# Properties

 Label 2520.2.bi.a.1801.1 Level $2520$ Weight $2$ Character 2520.1801 Analytic conductor $20.122$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2520.bi (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$20.1223013094$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 280) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1801.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2520.1801 Dual form 2520.2.bi.a.361.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{11} +(2.00000 + 3.46410i) q^{17} +(1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} -9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(2.00000 - 1.73205i) q^{35} +(-2.00000 + 3.46410i) q^{37} -1.00000 q^{41} +9.00000 q^{43} +(5.50000 + 4.33013i) q^{49} +(-5.00000 - 8.66025i) q^{53} -2.00000 q^{55} +(-5.00000 - 8.66025i) q^{59} +(-4.50000 + 7.79423i) q^{61} +(-2.50000 - 4.33013i) q^{67} -14.0000 q^{71} +(-6.00000 - 10.3923i) q^{73} +(-1.00000 - 5.19615i) q^{77} +(-7.00000 + 12.1244i) q^{79} -11.0000 q^{83} -4.00000 q^{85} +(-7.50000 + 12.9904i) q^{89} +(1.00000 + 1.73205i) q^{95} -18.0000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{5} - 5 q^{7}+O(q^{10})$$ 2 * q - q^5 - 5 * q^7 $$2 q - q^{5} - 5 q^{7} + 2 q^{11} + 4 q^{17} + 2 q^{19} + q^{23} - q^{25} - 18 q^{29} - 4 q^{31} + 4 q^{35} - 4 q^{37} - 2 q^{41} + 18 q^{43} + 11 q^{49} - 10 q^{53} - 4 q^{55} - 10 q^{59} - 9 q^{61} - 5 q^{67} - 28 q^{71} - 12 q^{73} - 2 q^{77} - 14 q^{79} - 22 q^{83} - 8 q^{85} - 15 q^{89} + 2 q^{95} - 36 q^{97}+O(q^{100})$$ 2 * q - q^5 - 5 * q^7 + 2 * q^11 + 4 * q^17 + 2 * q^19 + q^23 - q^25 - 18 * q^29 - 4 * q^31 + 4 * q^35 - 4 * q^37 - 2 * q^41 + 18 * q^43 + 11 * q^49 - 10 * q^53 - 4 * q^55 - 10 * q^59 - 9 * q^61 - 5 * q^67 - 28 * q^71 - 12 * q^73 - 2 * q^77 - 14 * q^79 - 22 * q^83 - 8 * q^85 - 15 * q^89 + 2 * q^95 - 36 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$$.

 $$n$$ $$281$$ $$631$$ $$1081$$ $$1261$$ $$2017$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ −2.50000 0.866025i −0.944911 0.327327i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i $$-0.0691756\pi$$
−0.674967 + 0.737848i $$0.735842\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i $$-0.00546033\pi$$
−0.514782 + 0.857321i $$0.672127\pi$$
$$18$$ 0 0
$$19$$ 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i $$-0.759652\pi$$
0.957635 + 0.287984i $$0.0929851\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i $$-0.800087\pi$$
0.913434 + 0.406986i $$0.133420\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −9.00000 −1.67126 −0.835629 0.549294i $$-0.814897\pi$$
−0.835629 + 0.549294i $$0.814897\pi$$
$$30$$ 0 0
$$31$$ −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i $$-0.283621\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 2.00000 1.73205i 0.338062 0.292770i
$$36$$ 0 0
$$37$$ −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i $$-0.939977\pi$$
0.653476 + 0.756948i $$0.273310\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1.00000 −0.156174 −0.0780869 0.996947i $$-0.524881\pi$$
−0.0780869 + 0.996947i $$0.524881\pi$$
$$42$$ 0 0
$$43$$ 9.00000 1.37249 0.686244 0.727372i $$-0.259258\pi$$
0.686244 + 0.727372i $$0.259258\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0 0
$$49$$ 5.50000 + 4.33013i 0.785714 + 0.618590i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −5.00000 8.66025i −0.686803 1.18958i −0.972867 0.231367i $$-0.925680\pi$$
0.286064 0.958211i $$-0.407653\pi$$
$$54$$ 0 0
$$55$$ −2.00000 −0.269680
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −5.00000 8.66025i −0.650945 1.12747i −0.982894 0.184172i $$-0.941040\pi$$
0.331949 0.943297i $$-0.392294\pi$$
$$60$$ 0 0
$$61$$ −4.50000 + 7.79423i −0.576166 + 0.997949i 0.419748 + 0.907641i $$0.362118\pi$$
