25$$ 14.7980 25.6308i 0.591918 1.02523i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 16.1969 + 9.35131i 0.558515 + 0.322459i 0.752549 0.658536i $$-0.228824\pi$$
−0.194034 + 0.980995i $$0.562157\pi$$
$$30$$ 0 0
$$31$$ −23.3990 40.5282i −0.754806 1.30736i −0.945471 0.325707i $$-0.894398\pi$$
0.190665 0.981655i $$-0.438936\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 50.2295i 1.43513i
$$36$$ 0 0
$$37$$ 49.5959 1.34043 0.670215 0.742167i $$-0.266202\pi$$
0.670215 + 0.742167i $$0.266202\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 34.5000 19.9186i 0.841463 0.485819i −0.0162980 0.999867i $$-0.505188\pi$$
0.857761 + 0.514048i $$0.171855\pi$$
$$42$$ 0 0
$$43$$ 22.0959 38.2713i 0.513859 0.890029i −0.486012 0.873952i $$-0.661549\pi$$
0.999871 0.0160771i $$-0.00511772\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 28.8031 + 16.6295i 0.612831 + 0.353818i 0.774073 0.633097i $$-0.218216\pi$$
−0.161242 + 0.986915i $$0.551550\pi$$
$$48$$ 0 0
$$49$$ 1.39388 + 2.41427i 0.0284465 + 0.0492707i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 10.1708i 0.191902i 0.995386 + 0.0959509i $$0.0305892\pi$$
−0.995386 + 0.0959509i $$0.969411\pi$$
$$54$$ 0 0
$$55$$ −45.2020 −0.821855
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 14.2980 8.25493i 0.242338 0.139914i −0.373913 0.927464i $$-0.621984\pi$$
0.616251 + 0.787550i $$0.288651\pi$$
$$60$$ 0 0
$$61$$ 10.6010 18.3615i 0.173787 0.301008i −0.765954 0.642896i $$-0.777733\pi$$
0.939741 + 0.341887i $$0.111066\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 107.490 + 62.0593i 1.65369 + 0.954758i
$$66$$ 0 0
$$67$$ 43.4898 + 75.3265i 0.649101 + 1.12428i 0.983338 + 0.181787i $$0.0581883\pi$$
−0.334236 + 0.942489i $$0.608478\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 30.2555i 0.426134i −0.977038 0.213067i $$-0.931655\pi$$
0.977038 0.213067i $$-0.0683453\pi$$
$$72$$ 0 0
$$73$$ −48.7878 −0.668325 −0.334163 0.942515i $$-0.608454\pi$$
−0.334163 + 0.942515i $$0.608454\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 36.0153 20.7934i 0.467731 0.270045i
$$78$$ 0 0
$$79$$ 55.7929 96.6361i 0.706239 1.22324i −0.260004 0.965608i $$-0.583724\pi$$
0.966243 0.257634i $$-0.0829428\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 85.0857 + 49.1243i 1.02513 + 0.591859i 0.915585 0.402123i $$-0.131728\pi$$
0.109544 + 0.993982i $$0.465061\pi$$
$$84$$ 0 0
$$85$$ −92.9898 161.063i −1.09400 1.89486i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 75.5103i 0.848431i −0.905561 0.424215i $$-0.860550\pi$$
0.905561 0.424215i $$-0.139450\pi$$
$$90$$ 0 0
$$91$$ −114.192 −1.25486
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −112.596 + 65.0073i −1.18522 + 0.684287i
$$96$$ 0 0
$$97$$ 70.2980 121.760i 0.724721 1.25525i −0.234367 0.972148i $$-0.575302\pi$$
0.959089 0.283106i $$-0.0913648\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 28.1969 + 16.2795i 0.279178 + 0.161183i 0.633051 0.774110i $$-0.281802\pi$$
−0.353873 + 0.935293i $$0.615136\pi$$
$$102$$ 0 0
$$103$$ 67.7929 + 117.421i 0.658183 + 1.14001i 0.981086 + 0.193574i $$0.0620081\pi$$
−0.322903 + 0.946432i $$0.604659\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 35.3409i 0.330289i −0.986269 0.165144i $$-0.947191\pi$$
0.986269 0.165144i $$-0.0528090\pi$$
$$108$$ 0 0
$$109$$ −53.5959 −0.491706 −0.245853 0.969307i $$-0.579068\pi$$
