# Properties

 Label 20.4.e.a.7.1 Level 20 Weight 4 Character 20.7 Analytic conductor 1.180 Analytic rank 0 Dimension 2 CM discriminant -4 Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$20 = 2^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 20.e (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.18003820011$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{4}]$

## Embedding invariants

 Embedding label 7.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 20.7 Dual form 20.4.e.a.3.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(2.00000 + 2.00000i) q^{2} +8.00000i q^{4} +(-2.00000 - 11.0000i) q^{5} +(-16.0000 + 16.0000i) q^{8} -27.0000i q^{9} +O(q^{10})$$ $$q+(2.00000 + 2.00000i) q^{2} +8.00000i q^{4} +(-2.00000 - 11.0000i) q^{5} +(-16.0000 + 16.0000i) q^{8} -27.0000i q^{9} +(18.0000 - 26.0000i) q^{10} +(-37.0000 + 37.0000i) q^{13} -64.0000 q^{16} +(99.0000 + 99.0000i) q^{17} +(54.0000 - 54.0000i) q^{18} +(88.0000 - 16.0000i) q^{20} +(-117.000 + 44.0000i) q^{25} -148.000 q^{26} -284.000i q^{29} +(-128.000 - 128.000i) q^{32} +396.000i q^{34} +216.000 q^{36} +(-91.0000 - 91.0000i) q^{37} +(208.000 + 144.000i) q^{40} +472.000 q^{41} +(-297.000 + 54.0000i) q^{45} +343.000i q^{49} +(-322.000 - 146.000i) q^{50} +(-296.000 - 296.000i) q^{52} +(-27.0000 + 27.0000i) q^{53} +(568.000 - 568.000i) q^{58} -468.000 q^{61} -512.000i q^{64} +(481.000 + 333.000i) q^{65} +(-792.000 + 792.000i) q^{68} +(432.000 + 432.000i) q^{72} +(253.000 - 253.000i) q^{73} -364.000i q^{74} +(128.000 + 704.000i) q^{80} -729.000 q^{81} +(944.000 + 944.000i) q^{82} +(891.000 - 1287.00i) q^{85} +176.000i q^{89} +(-702.000 - 486.000i) q^{90} +(-611.000 - 611.000i) q^{97} +(-686.000 + 686.000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 4q^{2} - 4q^{5} - 32q^{8} + O(q^{10})$$ $$2q + 4q^{2} - 4q^{5} - 32q^{8} + 36q^{10} - 74q^{13} - 128q^{16} + 198q^{17} + 108q^{18} + 176q^{20} - 234q^{25} - 296q^{26} - 256q^{32} + 432q^{36} - 182q^{37} + 416q^{40} + 944q^{41} - 594q^{45} - 644q^{50} - 592q^{52} - 54q^{53} + 1136q^{58} - 936q^{61} + 962q^{65} - 1584q^{68} + 864q^{72} + 506q^{73} + 256q^{80} - 1458q^{81} + 1888q^{82} + 1782q^{85} - 1404q^{90} - 1222q^{97} - 1372q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$$.