−0.995914 + 0.0903080i $$0.971215\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i $$-0.265465\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −14.0000 −1.66149 −0.830747 0.556650i $$-0.812086\pi$$
−0.830747 + 0.556650i $$0.812086\pi$$
$$72$$ 0 0
$$73$$ −6.00000 10.3923i −0.702247 1.21633i −0.967676 0.252197i $$-0.918847\pi$$
0.265429 0.964130i $$-0.414486\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −1.00000 5.19615i −0.113961 0.592157i
$$78$$ 0 0
$$79$$ −7.00000 + 12.1244i −0.787562 + 1.36410i 0.139895 + 0.990166i $$0.455323\pi$$
−0.927457 + 0.373930i $$0.878010\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −11.0000 −1.20741 −0.603703 0.797209i $$-0.706309\pi$$
−0.603703 + 0.797209i $$0.706309\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i $$0.459195\pi$$
−0.922840 + 0.385183i $$0.874138\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 1.00000 + 1.73205i 0.102598 + 0.177705i
$$96$$ 0 0
$$97$$ −18.0000 −1.82762 −0.913812 0.406138i $$-0.866875\pi$$
−0.913812 + 0.406138i $$0.866875\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i $$-0.118979\pi$$
−0.781697 + 0.623658i $$0.785646\pi$$
$$102$$ 0 0
$$103$$ 6.50000 11.2583i 0.640464 1.10932i −0.344865 0.938652i $$-0.612075\pi$$
0.985329 0.170664i $$-0.0545913\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 4.50000 7.79423i 0.435031 0.753497i −0.562267 0.826956i $$-0.690071\pi$$
0.997298 + 0.0734594i $$0.0234039\pi$$
$$108$$ 0 0
$$109$$ 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i $$-0.151417\pi$$
−0.841086 + 0.540901i $$0.818083\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ 0.500000 + 0.866025i 0.0466252 + 0.0807573i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −2.00000 10.3923i −0.183340 0.952661i
$$120$$ 0 0
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −4.00000 + 6.92820i −0.349482 + 0.605320i −0.986157 0.165812i $$-0.946976\pi$$
0.636676 + 0.771132i $$0.280309\pi$$
$$132$$ 0 0
$$133$$ −4.00000 + 3.46410i −0.346844 + 0.300376i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i $$0.00465636\pi$$
−0.487278 + 0.873247i $$0.662010\pi$$
$$138$$ 0 0
$$139$$ −2.00000 −0.169638 −0.0848189 0.996396i $$-0.527031\pi$$
−0.0848189 + 0.996396i $$0.527031\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 4.50000 7.79423i 0.373705 0.647275i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2.50000 + 4.33013i −0.204808 + 0.354738i −0.950072 0.312032i $$-0.898990\pi$$
0.745264 + 0.666770i $$0.232324\pi$$
$$150$$ 0 0
$$151$$ −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i $$-0.272204\pi$$
−0.981617 + 0.190864i $$0.938871\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 4.00000 0.321288
$$156$$ 0 0
$$157$$ −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i $$-0.192098\pi$$
−0.903167 + 0.429289i $$0.858764\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −2.00000 + 1.73205i −0.157622 + 0.136505i
$$162$$ 0 0
$$163$$ 10.0000 17.3205i 0.783260 1.35665i −0.146772 0.989170i $$-0.546888\pi$$
0.930033 0.367477i $$-0.119778\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −17.0000 −1.31550 −0.657750 0.753237i $$-0.728492\pi$$
−0.657750 + 0.753237i $$0.728492\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 8.00000 13.8564i 0.608229 1.05348i −0.383304 0.923622i $$-0.625214\pi$$
0.991532 0.129861i $$-0.0414530\pi$$
$$174$$ 0 0
$$175$$ 0.500000 + 2.59808i 0.0377964 + 0.196396i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i $$-0.0186389\pi$$
−0.549825 + 0.835280i $$0.685306\pi$$
$$180$$ 0 0
$$181$$ −25.0000 −1.85824 −0.929118 0.369784i $$-0.879432\pi$$
−0.929118 + 0.369784i $$0.879432\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −2.00000 3.46410i −0.147043 0.254686i
$$186$$ 0 0