−0.245853 + 0.969307i $$0.579068\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −143.076 + 82.6047i −1.26615 + 0.731015i −0.974258 0.225435i $$-0.927620\pi$$
−0.291897 + 0.956450i $$0.594286\pi$$
$$114$$ 0 0
$$115$$ 52.8939 91.6149i 0.459947 0.796651i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 148.182 + 85.5527i 1.24522 + 0.718930i
$$120$$ 0 0
$$121$$ −41.7878 72.3785i −0.345353 0.598170i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 33.9588i 0.271670i
$$126$$ 0 0
$$127$$ −11.9796 −0.0943275 −0.0471637 0.998887i $$-0.515018\pi$$
−0.0471637 + 0.998887i $$0.515018\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 13.3082 7.68347i 0.101589 0.0586525i −0.448345 0.893861i $$-0.647986\pi$$
0.549934 + 0.835208i $$0.314653\pi$$
$$132$$ 0 0
$$133$$ 59.8082 103.591i 0.449685 0.778878i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 47.7122 + 27.5467i 0.348265 + 0.201071i 0.663921 0.747803i $$-0.268891\pi$$
−0.315656 + 0.948874i $$0.602225\pi$$
$$138$$ 0 0
$$139$$ −50.4898 87.4509i −0.363236 0.629143i 0.625255 0.780420i $$-0.284995\pi$$
−0.988491 + 0.151277i $$0.951661\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 102.762i 0.718619i
$$144$$ 0 0
$$145$$ 138.192 0.953047
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 187.389 108.189i 1.25764 0.726100i 0.285027 0.958519i $$-0.407997\pi$$
0.972616 + 0.232419i $$0.0746641\pi$$
$$150$$ 0 0
$$151$$ −76.7929 + 133.009i −0.508562 + 0.880855i 0.491389 + 0.870940i $$0.336489\pi$$
−0.999951 + 0.00991488i $$0.996844\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −299.459 172.893i −1.93199 1.11544i
$$156$$ 0 0
$$157$$ 40.9847 + 70.9876i 0.261049 + 0.452150i 0.966521 0.256588i $$-0.0825983\pi$$
−0.705472 + 0.708738i $$0.749265\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 97.3271i 0.604516i
$$162$$ 0 0
$$163$$ 55.2122 0.338725 0.169363 0.985554i $$-0.445829\pi$$
0.169363 + 0.985554i $$0.445829\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −133.803 + 77.2512i −0.801216 + 0.462582i −0.843896 0.536507i $$-0.819744\pi$$
0.0426802 + 0.999089i $$0.486410\pi$$
$$168$$ 0 0
$$169$$ −56.5857 + 98.0093i −0.334827 + 0.579937i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 22.8031 + 13.1654i 0.131810 + 0.0761003i 0.564455 0.825464i $$-0.309086\pi$$
−0.432645 + 0.901564i $$0.642420\pi$$
$$174$$ 0 0
$$175$$ 100.596 + 174.237i 0.574834 + 0.995641i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 266.700i 1.48995i −0.667094 0.744973i $$-0.732462\pi$$
0.667094 0.744973i $$-0.267538\pi$$
$$180$$ 0 0
$$181$$ 58.4041 0.322674 0.161337 0.986899i $$-0.448419\pi$$
0.161337 + 0.986899i $$0.448419\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 317.363 183.230i 1.71548 0.990431i
$$186$$ 0 0
$$187$$ −76.9898 + 133.350i −0.411710 + 0.713103i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −99.5602 57.4811i −0.521258 0.300948i 0.216191 0.976351i $$-0.430636\pi$$
−0.737449 + 0.675403i $$0.763970\pi$$
$$192$$ 0 0
$$193$$ −108.490 187.910i −0.562123 0.973626i −0.997311 0.0732863i $$-0.976651\pi$$
0.435188 0.900340i $$-0.356682\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 171.105i 0.868555i 0.900779 + 0.434278i $$0.142996\pi$$
−0.900779 + 0.434278i $$0.857004\pi$$
$$198$$ 0 0
$$199$$ 62.0000 0.311558 0.155779 0.987792i $$-0.450211\pi$$
0.155779 + 0.987792i $$0.450211\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −110.106 + 63.5698i −0.542395 + 0.313152i
$$204$$ 0 0