 $$n$$ $$11$$ $$17$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 + 2.00000i 0.707107 + 0.707107i
$$3$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$4$$ 8.00000i 1.00000i
$$5$$ −2.00000 11.0000i −0.178885 0.983870i
$$6$$ 0 0
$$7$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$8$$ −16.0000 + 16.0000i −0.707107 + 0.707107i
$$9$$ 27.0000i 1.00000i
$$10$$ 18.0000 26.0000i 0.569210 0.822192i
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ −37.0000 + 37.0000i −0.789381 + 0.789381i −0.981393 0.192012i $$-0.938499\pi$$
0.192012 + 0.981393i $$0.438499\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −64.0000 −1.00000
$$17$$ 99.0000 + 99.0000i 1.41241 + 1.41241i 0.741874 + 0.670540i $$0.233937\pi$$
0.670540 + 0.741874i $$0.266063\pi$$
$$18$$ 54.0000 54.0000i 0.707107 0.707107i
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 88.0000 16.0000i 0.983870 0.178885i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$24$$ 0 0
$$25$$ −117.000 + 44.0000i −0.936000 + 0.352000i
$$26$$ −148.000 −1.11635
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 284.000i 1.81853i −0.416214 0.909267i $$-0.636643\pi$$
0.416214 0.909267i $$-0.363357\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ −128.000 128.000i −0.707107 0.707107i
$$33$$ 0 0
$$34$$ 396.000i 1.99745i
$$35$$ 0 0
$$36$$ 216.000 1.00000
$$37$$ −91.0000 91.0000i −0.404333 0.404333i 0.475424 0.879757i $$-0.342295\pi$$
−0.879757 + 0.475424i $$0.842295\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 208.000 + 144.000i 0.822192 + 0.569210i
$$41$$ 472.000 1.79790 0.898951 0.438048i $$-0.144330\pi$$
0.898951 + 0.438048i $$0.144330\pi$$
$$42$$ 0 0
$$43$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$44$$ 0 0
$$45$$ −297.000 + 54.0000i −0.983870 + 0.178885i
$$46$$ 0 0
$$47$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$48$$ 0 0
$$49$$ 343.000i 1.00000i
$$50$$ −322.000 146.000i −0.910754 0.412950i
$$51$$ 0 0
$$52$$ −296.000 296.000i −0.789381 0.789381i
$$53$$ −27.0000 + 27.0000i −0.0699761 + 0.0699761i −0.741229 0.671253i $$-0.765757\pi$$
0.671253 + 0.741229i $$0.265757\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 568.000 568.000i 1.28590 1.28590i
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −468.000 −0.982316 −0.491158 0.871071i $$-0.663426\pi$$
−0.491158 + 0.871071i $$0.663426\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 512.000i 1.00000i
$$65$$ 481.000 + 333.000i 0.917857 + 0.635439i
$$66$$ 0 0
$$67$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$68$$ −792.000 + 792.000i −1.41241 + 1.41241i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 432.000 + 432.000i 0.707107 + 0.707107i
$$73$$ 253.000 253.000i 0.405636 0.405636i −0.474578 0.880214i $$-0.657399\pi$$
0.880214 + 0.474578i $$0.157399\pi$$
$$74$$ 364.000i 0.571813i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 128.000 + 704.000i 0.178885 + 0.983870i
$$81$$ −729.000 −1.00000
$$82$$ 944.000 + 944.000i 1.27131 + 1.27131i
$$83$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$84$$ 0 0
$$85$$ 891.000 1287.00i 1.13697 1.64229i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 176.000i 0.209618i 0.994492 + 0.104809i $$0.0334231\pi$$
−0.994492 + 0.104809i $$0.966577\pi$$
$$90$$ −702.000 486.000i −0.822192 0.569210i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −611.000 611.000i −0.639563 0.639563i 0.310884 0.950448i $$-0.399375\pi$$
−0.950448 + 0.310884i $$0.899375\pi$$
$$98$$ −686.000 + 686.000i −0.707107 + 0.707107i
$$99$$ 0 0
$$100$$ −352.000 936.000i −0.352000 0.936000i
$$101$$ −598.000 −0.589141 −0.294570 0.955630i $$-0.595177\pi$$
−0.294570 + 0.955630i $$0.595177\pi$$
$$102$$ 0 0
$$103$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$104$$ 1184.00i 1.11635i
$$105$$ 0 0
$$106$$ −108.000 −0.0989612
$$107$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$108$$ 0 0
$$109$$ 1746.00i 1.53428i 0.641480 + 0.767140i $$0.278321\pi$$