$$187$$ −4.00000 + 6.92820i −0.292509 + 0.506640i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i $$-0.607592\pi$$
0.982828 0.184525i $$-0.0590746\pi$$
$$192$$ 0 0
$$193$$ 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i $$0.00142465\pi$$
−0.496119 + 0.868255i $$0.665242\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i $$-0.121385\pi$$
−0.786389 + 0.617731i $$0.788052\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 22.5000 + 7.79423i 1.57919 + 0.547048i
$$204$$ 0 0
$$205$$ 0.500000 0.866025i 0.0349215 0.0604858i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ 2.00000 0.137686 0.0688428 0.997628i $$-0.478069\pi$$
0.0688428 + 0.997628i $$0.478069\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −4.50000 + 7.79423i −0.306897 + 0.531562i
$$216$$ 0 0
$$217$$ 2.00000 + 10.3923i 0.135769 + 0.705476i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −4.00000 −0.267860 −0.133930 0.990991i $$-0.542760\pi$$
−0.133930 + 0.990991i $$0.542760\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −10.0000 17.3205i −0.663723 1.14960i −0.979630 0.200812i $$-0.935642\pi$$
0.315906 0.948790i $$-0.397691\pi$$
$$228$$ 0 0
$$229$$ 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i $$-0.726147\pi$$
0.982592 + 0.185776i $$0.0594799\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 4.00000 6.92820i 0.262049 0.453882i −0.704737 0.709468i $$-0.748935\pi$$
0.966786 + 0.255586i $$0.0822686\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 24.0000 1.55243 0.776215 0.630468i $$-0.217137\pi$$
0.776215 + 0.630468i $$0.217137\pi$$
$$240$$ 0 0
$$241$$ 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i $$0.0839937\pi$$
−0.256814 + 0.966461i $$0.582673\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −6.50000 + 2.59808i −0.415270 + 0.165985i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −8.00000 −0.504956 −0.252478 0.967603i $$-0.581245\pi$$
−0.252478 + 0.967603i $$0.581245\pi$$
$$252$$ 0 0
$$253$$ 2.00000 0.125739
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$258$$ 0 0
$$259$$ 8.00000 6.92820i 0.497096 0.430498i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −0.500000 0.866025i −0.0308313 0.0534014i 0.850198 0.526463i $$-0.176482\pi$$
−0.881029 + 0.473062i $$0.843149\pi$$
$$264$$ 0 0
$$265$$ 10.0000 0.614295
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −10.5000 18.1865i −0.640196 1.10885i −0.985389 0.170321i $$-0.945520\pi$$
0.345192 0.938532i $$-0.387814\pi$$
$$270$$ 0 0
$$271$$ −11.0000 + 19.0526i −0.668202 + 1.15736i 0.310204 + 0.950670i $$0.399603\pi$$
−0.978406 + 0.206691i $$0.933731\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.00000 1.73205i 0.0603023 0.104447i
$$276$$ 0 0
$$277$$ 14.0000 + 24.2487i 0.841178 + 1.45696i 0.888899 + 0.458103i $$0.151471\pi$$
−0.0477206 + 0.998861i $$0.515196\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i $$-0.128734\pi$$
−0.800439 + 0.599414i $$0.795400\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 2.50000 + 0.866025i 0.147570 + 0.0511199i
$$288$$ 0 0
$$289$$ 0.500000 0.866025i 0.0294118 0.0509427i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −12.0000 −0.701047 −0.350524 0.936554i $$-0.613996\pi$$
−0.350524 + 0.936554i $$0.613996\pi$$
$$294$$ 0 0
$$295$$ 10.0000 0.582223
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −22.5000 7.79423i −1.29688 0.449252i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −4.50000 7.79423i −0.257669 0.446296i
$$306$$ 0 0
$$307$$ 21.0000 1.19853 0.599267 0.800549i $$-0.295459\pi$$
0.599267 + 0.800549i $$0.295459\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 13.0000 + 22.5167i 0.737162 + 1.27680i 0.953768 + 0.300544i $$0.0971681\pi$$
−0.216606 + 0.976259i $$0.569499\pi$$
$$312$$ 0 0