$$205$$ 147.177 254.917i 0.717934 1.24350i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 93.2225 + 53.8220i 0.446040 + 0.257522i
$$210$$ 0 0
$$211$$ 64.7020 + 112.067i 0.306645 + 0.531124i 0.977626 0.210350i $$-0.0674603\pi$$
−0.670981 + 0.741474i $$0.734127\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 326.529i 1.51874i
$$216$$ 0 0
$$217$$ 318.131 1.46604
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 366.161 211.403i 1.65684 0.956576i
$$222$$ 0 0
$$223$$ 49.1867 85.1939i 0.220568 0.382036i −0.734412 0.678704i $$-0.762542\pi$$
0.954981 + 0.296668i $$0.0958755\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 383.651 + 221.501i 1.69009 + 0.975775i 0.954434 + 0.298423i $$0.0964607\pi$$
0.735659 + 0.677352i $$0.236873\pi$$
$$228$$ 0 0
$$229$$ −56.0051 97.0037i −0.244564 0.423597i 0.717445 0.696615i $$-0.245311\pi$$
−0.962009 + 0.273018i $$0.911978\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 80.8526i 0.347007i −0.984833 0.173503i $$-0.944491\pi$$
0.984833 0.173503i $$-0.0555088\pi$$
$$234$$ 0 0
$$235$$ 245.747 1.04573
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 37.3888 21.5864i 0.156438 0.0903197i −0.419737 0.907646i $$-0.637878\pi$$
0.576176 + 0.817326i $$0.304544\pi$$
$$240$$ 0 0
$$241$$ 140.904 244.053i 0.584664 1.01267i −0.410253 0.911972i $$-0.634560\pi$$
0.994917 0.100696i $$-0.0321071\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 17.8388 + 10.2992i 0.0728113 + 0.0420376i
$$246$$ 0 0
$$247$$ −147.788 255.976i −0.598331 1.03634i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 15.5131i 0.0618050i −0.999522 0.0309025i $$-0.990162\pi$$
0.999522 0.0309025i $$-0.00983814\pi$$
$$252$$ 0 0
$$253$$ −87.5857 −0.346189
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 312.035 180.153i 1.21414 0.700986i 0.250484 0.968121i $$-0.419410\pi$$
0.963659 + 0.267135i $$0.0860770\pi$$
$$258$$ 0 0
$$259$$ −168.576 + 291.981i −0.650871 + 1.12734i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −42.4296 24.4967i −0.161329 0.0931435i 0.417162 0.908832i $$-0.363025\pi$$
−0.578491 + 0.815689i $$0.696358\pi$$
$$264$$ 0 0
$$265$$ 37.5755 + 65.0827i 0.141794 + 0.245595i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 281.700i 1.04721i −0.851961 0.523606i $$-0.824587\pi$$
0.851961 0.523606i $$-0.175413\pi$$
$$270$$ 0 0
$$271$$ 89.5959 0.330612 0.165306 0.986242i $$-0.447139\pi$$
0.165306 + 0.986242i $$0.447139\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −156.798 + 90.5273i −0.570174 + 0.329190i
$$276$$ 0 0
$$277$$ 42.1969 73.0872i 0.152336 0.263853i −0.779750 0.626091i $$-0.784654\pi$$
0.932086 + 0.362238i $$0.117987\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 23.2673 + 13.4334i 0.0828019 + 0.0478057i 0.540829 0.841132i $$-0.318110\pi$$
−0.458027 + 0.888938i $$0.651444\pi$$
$$282$$ 0 0
$$283$$ −90.4898 156.733i −0.319752 0.553827i 0.660684 0.750664i $$-0.270266\pi$$
−0.980436 + 0.196837i $$0.936933\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 270.811i 0.943594i
$$288$$ 0 0
$$289$$ −344.535 −1.19216
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −407.985 + 235.550i −1.39244 + 0.803925i −0.993585 0.113089i $$-0.963925\pi$$
−0.398854 + 0.917014i $$0.630592\pi$$
$$294$$ 0 0
$$295$$ 60.9949 105.646i 0.206762 0.358123i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 208.278 + 120.249i 0.696580 + 0.402171i
$$300$$ 0 0
$$301$$ 150.207 + 260.166i 0.499027 + 0.864340i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 156.660i 0.513639i