−0.641480 + 0.767140i $$0.721679\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −337.000 + 337.000i −0.280551 + 0.280551i −0.833329 0.552778i $$-0.813568\pi$$
0.552778 + 0.833329i $$0.313568\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 2272.00 1.81853
$$117$$ 999.000 + 999.000i 0.789381 + 0.789381i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1331.00 1.00000
$$122$$ −936.000 936.000i −0.694602 0.694602i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 718.000 + 1199.00i 0.513759 + 0.857935i
$$126$$ 0 0
$$127$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$128$$ 1024.00 1024.00i 0.707107 0.707107i
$$129$$ 0 0
$$130$$ 296.000 + 1628.00i 0.199699 + 1.09835i
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ −3168.00 −1.99745
$$137$$ −2191.00 2191.00i −1.36635 1.36635i −0.865583 0.500766i $$-0.833052\pi$$
−0.500766 0.865583i $$-0.666948\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 1728.00i 1.00000i
$$145$$ −3124.00 + 568.000i −1.78920 + 0.325309i
$$146$$ 1012.00 0.573656
$$147$$ 0 0
$$148$$ 728.000 728.000i 0.404333 0.404333i
$$149$$ 3514.00i 1.93207i −0.258415 0.966034i $$-0.583200\pi$$
0.258415 0.966034i $$-0.416800\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 2673.00 2673.00i 1.41241 1.41241i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 1819.00 + 1819.00i 0.924662 + 0.924662i 0.997354 0.0726920i $$-0.0231590\pi$$
−0.0726920 + 0.997354i $$0.523159\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −1152.00 + 1664.00i −0.569210 + 0.822192i
$$161$$ 0 0
$$162$$ −1458.00 1458.00i −0.707107 0.707107i
$$163$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$164$$ 3776.00i 1.79790i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$168$$ 0 0
$$169$$ 541.000i 0.246245i
$$170$$ 4356.00 792.000i 1.96523 0.357315i
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −3047.00 + 3047.00i −1.33907 + 1.33907i −0.442108 + 0.896962i $$0.645769\pi$$
−0.896962 + 0.442108i $$0.854231\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −352.000 + 352.000i −0.148222 + 0.148222i
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ −432.000 2376.00i −0.178885 0.983870i
$$181$$ 3942.00 1.61882 0.809410 0.587243i $$-0.199787\pi$$
0.809410 + 0.587243i $$0.199787\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −819.000 + 1183.00i −0.325482 + 0.470140i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ −2717.00 + 2717.00i −1.01334 + 1.01334i −0.0134266 + 0.999910i $$0.504274\pi$$
−0.999910 + 0.0134266i $$0.995726\pi$$
$$194$$ 2444.00i 0.904479i
$$195$$ 0 0
$$196$$ −2744.00 −1.00000
$$197$$ 3289.00 + 3289.00i 1.18950 + 1.18950i 0.977206 + 0.212295i $$0.0680936\pi$$
0.212295 + 0.977206i $$0.431906\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 1168.00 2576.00i 0.412950 0.910754i
$$201$$ 0 0
$$202$$ −1196.00 1196.00i −0.416585 0.416585i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −944.000 5192.00i −0.321619 1.76890i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 2368.00 2368.00i 0.789381 0.789381i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ −216.000 216.000i −0.0699761 0.0699761i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −3492.00 + 3492.00i −1.08490 + 1.08490i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −7326.00 −2.22986
$$222$$ 0 0
$$223$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$224$$ 0 0
$$225$$ 1188.00 + 3159.00i 0.352000 + 0.936000i
$$226$$ −1348.00 −0.396759
$$227$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$228$$ 0 0
$$229$$ 2684.00i 0.774514i −0.921972 0.387257i $$-0.873423\pi$$
0.921972 0.387257i $$-0.126577\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 4544.00 + 4544.00i 1.28590 + 1.28590i
$$233$$ 3843.00 3843.00i 1.08053 1.08053i 0.0840693 0.996460i $$-0.473208\pi$$
0.996460 0.0840693i $$-0.0267917\pi$$
$$234$$ 3996.00i 1.11635i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 5272.00 1.40913 0.704563 0.709641i $$-0.251143\pi$$
0.704563 + 0.709641i $$0.251143\pi$$
$$242$$ 2662.00 + 2662.00i 0.707107 + 0.707107i