$$313$$ −8.00000 + 13.8564i −0.452187 + 0.783210i −0.998522 0.0543564i $$-0.982689\pi$$
0.546335 + 0.837567i $$0.316023\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −8.00000 + 13.8564i −0.449325 + 0.778253i −0.998342 0.0575576i $$-0.981669\pi$$
0.549017 + 0.835811i $$0.315002\pi$$
$$318$$ 0 0
$$319$$ −9.00000 15.5885i −0.503903 0.872786i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.00000 0.445132
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 5.00000 0.273179
$$336$$ 0 0
$$337$$ −2.00000 −0.108947 −0.0544735 0.998515i $$-0.517348\pi$$
−0.0544735 + 0.998515i $$0.517348\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 4.00000 6.92820i 0.216612 0.375183i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −3.50000 6.06218i −0.187890 0.325435i 0.756657 0.653812i $$-0.226831\pi$$
−0.944547 + 0.328378i $$0.893498\pi$$
$$348$$ 0 0
$$349$$ −19.0000 −1.01705 −0.508523 0.861048i $$-0.669808\pi$$
−0.508523 + 0.861048i $$0.669808\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 7.00000 + 12.1244i 0.372572 + 0.645314i 0.989960 0.141344i $$-0.0451425\pi$$
−0.617388 + 0.786659i $$0.711809\pi$$
$$354$$ 0 0
$$355$$ 7.00000 12.1244i 0.371521 0.643494i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i $$-0.730769\pi$$
0.979791 + 0.200026i $$0.0641026\pi$$
$$360$$ 0 0
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 12.0000 0.628109
$$366$$ 0 0
$$367$$ −3.50000 6.06218i −0.182699 0.316443i 0.760100 0.649806i $$-0.225150\pi$$
−0.942799 + 0.333363i $$0.891817\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 5.00000 + 25.9808i 0.259587 + 1.34885i
$$372$$ 0 0
$$373$$ 14.0000 24.2487i 0.724893 1.25555i −0.234126 0.972206i $$-0.575223\pi$$
0.959018 0.283344i $$-0.0914439\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −30.0000 −1.54100 −0.770498 0.637442i $$-0.779993\pi$$
−0.770498 + 0.637442i $$0.779993\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i $$-0.653070\pi$$
0.999088 0.0427020i $$-0.0135966\pi$$
$$384$$ 0 0
$$385$$ 5.00000 + 1.73205i 0.254824 + 0.0882735i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 13.0000 + 22.5167i 0.659126 + 1.14164i 0.980842 + 0.194804i $$0.0624070\pi$$
−0.321716 + 0.946836i $$0.604260\pi$$
$$390$$ 0 0
$$391$$ 4.00000 0.202289
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −7.00000 12.1244i −0.352208 0.610043i
$$396$$ 0 0
$$397$$ −3.00000 + 5.19615i −0.150566 + 0.260787i −0.931436 0.363906i $$-0.881443\pi$$
0.780870 + 0.624694i $$0.214776\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −8.50000 + 14.7224i −0.424470 + 0.735203i −0.996371 0.0851195i $$-0.972873\pi$$
0.571901 + 0.820323i $$0.306206\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −8.00000 −0.396545
$$408$$ 0 0
$$409$$ 10.5000 + 18.1865i 0.519192 + 0.899266i 0.999751 + 0.0223042i $$0.00710022\pi$$
−0.480560 + 0.876962i $$0.659566\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 5.00000 + 25.9808i 0.246034 + 1.27843i
$$414$$ 0 0
$$415$$ 5.50000 9.52628i 0.269984 0.467627i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −16.0000 −0.781651 −0.390826 0.920465i $$-0.627810\pi$$
−0.390826 + 0.920465i $$0.627810\pi$$
$$420$$ 0 0
$$421$$ −27.0000 −1.31590 −0.657950 0.753062i $$-0.728576\pi$$
−0.657950 + 0.753062i $$0.728576\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2.00000 3.46410i 0.0970143 0.168034i
$$426$$ 0 0
$$427$$ 18.0000 15.5885i 0.871081 0.754378i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 7.00000 + 12.1244i 0.337178 + 0.584010i 0.983901 0.178716i $$-0.0571942\pi$$
−0.646723 + 0.762725i $$0.723861\pi$$
$$432$$ 0 0
$$433$$ 30.0000 1.44171 0.720854 0.693087i $$-0.243750\pi$$
0.720854 + 0.693087i $$0.243750\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −1.00000 1.73205i −0.0478365 0.0828552i