$$306$$ 0 0
$$307$$ 464.747 1.51383 0.756917 0.653511i $$-0.226705\pi$$
0.756917 + 0.653511i $$0.226705\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −218.348 + 126.063i −0.702083 + 0.405348i −0.808123 0.589014i $$-0.799516\pi$$
0.106039 + 0.994362i $$0.466183\pi$$
$$312$$ 0 0
$$313$$ −98.1061 + 169.925i −0.313438 + 0.542891i −0.979104 0.203359i $$-0.934814\pi$$
0.665666 + 0.746250i $$0.268147\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 98.9847 + 57.1488i 0.312255 + 0.180280i 0.647935 0.761696i $$-0.275633\pi$$
−0.335680 + 0.941976i $$0.608966\pi$$
$$318$$ 0 0
$$319$$ −57.2071 99.0857i −0.179333 0.310613i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 442.891i 1.37118i
$$324$$ 0 0
$$325$$ 497.151 1.52970
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −195.802 + 113.046i −0.595143 + 0.343606i
$$330$$ 0 0
$$331$$ −27.2980 + 47.2815i −0.0824712 + 0.142844i −0.904311 0.426875i $$-0.859615\pi$$
0.821840 + 0.569719i $$0.192948\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 556.581 + 321.342i 1.66143 + 0.959230i
$$336$$ 0 0
$$337$$ 118.884 + 205.913i 0.352771 + 0.611016i 0.986734 0.162347i $$-0.0519063\pi$$
−0.633963 + 0.773363i $$0.718573\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 286.289i 0.839558i
$$342$$ 0 0
$$343$$ −352.051 −1.02639
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −108.349 + 62.5553i −0.312245 + 0.180275i −0.647931 0.761699i $$-0.724365\pi$$
0.335686 + 0.941974i $$0.391032\pi$$
$$348$$ 0 0
$$349$$ −269.985 + 467.627i −0.773595 + 1.33991i 0.161986 + 0.986793i $$0.448210\pi$$
−0.935581 + 0.353113i $$0.885123\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −254.490 146.930i −0.720934 0.416232i 0.0941622 0.995557i $$-0.469983\pi$$
−0.815096 + 0.579325i $$0.803316\pi$$
$$354$$ 0 0
$$355$$ −111.778 193.604i −0.314866 0.545364i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 422.550i 1.17702i −0.808490 0.588509i $$-0.799715\pi$$
0.808490 0.588509i $$-0.200285\pi$$
$$360$$ 0 0
$$361$$ −51.3837 −0.142337
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −312.192 + 180.244i −0.855320 + 0.493819i
$$366$$ 0 0
$$367$$ −131.358 + 227.519i −0.357924 + 0.619943i −0.987614 0.156904i $$-0.949849\pi$$
0.629690 + 0.776847i $$0.283182\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −59.8775 34.5703i −0.161395 0.0931814i
$$372$$ 0 0
$$373$$ 60.9847 + 105.629i 0.163498 + 0.283187i 0.936121 0.351679i $$-0.114389\pi$$
−0.772623 + 0.634865i $$0.781056\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 314.166i 0.833331i
$$378$$ 0 0
$$379$$ −641.151 −1.69169 −0.845846 0.533428i $$-0.820904\pi$$
−0.845846 + 0.533428i $$0.820904\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 640.681 369.897i 1.67280 0.965789i 0.706733 0.707481i $$-0.250168\pi$$
0.966063 0.258308i $$-0.0831650\pi$$
$$384$$ 0 0
$$385$$ 153.641 266.114i 0.399067 0.691204i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 75.7520 + 43.7355i 0.194735 + 0.112430i 0.594197 0.804319i $$-0.297470\pi$$
−0.399462 + 0.916750i $$0.630803\pi$$
$$390$$ 0 0
$$391$$ −180.182 312.084i −0.460823 0.798168i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 824.496i 2.08733i
$$396$$ 0 0
$$397$$ −483.090 −1.21685 −0.608425 0.793611i $$-0.708199\pi$$
−0.608425 + 0.793611i $$0.708199\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −317.682 + 183.414i −0.792224 + 0.457390i −0.840745 0.541432i $$-0.817882\pi$$