$$243$$ 0 0
$$244$$ 3744.00i 0.982316i
$$245$$ 3773.00 686.000i 0.983870 0.178885i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −962.000 + 3834.00i −0.243369 + 0.969934i
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 4096.00 1.00000
$$257$$ −3281.00 3281.00i −0.796355 0.796355i 0.186164 0.982519i $$-0.440394\pi$$
−0.982519 + 0.186164i $$0.940394\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −2664.00 + 3848.00i −0.635439 + 0.917857i
$$261$$ −7668.00 −1.81853
$$262$$ 0 0
$$263$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$264$$ 0 0
$$265$$ 351.000 + 243.000i 0.0813651 + 0.0563297i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 3406.00i 0.771998i 0.922499 + 0.385999i $$0.126143\pi$$
−0.922499 + 0.385999i $$0.873857\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ −6336.00 6336.00i −1.41241 1.41241i
$$273$$ 0 0
$$274$$ 8764.00i 1.93231i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −5221.00 5221.00i −1.13249 1.13249i −0.989762 0.142727i $$-0.954413\pi$$
−0.142727 0.989762i $$-0.545587\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 5792.00 1.22961 0.614807 0.788677i $$-0.289234\pi$$
0.614807 + 0.788677i $$0.289234\pi$$
$$282$$ 0 0
$$283$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −3456.00 + 3456.00i −0.707107 + 0.707107i
$$289$$ 14689.0i 2.98982i
$$290$$ −7384.00 5112.00i −1.49518 1.03513i
$$291$$ 0 0
$$292$$ 2024.00 + 2024.00i 0.405636 + 0.405636i
$$293$$ 2983.00 2983.00i 0.594774 0.594774i −0.344143 0.938917i $$-0.611831\pi$$
0.938917 + 0.344143i $$0.111831\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 2912.00 0.571813
$$297$$ 0 0
$$298$$ 7028.00 7028.00i 1.36618 1.36618i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 936.000 + 5148.00i 0.175722 + 0.966471i
$$306$$ 10692.0 1.99745
$$307$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ −937.000 + 937.000i −0.169209 + 0.169209i −0.786632 0.617423i $$-0.788177\pi$$
0.617423 + 0.786632i $$0.288177\pi$$
$$314$$ 7276.00i 1.30767i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2799.00 + 2799.00i 0.495923 + 0.495923i 0.910166 0.414243i $$-0.135954\pi$$
−0.414243 + 0.910166i $$0.635954\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −5632.00 + 1024.00i −0.983870 + 0.178885i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 5832.00i 1.00000i
$$325$$ 2701.00 5957.00i 0.460999 1.01672i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ −7552.00 + 7552.00i −1.27131 + 1.27131i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ −2457.00 + 2457.00i −0.404333 + 0.404333i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −6391.00 6391.00i −1.03306 1.03306i −0.999435 0.0336216i $$-0.989296\pi$$
−0.0336216 0.999435i $$-0.510704\pi$$
$$338$$ 1082.00 1082.00i 0.174121 0.174121i
$$339$$ 0 0
$$340$$ 10296.0 + 7128.00i 1.64229 + 1.13697i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −12188.0 −1.89373
$$347$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$348$$ 0 0
$$349$$ 8964.00i 1.37488i −0.726243 0.687438i $$-0.758735\pi$$
0.726243 0.687438i $$-0.241265\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 8073.00 8073.00i 1.21723 1.21723i 0.248633 0.968598i $$-0.420019\pi$$
0.968598 0.248633i $$-0.0799813\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −1408.00 −0.209618
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 3888.00 5616.00i 0.569210 0.822192i
$$361$$ −6859.00 −1.00000
$$362$$ 7884.00 + 7884.00i 1.14468 + 1.14468i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −3289.00 2277.00i −0.471655 0.326530i
$$366$$ 0 0
$$367$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$368$$ 0 0
$$369$$ 12744.0i 1.79790i
$$370$$ −4004.00 + 728.000i −0.562589 + 0.102289i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −9647.00 + 9647.00i −1.33915 + 1.33915i −0.442265 + 0.896884i $$0.645825\pi$$
−0.896884 + 0.442265i $$0.854175\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 10508.0 + 10508.0i 1.43552 + 1.43552i