$$438$$ 0 0
$$439$$ 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i $$-0.600405\pi$$
0.978412 0.206666i $$-0.0662612\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −5.50000 + 9.52628i −0.261313 + 0.452607i −0.966591 0.256323i $$-0.917489\pi$$
0.705278 + 0.708931i $$0.250822\pi$$
$$444$$ 0 0
$$445$$ −7.50000 12.9904i −0.355534 0.615803i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 41.0000 1.93491 0.967455 0.253044i $$-0.0814317\pi$$
0.967455 + 0.253044i $$0.0814317\pi$$
$$450$$ 0 0
$$451$$ −1.00000 1.73205i −0.0470882 0.0815591i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −4.00000 + 6.92820i −0.187112 + 0.324088i −0.944286 0.329125i $$-0.893246\pi$$
0.757174 + 0.653213i $$0.226579\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2.00000 −0.0931493 −0.0465746 0.998915i $$-0.514831\pi$$
−0.0465746 + 0.998915i $$0.514831\pi$$
$$462$$ 0 0
$$463$$ 39.0000 1.81248 0.906242 0.422760i $$-0.138939\pi$$
0.906242 + 0.422760i $$0.138939\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −3.50000 + 6.06218i −0.161961 + 0.280524i −0.935572 0.353137i $$-0.885115\pi$$
0.773611 + 0.633661i $$0.218448\pi$$
$$468$$ 0 0
$$469$$ 2.50000 + 12.9904i 0.115439 + 0.599840i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 9.00000 + 15.5885i 0.413820 + 0.716758i
$$474$$ 0 0
$$475$$ −2.00000 −0.0917663
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i $$-0.285779\pi$$
−0.988861 + 0.148842i $$0.952445\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 9.00000 15.5885i 0.408669 0.707835i
$$486$$ 0 0
$$487$$ 4.00000 + 6.92820i 0.181257 + 0.313947i 0.942309 0.334744i $$-0.108650\pi$$
−0.761052 + 0.648691i $$0.775317\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ 0 0
$$493$$ −18.0000 31.1769i −0.810679 1.40414i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 35.0000 + 12.1244i 1.56996 + 0.543852i
$$498$$ 0 0
$$499$$ 19.0000 32.9090i 0.850557 1.47321i −0.0301498 0.999545i $$-0.509598\pi$$
0.880707 0.473662i $$-0.157068\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 23.0000 1.02552 0.512760 0.858532i $$-0.328623\pi$$
0.512760 + 0.858532i $$0.328623\pi$$
$$504$$ 0 0
$$505$$ −3.00000 −0.133498
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −7.50000 + 12.9904i −0.332432 + 0.575789i −0.982988 0.183669i $$-0.941202\pi$$
0.650556 + 0.759458i $$0.274536\pi$$
$$510$$ 0 0
$$511$$ 6.00000 + 31.1769i 0.265424 + 1.37919i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 6.50000 + 11.2583i 0.286424 + 0.496101i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −21.0000 36.3731i −0.920027 1.59353i −0.799370 0.600839i $$-0.794833\pi$$
−0.120656 0.992694i $$-0.538500\pi$$
$$522$$ 0 0
$$523$$ −14.0000 + 24.2487i −0.612177 + 1.06032i 0.378695 + 0.925521i $$0.376373\pi$$
−0.990873 + 0.134801i $$0.956961\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 8.00000 13.8564i 0.348485 0.603595i
$$528$$ 0 0
$$529$$ 11.0000 + 19.0526i 0.478261 + 0.828372i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 4.50000 + 7.79423i 0.194552 + 0.336974i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −2.00000 + 13.8564i −0.0861461 + 0.596838i
$$540$$ 0 0
$$541$$ 6.50000 11.2583i 0.279457 0.484033i −0.691793 0.722096i $$-0.743179\pi$$
0.971250 + 0.238062i $$0.0765123\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −1.00000 −0.0428353
$$546$$ 0 0
$$547$$ −35.0000 −1.49649 −0.748246 0.663421i $$-0.769104\pi$$
−0.748246 + 0.663421i $$0.769104\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −9.00000 + 15.5885i −0.383413 + 0.664091i
$$552$$ 0 0
$$553$$ 28.0000 24.2487i 1.19068 1.03116i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 15.0000 + 25.9808i 0.635570 + 1.10084i 0.986394 + 0.164399i $$0.0525683\pi$$