0.0485212 + 0.998822i $$0.484549\pi$$
$$402$$ 0 0
$$403$$ 393.055 680.791i 0.975323 1.68931i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −262.757 151.703i −0.645595 0.372734i
$$408$$ 0 0
$$409$$ −267.641 463.567i −0.654379 1.13342i −0.982049 0.188625i $$-0.939597\pi$$
0.327671 0.944792i $$-0.393736\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 112.233i 0.271751i
$$414$$ 0 0
$$415$$ 725.949 1.74927
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −605.620 + 349.655i −1.44539 + 0.834499i −0.998202 0.0599386i $$-0.980910\pi$$
−0.447193 + 0.894438i $$0.647576\pi$$
$$420$$ 0 0
$$421$$ −180.772 + 313.107i −0.429388 + 0.743722i −0.996819 0.0796989i $$-0.974604\pi$$
0.567431 + 0.823421i $$0.307937\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −645.131 372.466i −1.51795 0.876391i
$$426$$ 0 0
$$427$$ 72.0653 + 124.821i 0.168771 + 0.292320i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 463.747i 1.07598i 0.842952 + 0.537989i $$0.180816\pi$$
−0.842952 + 0.537989i $$0.819184\pi$$
$$432$$ 0 0
$$433$$ −689.514 −1.59241 −0.796206 0.605026i $$-0.793163\pi$$
−0.796206 + 0.605026i $$0.793163\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −218.171 + 125.961i −0.499248 + 0.288241i
$$438$$ 0 0
$$439$$ −310.772 + 538.274i −0.707910 + 1.22614i 0.257721 + 0.966219i $$0.417028\pi$$
−0.965631 + 0.259917i $$0.916305\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 698.843 + 403.477i 1.57752 + 0.910784i 0.995204 + 0.0978236i $$0.0311881\pi$$
0.582320 + 0.812960i $$0.302145\pi$$
$$444$$ 0 0
$$445$$ −278.969 483.189i −0.626897 1.08582i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 317.554i 0.707248i 0.935388 + 0.353624i $$0.115051\pi$$
−0.935388 + 0.353624i $$0.884949\pi$$
$$450$$ 0 0
$$451$$ −243.706 −0.540368
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −730.711 + 421.876i −1.60596 + 0.927201i
$$456$$ 0 0
$$457$$ −285.843 + 495.094i −0.625477 + 1.08336i 0.362972 + 0.931800i $$0.381762\pi$$
−0.988448 + 0.151557i $$0.951571\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −478.550 276.291i −1.03807 0.599330i −0.118784 0.992920i $$-0.537899\pi$$
−0.919286 + 0.393591i $$0.871233\pi$$
$$462$$ 0 0
$$463$$ −60.1663 104.211i −0.129949 0.225078i 0.793708 0.608299i $$-0.208148\pi$$
−0.923657 + 0.383221i $$0.874815\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 880.440i 1.88531i −0.333767 0.942656i $$-0.608320\pi$$
0.333767 0.942656i $$-0.391680\pi$$
$$468$$ 0 0
$$469$$ −591.284 −1.26073
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −234.127 + 135.173i −0.494982 + 0.285778i
$$474$$ 0 0
$$475$$ −260.384 + 450.998i −0.548176 + 0.949469i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 593.793 + 342.826i 1.23965 + 0.715713i 0.969023 0.246971i $$-0.0794353\pi$$
0.270628 + 0.962684i $$0.412769\pi$$
$$480$$ 0 0
$$481$$ 416.555 + 721.495i 0.866019 + 1.49999i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 1038.85i 2.14196i
$$486$$ 0 0
$$487$$ −391.131 −0.803143 −0.401571 0.915828i $$-0.631536\pi$$
−0.401571 + 0.915828i $$0.631536\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −166.469 + 96.1111i −0.339042 + 0.195746i −0.659848 0.751399i $$-0.729379\pi$$
0.320807 + 0.947145i $$0.396046\pi$$
$$492$$ 0 0
$$493$$ 235.373 407.679i 0.477431 0.826935i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 178.120 + 102.838i 0.358391 + 0.206917i