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −10868.0 −1.43307
$$387$$ 0 0
$$388$$ 4888.00 4888.00i 0.639563 0.639563i
$$389$$ 374.000i 0.0487469i −0.999703 0.0243735i $$-0.992241\pi$$
0.999703 0.0243735i $$-0.00775908\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −5488.00 5488.00i −0.707107 0.707107i
$$393$$ 0 0
$$394$$ 13156.0i 1.68221i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 11089.0 + 11089.0i 1.40187 + 1.40187i 0.794168 + 0.607699i $$0.207907\pi$$
0.607699 + 0.794168i $$0.292093\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 7488.00 2816.00i 0.936000 0.352000i
$$401$$ −2398.00 −0.298629 −0.149315 0.988790i $$-0.547707\pi$$
−0.149315 + 0.988790i $$0.547707\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 4784.00i 0.589141i
$$405$$ 1458.00 + 8019.00i 0.178885 + 0.983870i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 7146.00i 0.863929i 0.901891 + 0.431964i $$0.142179\pi$$
−0.901891 + 0.431964i $$0.857821\pi$$
$$410$$ 8496.00 12272.0i 1.02338 1.47822i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 9472.00 1.11635
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 13412.0 1.55264 0.776319 0.630340i $$-0.217084\pi$$
0.776319 + 0.630340i $$0.217084\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 864.000i 0.0989612i
$$425$$ −15939.0 7227.00i −1.81919 0.824849i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ −11107.0 + 11107.0i −1.23272 + 1.23272i −0.269807 + 0.962914i $$0.586960\pi$$
−0.962914 + 0.269807i $$0.913040\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −13968.0 −1.53428
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 9261.00 1.00000
$$442$$ −14652.0 14652.0i −1.57675 1.57675i
$$443$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$444$$ 0 0
$$445$$ 1936.00 352.000i 0.206236 0.0374975i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 16114.0i 1.69369i −0.531840 0.846845i $$-0.678499\pi$$
0.531840 0.846845i $$-0.321501\pi$$
$$450$$ −3942.00 + 8694.00i −0.412950 + 0.910754i
$$451$$ 0 0
$$452$$ −2696.00 2696.00i −0.280551 0.280551i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −13481.0 13481.0i −1.37990 1.37990i −0.844768 0.535132i $$-0.820262\pi$$
−0.535132 0.844768i $$-0.679738\pi$$
$$458$$ 5368.00 5368.00i 0.547664 0.547664i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2318.00 −0.234187 −0.117093 0.993121i $$-0.537358\pi$$
−0.117093 + 0.993121i $$0.537358\pi$$
$$462$$ 0 0
$$463$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$464$$ 18176.0i 1.81853i
$$465$$ 0 0
$$466$$ 15372.0 1.52810
$$467$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$468$$ −7992.00 + 7992.00i −0.789381 + 0.789381i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 729.000 + 729.000i 0.0699761 + 0.0699761i
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 6734.00 0.638345
$$482$$ 10544.0 + 10544.0i 0.996403 + 0.996403i
$$483$$ 0 0
$$484$$ 10648.0i 1.00000i
$$485$$ −5499.00 + 7943.00i −0.514839 + 0.743656i
$$486$$ 0 0
$$487$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$488$$ 7488.00 7488.00i 0.694602 0.694602i
$$489$$ 0 0
$$490$$ 8918.00 + 6174.00i 0.822192 + 0.569210i
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 28116.0 28116.0i 2.56852 2.56852i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ −9592.00 + 5744.00i −0.857935 + 0.513759i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$504$$ 0 0
$$505$$ 1196.00 + 6578.00i 0.105389 + 0.579638i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 17996.0i 1.56711i 0.621323 + 0.783555i $$0.286596\pi$$
−0.621323 + 0.783555i $$0.713404\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 8192.00 + 8192.00i 0.707107 + 0.707107i
$$513$$ 0 0
$$514$$ 13124.0i 1.12622i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −13024.0 + 2368.00i −1.09835 + 0.199699i
$$521$$ −23738.0 −1.99612 −0.998062 0.0622265i $$-0.980180\pi$$
−0.998062 + 0.0622265i $$0.980180\pi$$
$$522$$ −15336.0 15336.0i −1.28590 1.28590i
$$523$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 12167.0i 1.00000i