−0.350824 + 0.936442i $$0.614098\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −22.5000 38.9711i −0.948262 1.64244i −0.749085 0.662474i $$-0.769506\pi$$
−0.199177 0.979963i $$-0.563827\pi$$
$$564$$ 0 0
$$565$$ 1.00000 1.73205i 0.0420703 0.0728679i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 23.0000 39.8372i 0.964210 1.67006i 0.252488 0.967600i $$-0.418751\pi$$
0.711722 0.702461i $$-0.247915\pi$$
$$570$$ 0 0
$$571$$ 13.0000 + 22.5167i 0.544033 + 0.942293i 0.998667 + 0.0516146i $$0.0164367\pi$$
−0.454634 + 0.890678i $$0.650230\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ −1.00000 1.73205i −0.0416305 0.0721062i 0.844459 0.535620i $$-0.179922\pi$$
−0.886090 + 0.463513i $$0.846589\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 27.5000 + 9.52628i 1.14089 + 0.395217i
$$582$$ 0 0
$$583$$ 10.0000 17.3205i 0.414158 0.717342i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ −8.00000 −0.329634
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 9.00000 15.5885i 0.369586 0.640141i −0.619915 0.784669i $$-0.712833\pi$$
0.989501 + 0.144528i $$0.0461663\pi$$
$$594$$ 0 0
$$595$$ 10.0000 + 3.46410i 0.409960 + 0.142014i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 2.00000 + 3.46410i 0.0817178 + 0.141539i 0.903988 0.427558i $$-0.140626\pi$$
−0.822270 + 0.569097i $$0.807293\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 3.50000 + 6.06218i 0.142295 + 0.246463i
$$606$$ 0 0
$$607$$ −13.5000 + 23.3827i −0.547948 + 0.949074i 0.450467 + 0.892793i $$0.351258\pi$$
−0.998415 + 0.0562808i $$0.982076\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 10.0000 + 17.3205i 0.403896 + 0.699569i 0.994192 0.107618i $$-0.0343224\pi$$
−0.590296 + 0.807187i $$0.700989\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 12.0000 0.483102 0.241551 0.970388i $$-0.422344\pi$$
0.241551 + 0.970388i $$0.422344\pi$$
$$618$$ 0 0
$$619$$ 17.0000 + 29.4449i 0.683288 + 1.18349i 0.973972 + 0.226670i $$0.0727838\pi$$
−0.290684 + 0.956819i $$0.593883\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 30.0000 25.9808i 1.20192 1.04090i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −16.0000 −0.637962
$$630$$ 0 0
$$631$$ −2.00000 −0.0796187 −0.0398094 0.999207i $$-0.512675\pi$$
−0.0398094 + 0.999207i $$0.512675\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −4.00000 + 6.92820i −0.158735 + 0.274937i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −9.50000 16.4545i −0.375227 0.649913i 0.615134 0.788423i $$-0.289102\pi$$
−0.990361 + 0.138510i $$0.955769\pi$$
$$642$$ 0 0
$$643$$ −4.00000 −0.157745 −0.0788723 0.996885i $$-0.525132\pi$$
−0.0788723 + 0.996885i $$0.525132\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 11.5000 + 19.9186i 0.452112 + 0.783080i 0.998517 0.0544405i $$-0.0173375\pi$$
−0.546405 + 0.837521i $$0.684004\pi$$
$$648$$ 0 0
$$649$$ 10.0000 17.3205i 0.392534 0.679889i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 18.0000 31.1769i 0.704394 1.22005i −0.262515 0.964928i $$-0.584552\pi$$
0.966910 0.255119i $$-0.0821147\pi$$
$$654$$ 0 0
$$655$$ −4.00000 6.92820i −0.156293 0.270707i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −2.00000 −0.0779089 −0.0389545 0.999241i $$-0.512403\pi$$
−0.0389545 + 0.999241i $$0.512403\pi$$
$$660$$ 0 0
$$661$$ 1.50000 + 2.59808i 0.0583432 + 0.101053i 0.893722 0.448622i $$-0.148085\pi$$
−0.835379 + 0.549675i $$0.814752\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −1.00000 5.19615i −0.0387783 0.201498i
$$666$$ 0 0
$$667$$ −4.50000 + 7.79423i −0.174241 + 0.301794i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −18.0000 −0.694882
$$672$$ 0 0
$$673$$ 24.0000 0.925132 0.462566 0.886585i $$-0.346929\pi$$
0.462566 + 0.886585i $$0.346929\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −12.0000 + 20.7846i −0.461197 + 0.798817i −0.999021 0.0442400i $$-0.985913\pi$$