$$498$$ 0 0
$$499$$ −304.692 527.742i −0.610605 1.05760i −0.991139 0.132832i $$-0.957593\pi$$
0.380534 0.924767i $$-0.375740\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 232.130i 0.461491i −0.973014 0.230746i $$-0.925883\pi$$
0.973014 0.230746i $$-0.0741165\pi$$
$$504$$ 0 0
$$505$$ 240.576 0.476387
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −223.136 + 128.827i −0.438381 + 0.253099i −0.702910 0.711278i $$-0.748117\pi$$
0.264530 + 0.964377i $$0.414783\pi$$
$$510$$ 0 0
$$511$$ 165.829 287.224i 0.324518 0.562081i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 867.610 + 500.915i 1.68468 + 0.972650i
$$516$$ 0 0
$$517$$ −101.732 176.204i −0.196773 0.340821i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 484.088i 0.929152i 0.885533 + 0.464576i $$0.153793\pi$$
−0.885533 + 0.464576i $$0.846207\pi$$
$$522$$ 0 0
$$523$$ −644.384 −1.23209 −0.616046 0.787711i $$-0.711266\pi$$
−0.616046 + 0.787711i $$0.711266\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −1020.10 + 588.955i −1.93567 + 1.11756i
$$528$$ 0 0
$$529$$ −162.010 + 280.610i −0.306257 + 0.530454i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 579.530 + 334.592i 1.08730 + 0.627752i
$$534$$ 0 0
$$535$$ −130.565 226.146i −0.244047 0.422702i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 17.0542i 0.0316405i
$$540$$ 0 0
$$541$$ 332.302 0.614237 0.307118 0.951671i $$-0.400635\pi$$
0.307118 + 0.951671i $$0.400635\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −342.959 + 198.008i −0.629283 + 0.363317i
$$546$$ 0 0
$$547$$ 157.329 272.501i 0.287621 0.498174i −0.685621 0.727959i $$-0.740469\pi$$
0.973241 + 0.229785i $$0.0738024\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −285.000 164.545i −0.517241 0.298629i
$$552$$ 0 0
$$553$$ 379.278 + 656.928i 0.685855 + 1.18793i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 664.080i 1.19224i 0.802894 + 0.596122i $$0.203293\pi$$
−0.802894 + 0.596122i $$0.796707\pi$$
$$558$$ 0 0
$$559$$ 742.333 1.32797
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 211.024 121.835i 0.374821 0.216403i −0.300741 0.953706i $$-0.597234\pi$$
0.675563 + 0.737302i $$0.263901\pi$$
$$564$$ 0 0
$$565$$ −610.358 + 1057.17i −1.08028 + 1.87110i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 502.155 + 289.919i 0.882522 + 0.509524i 0.871489 0.490415i $$-0.163155\pi$$
0.0110330 + 0.999939i $$0.496488\pi$$
$$570$$ 0 0
$$571$$ 356.843 + 618.070i 0.624944 + 1.08243i 0.988552 + 0.150882i $$0.0482114\pi$$
−0.363608 + 0.931552i $$0.618455\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 423.728i 0.736918i
$$576$$ 0 0
$$577$$ 829.433 1.43749 0.718746 0.695273i $$-0.244717\pi$$
0.718746 + 0.695273i $$0.244717\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −578.409 + 333.945i −0.995541 + 0.574776i
$$582$$ 0 0
$$583$$ 31.1102 53.8844i 0.0533623 0.0924261i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −777.480 448.878i −1.32450 0.764699i −0.340054 0.940406i $$-0.610445\pi$$
−0.984442 + 0.175707i $$0.943779\pi$$
$$588$$ 0 0
$$589$$ 411.727 + 713.131i 0.699026 + 1.21075i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 378.065i 0.637547i −0.947831 0.318774i $$-0.896729\pi$$
0.947831 0.318774i $$-0.103271\pi$$
$$594$$ 0 0
$$595$$ 1264.28 2.12484
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 822.438 474.835i 1.37302 0.792712i 0.381711 0.924282i $$-0.375335\pi$$
0.991307 + 0.131569i $$0.0420016\pi$$