$$530$$ 216.000 + 1188.00i 0.0177027 + 0.0973649i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −17464.0 + 17464.0i −1.41923 + 1.41923i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −6812.00 + 6812.00i −0.545885 + 0.545885i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 5922.00 0.470622 0.235311 0.971920i $$-0.424389\pi$$
0.235311 + 0.971920i $$0.424389\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 25344.0i 1.99745i
$$545$$ 19206.0 3492.00i 1.50953 0.274460i
$$546$$ 0 0
$$547$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$548$$ 17528.0 17528.0i 1.36635 1.36635i
$$549$$ 12636.0i 0.982316i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 20884.0i 1.60158i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −16731.0 16731.0i −1.27274 1.27274i −0.944646 0.328093i $$-0.893594\pi$$
−0.328093 0.944646i $$-0.606406\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 11584.0 + 11584.0i 0.869469 + 0.869469i
$$563$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$564$$ 0 0
$$565$$ 4381.00 + 3033.00i 0.326212 + 0.225839i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 26806.0i 1.97498i 0.157669 + 0.987492i $$0.449602\pi$$
−0.157669 + 0.987492i $$0.550398\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −13824.0 −1.00000
$$577$$ 15479.0 + 15479.0i 1.11681 + 1.11681i 0.992207 + 0.124603i $$0.0397657\pi$$
0.124603 + 0.992207i $$0.460234\pi$$
$$578$$ −29378.0 + 29378.0i −2.11412 + 2.11412i
$$579$$ 0 0
$$580$$ −4544.00 24992.0i −0.325309 1.78920i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 8096.00i 0.573656i
$$585$$ 8991.00 12987.0i 0.635439 0.917857i
$$586$$ 11932.0 0.841137
$$587$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 5824.00 + 5824.00i 0.404333 + 0.404333i
$$593$$ 4433.00 4433.00i 0.306984 0.306984i −0.536755 0.843738i $$-0.680350\pi$$
0.843738 + 0.536755i $$0.180350\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 28112.0 1.93207
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −24048.0 −1.63218 −0.816089 0.577927i $$-0.803862\pi$$
−0.816089 + 0.577927i $$0.803862\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −2662.00 14641.0i −0.178885 0.983870i
$$606$$ 0 0
$$607$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −8424.00 + 12168.0i −0.559144 + 0.807652i
$$611$$ 0 0
$$612$$ 21384.0 + 21384.0i 1.41241 + 1.41241i
$$613$$ −1837.00 + 1837.00i −0.121037 + 0.121037i −0.765031 0.643994i $$-0.777276\pi$$
0.643994 + 0.765031i $$0.277276\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 5499.00 + 5499.00i 0.358803 + 0.358803i 0.863372 0.504569i $$-0.168348\pi$$
−0.504569 + 0.863372i $$0.668348\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 11753.0 10296.0i 0.752192 0.658944i
$$626$$ −3748.00 −0.239297
$$627$$ 0 0
$$628$$ −14552.0 + 14552.0i −0.924662 + 0.924662i
$$629$$ 18018.0i 1.14217i
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 11196.0i 0.701341i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −12691.0 12691.0i −0.789381 0.789381i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −13312.0 9216.00i −0.822192 0.569210i
$$641$$ 14872.0 0.916394 0.458197 0.888851i $$-0.348495\pi$$
0.458197 + 0.888851i $$0.348495\pi$$
$$642$$ 0 0
$$643$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$648$$ 11664.0 11664.0i 0.707107 0.707107i
$$649$$ 0 0
$$650$$ 17316.0 6512.00i 1.04491 0.392956i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 16173.0 16173.0i 0.969217 0.969217i −0.0303236 0.999540i $$-0.509654\pi$$
0.999540 + 0.0303236i $$0.00965378\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −30208.0 −1.79790
$$657$$ −6831.00 6831.00i −0.405636 0.405636i
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ −22068.0 −1.29856 −0.649278 0.760551i $$-0.724929\pi$$
−0.649278 + 0.760551i $$0.724929\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −9828.00 −0.571813
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −19547.0 + 19547.0i −1.11959 + 1.11959i −0.127784 + 0.991802i $$0.540786\pi$$