0.537823 + 0.843057i $$0.319247\pi$$
$$678$$ 0 0
$$679$$ 45.0000 + 15.5885i 1.72694 + 0.598230i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 4.50000 + 7.79423i 0.172188 + 0.298238i 0.939184 0.343413i $$-0.111583\pi$$
−0.766997 + 0.641651i $$0.778250\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −25.0000 + 43.3013i −0.951045 + 1.64726i −0.207875 + 0.978155i $$0.566655\pi$$
−0.743170 + 0.669102i $$0.766679\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 1.00000 1.73205i 0.0379322 0.0657004i
$$696$$ 0 0
$$697$$ −2.00000 3.46410i −0.0757554 0.131212i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −9.00000 −0.339925 −0.169963 0.985451i $$-0.554365\pi$$
−0.169963 + 0.985451i $$0.554365\pi$$
$$702$$ 0 0
$$703$$ 4.00000 + 6.92820i 0.150863 + 0.261302i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −1.50000 7.79423i −0.0564133 0.293132i
$$708$$ 0 0
$$709$$ −10.5000 + 18.1865i −0.394336 + 0.683010i −0.993016 0.117978i $$-0.962359\pi$$
0.598680 + 0.800988i $$0.295692\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −4.00000 −0.149801
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −21.0000 + 36.3731i −0.783168 + 1.35649i 0.146920 + 0.989148i $$0.453064\pi$$
−0.930087 + 0.367338i $$0.880269\pi$$
$$720$$ 0 0
$$721$$ −26.0000 + 22.5167i −0.968291 + 0.838564i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 4.50000 + 7.79423i 0.167126 + 0.289470i
$$726$$ 0 0
$$727$$ −31.0000 −1.14973 −0.574863 0.818250i $$-0.694945\pi$$
−0.574863 + 0.818250i $$0.694945\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 18.0000 + 31.1769i 0.665754 + 1.15312i
$$732$$ 0 0
$$733$$ 13.0000 22.5167i 0.480166 0.831672i −0.519575 0.854425i $$-0.673910\pi$$
0.999741 + 0.0227529i $$0.00724310\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 5.00000 8.66025i 0.184177 0.319005i
$$738$$ 0 0
$$739$$ −5.00000 8.66025i −0.183928 0.318573i 0.759287 0.650756i $$-0.225548\pi$$
−0.943215 + 0.332184i $$0.892215\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −27.0000 −0.990534 −0.495267 0.868741i $$-0.664930\pi$$
−0.495267 + 0.868741i $$0.664930\pi$$
$$744$$ 0 0
$$745$$ −2.50000 4.33013i −0.0915929 0.158644i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −18.0000 + 15.5885i −0.657706 + 0.569590i
$$750$$ 0 0
$$751$$ −6.00000 + 10.3923i −0.218943 + 0.379221i −0.954485 0.298259i $$-0.903594\pi$$
0.735542 + 0.677479i $$0.236928\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ −24.0000 −0.872295 −0.436147 0.899875i $$-0.643657\pi$$
−0.436147 + 0.899875i $$0.643657\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −3.00000 + 5.19615i −0.108750 + 0.188360i −0.915264 0.402854i $$-0.868018\pi$$
0.806514 + 0.591215i $$0.201351\pi$$
$$762$$ 0 0
$$763$$ −0.500000 2.59808i −0.0181012 0.0940567i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 34.0000 1.22607 0.613036 0.790055i $$-0.289948\pi$$
0.613036 + 0.790055i $$0.289948\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$774$$ 0 0
$$775$$ −2.00000 + 3.46410i −0.0718421 + 0.124434i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1.00000 + 1.73205i −0.0358287 + 0.0620572i
$$780$$ 0 0
$$781$$ −14.0000 24.2487i −0.500959 0.867687i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 2.00000 0.0713831
$$786$$ 0 0
$$787$$ −22.5000 38.9711i −0.802038 1.38917i −0.918272 0.395949i $$-0.870416\pi$$
0.116234 0.993222i $$-0.462918\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 5.00000 + 1.73205i 0.177780 + 0.0615846i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −8.00000 −0.283375 −0.141687 0.989911i $$-0.545253\pi$$
−0.141687 + 0.989911i $$0.545253\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$