$$600$$ 0 0
$$601$$ −252.308 + 437.011i −0.419814 + 0.727139i −0.995920 0.0902356i $$-0.971238\pi$$
0.576107 + 0.817375i $$0.304571\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −534.798 308.766i −0.883964 0.510357i
$$606$$ 0 0
$$607$$ 429.954 + 744.702i 0.708326 + 1.22686i 0.965478 + 0.260486i $$0.0838828\pi$$
−0.257151 + 0.966371i $$0.582784\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 558.682i 0.914373i
$$612$$ 0 0
$$613$$ 655.253 1.06893 0.534464 0.845191i $$-0.320513\pi$$
0.534464 + 0.845191i $$0.320513\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 147.227 85.0013i 0.238617 0.137765i −0.375924 0.926650i $$-0.622675\pi$$
0.614541 + 0.788885i $$0.289341\pi$$
$$618$$ 0 0
$$619$$ −270.531 + 468.573i −0.437045 + 0.756983i −0.997460 0.0712282i $$-0.977308\pi$$
0.560415 + 0.828212i $$0.310641\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 444.545 + 256.658i 0.713555 + 0.411971i
$$624$$ 0 0
$$625$$ 244.490 + 423.469i 0.391184 + 0.677550i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 1248.33i 1.98463i
$$630$$ 0 0
$$631$$ −260.788 −0.413293 −0.206646 0.978416i $$-0.566255\pi$$
−0.206646 + 0.978416i $$0.566255\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −76.6571 + 44.2580i −0.120720 + 0.0696977i
$$636$$ 0 0
$$637$$ −23.4143 + 40.5547i −0.0367571 + 0.0636652i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −585.418 337.991i −0.913289 0.527288i −0.0318012 0.999494i $$-0.510124\pi$$
−0.881488 + 0.472206i $$0.843458\pi$$
$$642$$ 0 0
$$643$$ 378.318 + 655.267i 0.588364 + 1.01908i 0.994447 + 0.105241i $$0.0335613\pi$$
−0.406082 + 0.913837i $$0.633105\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 554.770i 0.857450i −0.903435 0.428725i $$-0.858963\pi$$
0.903435 0.428725i $$-0.141037\pi$$
$$648$$ 0 0
$$649$$ −101.000 −0.155624
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 174.499 100.747i 0.267227 0.154283i −0.360400 0.932798i $$-0.617360\pi$$
0.627627 + 0.778514i $$0.284026\pi$$
$$654$$ 0 0
$$655$$ 56.7724 98.3328i 0.0866755 0.150126i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 89.7122 + 51.7954i 0.136134 + 0.0785969i 0.566520 0.824048i $$-0.308289\pi$$
−0.430386 + 0.902645i $$0.641623\pi$$
$$660$$ 0 0
$$661$$ 109.207 + 189.152i 0.165215 + 0.286161i 0.936732 0.350048i $$-0.113835\pi$$
−0.771517 + 0.636209i $$0.780502\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 883.834i 1.32907i
$$666$$ 0 0
$$667$$ 267.767 0.401450
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −112.328 + 64.8523i −0.167403 + 0.0966503i
$$672$$ 0 0
$$673$$ −394.429 + 683.170i −0.586075 + 1.01511i 0.408665 + 0.912684i $$0.365994\pi$$
−0.994740 + 0.102428i $$0.967339\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −634.550 366.358i −0.937297 0.541149i −0.0481850 0.998838i $$-0.515344\pi$$
−0.889112 + 0.457690i $$0.848677\pi$$
$$678$$ 0 0
$$679$$ 477.883 + 827.717i 0.703804 + 1.21902i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1353.33i 1.98145i −0.135883 0.990725i $$-0.543387\pi$$
0.135883 0.990725i $$-0.456613\pi$$
$$684$$ 0 0
$$685$$ 407.080 0.594277
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −147.959 + 85.4243i −0.214745 + 0.123983i
$$690$$ 0 0
$$691$$ 368.257 637.840i 0.532934 0.923068i −0.466327 0.884613i $$-0.654423\pi$$
0.999260 0.0384555i $$-0.0122438\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −646.166 373.064i −0.929736 0.536783i