−0.991802 + 0.127784i $$0.959214\pi$$
$$674$$ 25564.0i 1.46096i
$$675$$ 0 0
$$676$$ 4328.00 0.246245
$$677$$ −15471.0 15471.0i −0.878285 0.878285i 0.115072 0.993357i $$-0.463290\pi$$
−0.993357 + 0.115072i $$0.963290\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 6336.00 + 34848.0i 0.357315 + 1.96523i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$684$$ 0 0
$$685$$ −19719.0 + 28483.0i −1.09989 + 1.58873i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 1998.00i 0.110476i
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ −24376.0 24376.0i −1.33907 1.33907i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 46728.0 + 46728.0i 2.53938 + 2.53938i
$$698$$ 17928.0 17928.0i 0.972185 0.972185i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 31252.0 1.68384 0.841920 0.539602i $$-0.181425\pi$$
0.841920 + 0.539602i $$0.181425\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 32292.0 1.72142
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 8404.00i 0.445161i −0.974914 0.222580i $$-0.928552\pi$$
0.974914 0.222580i $$-0.0714479\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −2816.00 2816.00i −0.148222 0.148222i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 19008.0 3456.00i 0.983870 0.178885i
$$721$$ 0 0
$$722$$ −13718.0 13718.0i −0.707107 0.707107i
$$723$$ 0 0
$$724$$ 31536.0i 1.61882i
$$725$$ 12496.0 + 33228.0i 0.640124 + 1.70215i
$$726$$ 0 0
$$727$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$728$$ 0 0
$$729$$ 19683.0i 1.00000i
$$730$$ −2024.00 11132.0i −0.102619 0.564402i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 14993.0 14993.0i 0.755497 0.755497i −0.220003 0.975499i $$-0.570607\pi$$
0.975499 + 0.220003i $$0.0706066\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 25488.0 25488.0i 1.27131 1.27131i
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ −9464.00 6552.00i −0.470140 0.325482i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$744$$ 0 0
$$745$$ −38654.0 + 7028.00i −1.90090 + 0.345619i
$$746$$ −38588.0 −1.89384
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 42032.0i 2.03013i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −28781.0 28781.0i −1.38185 1.38185i −0.841327 0.540527i $$-0.818225\pi$$
−0.540527 0.841327i $$-0.681775\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 31882.0 1.51869 0.759344 0.650689i $$-0.225520\pi$$
0.759344 + 0.650689i $$0.225520\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −34749.0 24057.0i −1.64229 1.13697i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 41544.0i 1.94813i −0.226260 0.974067i $$-0.572650\pi$$
0.226260 0.974067i $$-0.427350\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −21736.0 21736.0i −1.01334 1.01334i
$$773$$ −28197.0 + 28197.0i −1.31200 + 1.31200i −0.392060 + 0.919940i $$0.628237\pi$$
−0.919940 + 0.392060i $$0.871763\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 19552.0 0.904479
$$777$$ 0 0
$$778$$ 748.000 748.000i 0.0344693 0.0344693i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 21952.0i 1.00000i
$$785$$ 16371.0 23647.0i 0.744339 1.07516i
$$786$$ 0 0
$$787$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$788$$ −26312.0 + 26312.0i −1.18950 + 1.18950i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 17316.0 17316.0i 0.775421 0.775421i
$$794$$ 44356.0i 1.98254i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 12839.0 + 12839.0i 0.570616 + 0.570616i 0.932300 0.361685i $$-0.117798\pi$$
−0.361685 + 0.932300i $$0.617798\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 20608.0 + 9344.00i 0.910754 + 0.412950i
$$801$$ 4752.00 0.209618
$$802$$ −4796.00 4796.00i −0.211163 0.211163i
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 9568.00 9568.00i 0.416585 0.416585i
$$809$$ 39704.0i 1.72549i −0.505643 0.862743i $$-0.668745\pi$$
0.505643 0.862743i $$-0.331255\pi$$
$$810$$ −13122.0 + 18954.0i −0.569210 + 0.822192i
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 <