$$696$$ 0 0
$$697$$ −501.353 868.369i −0.719301 1.24587i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1068.34i 1.52403i 0.647561 + 0.762014i $$0.275789\pi$$
−0.647561 + 0.762014i $$0.724211\pi$$
$$702$$ 0 0
$$703$$ −872.686 −1.24137
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −191.682 + 110.667i −0.271120 + 0.156531i
$$708$$ 0 0
$$709$$ 136.944 237.194i 0.193151 0.334547i −0.753142 0.657858i $$-0.771463\pi$$
0.946293 + 0.323311i $$0.104796\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −580.247 335.006i −0.813811 0.469854i
$$714$$ 0 0
$$715$$ −379.651 657.575i −0.530980 0.919685i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 654.423i 0.910185i 0.890444 + 0.455092i $$0.150394\pi$$
−0.890444 + 0.455092i $$0.849606\pi$$
$$720$$ 0 0
$$721$$ −921.706 −1.27837
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 479.363 276.761i 0.661191 0.381739i
$$726$$ 0 0
$$727$$ 583.166 1010.07i 0.802155 1.38937i −0.116041 0.993244i $$-0.537020\pi$$
0.918195 0.396128i $$-0.129646\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −963.292 556.157i −1.31777 0.760816i
$$732$$ 0 0
$$733$$ 439.146 + 760.623i 0.599108 + 1.03768i 0.992953 + 0.118508i $$0.0378112\pi$$
−0.393845 + 0.919177i $$0.628855\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 532.103i 0.721984i
$$738$$ 0 0
$$739$$ −593.151 −0.802640 −0.401320 0.915938i $$-0.631448\pi$$
−0.401320 + 0.915938i $$0.631448\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −47.0561 + 27.1679i −0.0633326 + 0.0365651i −0.531332 0.847164i $$-0.678308\pi$$
0.467999 + 0.883729i $$0.344975\pi$$
$$744$$ 0 0
$$745$$ 799.398 1384.60i 1.07302 1.85852i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 208.059 + 120.123i 0.277783 + 0.160378i
$$750$$ 0 0
$$751$$ 455.570 + 789.071i 0.606618 + 1.05069i 0.991793 + 0.127850i $$0.0408077\pi$$
−0.385175 + 0.922844i $$0.625859\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 1134.83i 1.50309i
$$756$$ 0 0
$$757$$ −1272.22 −1.68061 −0.840304 0.542115i $$-0.817624\pi$$
−0.840304 + 0.542115i $$0.817624\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −399.480 + 230.640i −0.524940 + 0.303074i −0.738954 0.673756i $$-0.764680\pi$$
0.214013 + 0.976831i $$0.431346\pi$$
$$762$$ 0 0
$$763$$ 182.171 315.530i 0.238757 0.413539i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 240.177 + 138.666i 0.313138 + 0.180790i
$$768$$ 0 0
$$769$$ −269.439 466.682i −0.350376 0.606868i 0.635940 0.771739i $$-0.280613\pi$$
−0.986315 + 0.164871i $$0.947279\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1036.29i 1.34061i 0.742087 + 0.670304i $$0.233836\pi$$
−0.742087 + 0.670304i $$0.766164\pi$$
$$774$$ 0 0
$$775$$ −1385.03 −1.78713
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −607.059 + 350.486i −0.779280 + 0.449918i
$$780$$ 0 0
$$781$$ −92.5449 + 160.292i −0.118495 + 0.205240i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 524.520 + 302.832i 0.668179 + 0.385773i
$$786$$ 0 0
$$787$$ 706.096 + 1222.99i 0.897199 + 1.55399i 0.831059 + 0.556185i $$0.187735\pi$$
0.0661406 + 0.997810i $$0.478931\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 1123.09i 1.41983i
$$792$$ 0 0
$$793$$ 356.151 0.449119
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 60.4602 34.9067i 0.0758597 0.0437976i −0.461590 0.887093i $$-0.652721\pi$$
0.537450 + 0.843296i $$0.319388\pi$$
$$798$$ 0 0
$$799$$ 418.565 724.976i 0.523861 0.907355i
$$800$$